adalib/numpy-cond-gen-0 · Datasets at Hugging Face

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import matplotlib import matplotlib.collections import matplotlib.pyplot as plt import numpy as np from .entropy_approximate import entropy_approximate from .optim_complexity_delay import ( _embedding_delay_metric, _embedding_delay_plot, _embedding_delay_select, ) from .optim_complexity_dimension import ( _embedding_dimension_afn, _embedding_dimension_ffn, _embedding_dimension_plot, ) from .optim_complexity_tolerance import _optimize_tolerance_plot def complexity_optimize( signal, delay_max=50, delay_method="fraser1986", dimension_max=10, dimension_method="afnn", tolerance_method="maxApEn", show=False, kwargs ): """Joint-estimation of optimal complexity parameters** The selection of the parameters Dimension and Delay is a challenge. One approach is to select them (semi) independently (as dimension selection often requires the delay) from each other, using :func:`complexity_delay` and :func:`complexity_dimension`. Estimate optimal complexity parameters Dimension (m), Time Delay (tau) and tolerance (r). Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. delay_max : int See :func:`complexity_delay`. delay_method : str See :func:`complexity_delay`. dimension_max : int See :func:`complexity_dimension`. dimension_method : str See :func:`complexity_dimension`. tolerance_method : str See :func:`complexity_tolerance`. show : bool Defaults to ``False``. Returns ------- optimal_dimension : int Optimal dimension. optimal_delay : int Optimal time delay. optimal_tolerance : int Optimal tolerance See Also ------------ complexity_delay, complexity_dimension, complexity_tolerance Examples --------- .. ipython:: python import neurokit2 as nk signal = nk.signal_simulate(duration=10, frequency=[5, 7], noise=0.01) parameters = nk.complexity_optimize(signal, show=True) parameters References ----------- * <NAME>., <NAME>., & <NAME>. (2003, April). A differential entropy based method for determining the optimal embedding parameters of a signal. In 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP'03). (Vol. 6, pp. VI-29). IEEE. * <NAME>., & <NAME>. (2009). The role of the embedding dimension and time delay in time series forecasting. IFAC Proceedings Volumes, 42(7), 316-320. * <NAME>., <NAME>., & <NAME>. (1994). Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physica-Section D, 73(1), 82-98. * <NAME>. (1997). Practical method for determining the minimum embedding dimension of a scalar time series. Physica D: Nonlinear Phenomena, 110(1-2), 43-50. * <NAME>., <NAME>., <NAME>., <NAME>., & <NAME>. (2008). Automatic selection of the threshold value r for approximate entropy. IEEE Transactions on Biomedical Engineering, 55(8), 1966-1972. """ out = {} # Optimize delay tau_sequence, metric, metric_values, out["Delay"] = _complexity_delay( signal, delay_max=delay_max, method=delay_method ) # Optimize dimension dimension_seq, optimize_indices, out["Dimension"] = _complexity_dimension( signal, delay=out["Delay"], dimension_max=dimension_max, method=dimension_method, *kwargs ) # Optimize r tolerance_method = tolerance_method.lower() if tolerance_method in ["traditional"]: out["Tolerance"] = 0.2 np.std(signal, ddof=1) if tolerance_method in ["maxapen", "optimize"]: r_range, ApEn, out["Tolerance"] = _complexity_tolerance( signal, delay=out["Delay"], dimension=out["Dimension"] ) if show is True: if tolerance_method in ["traditional"]: raise ValueError( "NeuroKit error: complexity_optimize():" "show is not available for current tolerance_method" ) if tolerance_method in ["maxapen", "optimize"]: _complexity_plot( signal, out, tau_sequence, metric, metric_values, dimension_seq[:-1], optimize_indices, r_range, ApEn, dimension_method=dimension_method, ) return out # ============================================================================= # Plot # ============================================================================= def _complexity_plot( signal, out, tau_sequence, metric, metric_values, dimension_seq, optimize_indices, r_range, ApEn, dimension_method="afnn", ): # Prepare figure fig = plt.figure(constrained_layout=False) spec = matplotlib.gridspec.GridSpec( ncols=2, nrows=3, height_ratios=[1, 1, 1], width_ratios=[1 - 1.2 / np.pi, 1.2 / np.pi] ) ax_tau = fig.add_subplot(spec[0, :-1]) ax_dim = fig.add_subplot(spec[1, :-1]) ax_r = fig.add_subplot(spec[2, :-1]) if out["Dimension"] > 2: plot_type = "3D" ax_attractor = fig.add_subplot(spec[:, -1], projection="3d") else: plot_type = "2D" ax_attractor = fig.add_subplot(spec[:, -1]) fig.suptitle("Otimization of Complexity Parameters", fontweight="bold", fontsize=16) plt.subplots_adjust(hspace=0.4, wspace=0.05) # Plot tau optimization # Plot Attractor _embedding_delay_plot( signal, metric_values=metric_values, tau_sequence=tau_sequence, tau=out["Delay"], metric=metric, ax0=ax_tau, ax1=ax_attractor, plot=plot_type, ) # Plot dimension optimization if dimension_method.lower() in ["afnn"]: _embedding_dimension_plot( method=dimension_method, dimension_seq=dimension_seq, min_dimension=out["Dimension"], E1=optimize_indices[0], E2=optimize_indices[1], ax=ax_dim, ) if dimension_method.lower() in ["fnn"]: _embedding_dimension_plot( method=dimension_method, dimension_seq=dimension_seq, min_dimension=out["Dimension"], f1=optimize_indices[0], f2=optimize_indices[1], f3=optimize_indices[2], ax=ax_dim, ) # Plot r optimization _optimize_tolerance_plot(out["Tolerance"], {"Values": r_range, "Scores": ApEn}, ax=ax_r) return fig # ============================================================================= # Internals # ============================================================================== def _complexity_delay(signal, delay_max=100, method="fraser1986"): # Initalize vectors if isinstance(delay_max, int): tau_sequence = np.arange(1, delay_max) else: tau_sequence = np.array(delay_max) # Get metric # Method method = method.lower() if method in ["fraser", "fraser1986", "tdmi"]: metric = "Mutual Information" algorithm = "first local minimum" elif method in ["theiler", "theiler1990"]: metric = "Autocorrelation" algorithm = "first 1/e crossing" elif method in ["casdagli", "casdagli1991"]: metric = "Autocorrelation" algorithm = "first zero crossing" elif method in ["rosenstein", "rosenstein1993", "adfd"]: metric = "Displacement" algorithm = "closest to 40% of the slope" else: raise ValueError("NeuroKit error: complexity_delay(): 'method' not recognized.") metric_values = _embedding_delay_metric(signal, tau_sequence, metric=metric) # Get optimal tau optimal = _embedding_delay_select(metric_values, algorithm=algorithm) if ~	np.isnan(optimal)	numpy.isnan
# coding: utf-8 import os import sys sys.path.append(os.path.abspath(os.path.join(sys.path[0], '../'))) from model.model import ResNetLayer3Feat, ResNetLayer4Feat import torch import torch.nn.functional as F from torchvision import transforms import numpy as np from dataloader import TrainDataLoader from torch.autograd import Variable import outils from tqdm import tqdm import json import argparse parser = argparse.ArgumentParser() parser.add_argument( '--outDir', type=str , help='output model directory') ##---- Loss Parameter ----#### parser.add_argument( '--tripleLossThreshold', type=float , default = 1.0, help='threshold for triple loss') ##---- Search, Train, Validate Region ----#### parser.add_argument( '--searchRegion', type=int, default=1, help='feat size') ##---- Training parameters ----#### parser.add_argument( '--modelPth', type=str, default = '../model/net98_8.pth', help='finetune model weight path') parser.add_argument( '--searchDir', type=str, default= '../data/watermark/C_cross_domain/trainBG2/', help='searching directory') parser.add_argument( '--queryDir', type=str, default= '../data/watermark/C_cross_domain/trainBG2/', help='query image directory') parser.add_argument( '--nbEpoch', type=int , default = 300, help='Number of training epochs') parser.add_argument( '--lr', type=float , default = 1e-5, help='learning rate') parser.add_argument( '--batchSize', type=int , default = 8, help='batch size') parser.add_argument( '--cuda', action='store_true', help='cuda setting') parser.add_argument( '--nbSearchImgEpoch', type=int, default = 2000, help='maximum number of searching image in one epoch') parser.add_argument( '--featScaleBase', type=int, default= 22, help='median # of features in the scale list ') parser.add_argument( '--stepNbFeat', type=int, default= 3, help='difference nb feature in adjacent scales ') parser.add_argument( '--nbscale', type=int, default= 2, help='# of octaves') parser.add_argument( '--featLayer', type = str, default='conv4', choices=['conv4', 'conv5'], help='which feature, conv4 or conv5') parser.add_argument( '--labelInfo', type = str, default='../data/crossDomainTraining.json', help='label category') parser.add_argument( '--tmpTrainDir', type = str, default='./trainPair', help='temporal image directory to store training pairs') parser.add_argument( '--eta', type = float, default=1e-7, help='eta for calculate norm') parser.add_argument( '--margin', type = int, default=3, help='keep top K ') parser.add_argument( '--tolerance', type = float, default=4, help='tolerance') parser.add_argument( '--valK', type = int, default=300, help='keep top K for validation') parser.add_argument( '--K', type = int, default=300, help='keep top K ') parser.add_argument( '--dataset', type = str, default='watermark', choices = ['watermark', 'sketch'], help='running on which dataset') args = parser.parse_args() tqdm.monitor_interval = 0 print (args) if os.path.exists(args.tmpTrainDir) : cmd = 'rm -r {}'.format(args.tmpTrainDir) os.system(cmd) os.mkdir(args.tmpTrainDir) ## Dataset, Minimum dimension, Total patch during the training with open(args.labelInfo, 'r') as f : label = json.load(f) QueryImgList = sorted(label['queryImg']) SearchImgList = sorted(label['searchImg']) labelCategory = label['annotation'] nbPatchTotal = args.nbSearchImgEpoch imgFeatMin = args.searchRegion + 2 * args.margin + 1 ## Minimum dimension of feature map in a image tolerance = args.tolerance / float(args.featScaleBase) ## Loading model if args.dataset == 'watermark': normalize = transforms.Normalize(mean = [ 0.75, 0.70, 0.65 ], std = [ 0.14,0.15,0.16 ]) ## watermark classification normalization if args.featLayer == 'conv4' : net = ResNetLayer3Feat( None ) msg = 'loading weight from {}'.format(args.modelPth) print (msg) modelParams = torch.load(args.modelPth) for key in list(modelParams.keys()) : if 'layer4' in key or 'fc.fc1' in key: modelParams.pop(key, None) else : net = ResNetLayer4Feat( None ) msg = 'loading weight from {}'.format(args.modelPth) print (msg) for key in list(modelParams.keys()) : if 'fc.fc1' in key: modelParams.pop(key, None) modelParams = torch.load(args.modelPth) net.load_state_dict( modelParams ) else : normalize = transforms.Normalize(mean = [ 0.485, 0.456, 0.406 ], std = [ 0.229, 0.224, 0.225 ]) ## imagenet classification normalization if args.featLayer == 'conv4' : net = ResNetLayer3Feat( None ) msg = 'loading weight from {}'.format(args.modelPth) print (msg) modelParams = torch.load(args.modelPth) for key in list(modelParams.keys()) : if 'layer4' in key or 'fc' in key: modelParams.pop(key, None) else : net = ResNetLayer4Feat( None ) msg = 'loading weight from {}'.format(args.modelPth) print (msg) for key in list(modelParams.keys()) : if 'fc' in key: modelParams.pop(key, None) modelParams = torch.load(args.modelPth) net.load_state_dict( modelParams ) if args.cuda : net.cuda() featChannel = 256 if args.featLayer == 'conv4' else 512 ## stride size, min input size, channel of feature strideNet = 16 minNet = 15 PATIENCE = 10 # 10 epochs no improved, training will be stopped optimizer = torch.optim.Adam(net.parameters(), lr=args.lr, betas=(0.5, 0.999)) transform = transforms.Compose([ transforms.ToTensor(), normalize, ]) ## Scales scales = [args.featScaleBase - args.stepNbFeat * i for i in range(args.nbscale, 0, -1)] + [args.featScaleBase] + [args.featScaleBase + args.stepNbFeat * i for i in range(1, args.nbscale + 1)] msg = 'We search to match in {:d} scales, the max dimensions in the feature maps are:'.format(len(scales)) print (msg) print (scales) print ('\n\n') ## Output if not os.path.exists(args.outDir) : os.mkdir(args.outDir) history = {'posLoss':[], 'negaLoss':[], 'nbPos':[]} nbEpochNoImproved = 0 bestNbPos = 0 outHistory = os.path.join(args.outDir, 'history.json') if len(QueryImgList) <= args.nbSearchImgEpoch : valQueryImgList = QueryImgList valSearchImgList = SearchImgList else : index = np.linspace(0, len(QueryImgList)-1, args.nbSearchImgEpoch).astype(np.int64) valQueryImgList = [QueryImgList[i] for i in index] valSearchImgList = [SearchImgList[i] for i in index] ## Main Loop for i_ in range(args.nbEpoch) : logPosLoss = [] logNegaLoss = [] print ('Training Epoch {:d}'.format(i_)) print ('---> Get query...') net.eval() if len(QueryImgList) <= args.nbSearchImgEpoch : queryImgList = QueryImgList else : index = np.random.permutation(np.arange(len(QueryImgList)))[:args.nbSearchImgEpoch] queryImgList = [QueryImgList[i] for i in index] if len(SearchImgList) <= args.nbSearchImgEpoch : searchImgList = SearchImgList else : index = np.random.permutation(np.arange(len(SearchImgList)))[:args.nbSearchImgEpoch] searchImgList = [SearchImgList[i] for i in index] featQuery, queryNameList = outils.RandomQueryFeat(nbPatchTotal, featChannel, args.searchRegion, imgFeatMin, minNet, strideNet, transform, net, args.searchDir, args.margin, queryImgList, args.cuda, args.featScaleBase) print ('---> Get topK patches matching to query...') topkImg, topkScale, topkValue, topkW, topkH = outils.RetrievalRes(nbPatchTotal, searchImgList, args.searchDir, args.margin, args.searchRegion, scales, minNet, strideNet, transform, net, featQuery, args.cuda, min(len(searchImgList), args.K)) print ('---> Get training pairs...') posPair, negPair = outils.TrainPair(args.searchDir, searchImgList, topkImg, topkScale, topkW, topkH, transform, net, args.margin, args.cuda, featChannel, args.searchRegion, minNet, strideNet, labelCategory, min(len(searchImgList), args.K), queryNameList, tolerance) outils.saveTrainImgPair(posPair, negPair, args.tmpTrainDir, args.margin, args.searchDir, searchImgList, topkImg, topkScale, topkW, topkH, minNet, strideNet, args.searchRegion) msg = 'NB Pos Train Pair : {:d}, NB Neg Train Pair : {:d}'.format(len(posPair), len(negPair)) print (msg) if len(posPair) < args.batchSize : continue trainloader = TrainDataLoader(args.tmpTrainDir, len(posPair), transform, args.batchSize) ## Calculate Loss net.train() # switch to train mode net.trainFreezeBN() for batch in trainloader : p1, p2, n1, n2 = batch['posI1'], batch['posI2'], batch['negI1'], batch['negI2'] if args.cuda : p1, p2, n1, n2 = p1.cuda(), p2.cuda(), n1.cuda(), n2.cuda() optimizer.zero_grad() p1, p2, n1, n2 = net(p1), net(p2), net(n1), net(n2) posSimilarityBatch, negaSimilarityBatch = outils.CosSimilarity(p1, p2, n1, n2, args.margin, args.eta) ## Triplet Loss loss = torch.clamp(negaSimilarityBatch + args.tripleLossThreshold - 1, min=0) + torch.clamp(args.tripleLossThreshold - posSimilarityBatch, min=0) ## make sure that gradient is not zero if (loss > 0).any() : loss = loss.mean() loss.backward() optimizer.step() logPosLoss.append( posSimilarityBatch.mean().item() ) logNegaLoss.append( negaSimilarityBatch.mean().item() ) # Save model, training history; print loss msg = 'EPOCH {:d}, positive pairs similarity: {:.4f}, negative pairs similarity: {:.4f}'.format(i_, np.mean(logPosLoss), np.mean(logNegaLoss)) print (msg) history['posLoss'].append(np.mean(logPosLoss)) history['negaLoss'].append(	np.mean(logNegaLoss)	numpy.mean
# Lint as: python3 # Copyright 2021 The TensorFlow Authors. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ============================================================================== """Tests for whitening module.""" import numpy as np import tensorflow as tf from delf.python import whiten class WhitenTest(tf.test.TestCase): def testApplyWhitening(self): # Testing the application of the learned whitening. vectors = np.array([[0.14022471, 0.96360618], [0.37601032, 0.25528411]]) # Learn whitening for the `vectors`. First element in the `vectors` is # viewed is the example query and the second element is the corresponding # positive. mean_vector, projection = whiten.learn_whitening(vectors, [0], [1]) # Apply the computed whitening. whitened_vectors = whiten.apply_whitening(vectors, mean_vector, projection) expected_whitened_vectors = np.array([[0., 9.99999000e-01], [0., -2.81240452e-13]]) # Compare the obtained whitened vectors with the expected result. self.assertAllClose(whitened_vectors, expected_whitened_vectors) def testLearnWhitening(self): # Testing whitening learning function. input = np.array([[0.14022471, 0.96360618], [0.37601032, 0.25528411]]) # Obtain the mean descriptor vector and the projection matrix. mean_vector, projection = whiten.learn_whitening(input, [0], [1]) expected_mean_vector = np.array([[0.14022471], [0.37601032]]) expected_projection = np.array([[1.18894378e+00, -1.74326044e-01], [1.45071361e+04, 9.89421193e+04]]) # Check that the both calculated values are close to the expected values. self.assertAllClose(mean_vector, expected_mean_vector) self.assertAllClose(projection, expected_projection) def testCholeskyPositiveDefinite(self): # Testing the Cholesky decomposition for the positive definite matrix. input = np.array([[1, -2j], [2j, 5]]) output = whiten.cholesky(input) expected_output = np.array([[1. + 0.j, 0. + 0.j], [0. + 2.j, 1. + 0.j]]) # Check that the expected output is obtained. self.assertAllClose(output, expected_output) # Check that the properties of the Cholesky decomposition are satisfied. self.assertAllClose(np.matmul(output, output.T.conj()), input) def testCholeskyNonPositiveDefinite(self): # Testing the Cholesky decomposition for a non-positive definite matrix. input_matrix = np.array([[1., 2.], [-2., 1.]]) decomposition = whiten.cholesky(input_matrix) expected_output =	np.array([[2., -2.], [-2., 2.]])	numpy.array
from __future__ import division, print_function import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt from matplotlib.backends.backend_pdf import PdfPages from mpl_toolkits.axes_grid1 import make_axes_locatable from mpl_toolkits.mplot3d import Axes3D import streakline #import streakline2 import myutils import ffwd from streams import load_stream, vcirc_potential, store_progparams, wrap_angles, progenitor_prior #import streams import astropy import astropy.units as u from astropy.constants import G from astropy.table import Table import astropy.coordinates as coord import gala.coordinates as gc import scipy.linalg as la import scipy.interpolate import scipy.optimize import zscale import itertools import copy import pickle # observers # defaults taken as in astropy v2.0 icrs mw_observer = {'z_sun': 27.u.pc, 'galcen_distance': 8.3u.kpc, 'roll': 0u.deg, 'galcen_coord': coord.SkyCoord(ra=266.4051u.deg, dec=-28.936175u.deg, frame='icrs')} vsun = {'vcirc': 237.8u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]u.km/u.s} vsun0 = {'vcirc': 237.8u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]u.km/u.s} gc_observer = {'z_sun': 27.u.pc, 'galcen_distance': 0.1u.kpc, 'roll': 0u.deg, 'galcen_coord': coord.SkyCoord(ra=266.4051u.deg, dec=-28.936175u.deg, frame='icrs')} vgc = {'vcirc': 0u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]u.km/u.s} vgc0 = {'vcirc': 0u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]u.km/u.s} MASK = -9999 pparams_fid = [np.log10(0.5e10)u.Msun, 0.7u.kpc, np.log10(6.8e10)u.Msun, 3u.kpc, 0.28u.kpc, 430u.km/u.s, 30u.kpc, 1.57u.rad, 1u.Unit(1), 1u.Unit(1), 1u.Unit(1), 0.u.pc/u.Myr*2, 0.u.pc/u.Myr*2, 0.u.pc/u.Myr*2, 0.u.Gyr*-2, 0.u.Gyr*-2, 0.u.Gyr*-2, 0.u.Gyr*-2, 0.u.Gyr*-2, 0.u.Gyr*-2u.kpc*-1, 0.u.Gyr*-2u.kpc*-1, 0.u.Gyr*-2u.kpc*-1, 0.u.Gyr*-2u.kpc*-1, 0.u.Gyr*-2u.kpc*-1, 0.u.Gyr*-2u.kpc*-1, 0.u.Gyr*-2u.kpc*-1, 0u.deg, 0u.deg, 0u.kpc, 0u.km/u.s, 0u.mas/u.yr, 0u.mas/u.yr] #pparams_fid = [0.5e-5u.Msun, 0.7u.kpc, 6.8e-5u.Msun, 3u.kpc, 0.28u.kpc, 430u.km/u.s, 30u.kpc, 1.57u.rad, 1u.Unit(1), 1u.Unit(1), 1u.Unit(1), 0.u.pc/u.Myr2, 0.u.pc/u.Myr*2, 0.u.pc/u.Myr*2, 0.u.Gyr*-2, 0.u.Gyr*-2, 0.u.Gyr*-2, 0.u.Gyr*-2, 0.u.Gyr*-2, 0u.deg, 0u.deg, 0u.kpc, 0u.km/u.s, 0u.mas/u.yr, 0u.mas/u.yr] class Stream(): def __init__(self, x0=[]u.kpc, v0=[]u.km/u.s, progenitor={'coords': 'galactocentric', 'observer': {}, 'pm_polar': False}, potential='nfw', pparams=[], minit=2e4u.Msun, mfinal=2e4u.Msun, rcl=20u.pc, dr=0.5, dv=2u.km/u.s, dt=1u.Myr, age=6u.Gyr, nstars=600, integrator='lf'): """Initialize """ setup = {} if progenitor['coords']=='galactocentric': setup['x0'] = x0 setup['v0'] = v0 elif (progenitor['coords']=='equatorial') & (len(progenitor['observer'])!=0): if progenitor['pm_polar']: a = v0[1].value phi = v0[2].value v0[1] = anp.sin(phi)u.mas/u.yr v0[2] = anp.cos(phi)u.mas/u.yr # convert positions xeq = coord.SkyCoord(x0[0], x0[1], x0[2], progenitor['observer']) xgal = xeq.transform_to(coord.Galactocentric) setup['x0'] = [xgal.x.to(u.kpc), xgal.y.to(u.kpc), xgal.z.to(u.kpc)]u.kpc # convert velocities setup['v0'] = gc.vhel_to_gal(xeq.icrs, rv=v0[0], pm=v0[1:], *vsun) #setup['v0'] = [v.to(u.km/u.s) for v in vgal]u.km/u.s else: raise ValueError('Observer position needed!') setup['dr'] = dr setup['dv'] = dv setup['minit'] = minit setup['mfinal'] = mfinal setup['rcl'] = rcl setup['dt'] = dt setup['age'] = age setup['nstars'] = nstars setup['integrator'] = integrator setup['potential'] = potential setup['pparams'] = pparams self.setup = setup self.setup_aux = {} self.fill_intid() self.fill_potid() self.st_params = self.format_input() def fill_intid(self): """Assign integrator ID for a given integrator choice Assumes setup dictionary has an 'integrator' key""" if self.setup['integrator']=='lf': self.setup_aux['iaux'] = 0 elif self.setup['integrator']=='rk': self.setup_aux['iaux'] = 1 def fill_potid(self): """Assign potential ID for a given potential choice Assumes d has a 'potential' key""" if self.setup['potential']=='nfw': self.setup_aux['paux'] = 3 elif self.setup['potential']=='log': self.setup_aux['paux'] = 2 elif self.setup['potential']=='point': self.setup_aux['paux'] = 0 elif self.setup['potential']=='gal': self.setup_aux['paux'] = 4 elif self.setup['potential']=='lmc': self.setup_aux['paux'] = 6 elif self.setup['potential']=='dipole': self.setup_aux['paux'] = 8 elif self.setup['potential']=='quad': self.setup_aux['paux'] = 9 elif self.setup['potential']=='octu': self.setup_aux['paux'] = 10 def format_input(self): """Format input parameters for streakline.stream""" p = [None]12 # progenitor position p[0] = self.setup['x0'].si.value p[1] = self.setup['v0'].si.value # potential parameters p[2] = [x.si.value for x in self.setup['pparams']] # stream smoothing offsets p[3] = [self.setup['dr'], self.setup['dv'].si.value] # potential and integrator choice p[4] = self.setup_aux['paux'] p[5] = self.setup_aux['iaux'] # number of steps and stream stars p[6] = int(self.setup['age']/self.setup['dt']) p[7] = int(p[6]/self.setup['nstars']) # cluster properties p[8] = self.setup['minit'].si.value p[9] = self.setup['mfinal'].si.value p[10] = self.setup['rcl'].si.value # time step p[11] = self.setup['dt'].si.value return p def generate(self): """Create streakline model for a stream of set parameters""" #xm1, xm2, xm3, xp1, xp2, xp3, vm1, vm2, vm3, vp1, vp2, vp3 = streakline.stream(p) stream = streakline.stream(self.st_params) self.leading = {} self.leading['x'] = stream[:3]u.m self.leading['v'] = stream[6:9]u.m/u.s self.trailing = {} self.trailing['x'] = stream[3:6]u.m self.trailing['v'] = stream[9:12]u.m/u.s def observe(self, mode='cartesian', wangle=0u.deg, units=[], errors=[], nstars=-1, sequential=False, present=[], logerr=False, observer={'z_sun': 0.u.pc, 'galcen_distance': 8.3u.kpc, 'roll': 0u.deg, 'galcen_ra': 300u.deg, 'galcen_dec': 20u.deg}, vobs={'vcirc': 237.8u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]u.km/u.s}, footprint='none', rotmatrix=None): """Observe the stream stream.obs holds all observations stream.err holds all errors""" x = np.concatenate((self.leading['x'].to(u.kpc).value, self.trailing['x'].to(u.kpc).value), axis=1) u.kpc v = np.concatenate((self.leading['v'].to(u.km/u.s).value, self.trailing['v'].to(u.km/u.s).value), axis=1) * u.km/u.s if mode=='cartesian': # returns coordinates in following order # x(x, y, z), v(vx, vy, vz) if len(units)<2: units.append(self.trailing['x'].unit) units.append(self.trailing['v'].unit) if len(errors)<2: errors.append(0.2u.kpc) errors.append(2u.km/u.s) # positions x = x.to(units[0]) ex = np.ones(np.shape(x))errors[0] ex = ex.to(units[0]) # velocities v = v.to(units[1]) ev = np.ones(np.shape(v))errors[1] ev = ev.to(units[1]) self.obs = np.concatenate([x,v]).value self.err = np.concatenate([ex,ev]).value elif mode=='equatorial': # assumes coordinates in the following order: # ra, dec, distance, vrad, mualpha, mudelta if len(units)!=6: units = [u.deg, u.deg, u.kpc, u.km/u.s, u.mas/u.yr, u.mas/u.yr] if len(errors)!=6: errors = [0.2u.deg, 0.2u.deg, 0.5u.kpc, 1u.km/u.s, 0.2u.mas/u.yr, 0.2u.mas/u.yr] # define reference frame xgal = coord.Galactocentric(x, observer) #frame = coord.Galactocentric(observer) # convert xeq = xgal.transform_to(coord.ICRS) veq = gc.vgal_to_hel(xeq, v, *vobs) # store coordinates ra, dec, dist = [xeq.ra.to(units[0]).wrap_at(wangle), xeq.dec.to(units[1]), xeq.distance.to(units[2])] vr, mua, mud = [veq[2].to(units[3]), veq[0].to(units[4]), veq[1].to(units[5])] obs = np.hstack([ra, dec, dist, vr, mua, mud]).value obs = np.reshape(obs,(6,-1)) if footprint=='sdss': infoot = dec > -2.5u.deg obs = obs[:,infoot] if np.allclose(rotmatrix, np.eye(3))!=1: xi, eta = myutils.rotate_angles(obs[0], obs[1], rotmatrix) obs[0] = xi obs[1] = eta self.obs = obs # store errors err = np.ones(np.shape(self.obs)) if logerr: for i in range(6): err[i] = np.exp(errors[i].to(units[i]).value) else: for i in range(6): err[i] = errors[i].to(units[i]).value self.err = err self.obsunit = units self.obserror = errors # randomly select nstars from the stream if nstars>-1: if sequential: select = np.linspace(0, np.shape(self.obs)[1], nstars, endpoint=False, dtype=int) else: select = np.random.randint(low=0, high=np.shape(self.obs)[1], size=nstars) self.obs = self.obs[:,select] self.err = self.err[:,select] # include only designated dimensions if len(present)>0: self.obs = self.obs[present] self.err = self.err[present] self.obsunit = [ self.obsunit[x] for x in present ] self.obserror = [ self.obserror[x] for x in present ] def prog_orbit(self): """Generate progenitor orbital history""" orbit = streakline.orbit(self.st_params[0], self.st_params[1], self.st_params[2], self.st_params[4], self.st_params[5], self.st_params[6], self.st_params[11], -1) self.orbit = {} self.orbit['x'] = orbit[:3]u.m self.orbit['v'] = orbit[3:]u.m/u.s def project(self, name, N=1000, nbatch=-1): """Project the stream from observed to native coordinates""" poly = np.loadtxt("../data/{0:s}_all.txt".format(name)) self.streak = np.poly1d(poly) self.streak_x = np.linspace(np.min(self.obs[0])-2, np.max(self.obs[0])+2, N) self.streak_y = np.polyval(self.streak, self.streak_x) self.streak_b = np.zeros(N) self.streak_l = np.zeros(N) pdot = np.polyder(poly) for i in range(N): length = scipy.integrate.quad(self._delta_path, self.streak_x[0], self.streak_x[i], args=(pdot,)) self.streak_l[i] = length[0] XB = np.transpose(np.vstack([self.streak_x, self.streak_y])) n = np.shape(self.obs)[1] if nbatch<0: nstep = 0 nbatch = -1 else: nstep = np.int(n/nbatch) i1 = 0 i2 = nbatch for i in range(nstep): XA = np.transpose(np.vstack([np.array(self.obs[0][i1:i2]), np.array(self.obs[1][i1:i2])])) self.emdist(XA, XB, i1=i1, i2=i2) i1 += nbatch i2 += nbatch XA = np.transpose(np.vstack([np.array(self.catalog['ra'][i1:]), np.array(self.catalog['dec'][i1:])])) self.emdist(XA, XB, i1=i1, i2=n) #self.catalog.write("../data/{0:s}_footprint_catalog.txt".format(self.name), format='ascii.commented_header') def emdist(self, XA, XB, i1=0, i2=-1): """""" distances = scipy.spatial.distance.cdist(XA, XB) self.catalog['b'][i1:i2] = np.min(distances, axis=1) imin = np.argmin(distances, axis=1) self.catalog['b'][i1:i2][self.catalog['dec'][i1:i2]<self.streak_y[imin]] = -1 self.catalog['l'][i1:i2] = self.streak_l[imin] def _delta_path(self, x, pdot): """Return integrand for calculating length of a path along a polynomial""" return np.sqrt(1 + np.polyval(pdot, x)2) def plot(self, mode='native', fig=None, color='k', kwargs): """Plot stream""" # Plotting if fig==None: plt.close() plt.figure() ax = plt.axes([0.12,0.1,0.8,0.8]) if mode=='native': # Color setup cindices = np.arange(self.setup['nstars']) # colors of stream particles nor = mpl.colors.Normalize(vmin=0, vmax=self.setup['nstars']) # colormap normalization plt.plot(self.setup['x0'][0].to(u.kpc).value, self.setup['x0'][2].to(u.kpc).value, 'wo', ms=10, mew=2, zorder=3) plt.scatter(self.trailing['x'][0].to(u.kpc).value, self.trailing['x'][2].to(u.kpc).value, s=30, c=cindices, cmap='winter', norm=nor, marker='o', edgecolor='none', lw=0, alpha=0.1) plt.scatter(self.leading['x'][0].to(u.kpc).value, self.leading['x'][2].to(u.kpc).value, s=30, c=cindices, cmap='autumn', norm=nor, marker='o', edgecolor='none', lw=0, alpha=0.1) plt.xlabel("X (kpc)") plt.ylabel("Z (kpc)") elif mode=='observed': plt.subplot(221) plt.plot(self.obs[0], self.obs[1], 'o', color=color, kwargs) plt.xlabel("RA") plt.ylabel("Dec") plt.subplot(223) plt.plot(self.obs[0], self.obs[2], 'o', color=color, kwargs) plt.xlabel("RA") plt.ylabel("Distance") plt.subplot(222) plt.plot(self.obs[3], self.obs[4], 'o', color=color, kwargs) plt.xlabel("V$_r$") plt.ylabel("$\mu\\alpha$") plt.subplot(224) plt.plot(self.obs[3], self.obs[5], 'o', color=color, kwargs) plt.xlabel("V$_r$") plt.ylabel("$\mu\delta$") plt.tight_layout() #plt.minorticks_on() def read(self, fname, units={'x': u.kpc, 'v': u.km/u.s}): """Read stream star positions from a file""" t = np.loadtxt(fname).T n = np.shape(t)[1] ns = int((n-1)/2) self.setup['nstars'] = ns # progenitor self.setup['x0'] = t[:3,0] units['x'] self.setup['v0'] = t[3:,0] * units['v'] # leading tail self.leading = {} self.leading['x'] = t[:3,1:ns+1] * units['x'] self.leading['v'] = t[3:,1:ns+1] * units['v'] # trailing tail self.trailing = {} self.trailing['x'] = t[:3,ns+1:] * units['x'] self.trailing['v'] = t[3:,ns+1:] * units['v'] def save(self, fname): """Save stream star positions to a file""" # define table t = Table(names=('x', 'y', 'z', 'vx', 'vy', 'vz')) # add progenitor info t.add_row(np.ravel([self.setup['x0'].to(u.kpc).value, self.setup['v0'].to(u.km/u.s).value])) # add leading tail infoobsmode tt = Table(np.concatenate((self.leading['x'].to(u.kpc).value, self.leading['v'].to(u.km/u.s).value)).T, names=('x', 'y', 'z', 'vx', 'vy', 'vz')) t = astropy.table.vstack([t,tt]) # add trailing tail info tt = Table(np.concatenate((self.trailing['x'].to(u.kpc).value, self.trailing['v'].to(u.km/u.s).value)).T, names=('x', 'y', 'z', 'vx', 'vy', 'vz')) t = astropy.table.vstack([t,tt]) # save to file t.write(fname, format='ascii.commented_header') # make a streakline model of a stream def stream_model(name='gd1', pparams0=pparams_fid, dt=0.2u.Myr, rotmatrix=np.eye(3), graph=False, graphsave=False, observer=mw_observer, vobs=vsun, footprint='', obsmode='equatorial'): """Create a streakline model of a stream baryonic component as in kupper+2015: 3.4e10u.Msun, 0.7u.kpc, 1e11u.Msun, 6.5u.kpc, 0.26u.kpc""" # vary progenitor parameters mock = pickle.load(open('../data/mock_{}.params'.format(name), 'rb')) for i in range(3): mock['x0'][i] += pparams0[26+i] mock['v0'][i] += pparams0[29+i] # vary potential parameters potential = 'octu' pparams = pparams0[:26] #print(pparams[0]) pparams[0] = (10*pparams0[0].value)pparams0[0].unit pparams[2] = (10*pparams0[2].value)pparams0[2].unit #pparams[0] = pparams0[0]1e15 #pparams[2] = pparams0[2]1e15 #print(pparams[0]) # adjust circular velocity in this halo vobs['vcirc'] = vcirc_potential(observer['galcen_distance'], pparams=pparams) # create a model stream with these parameters params = {'generate': {'x0': mock['x0'], 'v0': mock['v0'], 'progenitor': {'coords': 'equatorial', 'observer': mock['observer'], 'pm_polar': False}, 'potential': potential, 'pparams': pparams, 'minit': mock['mi'], 'mfinal': mock['mf'], 'rcl': 20u.pc, 'dr': 0., 'dv': 0u.km/u.s, 'dt': dt, 'age': mock['age'], 'nstars': 400, 'integrator': 'lf'}, 'observe': {'mode': mock['obsmode'], 'wangle': mock['wangle'], 'nstars':-1, 'sequential':True, 'errors': [2e-4u.deg, 2e-4u.deg, 0.5u.kpc, 5u.km/u.s, 0.5u.mas/u.yr, 0.5u.mas/u.yr], 'present': [0,1,2,3,4,5], 'observer': mock['observer'], 'vobs': mock['vobs'], 'footprint': mock['footprint'], 'rotmatrix': rotmatrix}} stream = Stream(params['generate']) stream.generate() stream.observe(params['observe']) ################################ # Plot observed stream and model if graph: observed = load_stream(name) Ndim = np.shape(observed.obs)[0] modcol = 'k' obscol = 'orange' ylabel = ['Dec (deg)', 'Distance (kpc)', 'Radial velocity (km/s)'] plt.close() fig, ax = plt.subplots(1, 3, figsize=(12,4)) for i in range(3): plt.sca(ax[i]) plt.gca().invert_xaxis() plt.xlabel('R.A. (deg)') plt.ylabel(ylabel[i]) plt.plot(observed.obs[0], observed.obs[i+1], 's', color=obscol, mec='none', ms=8, label='Observed stream') plt.plot(stream.obs[0], stream.obs[i+1], 'o', color=modcol, mec='none', ms=4, label='Fiducial model') if i==0: plt.legend(frameon=False, handlelength=0.5, fontsize='small') plt.tight_layout() if graphsave: plt.savefig('../plots/mock_observables_{}_p{}.png'.format(name, potential), dpi=150) return stream def progenitor_params(n): """Return progenitor parameters for a given stream""" if n==-1: age = 1.6u.Gyr mi = 1e4u.Msun mf = 2e-1u.Msun x0, v0 = gd1_coordinates(observer=mw_observer) elif n==-2: age = 2.7u.Gyr mi = 1e5u.Msun mf = 2e4u.Msun x0, v0 = pal5_coordinates(observer=mw_observer, vobs=vsun0) elif n==-3: age = 3.5u.Gyr mi = 5e4u.Msun mf = 2e-1u.Msun x0, v0 = tri_coordinates(observer=mw_observer) elif n==-4: age = 2u.Gyr mi = 2e4u.Msun mf = 2e-1u.Msun x0, v0 = atlas_coordinates(observer=mw_observer) out = {'x0': x0, 'v0': v0, 'age': age, 'mi': mi, 'mf': mf} return out def gal2eq(x, v, observer=mw_observer, vobs=vsun0): """""" # define reference frame xgal = coord.Galactocentric(np.array(x)[:,np.newaxis]u.kpc, observer) # convert xeq = xgal.transform_to(coord.ICRS) veq = gc.vgal_to_hel(xeq, np.array(v)[:,np.newaxis]u.km/u.s, *vobs) # store coordinates units = [u.deg, u.deg, u.kpc, u.km/u.s, u.mas/u.yr, u.mas/u.yr] xobs = [xeq.ra.to(units[0]), xeq.dec.to(units[1]), xeq.distance.to(units[2])] vobs = [veq[2].to(units[3]), veq[0].to(units[4]), veq[1].to(units[5])] return(xobs, vobs) def gd1_coordinates(observer=mw_observer): """Approximate GD-1 progenitor coordinates""" x = coord.SkyCoord(ra=154.377u.deg, dec=41.5309u.deg, distance=8.2u.kpc, *observer) x_ = x.galactocentric x0 = [x_.x.value, x_.y.value, x_.z.value] v0 = [-90, -250, -120] return (x0, v0) def pal5_coordinates(observer=mw_observer, vobs=vsun0): """Pal5 coordinates""" # sdss ra = 229.0128u.deg dec = -0.1082u.deg # bob's rrlyrae d = 21.7u.kpc # harris #d = 23.2u.kpc # odenkirchen 2002 vr = -58.7u.km/u.s # fritz & kallivayalil 2015 mua = -2.296u.mas/u.yr mud = -2.257u.mas/u.yr d = 24u.kpc x = coord.SkyCoord(ra=ra, dec=dec, distance=d, observer) x0 = x.galactocentric v0 = gc.vhel_to_gal(x.icrs, rv=vr, pm=[mua, mud], vobs).to(u.km/u.s) return ([x0.x.value, x0.y.value, x0.z.value], v0.value.tolist()) def tri_coordinates(observer=mw_observer): """Approximate Triangulum progenitor coordinates""" x = coord.SkyCoord(ra=22.38u.deg, dec=30.26u.deg, distance=33u.kpc, *observer) x_ = x.galactocentric x0 = [x_.x.value, x_.y.value, x_.z.value] v0 = [-40, 155, 155] return (x0, v0) def atlas_coordinates(observer=mw_observer): """Approximate ATLAS progenitor coordinates""" x = coord.SkyCoord(ra=20u.deg, dec=-27u.deg, distance=20u.kpc, *observer) x_ = x.galactocentric x0 = [x_.x.value, x_.y.value, x_.z.value] v0 = [40, 150, -120] return (x0, v0) # great circle orientation def find_greatcircle(stream=None, name='gd1', pparams=pparams_fid, dt=0.2u.Myr, save=True, graph=True): """Save rotation matrix for a stream model""" if stream==None: stream = stream_model(name, pparams0=pparams, dt=dt) # find the pole ra = np.radians(stream.obs[0]) dec = np.radians(stream.obs[1]) rx = np.cos(ra) * np.cos(dec) ry = np.sin(ra) * np.cos(dec) rz = np.sin(dec) r = np.column_stack((rx, ry, rz)) # fit the plane x0 = np.array([0, 1, 0]) lsq = scipy.optimize.minimize(wfit_plane, x0, args=(r,)) x0 = lsq.x/np.linalg.norm(lsq.x) ra0 = np.arctan2(x0[1], x0[0]) dec0 = np.arcsin(x0[2]) ra0 += np.pi dec0 = np.pi/2 - dec0 # euler rotations R0 = myutils.rotmatrix(np.degrees(-ra0), 2) R1 = myutils.rotmatrix(np.degrees(dec0), 1) R2 = myutils.rotmatrix(0, 2) R = np.dot(R2, np.matmul(R1, R0)) xi, eta = myutils.rotate_angles(stream.obs[0], stream.obs[1], R) # put xi = 50 at the beginning of the stream xi[xi>180] -= 360 xi += 360 xi0 = np.min(xi) - 50 R2 = myutils.rotmatrix(-xi0, 2) R = np.dot(R2, np.matmul(R1, R0)) xi, eta = myutils.rotate_angles(stream.obs[0], stream.obs[1], R) if save: np.save('../data/rotmatrix_{}'.format(name), R) f = open('../data/mock_{}.params'.format(name), 'rb') mock = pickle.load(f) mock['rotmatrix'] = R f.close() f = open('../data/mock_{}.params'.format(name), 'wb') pickle.dump(mock, f) f.close() if graph: plt.close() fig, ax = plt.subplots(1,2,figsize=(10,5)) plt.sca(ax[0]) plt.plot(stream.obs[0], stream.obs[1], 'ko') plt.xlabel('R.A. (deg)') plt.ylabel('Dec (deg)') plt.sca(ax[1]) plt.plot(xi, eta, 'ko') plt.xlabel('$\\xi$ (deg)') plt.ylabel('$\\eta$ (deg)') plt.ylim(-5, 5) plt.tight_layout() plt.savefig('../plots/gc_orientation_{}.png'.format(name)) return R def wfit_plane(x, r, p=None): """Fit a plane to a set of 3d points""" Np = np.shape(r)[0] if np.any(p)==None: p = np.ones(Np) Q = np.zeros((3,3)) for i in range(Np): Q += p[i]*2 np.outer(r[i], r[i]) x = x/np.linalg.norm(x) lsq = np.inner(x, np.inner(Q, x)) return lsq # observed streams #def load_stream(n): #"""Load stream observations""" #if n==-1: #observed = load_gd1(present=[0,1,2,3]) #elif n==-2: #observed = load_pal5(present=[0,1,2,3]) #elif n==-3: #observed = load_tri(present=[0,1,2,3]) #elif n==-4: #observed = load_atlas(present=[0,1,2,3]) #return observed def endpoints(name): """""" stream = load_stream(name) # find endpoints amin = np.argmin(stream.obs[0]) amax = np.argmax(stream.obs[0]) ra = np.array([stream.obs[0][i] for i in [amin, amax]]) dec = np.array([stream.obs[1][i] for i in [amin, amax]]) f = open('../data/mock_{}.params'.format(name), 'rb') mock = pickle.load(f) # rotate endpoints R = mock['rotmatrix'] xi, eta = myutils.rotate_angles(ra, dec, R) #xi, eta = myutils.rotate_angles(stream.obs[0], stream.obs[1], R) mock['ra_range'] = ra mock['xi_range'] = xi #np.percentile(xi, [10,90]) f.close() f = open('../data/mock_{}.params'.format(name), 'wb') pickle.dump(mock, f) f.close() def load_pal5(present, nobs=50, potential='gal'): """""" if len(present)==2: t = Table.read('../data/pal5_members.txt', format='ascii.commented_header') dist = 21.7 deltadist = 0.7 np.random.seed(34) t = t[np.random.randint(0, high=len(t), size=nobs)] nobs = len(t) d = np.random.randn(nobs)deltadist + dist obs = np.array([t['ra'], t['dec'], d]) obsunit = [u.deg, u.deg, u.kpc] err = np.repeat( np.array([2e-4, 2e-4, 0.7]), nobs ).reshape(3, -1) obserr = [2e-4u.deg, 2e-4u.deg, 0.5u.kpc] if len(present)==3: #t = Table.read('../data/pal5_kinematic.txt', format='ascii.commented_header') t = Table.read('../data/pal5_allmembers.txt', format='ascii.commented_header') obs = np.array([t['ra'], t['dec'], t['d']]) obsunit = [u.deg, u.deg, u.kpc] err = np.array([t['err_ra'], t['err_dec'], t['err_d']]) obserr = [2e-4u.deg, 2e-4u.deg, 0.5u.kpc] if len(present)==4: #t = Table.read('../data/pal5_kinematic.txt', format='ascii.commented_header') t = Table.read('../data/pal5_allmembers.txt', format='ascii.commented_header') obs = np.array([t['ra'], t['dec'], t['d'], t['vr']]) obsunit = [u.deg, u.deg, u.kpc, u.km/u.s] err = np.array([t['err_ra'], t['err_dec'], t['err_d'], t['err_vr']]) obserr = [2e-4u.deg, 2e-4u.deg, 0.5u.kpc, 5u.km/u.s] observed = Stream(potential=potential) observed.obs = obs observed.obsunit = obsunit observed.err = err observed.obserror = obserr return observed def load_gd1(present, nobs=50, potential='gal'): """""" if len(present)==3: t = Table.read('../data/gd1_members.txt', format='ascii.commented_header') dist = 0 deltadist = 0.5 np.random.seed(34) t = t[np.random.randint(0, high=len(t), size=nobs)] nobs = len(t) d = np.random.randn(nobs)deltadist + dist d += t['l']0.04836 + 9.86 obs = np.array([t['ra'], t['dec'], d]) obsunit = [u.deg, u.deg, u.kpc] err = np.repeat( np.array([2e-4, 2e-4, 0.5]), nobs ).reshape(3, -1) obserr = [2e-4u.deg, 2e-4u.deg, 0.5u.kpc] if len(present)==4: #t = Table.read('../data/gd1_kinematic.txt', format='ascii.commented_header') t = Table.read('../data/gd1_allmembers.txt', format='ascii.commented_header') obs = np.array([t['ra'], t['dec'], t['d'], t['vr']]) obsunit = [u.deg, u.deg, u.kpc, u.km/u.s] err = np.array([t['err_ra'], t['err_dec'], t['err_d'], t['err_vr']]) obserr = [2e-4u.deg, 2e-4u.deg, 0.5u.kpc, 5u.km/u.s] ind = np.all(obs!=MASK, axis=0) observed = Stream(potential=potential) observed.obs = obs#[np.array(present)] observed.obsunit = obsunit observed.err = err#[np.array(present)] observed.obserror = obserr return observed def load_tri(present, nobs=50, potential='gal'): """""" if len(present)==4: t = Table.read('../data/tri_allmembers.txt', format='ascii.commented_header') obs = np.array([t['ra'], t['dec'], t['d'], t['vr']]) obsunit = [u.deg, u.deg, u.kpc, u.km/u.s] err = np.array([t['err_ra'], t['err_dec'], t['err_d'], t['err_vr']]) obserr = [2e-4u.deg, 2e-4u.deg, 0.5u.kpc, 5u.km/u.s] if len(present)==3: t = Table.read('../data/tri_allmembers.txt', format='ascii.commented_header') obs = np.array([t['ra'], t['dec'], t['d']]) obsunit = [u.deg, u.deg, u.kpc] err = np.array([t['err_ra'], t['err_dec'], t['err_d']]) obserr = [2e-4u.deg, 2e-4u.deg, 0.5u.kpc] ind = np.all(obs!=MASK, axis=0) observed = Stream(potential=potential) observed.obs = obs observed.obsunit = obsunit observed.err = err observed.obserror = obserr return observed def load_atlas(present, nobs=50, potential='gal'): """""" ra, dec = atlas_track() n = np.size(ra) d = np.random.randn(n)2 + 20 obs = np.array([ra, dec, d]) obsunit = [u.deg, u.deg, u.kpc] err = np.array([np.ones(n)0.05, np.ones(n)0.05, np.ones(n)2]) obserr = [2e-4u.deg, 2e-4u.deg, 0.5u.kpc, 5u.km/u.s] observed = Stream(potential=potential) observed.obs = obs observed.obsunit = obsunit observed.err = err observed.obserror = obserr return observed def atlas_track(): """""" ra0, dec0 = np.radians(77.16), np.radians(46.92 - 90) # euler rotations D = np.array([[np.cos(ra0), np.sin(ra0), 0], [-np.sin(ra0), np.cos(ra0), 0], [0, 0, 1]]) C = np.array([[np.cos(dec0), 0, np.sin(dec0)], [0, 1, 0], [-np.sin(dec0), 0, np.cos(dec0)]]) B = np.diag(np.ones(3)) R = np.dot(B, np.dot(C, D)) Rinv = np.linalg.inv(R) l0 = np.linspace(0, 2np.pi, 500) b0 = np.zeros(500) xeq, yeq, zeq = myutils.eq2car(l0, b0) eq = np.column_stack((xeq, yeq, zeq)) eq_rot = np.zeros(np.shape(eq)) for i in range(np.size(l0)): eq_rot[i] = np.dot(Rinv, eq[i]) l0_rot, b0_rot = myutils.car2eq(eq_rot[:, 0], eq_rot[:, 1], eq_rot[:, 2]) ra_s, dec_s = np.degrees(l0_rot), np.degrees(b0_rot) ind_s = (ra_s>17) & (ra_s<30) ra_s = ra_s[ind_s] dec_s = dec_s[ind_s] return (ra_s, dec_s) def fancy_name(n): """Return nicely formatted stream name""" names = {-1: 'GD-1', -2: 'Palomar 5', -3: 'Triangulum', -4: 'ATLAS'} return names[n] # model parameters def get_varied_pars(vary): """Return indices and steps for a preset of varied parameters, and a label for varied parameters Parameters: vary - string setting the parameter combination to be varied, options: 'potential', 'progenitor', 'halo', or a list thereof""" if type(vary) is not list: vary = [vary] Nt = len(vary) vlabel = '_'.join(vary) pid = [] dp = [] for v in vary: o1, o2 = get_varied_bytype(v) pid += o1 dp += o2 return (pid, dp, vlabel) def get_varied_bytype(vary): """Get varied parameter of a particular type""" if vary=='potential': pid = [5,6,8,10,11] dp = [20u.km/u.s, 2u.kpc, 0.05u.Unit(1), 0.05u.Unit(1), 0.4e11u.Msun] elif vary=='bary': pid = [0,1,2,3,4] # gd1 dp = [1e-1u.Msun, 0.005u.kpc, 1e-1u.Msun, 0.002u.kpc, 0.002u.kpc] ## atlas & triangulum #dp = [0.4e5u.Msun, 0.0005u.kpc, 0.5e6u.Msun, 0.0002u.kpc, 0.002u.kpc] # pal5 dp = [1e-2u.Msun, 0.000005u.kpc, 1e-2u.Msun, 0.000002u.kpc, 0.00002u.kpc] dp = [1e-7u.Msun, 0.5u.kpc, 1e-7u.Msun, 0.5u.kpc, 0.5u.kpc] dp = [1e-2u.Msun, 0.5u.kpc, 1e-2u.Msun, 0.5u.kpc, 0.5u.kpc] elif vary=='halo': pid = [5,6,8,10] dp = [20u.km/u.s, 2u.kpc, 0.05u.Unit(1), 0.05u.Unit(1)] dp = [35u.km/u.s, 2.9u.kpc, 0.05u.Unit(1), 0.05u.Unit(1)] elif vary=='progenitor': pid = [26,27,28,29,30,31] dp = [1u.deg, 1u.deg, 0.5u.kpc, 20u.km/u.s, 0.3u.mas/u.yr, 0.3u.mas/u.yr] elif vary=='dipole': pid = [11,12,13] #dp = [1e-11u.Unit(1), 1e-11u.Unit(1), 1e-11u.Unit(1)] dp = [0.05u.pc/u.Myr*2, 0.05u.pc/u.Myr*2, 0.05u.pc/u.Myr*2] elif vary=='quad': pid = [14,15,16,17,18] dp = [0.5u.Gyr*-2 for x in range(5)] elif vary=='octu': pid = [19,20,21,22,23,24,25] dp = [0.001u.Gyr*-2u.kpc*-1 for x in range(7)] else: pid = [] dp = [] return (pid, dp) def get_parlabel(pid): """Return label for a list of parameter ids Parameter: pid - list of parameter ids""" master = ['log $M_b$', '$a_b$', 'log $M_d$', '$a_d$', '$b_d$', '$V_h$', '$R_h$', '$\phi$', '$q_x$', '$q_y$', '$q_z$', '$a_{1,-1}$', '$a_{1,0}$', '$a_{1,1}$', '$a_{2,-2}$', '$a_{2,-1}$', '$a_{2,0}$', '$a_{2,1}$', '$a_{2,2}$', '$a_{3,-3}$', '$a_{3,-2}$', '$a_{3,-1}$', '$a_{3,0}$', '$a_{3,1}$', '$a_{3,2}$', '$a_{3,3}$', '$RA_p$', '$Dec_p$', '$d_p$', '$V_{r_p}$', '$\mu_{\\alpha_p}$', '$\mu_{\delta_p}$', ] master_units = ['dex', 'kpc', 'dex', 'kpc', 'kpc', 'km/s', 'kpc', 'rad', '', '', '', 'pc/Myr$^2$', 'pc/Myr$^2$', 'pc/Myr$^2$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'deg', 'deg', 'kpc', 'km/s', 'mas/yr', 'mas/yr', ] if type(pid) is list: labels = [] units = [] for i in pid: labels += [master[i]] units += [master_units[i]] else: labels = master[pid] units = master_units[pid] return (labels, units) def get_steps(Nstep=50, log=False): """Return deltax steps in both directions Paramerets: Nstep - number of steps in one direction (default: 50) log - if True, steps are logarithmically spaced (default: False)""" if log: step = np.logspace(-10, 1, Nstep) else: step = np.linspace(0.1, 10, Nstep) step = np.concatenate([-step[::-1], step]) return (Nstep, step) def lmc_position(): """""" ra = 80.8939u.deg dec = -69.7561u.deg dm = 18.48 d = 10(1 + dm/5)u.pc x = coord.SkyCoord(ra=ra, dec=dec, distance=d) xgal = [x.galactocentric.x.si, x.galactocentric.y.si, x.galactocentric.z.si] print(xgal) def lmc_properties(): """""" # penarrubia 2016 mass = 2.5e11u.Msun ra = 80.8939u.deg dec = -69.7561u.deg dm = 18.48 d = 10(1 + dm/5)u.pc c1 = coord.SkyCoord(ra=ra, dec=dec, distance=d) cgal1 = c1.transform_to(coord.Galactocentric) xgal = np.array([cgal1.x.to(u.kpc).value, cgal1.y.to(u.kpc).value, cgal1.z.to(u.kpc).value])u.kpc return (mass, xgal) # fit bspline to a stream model def fit_bspline(n, pparams=pparams_fid, dt=0.2u.Myr, align=False, save='', graph=False, graphsave='', fiducial=False): """Fit bspline to a stream model and save to file""" Ndim = 6 fits = [None](Ndim-1) if align: rotmatrix = np.load('../data/rotmatrix_{}.npy'.format(n)) else: rotmatrix = None stream = stream_model(n, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) Nobs = 10 k = 3 isort = np.argsort(stream.obs[0]) ra = np.linspace(np.min(stream.obs[0])1.05, np.max(stream.obs[0])0.95, Nobs) t = np.r_[(stream.obs[0][isort][0],)(k+1), ra, (stream.obs[0][isort][-1],)(k+1)] for j in range(Ndim-1): fits[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][isort], stream.obs[j+1][isort], t, k=k) if len(save)>0: np.savez('../data/{:s}'.format(save), fits=fits) if graph: xlims, ylims = get_stream_limits(n, align) ylabel = ['R.A. (deg)', 'Dec (deg)', 'd (kpc)', '$V_r$ (km/s)', '$\mu_\\alpha$ (mas/yr)', '$\mu_\delta$ (mas/yr)'] if align: ylabel[:2] = ['$\\xi$ (deg)', '$\\eta$ (deg)'] if fiducial: stream_fid = stream_model(n, pparams0=pparams_fid, dt=dt, rotmatrix=rotmatrix) fidsort = np.argsort(stream_fid.obs[0]) ra = np.linspace(np.min(stream_fid.obs[0])1.05, np.max(stream_fid.obs[0])0.95, Nobs) tfid = np.r_[(stream_fid.obs[0][fidsort][0],)(k+1), ra, (stream_fid.obs[0][fidsort][-1],)(k+1)] llabel = 'b-spline fit' else: llabel = '' plt.close() fig, ax = plt.subplots(2,5,figsize=(20,5), sharex=True, gridspec_kw = {'height_ratios':[3, 1]}) for i in range(Ndim-1): plt.sca(ax[0][i]) plt.plot(stream.obs[0], stream.obs[i+1], 'ko') plt.plot(stream.obs[0][isort], fits[i](stream.obs[0][isort]), 'r-', lw=2, label=llabel) if fiducial: fits_fid = scipy.interpolate.make_lsq_spline(stream_fid.obs[0][fidsort], stream_fid.obs[i+1][fidsort], tfid, k=k) plt.plot(stream_fid.obs[0], stream_fid.obs[i+1], 'wo', mec='k', alpha=0.1) plt.plot(stream_fid.obs[0][fidsort], fits_fid(stream_fid.obs[0][fidsort]), 'b-', lw=2, label='Fiducial') plt.ylabel(ylabel[i+1]) plt.xlim(xlims[0], xlims[1]) plt.ylim(ylims[i][0], ylims[i][1]) plt.sca(ax[1][i]) if fiducial: yref = fits_fid(stream.obs[0]) ycolor = 'b' else: yref = fits[i](stream.obs[0]) ycolor = 'r' plt.axhline(0, color=ycolor, lw=2) if fiducial: plt.plot(stream.obs[0][isort], stream.obs[i+1][isort] - stream_fid.obs[i+1][fidsort], 'wo', mec='k', alpha=0.1) plt.plot(stream.obs[0], stream.obs[i+1] - yref, 'ko') if fiducial: fits_diff = scipy.interpolate.make_lsq_spline(stream.obs[0][isort], stream.obs[i+1][isort] - stream_fid.obs[i+1][fidsort], t, k=k) plt.plot(stream.obs[0][isort], fits_diff(stream.obs[0][isort]), 'r--') plt.plot(stream.obs[0][isort], fits[i](stream.obs[0][isort]) - yref[isort], 'r-', lw=2, label=llabel) plt.xlabel(ylabel[0]) plt.ylabel('$\Delta$ {}'.format(ylabel[i+1].split(' ')[0])) if fiducial: plt.sca(ax[0][Ndim-2]) plt.legend(fontsize='small') plt.tight_layout() if len(graphsave)>0: plt.savefig('../plots/{:s}.png'.format(graphsave)) def fitbyt_bspline(n, pparams=pparams_fid, dt=0.2u.Myr, align=False, save='', graph=False, graphsave='', fiducial=False): """Fit each tail individually""" Ndim = 6 fits = [None](Ndim-1) if align: rotmatrix = np.load('../data/rotmatrix_{}.npy'.format(n)) else: rotmatrix = None stream = stream_model(n, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) Nobs = 10 k = 3 isort = np.argsort(stream.obs[0]) ra = np.linspace(np.min(stream.obs[0])1.05, np.max(stream.obs[0])0.95, Nobs) t = np.r_[(stream.obs[0][isort][0],)(k+1), ra, (stream.obs[0][isort][-1],)(k+1)] for j in range(Ndim-1): fits[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][isort], stream.obs[j+1][isort], t, k=k) if len(save)>0: np.savez('../data/{:s}'.format(save), fits=fits) if graph: xlims, ylims = get_stream_limits(n, align) ylabel = ['R.A. (deg)', 'Dec (deg)', 'd (kpc)', '$V_r$ (km/s)', '$\mu_\\alpha$ (mas/yr)', '$\mu_\delta$ (mas/yr)'] if align: ylabel[:2] = ['$\\xi$ (deg)', '$\\eta$ (deg)'] if fiducial: stream_fid = stream_model(n, pparams0=pparams_fid, dt=dt, rotmatrix=rotmatrix) plt.close() fig, ax = plt.subplots(2,Ndim,figsize=(20,4), sharex=True, gridspec_kw = {'height_ratios':[3, 1]}) for i in range(Ndim): plt.sca(ax[0][i]) Nhalf = int(0.5np.size(stream.obs[i])) plt.plot(stream.obs[i][:Nhalf], 'o') plt.plot(stream.obs[i][Nhalf:], 'o') if fiducial: plt.plot(stream_fid.obs[i][:Nhalf], 'wo', mec='k', mew=0.2, alpha=0.5) plt.plot(stream_fid.obs[i][Nhalf:], 'wo', mec='k', mew=0.2, alpha=0.5) plt.ylabel(ylabel[i]) plt.sca(ax[1][i]) if fiducial: plt.plot(stream.obs[i][:Nhalf] - stream_fid.obs[i][:Nhalf], 'o') plt.plot(stream.obs[i][Nhalf:] - stream_fid.obs[i][Nhalf:], 'o') if fiducial: plt.sca(ax[0][Ndim-1]) plt.legend(fontsize='small') plt.tight_layout() if len(graphsave)>0: plt.savefig('../plots/{:s}.png'.format(graphsave)) else: return fig def get_stream_limits(n, align=False): """Return lists with limiting values in different dimensions""" if n==-1: xlims = [260, 100] ylims = [[-20, 70], [5, 15], [-400, 400], [-15,5], [-15, 5]] elif n==-2: xlims = [250, 210] ylims = [[-20, 15], [17, 27], [-80, -20], [-5,0], [-5, 0]] elif n==-3: xlims = [27, 17] ylims = [[10, 50], [34, 36], [-175, -50], [0.45, 1], [0.1, 0.7]] elif n==-4: xlims = [35, 10] ylims = [[-40, -20], [15, 25], [50, 200], [-0.5,0.5], [-1.5, -0.5]] if align: ylims[0] = [-5, 5] xup = [110, 110, 80, 80] xlims = [xup[np.abs(n)-1], 40] return (xlims, ylims) # step sizes for derivatives def iterate_steps(n): """Calculate derivatives for different parameter classes, and plot""" for vary in ['bary', 'halo', 'progenitor']: print(n, vary) step_convergence(n, Nstep=10, vary=vary) choose_step(n, Nstep=10, vary=vary) def iterate_plotsteps(n): """Plot stream models for a variety of model parameters""" for vary in ['bary', 'halo', 'progenitor']: print(n, vary) pid, dp, vlabel = get_varied_pars(vary) for p in range(len(pid)): plot_steps(n, p=p, Nstep=5, vary=vary, log=False) def plot_steps(n, p=0, Nstep=20, log=True, dt=0.2u.Myr, vary='halo', verbose=False, align=True, observer=mw_observer, vobs=vsun): """Plot stream for different values of a potential parameter""" if align: rotmatrix = np.load('../data/rotmatrix_{}.npy'.format(n)) else: rotmatrix = None pparams0 = pparams_fid pid, dp, vlabel = get_varied_pars(vary) plabel, punit = get_parlabel(pid[p]) Nstep, step = get_steps(Nstep=Nstep, log=log) plt.close() fig, ax = plt.subplots(5,5,figsize=(20,10), sharex=True, gridspec_kw = {'height_ratios':[3, 1, 1, 1, 1]}) # fiducial model stream0 = stream_model(n, pparams0=pparams0, dt=dt, rotmatrix=rotmatrix, observer=observer, vobs=vobs) Nobs = 10 k = 3 isort = np.argsort(stream0.obs[0]) ra = np.linspace(np.min(stream0.obs[0])1.05, np.max(stream0.obs[0])0.95, Nobs) t = np.r_[(stream0.obs[0][isort][0],)(k+1), ra, (stream0.obs[0][isort][-1],)(k+1)] fits = [None]5 for j in range(5): fits[j] = scipy.interpolate.make_lsq_spline(stream0.obs[0][isort], stream0.obs[j+1][isort], t, k=k) # excursions stream_fits = [[None] * 5 for x in range(2 * Nstep)] for i, s in enumerate(step[:]): pparams = [x for x in pparams0] pparams[pid[p]] = pparams[pid[p]] + sdp[p] stream = stream_model(n, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) color = mpl.cm.RdBu(i/(2Nstep-1)) #print(i, dp[p], pparams) # fits iexsort = np.argsort(stream.obs[0]) raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs) tex = np.r_[(stream.obs[0][iexsort][0],)(k+1), raex, (stream.obs[0][iexsort][-1],)(k+1)] fits_ex = [None]5 for j in range(5): fits_ex[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[j+1][iexsort], tex, k=k) stream_fits[i][j] = fits_ex[j] plt.sca(ax[0][j]) plt.plot(stream.obs[0], stream.obs[j+1], 'o', color=color, ms=2) plt.sca(ax[1][j]) plt.plot(stream.obs[0], stream.obs[j+1] - fits[j](stream.obs[0]), 'o', color=color, ms=2) plt.sca(ax[2][j]) plt.plot(stream.obs[0], fits_ex[j](stream.obs[0]) - fits[j](stream.obs[0]), 'o', color=color, ms=2) plt.sca(ax[3][j]) plt.plot(stream.obs[0], (fits_ex[j](stream.obs[0]) - fits[j](stream.obs[0]))/(sdp[p]), 'o', color=color, ms=2) # symmetric derivatives ra_der = np.linspace(np.min(stream0.obs[0])1.05, np.max(stream0.obs[0])0.95, 100) for i in range(Nstep): color = mpl.cm.Greys_r(i/Nstep) for j in range(5): dy = stream_fits[i][j](ra_der) - stream_fits[-i-1][j](ra_der) dydx = -dy / np.abs(2step[i]dp[p]) plt.sca(ax[4][j]) plt.plot(ra_der, dydx, '-', color=color, lw=2, zorder=Nstep-i) # labels, limits xlims, ylims = get_stream_limits(n, align) ylabel = ['R.A. (deg)', 'Dec (deg)', 'd (kpc)', '$V_r$ (km/s)', '$\mu_\\alpha$ (mas/yr)', '$\mu_\delta$ (mas/yr)'] if align: ylabel[:2] = ['$\\xi$ (deg)', '$\\eta$ (deg)'] for j in range(5): plt.sca(ax[0][j]) plt.ylabel(ylabel[j+1]) plt.xlim(xlims[0], xlims[1]) plt.ylim(ylims[j][0], ylims[j][1]) plt.sca(ax[1][j]) plt.ylabel('$\Delta$ {}'.format(ylabel[j+1].split(' ')[0])) plt.sca(ax[2][j]) plt.ylabel('$\Delta$ {}'.format(ylabel[j+1].split(' ')[0])) plt.sca(ax[3][j]) plt.ylabel('$\Delta${}/$\Delta${}'.format(ylabel[j+1].split(' ')[0], plabel)) plt.sca(ax[4][j]) plt.xlabel(ylabel[0]) plt.ylabel('$\langle$$\Delta${}/$\Delta${}$\\rangle$'.format(ylabel[j+1].split(' ')[0], plabel)) #plt.suptitle('Varying {}'.format(plabel), fontsize='small') plt.tight_layout() plt.savefig('../plots/observable_steps_{:d}_{:s}_p{:d}_Ns{:d}.png'.format(n, vlabel, p, Nstep)) def step_convergence(name='gd1', Nstep=20, log=True, layer=1, dt=0.2u.Myr, vary='halo', align=True, graph=False, verbose=False, Nobs=10, k=3, ra_der=np.nan, Nra=50): """Check deviations in numerical derivatives for consecutive step sizes""" mock = pickle.load(open('../data/mock_{}.params'.format(name),'rb')) if align: rotmatrix = mock['rotmatrix'] xmm = mock['xi_range'] else: rotmatrix = np.eye(3) xmm = mock['ra_range'] # fiducial model pparams0 = pparams_fid stream0 = stream_model(name=name, pparams0=pparams0, dt=dt, rotmatrix=rotmatrix) if np.any(~np.isfinite(ra_der)): ra_der = np.linspace(xmm[0]1.05, xmm[1]0.95, Nra) Nra = np.size(ra_der) # parameters to vary pid, dp, vlabel = get_varied_pars(vary) Np = len(pid) dpvec = np.array([x.value for x in dp]) Nstep, step = get_steps(Nstep=Nstep, log=log) dydx_all = np.empty((Np, Nstep, 5, Nra)) dev_der = np.empty((Np, Nstep-2layer)) step_der = np.empty((Np, Nstep-2layer)) for p in range(Np): plabel = get_parlabel(pid[p]) if verbose: print(p, plabel) # excursions stream_fits = [[None] 5 for x in range(2 * Nstep)] for i, s in enumerate(step[:]): if verbose: print(i, s) pparams = [x for x in pparams0] pparams[pid[p]] = pparams[pid[p]] + sdp[p] stream = stream_model(name=name, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) # fits iexsort = np.argsort(stream.obs[0]) raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs) tex = np.r_[(stream.obs[0][iexsort][0],)(k+1), raex, (stream.obs[0][iexsort][-1],)(k+1)] fits_ex = [None]5 for j in range(5): fits_ex[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[j+1][iexsort], tex, k=k) stream_fits[i][j] = fits_ex[j] # symmetric derivatives dydx = np.empty((Nstep, 5, Nra)) for i in range(Nstep): color = mpl.cm.Greys_r(i/Nstep) for j in range(5): dy = stream_fits[i][j](ra_der) - stream_fits[-i-1][j](ra_der) dydx[i][j] = -dy / np.abs(2step[i]dp[p]) dydx_all[p] = dydx # deviations from adjacent steps step_der[p] = -step[layer:Nstep-layer] * dp[p] for i in range(layer, Nstep-layer): dev_der[p][i-layer] = 0 for j in range(5): for l in range(layer): dev_der[p][i-layer] += np.sum((dydx[i][j] - dydx[i-l-1][j])2) dev_der[p][i-layer] += np.sum((dydx[i][j] - dydx[i+l+1][j])2) np.savez('../data/step_convergence_{}_{}_Ns{}_log{}_l{}'.format(name, vlabel, Nstep, log, layer), step=step_der, dev=dev_der, ders=dydx_all, steps_all=np.outer(dpvec,step[Nstep:])) if graph: plt.close() fig, ax = plt.subplots(1,Np,figsize=(4Np,4)) for p in range(Np): plt.sca(ax[p]) plt.plot(step_der[p], dev_der[p], 'ko') #plabel = get_parlabel(pid[p]) #plt.xlabel('$\Delta$ {}'.format(plabel)) plt.ylabel('D') plt.gca().set_yscale('log') plt.tight_layout() plt.savefig('../plots/step_convergence_{}_{}_Ns{}_log{}_l{}.png'.format(name, vlabel, Nstep, log, layer)) def choose_step(name='gd1', tolerance=2, Nstep=20, log=True, layer=1, vary='halo'): """""" pid, dp, vlabel = get_varied_pars(vary) Np = len(pid) plabels, units = get_parlabel(pid) punits = ['({})'.format(x) if len(x) else '' for x in units] t = np.load('../data/step_convergence_{}_{}_Ns{}_log{}_l{}.npz'.format(name, vlabel, Nstep, log, layer)) dev = t['dev'] step = t['step'] dydx = t['ders'] steps_all = t['steps_all'][:,::-1] Nra = np.shape(dydx)[-1] best = np.empty(Np) # plot setup da = 4 nrow = 2 ncol = Np plt.close() fig, ax = plt.subplots(nrow, ncol, figsize=(dancol, da1.3), squeeze=False, sharex='col', gridspec_kw = {'height_ratios':[1.2, 3]}) for p in range(Np): # choose step dmin = np.min(dev[p]) dtol = tolerance dmin opt_step = np.min(step[p][dev[p]<dtol]) opt_id = step[p]==opt_step best[p] = opt_step ## largest step w deviation smaller than 1e-4 #opt_step = np.max(step[p][dev[p]<1e-4]) #opt_id = step[p]==opt_step #best[p] = opt_step plt.sca(ax[0][p]) for i in range(5): for j in range(10): plt.plot(steps_all[p], np.tanh(dydx[p,:,i,np.int64(jNra/10)]), '-', color='{}'.format(i/5), lw=0.5, alpha=0.5) plt.axvline(opt_step, ls='-', color='r', lw=2) plt.ylim(-1,1) plt.ylabel('Derivative') plt.title('{}'.format(plabels[p])+'$_{best}$ = '+'{:2.2g}'.format(opt_step), fontsize='small') plt.sca(ax[1][p]) plt.plot(step[p], dev[p], 'ko') plt.axvline(opt_step, ls='-', color='r', lw=2) plt.plot(step[p][opt_id], dev[p][opt_id], 'ro') plt.axhline(dtol, ls='-', color='orange', lw=1) y0, y1 = plt.gca().get_ylim() plt.axhspan(y0, dtol, color='orange', alpha=0.3, zorder=0) plt.gca().set_yscale('log') plt.gca().set_xscale('log') plt.xlabel('$\Delta$ {} {}'.format(plabels[p], punits[p])) plt.ylabel('Derivative deviation') np.save('../data/optimal_step_{}_{}'.format(name, vlabel), best) plt.tight_layout(h_pad=0) plt.savefig('../plots/step_convergence_{}_{}_Ns{}_log{}_l{}.png'.format(name, vlabel, Nstep, log, layer)) def read_optimal_step(name, vary, equal=False): """Return optimal steps for a range of parameter types""" if type(vary) is not list: vary = [vary] dp = np.empty(0) for v in vary: dp_opt = np.load('../data/optimal_step_{}_{}.npy'.format(name, v)) dp = np.concatenate([dp, dp_opt]) if equal: dp = np.array([0.05, 0.05, 0.2, 1, 0.01, 0.01, 0.05, 0.1, 0.05, 0.1, 0.1, 10, 1, 0.01, 0.01]) return dp def visualize_optimal_steps(name='gd1', vary=['progenitor', 'bary', 'halo'], align=True, dt=0.2u.Myr, Nobs=50, k=3): """""" mock = pickle.load(open('../data/mock_{}.params'.format(name),'rb')) if align: rotmatrix = mock['rotmatrix'] xmm = mock['xi_range'] else: rotmatrix = np.eye(3) xmm = mock['ra_range'] # varied parameters pparams0 = pparams_fid pid, dp_fid, vlabel = get_varied_pars(vary) Np = len(pid) dp_opt = read_optimal_step(name, vary) dp = [xy.unit for x,y in zip(dp_opt, dp_fid)] fiducial = stream_model(name=name, pparams0=pparams0, dt=dt, rotmatrix=rotmatrix) iexsort = np.argsort(fiducial.obs[0]) raex = np.linspace(np.percentile(fiducial.obs[0], 10), np.percentile(fiducial.obs[0], 90), Nobs) tex = np.r_[(fiducial.obs[0][iexsort][0],)(k+1), raex, (fiducial.obs[0][iexsort][-1],)(k+1)] fit = scipy.interpolate.make_lsq_spline(fiducial.obs[0][iexsort], fiducial.obs[1][iexsort], tex, k=k) nrow = 2 ncol = np.int64((Np+1)/nrow) da = 4 c = ['b', 'b', 'b', 'r', 'r', 'r'] plt.close() fig, ax = plt.subplots(nrow, ncol, figsize=(ncolda, nrowda), squeeze=False) for p in range(Np): plt.sca(ax[p%2][int(p/2)]) for i, s in enumerate([-1.1, -1, -0.9, 0.9, 1, 1.1]): pparams = [x for x in pparams0] pparams[pid[p]] = pparams[pid[p]] + sdp[p] stream = stream_model(name=name, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) # bspline fits to stream centerline iexsort = np.argsort(stream.obs[0]) raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs) tex = np.r_[(stream.obs[0][iexsort][0],)(k+1), raex, (stream.obs[0][iexsort][-1],)(k+1)] fitex = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[1][iexsort], tex, k=k) plt.plot(raex, fitex(raex) - fit(raex), '-', color=c[i]) plt.xlabel('R.A. (deg)') plt.ylabel('Dec (deg)') #print(get_parlabel(p)) plt.title('$\Delta$ {} = {:.2g}'.format(get_parlabel(p)[0], dp[p]), fontsize='medium') plt.tight_layout() plt.savefig('../plots/{}_optimal_steps.png'.format(name), dpi=200) # observing modes def define_obsmodes(): """Output a pickled dictionary with typical uncertainties and dimensionality of data for a number of observing modes""" obsmodes = {} obsmodes['fiducial'] = {'sig_obs': np.array([0.1, 2, 5, 0.1, 0.1]), 'Ndim': [3,4,6]} obsmodes['binospec'] = {'sig_obs': np.array([0.1, 2, 10, 0.1, 0.1]), 'Ndim': [3,4,6]} obsmodes['hectochelle'] = {'sig_obs': np.array([0.1, 2, 1, 0.1, 0.1]), 'Ndim': [3,4,6]} obsmodes['desi'] = {'sig_obs': np.array([0.1, 2, 10, np.nan, np.nan]), 'Ndim': [4,]} obsmodes['gaia'] = {'sig_obs': np.array([0.1, 0.2, 10, 0.2, 0.2]), 'Ndim': [6,]} obsmodes['exgal'] = {'sig_obs': np.array([0.5, np.nan, 20, np.nan, np.nan]), 'Ndim': [3,]} pickle.dump(obsmodes, open('../data/observing_modes.info','wb')) def obsmode_name(mode): """Return full name of the observing mode""" if type(mode) is not list: mode = [mode] full_names = {'fiducial': 'Fiducial', 'binospec': 'Binospec', 'hectochelle': 'Hectochelle', 'desi': 'DESI-like', 'gaia': 'Gaia-like', 'exgal': 'Extragalactic'} keys = full_names.keys() names = [] for m in mode: if m in keys: name = full_names[m] else: name = m names += [name] return names # crbs using bspline def calculate_crb(name='gd1', dt=0.2u.Myr, vary=['progenitor', 'bary', 'halo'], ra=np.nan, dd=0.5, Nmin=15, verbose=False, align=True, scale=False, errmode='fiducial', k=3): """""" mock = pickle.load(open('../data/mock_{}.params'.format(name),'rb')) if align: rotmatrix = mock['rotmatrix'] xmm = np.sort(mock['xi_range']) else: rotmatrix = np.eye(3) xmm = np.sort(mock['ra_range']) # typical uncertainties and data availability obsmodes = pickle.load(open('../data/observing_modes.info', 'rb')) if errmode not in obsmodes.keys(): errmode = 'fiducial' sig_obs = obsmodes[errmode]['sig_obs'] data_dim = obsmodes[errmode]['Ndim'] # mock observations if np.any(~np.isfinite(ra)): if (np.int64((xmm[1]-xmm[0])/dd + 1) < Nmin): dd = (xmm[1]-xmm[0])/Nmin ra = np.arange(xmm[0], xmm[1]+dd, dd) #ra = np.linspace(xmm[0]1.05, xmm[1]0.95, Nobs) #else: Nobs = np.size(ra) print(name, Nobs) err = np.tile(sig_obs, Nobs).reshape(Nobs,-1) # varied parameters pparams0 = pparams_fid pid, dp_fid, vlabel = get_varied_pars(vary) Np = len(pid) dp_opt = read_optimal_step(name, vary) dp = [xy.unit for x,y in zip(dp_opt, dp_fid)] fits_ex = [[[None]5 for x in range(2)] for y in range(Np)] if scale: dp_unit = unity_scale(dp) dps = [xy for x,y in zip(dp, dp_unit)] # calculate derivatives for all parameters for p in range(Np): for i, s in enumerate([-1, 1]): pparams = [x for x in pparams0] pparams[pid[p]] = pparams[pid[p]] + sdp[p] stream = stream_model(name=name, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) # bspline fits to stream centerline iexsort = np.argsort(stream.obs[0]) raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs) tex = np.r_[(stream.obs[0][iexsort][0],)(k+1), raex, (stream.obs[0][iexsort][-1],)(k+1)] for j in range(5): fits_ex[p][i][j] = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[j+1][iexsort], tex, k=k) # populate matrix of derivatives and calculate CRB for Ndim in data_dim: #for Ndim in [6,]: Ndata = Nobs (Ndim - 1) cyd = np.empty(Ndata) dydx = np.empty((Np, Ndata)) dy2 = np.empty((2, Np, Ndata)) for j in range(1, Ndim): for p in range(Np): dy = fits_ex[p][0][j-1](ra) - fits_ex[p][1][j-1](ra) dy2[0][p][(j-1)Nobs:jNobs] = fits_ex[p][0][j-1](ra) dy2[1][p][(j-1)Nobs:jNobs] = fits_ex[p][1][j-1](ra) #positive = np.abs(dy)>0 #if verbose: print('{:d},{:d} {:s} min{:.1e} max{:1e} med{:.1e}'.format(j, p, get_parlabel(pid[p])[0], np.min(np.abs(dy[positive])), np.max(np.abs(dy)), np.median(np.abs(dy)))) if scale: dydx[p][(j-1)Nobs:jNobs] = -dy / np.abs(2dps[p].value) else: dydx[p][(j-1)Nobs:jNobs] = -dy / np.abs(2dp[p].value) #if verbose: print('{:d},{:d} {:s} min{:.1e} max{:1e} med{:.1e}'.format(j, p, get_parlabel(pid[p])[0], np.min(np.abs(dydx[p][(j-1)Nobs:jNobs][positive])), np.max(np.abs(dydx[p][(j-1)Nobs:jNobs])), np.median(np.abs(dydx[p][(j-1)Nobs:jNobs])))) #print(j, p, get_parlabel(pid[p])[0], dp[p], np.min(np.abs(dy)), np.max(np.abs(dy)), np.median(dydx[p][(j-1)Nobs:jNobs])) cyd[(j-1)Nobs:jNobs] = err[:,j-1]*2 np.savez('../data/crb/components_{:s}{:1d}_{:s}_a{:1d}_{:s}'.format(errmode, Ndim, name, align, vlabel), dydx=dydx, y=dy2, cyd=cyd, dp=dp_opt) # data component of the Fisher matrix cy = np.diag(cyd) cyi = np.diag(1. / cyd) caux = np.matmul(cyi, dydx.T) dxi = np.matmul(dydx, caux) # component based on prior knowledge of model parameters pxi = priors(name, vary) # full Fisher matrix cxi = dxi + pxi if verbose: cx = np.linalg.inv(cxi) cx = np.matmul(np.linalg.inv(np.matmul(cx, cxi)), cx) # iteration to improve inverse at large cond numbers sx = np.sqrt(np.diag(cx)) print('CRB', sx) print('condition {:g}'.format(np.linalg.cond(cxi))) print('standard inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0]))) cx = stable_inverse(cxi) print('stable inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0]))) np.savez('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}'.format(errmode, Ndim, name, align, vlabel), cxi=cxi, dxi=dxi, pxi=pxi) def priors(name, vary): """Return covariance matrix with prior knowledge about parameters""" mock = pickle.load(open('../data/mock_{}.params'.format(name), 'rb')) cprog = mock['prog_prior'] cbary = np.array([0.1x.value for x in pparams_fid[:5]])*-2 chalo = np.zeros(4) cdipole = np.zeros(3) cquad = np.zeros(5) coctu = np.zeros(7) priors = {'progenitor': cprog, 'bary': cbary, 'halo': chalo, 'dipole': cdipole, 'quad': cquad, 'octu': coctu} cprior = np.empty(0) for v in vary: cprior = np.concatenate([cprior, priors[v]]) pxi = np.diag(cprior) return pxi def scale2invert(name='gd1', Ndim=6, vary=['progenitor', 'bary', 'halo'], verbose=False, align=True, errmode='fiducial'): """""" pid, dp_fid, vlabel = get_varied_pars(vary) #dp = read_optimal_step(name, vary) d = np.load('../data/crb/components_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel)) dydx = d['dydx'] cyd = d['cyd'] y = d['y'] dp = d['dp'] dy = (y[1,:,:] - y[0,:,:]) dydx = (y[1,:,:] - y[0,:,:]) / (2dp[:,np.newaxis]) scaling_par = np.median(np.abs(dydx), axis=1) dydx = dydx / scaling_par[:,np.newaxis] dydx_ = np.reshape(dydx, (len(dp), Ndim-1, -1)) scaling_dim = np.median(np.abs(dydx_), axis=(2,0)) dydx_ = dydx_ / scaling_dim[np.newaxis,:,np.newaxis] cyd_ = np.reshape(cyd, (Ndim-1, -1)) cyd_ = cyd_ / scaling_dim[:,np.newaxis] cyd = np.reshape(cyd_, (-1)) dydx = np.reshape(dydx_, (len(dp), -1)) mmin = np.min(np.abs(dy), axis=0) mmax = np.max(np.abs(dy), axis=0) mmed = np.median(np.abs(dydx), axis=1) dyn_range = mmax/mmin #print(dyn_range) print(np.min(dyn_range), np.max(dyn_range), np.std(dyn_range)) cy = np.diag(cyd) cyi = np.diag(1. / cyd) caux = np.matmul(cyi, dydx.T) cxi = np.matmul(dydx, caux) print('condition {:e}'.format(np.linalg.cond(cxi))) cx = np.linalg.inv(cxi) cx = np.matmul(np.linalg.inv(np.matmul(cx, cxi)), cx) # iteration to improve inverse at large cond numbers print('standard inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0]))) cx = stable_inverse(cxi, maxiter=30) print('stable inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0]))) def unity_scale(dp): """""" dim_scale = 10np.array([2, 3, 3, 2, 4, 3, 7, 7, 5, 7, 7, 4, 4, 4, 4, 3, 3, 3, 4, 3, 4, 4, 4]) dim_scale = 10np.array([3, 2, 3, 4, 0, 2, 2, 3, 2, 2, 2, 4, 3, 2, 2, 3]) #dim_scale = 10np.array([2, 3, 3, 1, 3, 2, 5, 5, 3, 5, 5, 2, 2, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3]) #dim_scale = 10np.array([2, 3, 3, 1, 3, 2, 5, 5, 3, 5, 5, 2, 2, 4, 4, 3, 3, 3]) dp_unit = [(dp[x].valuedim_scale[x])-1 for x in range(len(dp))] return dp_unit def test_inversion(name='gd1', Ndim=6, vary=['progenitor', 'bary', 'halo'], align=True, errmode='fiducial'): """""" pid, dp, vlabel = get_varied_pars(vary) d = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel)) cxi = d['cxi'] N = np.shape(cxi)[0] cx_ = np.linalg.inv(cxi) cx = stable_inverse(cxi, verbose=True, maxiter=100) #cx_ii = stable_inverse(cx, verbose=True, maxiter=50) print('condition {:g}'.format(np.linalg.cond(cxi))) print('linalg inverse', np.allclose(np.matmul(cx_,cxi), np.eye(N))) print('stable inverse', np.allclose(np.matmul(cx,cxi), np.eye(N))) #print(np.matmul(cx,cxi)) #print('inverse inverse', np.allclose(cx_ii, cxi)) def stable_inverse(a, maxiter=20, verbose=False): """Invert a matrix with a bad condition number""" N = np.shape(a)[0] # guess q = np.linalg.inv(a) qa = np.matmul(q,a) # iterate for i in range(maxiter): if verbose: print(i, np.sqrt(np.sum((qa - np.eye(N))2)), np.allclose(qa, np.eye(N))) if np.allclose(qa, np.eye(N)): return q qai = np.linalg.inv(qa) q = np.matmul(qai,q) qa = np.matmul(q,a) return q def crb_triangle(n, vary, Ndim=6, align=True, plot='all', fast=False): """""" pid, dp, vlabel = get_varied_pars(vary) plabels, units = get_parlabel(pid) params = ['$\Delta$' + x + '({})'.format(y) for x,y in zip(plabels, units)] if align: alabel = '_align' else: alabel = '' fm = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel)) cxi = fm['cxi'] if fast: cx = np.linalg.inv(cxi) else: cx = stable_inverse(cxi) #print(cx[0][0]) if plot=='halo': cx = cx[:4, :4] params = params[:4] elif plot=='bary': cx = cx[4:9, 4:9] params = params[4:9] elif plot=='progenitor': cx = cx[9:, 9:] params = params[9:] Nvar = len(params) plt.close() dax = 2 fig, ax = plt.subplots(Nvar-1, Nvar-1, figsize=(daxNvar, daxNvar), sharex='col', sharey='row') for i in range(0,Nvar-1): for j in range(i+1,Nvar): plt.sca(ax[j-1][i]) cx_2d = np.array([[cx[i][i], cx[i][j]], [cx[j][i], cx[j][j]]]) w, v = np.linalg.eig(cx_2d) if np.all(np.isreal(v)): theta = np.degrees(np.arccos(v[0][0])) width = np.sqrt(w[0])2 height = np.sqrt(w[1])2 e = mpl.patches.Ellipse((0,0), width=width, height=height, angle=theta, fc='none', ec=mpl.cm.bone(0.5), lw=2) plt.gca().add_patch(e) plt.gca().autoscale_view() #plt.xlim(-ylim[i],ylim[i]) #plt.ylim(-ylim[j], ylim[j]) if j==Nvar-1: plt.xlabel(params[i]) if i==0: plt.ylabel(params[j]) # turn off unused axes for i in range(0,Nvar-1): for j in range(i+1,Nvar-1): plt.sca(ax[i][j]) plt.axis('off') plt.tight_layout() plt.savefig('../plots/crb_triangle_{:s}_{:d}_{:s}_{:d}_{:s}.pdf'.format(alabel, n, vlabel, Ndim, plot)) def crb_triangle_alldim(name='gd1', vary=['progenitor', 'bary', 'halo'], align=True, plot='all', fast=False, scale=False, errmode='fiducial'): """Show correlations in CRB between a chosen set of parameters in a triangle plot""" pid, dp_fid, vlabel = get_varied_pars(vary) dp_opt = read_optimal_step(name, vary) dp = [xy.unit for x,y in zip(dp_opt, dp_fid)] plabels, units = get_parlabel(pid) punits = [' ({})'.format(x) if len(x) else '' for x in units] params = ['$\Delta$ {}{}'.format(x, y) for x,y in zip(plabels, punits)] if plot=='halo': i0 = 11 i1 = 15 elif plot=='bary': i0 = 6 i1 = 11 elif plot=='progenitor': i0 = 0 i1 = 6 elif plot=='dipole': i0 = 15 i1 = len(params) else: i0 = 0 i1 = len(params) Nvar = i1 - i0 params = params[i0:i1] if scale: dp_unit = unity_scale(dp) #print(dp_unit) dp_unit = dp_unit[i0:i1] pid = pid[i0:i1] label = ['RA, Dec, d', 'RA, Dec, d, $V_r$', 'RA, Dec, d, $V_r$, $\mu_\\alpha$, $\mu_\delta$'] plt.close() dax = 2 fig, ax = plt.subplots(Nvar-1, Nvar-1, figsize=(daxNvar, daxNvar), sharex='col', sharey='row') for l, Ndim in enumerate([3, 4, 6]): fm = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel)) cxi = fm['cxi'] #cxi = np.load('../data/crb/bspline_cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npy'.format(errmode, Ndim, name, align, vlabel)) if fast: cx = np.linalg.inv(cxi) else: cx = stable_inverse(cxi) cx = cx[i0:i1,i0:i1] for i in range(0,Nvar-1): for j in range(i+1,Nvar): plt.sca(ax[j-1][i]) if scale: cx_2d = np.array([[cx[i][i]/dp_unit[i]*2, cx[i][j]/(dp_unit[i]dp_unit[j])], [cx[j][i]/(dp_unit[j]dp_unit[i]), cx[j][j]/dp_unit[j]2]]) else: cx_2d = np.array([[cx[i][i], cx[i][j]], [cx[j][i], cx[j][j]]]) w, v = np.linalg.eig(cx_2d) if np.all(np.isreal(v)): theta = np.degrees(np.arctan2(v[1][0], v[0][0])) width = np.sqrt(w[0])2 height = np.sqrt(w[1])2 e = mpl.patches.Ellipse((0,0), width=width, height=height, angle=theta, fc='none', ec=mpl.cm.bone(0.1+l/4), lw=2, label=label[l]) plt.gca().add_patch(e) if l==1: plt.gca().autoscale_view() if j==Nvar-1: plt.xlabel(params[i]) if i==0: plt.ylabel(params[j]) # turn off unused axes for i in range(0,Nvar-1): for j in range(i+1,Nvar-1): plt.sca(ax[i][j]) plt.axis('off') plt.sca(ax[int(Nvar/2-1)][int(Nvar/2-1)]) plt.legend(loc=2, bbox_to_anchor=(1,1)) plt.tight_layout() plt.savefig('../plots/cxi_{:s}_{:s}_a{:1d}_{:s}_{:s}.pdf'.format(errmode, name, align, vlabel, plot)) def compare_optimal_steps(): """""" vary = ['progenitor', 'bary', 'halo', 'dipole', 'quad'] vary = ['progenitor', 'bary', 'halo'] for name in ['gd1', 'tri']: print(name) print(read_optimal_step(name, vary)) def get_crb(name, Nstep=10, vary=['progenitor', 'bary', 'halo'], first=True): """""" if first: store_progparams(name) wrap_angles(name, save=True) progenitor_prior(name) find_greatcircle(name=name) endpoints(name) for v in vary: step_convergence(name=name, Nstep=Nstep, vary=v) choose_step(name=name, Nstep=Nstep, vary=v) calculate_crb(name=name, vary=vary, verbose=True) crb_triangle_alldim(name=name, vary=vary) ######################## # cartesian coordinates # accelerations def acc_kepler(x, p=1u.Msun): """Keplerian acceleration""" r = np.linalg.norm(x)u.kpc a = -G p * 1e11 * r*-3 x return a.to(u.pcu.Myr-2) def acc_bulge(x, p=[pparams_fid[j] for j in range(2)]): """""" r = np.linalg.norm(x)u.kpc a = -(Gp[0]x/(r * (r + p[1])*2)).to(u.pcu.Myr*-2) return a def acc_disk(x, p=[pparams_fid[j] for j in range(2,5)]): """""" R = np.linalg.norm(x[:2])u.kpc z = x[2] a = -(Gp[0]x * (R2 + (p[1] + np.sqrt(z2 + p[2]2))2)*-1.5).to(u.pcu.Myr*-2) a[2] = (1 + p[2]/np.sqrt(z2 + p[2]2)) return a def acc_nfw(x, p=[pparams_fid[j] for j in [5,6,8,10]]): """""" r = np.linalg.norm(x)u.kpc q = np.array([1u.Unit(1), p[2], p[3]]) a = (p[0]*2 p[1] * r*-3 (1/(1+p[1]/r) - np.log(1+r/p[1])) * x * q*-2).to(u.pcu.Myr*-2) return a def acc_dipole(x, p=[pparams_fid[j] for j in range(11,14)]): """Acceleration due to outside dipole perturbation""" pv = [x.value for x in p] a = np.sqrt(3/(4np.pi)) * np.array([pv[2], pv[0], pv[1]])u.pcu.Myr*-2 return a def acc_quad(x, p=[pparams_fid[j] for j in range(14,19)]): """Acceleration due to outside quadrupole perturbation""" a = np.zeros(3)u.pcu.Myr-2 f = 0.5np.sqrt(15/np.pi) a[0] = x[0](fp[4] - f/np.sqrt(3)p[2]) + x[1]fp[0] + x[2]fp[3] a[1] = x[0]fp[0] - x[1](fp[4] + f/np.sqrt(3)p[2]) + x[2]fp[1] a[2] = x[0]fp[3] + x[1]fp[1] + x[2]2f/np.sqrt(3)p[2] return a.to(u.pcu.Myr*-2) def acc_octu(x, p=[pparams_fid[j] for j in range(19,26)]): """Acceleration due to outside octupole perturbation""" a = np.zeros(3)u.pcu.Myr-2 f = np.array([0.25np.sqrt(35/(2np.pi)), 0.5np.sqrt(105/np.pi), 0.25np.sqrt(21/(2np.pi)), 0.25np.sqrt(7/np.pi), 0.25np.sqrt(21/(2np.pi)), 0.25np.sqrt(105/np.pi), 0.25np.sqrt(35/(2np.pi))]) xu = x.unit pu = p[0].unit pvec = np.array([i.value for i in p]) * pu dmat = np.ones((3,7)) * f * pvec * xu*2 x = np.array([i.value for i in x]) dmat[0] = np.array([6x[0]x[1], x[1]x[2], -2x[0]x[1], -6x[0]x[2], 4x[2]2-x[1]2-3x[0]2, 2x[0]x[2], 3x[0]*2-3x[1]*2]) dmat[1] = np.array([3x[0]2-3x[1]*2, x[0]x[2], 4x[2]2-x[0]2-3x[1]*2, -6x[1]x[2], -2x[0]x[1], -2x[1]x[2], -6x[0]x[1]]) dmat[2] = np.array([0, x[0]x[1], 8x[1]x[2], 6x[2]*2-3x[0]*2-3x[1]*2, 8x[0]x[2], x[0]2-x[1]2, 0]) a = np.einsum('ij->i', dmat) dmat.unit return a.to(u.pcu.Myr-2) # derivatives def der_kepler(x, p=1u.Msun): """Derivative of Kepler potential parameters wrt cartesian components of the acceleration""" r = np.linalg.norm(x)u.kpc dmat = np.zeros((3,1)) u.pc*-1 u.Myr*2 u.Msun dmat[:,0] = (-r*3/(Gx)).to(u.pc*-1 u.Myr*2 u.Msun) * 1e-11 return dmat.value def pder_kepler(x, p=1u.Msun): """Derivative of cartesian components of the acceleration wrt to Kepler potential parameter""" r = np.linalg.norm(x)u.kpc dmat = np.zeros((3,1)) * u.pc * u.Myr*-2 u.Msun*-1 dmat[:,0] = (-Gxr-3).to(u.pc u.Myr*-2 u.Msun*-1) 1e11 return dmat.value def pder_nfw(x, pu=[pparams_fid[j] for j in [5,6,8,10]]): """Calculate derivatives of cartesian components of the acceleration wrt halo potential parameters""" p = pu q = np.array([1, p[2], p[3]]) # physical quantities r = np.linalg.norm(x)u.kpc a = acc_nfw(x, p=pu) # derivatives dmat = np.zeros((3, 4)) # Vh dmat[:,0] = 2a/p[0] # Rh dmat[:,1] = a/p[1] + p[0]*2 p[1] * r*-3 (1/(p[1]+p[1]*2/r) - 1/(r(1+p[1]/r)*2)) x * q*-2 # qy, qz for i in [1,2]: dmat[i,i+1] = (-2a[i]/q[i]).value return dmat def pder_bulge(x, pu=[pparams_fid[j] for j in range(2)]): """Calculate derivarives of cartesian components of the acceleration wrt Hernquist bulge potential parameters""" # coordinates r = np.linalg.norm(x)u.kpc # accelerations ab = acc_bulge(x, p=pu[:2]) # derivatives dmat = np.zeros((3, 2)) # Mb dmat[:,0] = ab/pu[0] # ab dmat[:,1] = 2 ab / (r + pu[1]) return dmat def pder_disk(x, pu=[pparams_fid[j] for j in range(2,5)]): """Calculate derivarives of cartesian components of the acceleration wrt Miyamoto-Nagai disk potential parameters""" # coordinates R = np.linalg.norm(x[:2])u.kpc z = x[2] aux = np.sqrt(z2 + pu[2]2) # accelerations ad = acc_disk(x, p=pu) # derivatives dmat = np.zeros((3, 3)) # Md dmat[:,0] = ad / pu[0] # ad dmat[:,1] = 3 ad * (pu[1] + aux) / (R2 + (pu[1] + aux)2) # bd dmat[:2,2] = 3 * ad[:2] * (pu[1] + aux) / (R2 + (pu[1] + aux)2) * pu[2] / aux dmat[2,2] = (3 * ad[2] * (pu[1] + aux) / (R2 + (pu[1] + aux)2) * pu[2] / aux - G * pu[0] * z * (R2 + (pu[1] + aux)2)*-1.5 z*2 (pu[2]2 + z2)*-1.5).value return dmat def der_dipole(x, pu=[pparams_fid[j] for j in range(11,14)]): """Calculate derivatives of dipole potential parameters wrt (Cartesian) components of the acceleration vector a""" # shape: 3, Npar dmat = np.zeros((3,3)) f = np.sqrt((4np.pi)/3) dmat[0,2] = f dmat[1,0] = f dmat[2,1] = f return dmat def pder_dipole(x, pu=[pparams_fid[j] for j in range(11,14)]): """Calculate derivatives of (Cartesian) components of the acceleration vector a wrt dipole potential parameters""" # shape: 3, Npar dmat = np.zeros((3,3)) f = np.sqrt(3/(4np.pi)) dmat[0,2] = f dmat[1,0] = f dmat[2,1] = f return dmat def der_quad(x, p=[pparams_fid[j] for j in range(14,19)]): """Caculate derivatives of quadrupole potential parameters wrt (Cartesian) components of the acceleration vector a""" f = 2/np.sqrt(15/np.pi) s = np.sqrt(3) x = [1e-3/i.value for i in x] dmat = np.ones((3,5)) f dmat[0] = np.array([x[1], 0, -sx[0], x[2], x[0]]) dmat[1] = np.array([x[0], x[2], -sx[1], 0, -x[1]]) dmat[2] = np.array([0, x[1], 0.5sx[2], x[0], 0]) return dmat def pder_quad(x, p=[pparams_fid[j] for j in range(14,19)]): """Caculate derivatives of (Cartesian) components of the acceleration vector a wrt quadrupole potential parameters""" f = 0.5np.sqrt(15/np.pi) s = 1/np.sqrt(3) x = [1e-3i.value for i in x] dmat = np.ones((3,5)) * f dmat[0] = np.array([x[1], 0, -sx[0], x[2], x[0]]) dmat[1] = np.array([x[0], x[2], -sx[1], 0, -x[1]]) dmat[2] = np.array([0, x[1], 2sx[2], x[0], 0]) return dmat def pder_octu(x, p=[pparams_fid[j] for j in range(19,26)]): """Caculate derivatives of (Cartesian) components of the acceleration vector a wrt octupole potential parameters""" f = np.array([0.25np.sqrt(35/(2np.pi)), 0.5np.sqrt(105/np.pi), 0.25np.sqrt(21/(2np.pi)), 0.25np.sqrt(7/np.pi), 0.25np.sqrt(21/(2np.pi)), 0.25np.sqrt(105/np.pi), 0.25np.sqrt(35/(2np.pi))]) x = [1e-3i.value for i in x] dmat = np.ones((3,7)) f dmat[0] = np.array([6x[0]x[1], x[1]x[2], -2x[0]x[1], -6x[0]x[2], 4x[2]2-x[1]2-3x[0]*2, 2x[0]x[2], 3x[0]*2-3x[1]*2]) dmat[1] = np.array([3x[0]2-3x[1]*2, x[0]x[2], 4x[2]2-x[0]2-3x[1]*2, -6x[1]x[2], -2x[0]x[1], -2x[1]x[2], -6x[0]x[1]]) dmat[2] = np.array([0, x[0]x[1], 8x[1]x[2], 6x[2]*2-3x[0]*2-3x[1]*2, 8x[0]x[2], x[0]2-x[1]2, 0]) return dmat def crb_ax(n, Ndim=6, vary=['halo', 'bary', 'progenitor'], align=True, fast=False): """Calculate CRB inverse matrix for 3D acceleration at position x in a halo potential""" pid, dp, vlabel = get_varied_pars(vary) if align: alabel = '_align' else: alabel = '' # read in full inverse CRB for stream modeling cxi = np.load('../data/crb/bspline_cxi{:s}_{:d}_{:s}_{:d}.npy'.format(alabel, n, vlabel, Ndim)) if fast: cx = np.linalg.inv(cxi) else: cx = stable_inverse(cxi) # subset halo parameters Nhalo = 4 cq = cx[:Nhalo,:Nhalo] if fast: cqi = np.linalg.inv(cq) else: cqi = stable_inverse(cq) xi = np.array([-8.3, 0.1, 0.1])u.kpc x0, v0 = gd1_coordinates() #xi = np.array(x0)u.kpc d = 50 Nb = 20 x = np.linspace(x0[0]-d, x0[0]+d, Nb) y = np.linspace(x0[1]-d, x0[1]+d, Nb) x = np.linspace(-d, d, Nb) y = np.linspace(-d, d, Nb) xv, yv = np.meshgrid(x, y) xf = np.ravel(xv) yf = np.ravel(yv) af = np.empty((Nb2, 3)) plt.close() fig, ax = plt.subplots(3,3,figsize=(11,10)) dimension = ['x', 'y', 'z'] xlabel = ['y', 'x', 'x'] ylabel = ['z', 'z', 'y'] for j in range(3): if j==0: xin = np.array([np.repeat(x0[j], Nb2), xf, yf]).T elif j==1: xin = np.array([xf, np.repeat(x0[j], Nb2), yf]).T elif j==2: xin = np.array([xf, yf, np.repeat(x0[j], Nb2)]).T for i in range(Nb2): #xi = np.array([xf[i], yf[i], x0[2]])u.kpc xi = xin[i]u.kpc a = acc_nfw(xi) dqda = halo_accelerations(xi) cai = np.matmul(dqda, np.matmul(cqi, dqda.T)) if fast: ca = np.linalg.inv(cai) else: ca = stable_inverse(cai) a_crb = (np.sqrt(np.diag(ca)) u.km*2 u.kpc*-1 u.s*-2).to(u.pcu.Myr*-2) af[i] = np.abs(a_crb/a) af[i] = a_crb for i in range(3): plt.sca(ax[j][i]) im = plt.imshow(af[:,i].reshape(Nb,Nb), extent=[-d, d, -d, d], cmap=mpl.cm.gray) #, norm=mpl.colors.LogNorm(), vmin=1e-2, vmax=0.1) plt.xlabel(xlabel[j]+' (kpc)') plt.ylabel(ylabel[j]+' (kpc)') divider = make_axes_locatable(plt.gca()) cax = divider.append_axes("top", size="4%", pad=0.05) plt.colorbar(im, cax=cax, orientation='horizontal') plt.gca().xaxis.set_ticks_position('top') cax.tick_params(axis='x', labelsize='xx-small') if j==0: plt.title('a$_{}$'.format(dimension[i]), y=4) plt.tight_layout(rect=[0,0,1,0.95]) plt.savefig('../plots/acc_{}_{}_{}.png'.format(n, vlabel, Ndim)) def acc_cart(x, components=['bary', 'halo', 'dipole']): """""" acart = np.zeros(3) u.pcu.Myr-2 dict_acc = {'bary': [acc_bulge, acc_disk], 'halo': [acc_nfw], 'dipole': [acc_dipole], 'quad': [acc_quad], 'octu': [acc_octu], 'point': [acc_kepler]} accelerations = [] for c in components: accelerations += dict_acc[c] for acc in accelerations: a_ = acc(x) acart += a_ return acart def acc_rad(x, components=['bary', 'halo', 'dipole']): """Return radial acceleration""" r = np.linalg.norm(x) x.unit theta = np.arccos(x[2].value/r.value) phi = np.arctan2(x[1].value, x[0].value) trans = np.array([np.sin(theta)np.cos(phi), np.sin(theta)np.sin(phi), np.cos(theta)]) a_cart = acc_cart(x, components=components) a_rad = np.dot(a_cart, trans) return a_rad def ader_cart(x, components=['bary', 'halo', 'dipole']): """""" dacart = np.empty((3,0)) dict_der = {'bary': [der_bulge, der_disk], 'halo': [der_nfw], 'dipole': [der_dipole], 'quad': [der_quad], 'point': [der_kepler]} derivatives = [] for c in components: derivatives += dict_der[c] for ader in derivatives: da_ = ader(x) dacart = np.hstack((dacart, da_)) return dacart def apder_cart(x, components=['bary', 'halo', 'dipole']): """""" dacart = np.empty((3,0)) dict_der = {'bary': [pder_bulge, pder_disk], 'halo': [pder_nfw], 'dipole': [pder_dipole], 'quad': [pder_quad], 'octu': [pder_octu], 'point': [pder_kepler]} derivatives = [] for c in components: derivatives += dict_der[c] for ader in derivatives: da_ = ader(x) dacart = np.hstack((dacart, da_)) return dacart def apder_rad(x, components=['bary', 'halo', 'dipole']): """Return dar/dx_pot (radial acceleration/potential parameters) evaluated at vector x""" r = np.linalg.norm(x) * x.unit theta = np.arccos(x[2].value/r.value) phi = np.arctan2(x[1].value, x[0].value) trans = np.array([np.sin(theta)np.cos(phi), np.sin(theta)np.sin(phi), np.cos(theta)]) dadq_cart = apder_cart(x, components=components) dadq_rad = np.einsum('ij,i->j', dadq_cart, trans) return dadq_rad def crb_acart(n, Ndim=6, vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], component='all', align=True, d=20, Nb=50, fast=False, scale=False, relative=True, progenitor=False, errmode='fiducial'): """""" pid, dp_fid, vlabel = get_varied_pars(vary) if align: alabel = '_align' else: alabel = '' if relative: vmin = 1e-2 vmax = 1 rlabel = ' / a' else: vmin = 3e-1 vmax = 1e1 rlabel = ' (pc Myr$^{-2}$)' # read in full inverse CRB for stream modeling cxi = np.load('../data/crb/bspline_cxi{:s}_{:s}_{:d}_{:s}_{:d}.npy'.format(alabel, errmode, n, vlabel, Ndim)) if fast: cx = np.linalg.inv(cxi) else: cx = stable_inverse(cxi) # choose the appropriate components: Nprog, Nbary, Nhalo, Ndipole, Npoint = [6, 5, 4, 3, 1] if 'progenitor' not in vary: Nprog = 0 nstart = {'bary': Nprog, 'halo': Nprog + Nbary, 'dipole': Nprog + Nbary + Nhalo, 'all': Nprog, 'point': 0} nend = {'bary': Nprog + Nbary, 'halo': Nprog + Nbary + Nhalo, 'dipole': Nprog + Nbary + Nhalo + Ndipole, 'all': np.shape(cx)[0], 'point': 1} if 'progenitor' not in vary: nstart['dipole'] = Npoint nend['dipole'] = Npoint + Ndipole if component in ['bary', 'halo', 'dipole', 'point']: components = [component] else: components = [x for x in vary if x!='progenitor'] cq = cx[nstart[component]:nend[component], nstart[component]:nend[component]] Npot = np.shape(cq)[0] if fast: cqi = np.linalg.inv(cq) else: cqi = stable_inverse(cq) if scale: dp_opt = read_optimal_step(n, vary) dp = [xy.unit for x,y in zip(dp_opt, dp_fid)] scale_vec = np.array([x.value for x in dp[nstart[component]:nend[component]]]) scale_mat = np.outer(scale_vec, scale_vec) cqi = scale_mat if progenitor: x0, v0 = gd1_coordinates() else: x0 = np.array([4, 4, 0]) Rp = np.linalg.norm(x0[:2]) zp = x0[2] R = np.linspace(-d, d, Nb) k = x0[1]/x0[0] x = R/np.sqrt(1+k*2) y = k x z = np.linspace(-d, d, Nb) xv, zv = np.meshgrid(x, z) yv, zv = np.meshgrid(y, z) xin = np.array([np.ravel(xv), np.ravel(yv), np.ravel(zv)]).T Npix = np.size(xv) af = np.empty((Npix, 3)) derf = np.empty((Npix, 3, Npot)) for i in range(Npix): xi = xin[i]u.kpc a = acc_cart(xi, components=components) dadq = apder_cart(xi, components=components) derf[i] = dadq ca = np.matmul(dadq, np.matmul(cq, dadq.T)) a_crb = np.sqrt(np.diag(ca)) u.pc * u.Myr*-2 if relative: af[i] = np.abs(a_crb/a) else: af[i] = a_crb #print(xi, a_crb) # save np.savez('../data/crb_acart{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}'.format(alabel, errmode, n, vlabel, component, Ndim, d, Nb, relative), acc=af, x=xin, der=derf) plt.close() fig, ax = plt.subplots(1, 3, figsize=(15, 5)) label = ['$\Delta$ $a_X$', '$\Delta$ $a_Y$', '$\Delta$ $a_Z$'] for i in range(3): plt.sca(ax[i]) im = plt.imshow(af[:,i].reshape(Nb, Nb), origin='lower', extent=[-d, d, -d, d], cmap=mpl.cm.gray, vmin=vmin, vmax=vmax, norm=mpl.colors.LogNorm()) if progenitor: plt.plot(Rp, zp, 'r', ms=10) plt.xlabel('R (kpc)') plt.ylabel('Z (kpc)') divider = make_axes_locatable(plt.gca()) cax = divider.append_axes("right", size="3%", pad=0.1) plt.colorbar(im, cax=cax) plt.ylabel(label[i] + rlabel) plt.tight_layout() plt.savefig('../plots/crb_acc_cart{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}.png'.format(alabel, errmode, n, vlabel, component, Ndim, d, Nb, relative)) def crb_acart_cov(n, Ndim=6, vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], component='all', j=0, align=True, d=20, Nb=30, fast=False, scale=False, relative=True, progenitor=False, batch=False, errmode='fiducial'): """""" pid, dp_fid, vlabel = get_varied_pars(vary) if align: alabel = '_align' else: alabel = '' if relative: vmin = 1e-2 vmax = 1 rlabel = ' / a' else: vmin = -0.005 vmax = 0.005 #vmin = 1e-2 #vmax = 1e0 rlabel = ' (pc Myr$^{-2}$)' # read in full inverse CRB for stream modeling cxi = np.load('../data/crb/bspline_cxi{:s}_{:s}_{:d}_{:s}_{:d}.npy'.format(alabel, errmode, n, vlabel, Ndim)) if fast: cx = np.linalg.inv(cxi) else: cx = stable_inverse(cxi) # choose the appropriate components: Nprog, Nbary, Nhalo, Ndipole, Nquad, Npoint = [6, 5, 4, 3, 5, 1] if 'progenitor' not in vary: Nprog = 0 nstart = {'bary': Nprog, 'halo': Nprog + Nbary, 'dipole': Nprog + Nbary + Nhalo, 'quad': Nprog + Nbary + Nhalo + Ndipole, 'all': Nprog, 'point': 0} nend = {'bary': Nprog + Nbary, 'halo': Nprog + Nbary + Nhalo, 'dipole': Nprog + Nbary + Nhalo + Ndipole, 'quad': Nprog + Nbary + Nhalo + Ndipole + Nquad, 'all': np.shape(cx)[0], 'point': 1} if 'progenitor' not in vary: nstart['dipole'] = Npoint nend['dipole'] = Npoint + Ndipole if component in ['bary', 'halo', 'dipole', 'quad', 'point']: components = [component] else: components = [x for x in vary if x!='progenitor'] cq = cx[nstart[component]:nend[component], nstart[component]:nend[component]] Npot = np.shape(cq)[0] if fast: cqi = np.linalg.inv(cq) else: cqi = stable_inverse(cq) if scale: dp_opt = read_optimal_step(n, vary) dp = [xy.unit for x,y in zip(dp_opt, dp_fid)] scale_vec = np.array([x.value for x in dp[nstart[component]:nend[component]]]) scale_mat = np.outer(scale_vec, scale_vec) cqi = scale_mat if progenitor: prog_coords = {-1: gd1_coordinates(), -2: pal5_coordinates(), -3: tri_coordinates(), -4: atlas_coordinates()} x0, v0 = prog_coords[n] print(x0) else: x0 = np.array([4, 4, 0]) Rp = np.linalg.norm(x0[:2]) zp = x0[2] R = np.linspace(-d, d, Nb) k = x0[1]/x0[0] x = R/np.sqrt(1+k*2) y = k x z = np.linspace(-d, d, Nb) xv, zv = np.meshgrid(x, z) yv, zv = np.meshgrid(y, z) xin = np.array([np.ravel(xv), np.ravel(yv), np.ravel(zv)]).T Npix = np.size(xv) af = np.empty((Npix, 3)) derf = np.empty((Npix3, Npot)) for i in range(Npix): xi = xin[i]u.kpc a = acc_cart(xi, components=components) dadq = apder_cart(xi, components=components) derf[i3:(i+1)3] = dadq ca = np.matmul(derf, np.matmul(cq, derf.T)) Nx = Npot Nw = Npix3 vals, vecs = la.eigh(ca, eigvals=(Nw - Nx - 2, Nw - 1)) ## check orthogonality: #for i in range(Npot-1): #for k in range(i+1, Npot): #print(i, k) #print(np.dot(vecs[:,i], vecs[:,k])) #print(np.dot(vecs[::3,i], vecs[::3,k]), np.dot(vecs[1::3,i], vecs[1::3,k]), np.dot(vecs[1::3,i], vecs[1::3,k])) # save np.savez('../data/crb_acart_cov{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}_{:d}'.format(alabel, errmode, n, vlabel, component, Ndim, d, Nb, relative, progenitor), x=xin, der=derf, c=ca) plt.close() fig, ax = plt.subplots(1, 3, figsize=(15, 5)) if j==0: vcomb = np.sqrt(np.sum(vecs2vals, axis=1)) label = ['($\Sigma$ Eigval $\\times$ Eigvec$^2$ $a_{}$'.format(x)+')$^{1/2}$' for x in ['X', 'Y', 'Z']] vmin = 1e-2 vmax = 5e0 norm = mpl.colors.LogNorm() else: vcomb = vecs[:,j] label = ['Eig {} $a_{}$'.format(np.abs(j), x) for x in ['X', 'Y', 'Z']] vmin = -0.025 vmax = 0.025 norm = None for i in range(3): plt.sca(ax[i]) #im = plt.imshow(vecs[i::3,j].reshape(Nb, Nb), origin='lower', extent=[-d, d, -d, d], cmap=mpl.cm.gray, vmin=vmin, vmax=vmax) im = plt.imshow(vcomb[i::3].reshape(Nb, Nb), origin='lower', extent=[-d, d, -d, d], cmap=mpl.cm.gray, vmin=vmin, vmax=vmax, norm=norm) if progenitor: plt.plot(Rp, zp, 'r', ms=10) plt.xlabel('R (kpc)') plt.ylabel('Z (kpc)') divider = make_axes_locatable(plt.gca()) cax = divider.append_axes("right", size="3%", pad=0.1) plt.colorbar(im, cax=cax) plt.ylabel(label[i]) plt.tight_layout() if batch: return fig else: plt.savefig('../plots/crb_acc_cart_cov{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}_{:d}_{:d}.png'.format(alabel, errmode, n, vlabel, component, np.abs(j), Ndim, d, Nb, relative, progenitor)) def a_vecfield(vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], component='all', d=20, Nb=10): """Plot acceleration field in R,z plane""" if component in ['bary', 'halo', 'dipole', 'quad', 'point']: components = [component] else: components = [x for x in vary if x!='progenitor'] x0 = np.array([4, 4, 0]) R = np.linspace(-d, d, Nb) k = x0[1]/x0[0] x = R/np.sqrt(1+k2) y = k x z = np.linspace(-d, d, Nb) xv, zv = np.meshgrid(x, z) yv, zv = np.meshgrid(y, z) xin = np.array([np.ravel(xv), np.ravel(yv),	np.ravel(zv)	numpy.ravel
# Copyright 2019 Division of Medical Image Computing, German Cancer Research Center (DKFZ), Heidelberg, Germany # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. import argparse import numpy as np from batchgenerators.augmentations.utils import resize_segmentation from uuunet.experiment_planning.plan_and_preprocess_task import get_caseIDs_from_splitted_dataset_folder from uuunet.inference.segmentation_export import save_segmentation_nifti_from_softmax from batchgenerators.utilities.file_and_folder_operations import * from multiprocessing import Process, Queue import torch import threading import matplotlib import matplotlib.pyplot as plt import matplotlib.animation as animation from mpl_toolkits.mplot3d import Axes3D import SimpleITK as sitk import shutil from multiprocessing import Pool from uuunet.training.model_restore import load_model_and_checkpoint_files from uuunet.training.network_training.nnUNetTrainer import nnUNetTrainer from uuunet.utilities.one_hot_encoding import to_one_hot def plot_images(img, img2=None): """ Plot at most 2 images. Support passing in ndarray or image path string. """ fig = plt.figure(figsize=(20,10)) if isinstance(img, str): img = imread(img) if isinstance(img2, str): img2 = imread(img2) if img2 is None: ax = fig.add_subplot(111) ax.imshow(img) else: height, width = img.shape[0], img.shape[1] if height < width: ax = fig.add_subplot(211) ax2 = fig.add_subplot(212) else: ax = fig.add_subplot(121) ax2 = fig.add_subplot(122) ax.imshow(img) ax2.imshow(img2) plt.show() def view_batch(imgs, lbls, labels=['image', 'label'], stack=False): ''' imgs: [D, H, W, C], the depth or batch dimension should be the first. ''' fig = plt.figure() ax1 = fig.add_subplot(121) ax2 = fig.add_subplot(122) ax1.set_title(labels[0]) ax2.set_title(labels[1]) """ if init with zeros, the animation may not update? seems bug in animation. """ if stack: lbls = np.stack((lbls, imgs, imgs), -1) img1 = ax1.imshow(np.random.rand(imgs.shape[1:])) img2 = ax2.imshow(np.random.rand(lbls.shape[1:])) def update(i): plt.suptitle(str(i)) img1.set_data(imgs[i]) img2.set_data(lbls[i]) return img1, img2 ani = animation.FuncAnimation(fig, update, frames=len(imgs), interval=10, blit=False, repeat_delay=0) plt.show() def predict_save_to_queue(preprocess_fn, q, list_of_lists, output_files, segs_from_prev_stage, classes): errors_in = [] for i, l in enumerate(list_of_lists): try: output_file = output_files[i] print("preprocessing", output_file) d, _, dct = preprocess_fn(l) print(output_file, dct) if segs_from_prev_stage[i] is not None: assert isfile(segs_from_prev_stage[i]) and segs_from_prev_stage[i].endswith(".nii.gz"), "segs_from_prev_stage" \ " must point to a " \ "segmentation file" seg_prev = sitk.GetArrayFromImage(sitk.ReadImage(segs_from_prev_stage[i])) # check to see if shapes match img = sitk.GetArrayFromImage(sitk.ReadImage(l[0])) assert all([i == j for i, j in zip(seg_prev.shape, img.shape)]), "image and segmentation from previous " \ "stage don't have the same pixel array " \ "shape! image: %s, seg_prev: %s" % \ (l[0], segs_from_prev_stage[i]) seg_reshaped = resize_segmentation(seg_prev, d.shape[1:], order=1, cval=0) seg_reshaped = to_one_hot(seg_reshaped, classes) d = np.vstack((d, seg_reshaped)).astype(np.float32) """There is a problem with python process communication that prevents us from communicating obejcts larger than 2 GB between processes (basically when the length of the pickle string that will be sent is communicated by the multiprocessing.Pipe object then the placeholder (\%i I think) does not allow for long enough strings (lol). This could be fixed by changing i to l (for long) but that would require manually patching system python code. We circumvent that problem here by saving softmax_pred to a npy file that will then be read (and finally deleted) by the Process. save_segmentation_nifti_from_softmax can take either filename or np.ndarray and will handle this automatically""" print(d.shape) if np.prod(d.shape) > (2e9 / 4 * 0.9): # 0.9 just to be save, 4 because float32 is 4 bytes print( "This output is too large for python process-process communication. " "Saving output temporarily to disk") np.save(output_file[:-7] + ".npy", d) d = output_file[:-7] + ".npy" q.put((output_file, (d, dct))) except KeyboardInterrupt: raise KeyboardInterrupt except Exception as e: print("error in", l) print(e) q.put("end") if len(errors_in) > 0: print("There were some errors in the following cases:", errors_in) print("These cases were ignored.") else: print("This worker has ended successfully, no errors to report") def preprocess_multithreaded(trainer, list_of_lists, output_files, num_processes=2, segs_from_prev_stage=None): if segs_from_prev_stage is None: segs_from_prev_stage = [None] len(list_of_lists) classes = list(range(1, trainer.num_classes)) assert isinstance(trainer, nnUNetTrainer) q = Queue(1) processes = [] for i in range(num_processes): pr = Process(target=predict_save_to_queue, args=(trainer.preprocess_patient, q, list_of_lists[i::num_processes], output_files[i::num_processes], segs_from_prev_stage[i::num_processes], classes)) pr.start() processes.append(pr) try: end_ctr = 0 while end_ctr != num_processes: item = q.get() if item == "end": end_ctr += 1 continue else: yield item finally: for p in processes: if p.is_alive(): p.terminate() # this should not happen but better safe than sorry right p.join() q.close() def predict_cases(model, list_of_lists, output_filenames, folds, save_npz, num_threads_preprocessing, num_threads_nifti_save, segs_from_prev_stage=None, do_tta=True, overwrite_existing=False, data_type='2d', modality=0): assert len(list_of_lists) == len(output_filenames) if segs_from_prev_stage is not None: assert len(segs_from_prev_stage) == len(output_filenames) prman = Pool(num_threads_nifti_save) results = [] cleaned_output_files = [] for o in output_filenames: dr, f = os.path.split(o) if len(dr) > 0: maybe_mkdir_p(dr) if not f.endswith(".nii.gz"): f, _ = os.path.splitext(f) f = f + ".nii.gz" cleaned_output_files.append(join(dr, f)) if not overwrite_existing: print("number of cases:", len(list_of_lists)) not_done_idx = [i for i, j in enumerate(cleaned_output_files) if not isfile(j)] cleaned_output_files = [cleaned_output_files[i] for i in not_done_idx] list_of_lists = [list_of_lists[i] for i in not_done_idx] if segs_from_prev_stage is not None: segs_from_prev_stage = [segs_from_prev_stage[i] for i in not_done_idx] print("number of cases that still need to be predicted:", len(cleaned_output_files)) print("emptying cuda cache") torch.cuda.empty_cache() ################################## # Damn, finally find the model. print("loading parameters for folds,", folds) trainer, params = load_model_and_checkpoint_files(model, folds) trainer.modality = modality print("starting preprocessing generator") preprocessing = preprocess_multithreaded(trainer, list_of_lists, cleaned_output_files, num_threads_preprocessing, segs_from_prev_stage) print("starting prediction...") for preprocessed in preprocessing: output_filename, (d, dct) = preprocessed if isinstance(d, str): data = np.load(d) os.remove(d) d = data print("predicting", output_filename) softmax = [] for p in params: trainer.load_checkpoint_ram(p, False) softmax.append(trainer.predict_preprocessed_data_return_softmax(d, do_tta, 1, False, 1, trainer.data_aug_params['mirror_axes'], True, True, 2, trainer.patch_size, True, data_type=data_type)[None]) softmax =	np.vstack(softmax)	numpy.vstack
import numpy as np import matplotlib.pyplot as plt from os import makedirs from os.path import isfile, exists from scipy.constants import mu_0 # from numba import njit def calcDipolMomentAnalytical(remanence, volume): """ Calculating the magnetic moment from the remanence in T and the volume in m^3""" m = remanence * volume / mu_0 # [A * m^2] return m def plotSimple(data, FOV, fig, ax, cbar=True, args): """ Generate simple colorcoded plot of 2D grid data with contour. Returns axes object.""" im = ax.imshow(data, extent=FOV, origin="lower", args) cs = ax.contour(data, colors="k", extent=FOV, origin="lower", linestyles="dotted") class nf(float): def __repr__(self): s = f"{self:.1f}" return f"{self:.0f}" if s[-1] == "0" else s cs.levels = [nf(val) for val in cs.levels] if plt.rcParams["text.usetex"]: fmt = r"%r" else: fmt = "%r" ax.clabel(cs, cs.levels, inline=True, fmt=fmt, fontsize=10) if cbar == True: fig.colorbar(im, ax=ax) return im def centerCut(field, axis): """return a slice of the data at the center for the specified axis""" dims = np.shape(field) return np.take(field, indices=int(dims[axis] / 2), axis=axis) def isHarmonic(field, sphericalMask, shellMask): """Checks if the extrema of the field are in the shell.""" fullField = np.multiply(field, sphericalMask) # [T] reducedField = np.multiply(field, shellMask) if int(ptpPPM(fullField)) > int(ptpPPM(reducedField)): print( "ptpPPM of field:", ptpPPM(fullField), "ptpPPM on surface", ptpPPM(reducedField), ) print("Masked field is NOT a harmonic function...") return False else: print( "ptpPPM of field:", ptpPPM(fullField), "ptpPPM on surface", ptpPPM(reducedField), ) print("Masked field is harmonic.") sizeSpherical = int(np.nansum(sphericalMask)) sizeShell = int(np.nansum(shellMask)) print( "Reduced size of field from {} to {} ({}%)".format( sizeSpherical, sizeShell, int(100 * sizeShell / sizeSpherical) ) ) return True def genQmesh(field, resolution): """Generate a mesh of quadratic coordinates""" mask = np.zeros(np.shape(field)) xAxis = np.linspace( -(np.size(field, 0) - 1) * resolution / 2, (np.size(field, 0) - 1) * resolution / 2, np.size(field, 0), ) yAxis = np.linspace( -(np.size(field, 1) - 1) * resolution / 2, (np.size(field, 1) - 1) * resolution / 2, np.size(field, 1), ) zAxis = np.linspace( -(np.size(field, 2) - 1) * resolution / 2, (np.size(field, 2) - 1) * resolution / 2, np.size(field, 2), ) xAxis, yAxis, zAxis = np.meshgrid(xAxis, yAxis, zAxis) xAxisSquare = np.square(xAxis) yAxisSquare = np.square(yAxis) zAxisSquare = np.square(zAxis) return mask, xAxisSquare, yAxisSquare, zAxisSquare def genMask( field, resolution, diameter=False, shellThickness=False, axis=False, debug=False ): """Generate a mask for a spherical shell""" mask, xAxisSquare, yAxisSquare, zAxisSquare = genQmesh(field, resolution) if (shellThickness != False) and (diameter != False): if debug == True: print( "Creating shell mask. (resolution = {}, diameter = {}, shellThickness = {})".format( resolution, diameter, shellThickness ) ) print("The shell is added inside the sphere surface!") rAxisSquare = xAxisSquare + yAxisSquare + zAxisSquare innerRadiusSquare = (diameter / 2 - shellThickness) 2 outerRadiusSquare = (diameter / 2) 2 mask[ (rAxisSquare <= outerRadiusSquare) & (rAxisSquare >= innerRadiusSquare) ] = 1 mask[mask == 0] = "NaN" return mask def genSphericalMask(field, diameter, resolution): """generate spherical mask with >>diameter<< for a >>field<< and a given >>resolution<< """ mask, xAxisSquare, yAxisSquare, zAxisSquare = genQmesh(field, resolution) mask[xAxisSquare + yAxisSquare + zAxisSquare <= (diameter / 2) 2] = 1 mask[mask == 0] = "NaN" return mask def genSliceMask(field, diameter, resolution, axis="x"): """generate mask for a circular slice with >>diameter<< for a >>field<< and a given >>resolution<< Every input variable has to have the same unit (mm or m or ...) """ mask, xAxisSquare, yAxisSquare, zAxisSquare = genQmesh(field, resolution) if axis == "z": mask[ (xAxisSquare + yAxisSquare <= (diameter / 2) 2) & (zAxisSquare == 0) ] = 1 if axis == "y": mask[ (xAxisSquare + zAxisSquare <= (diameter / 2) 2) & (yAxisSquare == 0) ] = 1 if axis == "x": mask[ (yAxisSquare + zAxisSquare <= (diameter / 2) 2) & (xAxisSquare == 0) ] = 1 mask[mask == 0] = "NaN" return mask def genEllipseSliceMask(field, a, b, resolution, axis="x"): """generate mask for a circulat slice with >>diameter<< for a >>field<< and a given >>resolution<< Every input variable has to have the same unit (mm or m or ...) """ # generate spherical mask mask, xAxisSquare, yAxisSquare, zAxisSquare = genQmesh(field, resolution) if axis == "z": mask[ (xAxisSquare / (a / 2) 2 + yAxisSquare / (b / 2) 2 <= 1) & (zAxisSquare == 0) ] = 1 elif axis == "y": mask[ (xAxisSquare / (a / 2) 2 + zAxisSquare / (b / 2) 2 <= 1) & (yAxisSquare == 0) ] = 1 elif axis == "x": mask[ (yAxisSquare / (a / 2) 2 + zAxisSquare / (b / 2) 2 <= 1) & (xAxisSquare == 0) ] = 1 mask[mask == 0] = "NaN" return mask def ptpPPM(field): """Calculate the peak-to-peak homogeneity in ppm.""" return 1e6 * (np.nanmax(field) - np.nanmin(field)) / np.nanmean(field) def saveParameters(parameters, folder): """Saving a dict to the file parameters.npy . If the file exist it is beeing updated, if the parameters are not stored already. __future__: Fix usecase: Some parameters are in dict which are identical to the stored ones and some are new! """ try: print("Saving parameters to file...", end=" ") print("\x1b[6;30;42m", parameters.keys(), "\x1b[0m", end=" ") oldParameters = loadParameters(folder) if parameters.items() <= oldParameters.items(): print(" ... the parameters are already saved and identical.") elif set(parameters).issubset( set(oldParameters) ): # here just keys are compared! print( " ...\x1b[6;37;41m" + " parameters are NOT saved. Other parameters are stored. Please cleanup! " + "\x1b[0m" ) else: oldParameters.update(parameters) np.save(folder + "/parameters", oldParameters) print(" ... added.") except FileNotFoundError or AttributeError: np.save(folder + "/parameters", parameters) oldParameters = parameters # print('The following parameters are currently stored:\n', oldParameters.keys()) def loadParameters(folder): return np.load(folder + "/parameters.npy", allow_pickle=True).item() def loadParameter(key, folder): return loadParameters(folder)[key] def displayParameters(folder): print(loadParameters(folder)) def createShimfieldsShimRingV2( numMagnets=(32, 44), rings=4, radii=(0.074, 0.097), zRange=(-0.08, -0.039, 0.039, 0.08), resolution=1000, kValue=2, simDimensions=(0.04, 0.04, 0.04), numRotations=2, ): """ Calculating the magnetic field distributions for a single or multiple Halbach Rings. This has to be multiplied with the magnetic moment amplitude of a magnet to get the real distribution For every magnet position we set 4 different rotations: 0°, 45°, 90°, 135°. This has to be considered in the cost function otherwise two magnets are placed in one position resolution is the amount of sample points times data points in one dimension """ mu = mu_0 # positioning of the magnets in a circle if len(zRange) == 2: rings = np.linspace(zRange[0], zRange[1], rings) elif rings == len(zRange): rings = np.array(zRange) else: print("No clear definition how to place shims...") rotation_elements = np.linspace(0, np.pi, numRotations, endpoint=False) # create array to store field data count = 0 if type(numMagnets) in (list, tuple): totalNumMagnets = np.sum(numMagnets) * np.size(rings) * numRotations else: totalNumMagnets = numMagnets * np.size(rings) * numRotations * len(radii) print(totalNumMagnets, numMagnets, np.size(rings), np.size(numRotations)) shimFields = np.zeros( ( int(simDimensions[0] * resolution) + 1, int(simDimensions[1] * resolution) + 1, int(simDimensions[2] * resolution) + 1, 3, totalNumMagnets, ), dtype=np.float32, ) for rotation in rotation_elements: # create halbach array for row in rings: for i, radius in enumerate(radii): angle_elements = np.linspace( -np.pi, np.pi, numMagnets[i], endpoint=False ) for angle in angle_elements: print( "Simulating magnet " + str(count + 1) + " of " + str(totalNumMagnets), end="\t", ) position = (row, radius * np.cos(angle), radius * np.sin(angle)) print( "@ position {:2.2},\t {:2.2},\t {:2.2}".format(position), end="\r", ) angle = kValue angle + rotation dip_vec = [0, np.sin(angle), -np.cos(angle)] dip_vec = np.multiply(dip_vec, mu) dip_vec = np.divide(dip_vec, 4 * np.pi) # create mesh coordinates x = np.linspace( -simDimensions[0] / 2 + position[0], simDimensions[0] / 2 + position[0], int(simDimensions[0] * resolution) + 1, dtype=np.float32, ) y = np.linspace( -simDimensions[1] / 2 + position[1], simDimensions[1] / 2 + position[1], int(simDimensions[1] * resolution) + 1, dtype=np.float32, ) z = np.linspace( -simDimensions[2] / 2 + position[2], simDimensions[2] / 2 + position[2], int(simDimensions[2] * resolution) + 1, dtype=np.float32, ) x, y, z = np.meshgrid(x, y, z) vec_dot_dip = 3 * (y * dip_vec[1] + z * dip_vec[2]) # calculate the distance of each mesh point to magnet, optimised for speed # for improved memory performance move in to b0 calculations vec_mag = np.square(x) + np.square(y) + np.square(z) # if the magnet is in the origin, we divide by 0, therefore we set it to nan to # avoid getting and error. if this has any effect on speed just leave it out # as we do not care about the values outside of the FOV and even less inside the magnets vec_mag[(vec_mag <= 1e-15) & (vec_mag >= -1e-15)] = "NaN" vec_mag_3 = np.power(vec_mag, 1.5) vec_mag_5 = np.power(vec_mag, 2.5) del vec_mag # calculate contributions of magnet to total field, dipole always points in yz plane # so second term is zero for the x component shimFields[:, :, :, 0, count] = np.divide( np.multiply(x, vec_dot_dip), vec_mag_5 ) shimFields[:, :, :, 1, count] = np.divide( np.multiply(y, vec_dot_dip), vec_mag_5 ) - np.divide(dip_vec[1], vec_mag_3) shimFields[:, :, :, 2, count] = np.divide(	np.multiply(z, vec_dot_dip)	numpy.multiply
import numpy as np import pandas as pd import plotly.graph_objects as go import toolsClass import multiprocessing import time from scipy.interpolate import interp1d import scipy.integrate as integrate #from tqdm.contrib.concurrent import process_map #for process bar. very slow... tools = toolsClass.tools() import logging log = logging.getLogger(__name__) class GYRO: def __init__(self, rootDir, dataPath): """ rootDir is root location of python modules (where dashGUI.py lives) dataPath is the location where we write all output to """ self.rootDir = rootDir tools.rootDir = self.rootDir self.dataPath = dataPath tools.dataPath = self.dataPath return def allowed_class_vars(self): """ Writes a list of recognized class variables to HEAT object Used for error checking input files and for initialization Here is a list of variables with description: testvar dummy for testing """ self.allowed_vars = [ 'N_gyroSteps', 'gyroDeg', 'gyroT_eV', 'N_vSlice', 'N_vPhase', 'N_gyroPhase', 'ionMassAMU', 'vMode', 'ionFrac' ] return def setTypes(self): """ Set variable types for the stuff that isnt a string from the input file """ integers = [ 'N_gyroSteps', 'gyroDeg', 'N_vSlice', 'N_vPhase', 'N_gyroPhase', ] floats = [ 'ionFrac', 'gyroT_eV', 'ionMassAMU', ] for var in integers: if (getattr(self, var) is not None) and (~np.isnan(float(getattr(self, var)))): try: setattr(self, var, int(getattr(self, var))) except: print("Error with input file var "+var+". Perhaps you have invalid input values?") log.info("Error with input file var "+var+". Perhaps you have invalid input values?") for var in floats: if var is not None: if (getattr(self, var) is not None) and (~np.isnan(float(getattr(self, var)))): try: setattr(self, var, float(getattr(self, var))) except: print("Error with input file var "+var+". Perhaps you have invalid input values?") log.info("Error with input file var "+var+". Perhaps you have invalid input values?") return def setupConstants(self, ionMassAMU=2.014): """ Sets up constants default mass is deuterium 2.014 MeV/c^2 """ #unit conversions self.kg2eV = 5.609e35 #1kg = 5.609e35 eV/c^2 self.eV2K = 1.160e4 #1ev=1.160e4 K #constants self.AMU = 931.494e6 #ev/c^2 self.kB = 8.617e-5 #ev/K self.e = 1.602e-19 # C self.c = 299792458 #m/s self.diamag = -1 #diamagnetism = -1 for ions, 1 for electrons self.mass_eV = ionMassAMU * self.AMU self.Z=1 #assuming isotopes of hydrogen here return def temp2thermalVelocity(self, T_eV): """ Calculates thermal velocity from a temperature, where thermal velocity is defined as the most probable speed T_eV is temperature in eV can also be found with: d/dv( vf(v) ) = 0 note that this is for v, not vPerp or v\|\| """ return np.sqrt(2.0T_eV/(self.mass_eV/self.c*2)) def setupFreqs(self, B): """ Calculates frequencies, periods, that are dependent upon B These definitions follow Freidberg Section 7.7. B is magnetic field magnitude """ self.omegaGyro = self.Z self.e * B / (self.mass_eV / self.kg2eV) if np.isscalar(self.omegaGyro): self.omegaGyro = np.array([self.omegaGyro]) self.fGyro = np.abs(self.omegaGyro)/(2np.pi) self.TGyro = 1.0/self.fGyro return def setupRadius(self, vPerp): """ calculates gyro radius. rGyro has a column for each MC run (N_MC columns), and a row for each point on the PFC (N_pts), so it is a matrix of shape: N_pts X N_MC """ N_pts = len(self.omegaGyro) #get number of vPerps if np.isscalar(vPerp): vPerp = np.array([vPerp]) N_MC = 1 else: N_MC = len(vPerp) self.rGyro = np.zeros((N_pts,N_MC)) for i in range(N_MC): self.rGyro[:,i] = vPerp[i] / np.abs(self.omegaGyro) return def setupVelocities(self, N): """ sets up velocities based upon vMode input from GUI N is the number of source mesh elements (ie len(PFC.centers) ) len(self.t1) is number of points in divertor we are calculating HF on """ #get velocity space phase angles self.uniformVelPhaseAngle() if self.vMode == 'single': print("Gyro orbit calculation from single plasma temperature") log.info("Gyro orbit calculation from single plasma temperature") self.T0 = np.ones((N))self.gyroT_eV #get average velocity for each temperature point self.vThermal = self.temp2thermalVelocity(self.T0) #set upper bound of vf(v) (note that this cuts off high energy particles) self.vMax = 5 self.vThermal #get 100 points to initialize functional form of f(v) (note this is a 2D matrix cause vMax is 2D) self.vScan = np.linspace(0,self.vMax,10000).T #get velocity slices for each T0 self.pullEqualProbabilityVelocities() else: #TO ADD THIS YOU WILL NEED TO PASS IN XYZ COORDINATES OF CTRS AND INTERPOLATE print("3D plasma temperature interpolation from file not yet supported. Run gyro orbits in single mode") log.info("3D plasma temperature interpolation from file not yet supported. Run gyro orbits in single mode") return def pullEqualProbabilityVelocities(self): """ creates vSlices: array of velocities indexed to match T0 array (or PFC.centers) each vSlice is positioned at a place in the PDF so it has an equal probability of occuring. ie the area under the PDF curve between each vSlice is equal. in loop, i is mesh element index """ self.vSlices = np.ones((len(self.T0),self.N_vSlice))np.nan self.energySlices = np.zeros((len(self.T0),self.N_vSlice)) self.energyIntegrals = np.zeros((len(self.T0),self.N_vSlice)) self.energyFracs = np.zeros((len(self.T0),self.N_vSlice)) self.vBounds = np.zeros((len(self.T0),self.N_vSlice+1)) for i in range(len(self.T0)): #get speed range for this T0 v = self.vScan[i,:] #generate the (here maxwellian) velocity vector PDF #pdf = lambda x: (self.mass_eV/self.c2) / (self.T0[i]) np.exp(-(self.mass_eV/self.c*2 x*2) / (2self.T0[i]) ) pdf = lambda x: ( (self.mass_eV/self.c*2) / (2 np.pi * self.T0[i]) )*(3.0/2.0) np.exp(-(self.mass_eV/self.c*2 x*2) / (2self.T0[i]) ) #speed pdf (integrate over solid angle) v_pdf = 4np.pi v*2 pdf(v) #generate the CDF v_cdf = np.cumsum(v_pdf[1:])np.diff(v) v_cdf = np.insert(v_cdf, 0, 0) #create bspline interpolators for the cdf and cdf inverse inverseCDF = interp1d(v_cdf, v, kind='linear') forwardCDF = interp1d(v, v_cdf, kind='linear') #CDF location of vSlices and bin boundaries cdfBounds = np.linspace(0,v_cdf[-1],self.N_vSlice+1) #CDF location of velocity bin bounds omitting 0 and 1 #old method does not make vSlices truly bin centers #cdfBounds = np.linspace(0,1,self.N_vSlice+1)[1:-1] #old method 2 spaces centers uniformly # #calculate N_vSlice velocities for each pdf each with equal area (probability) # cdfMax = v_cdf[-1] # cdfMin = v_cdf[0] # sliceWidth = cdfMax / (self.N_vSlice+1) # #CDF location of vSlices omitting 0 and 1 # cdfSlices = np.linspace(0,1,self.N_vSlice+2)[1:-1] # #CDF location of velocity bin bounds omitting 0 and 1 # #old method does not make vSlices truly bin centers # #cdfBounds = np.linspace(0,1,self.N_vSlice+1)[1:-1] # #new method makes vSlices bin centers, except for the end bins # cdfBounds = np.diff(cdfSlices)/2.0 + cdfSlices[:-1] # #vSlices are Maxwellian distribution sample locations (@ bin centers) # self.vSlices[i,:] = inverseCDF(cdfSlices) # vBounds = inverseCDF(cdfBounds) # vBounds = np.insert(vBounds,0,0) # vBounds = np.append(vBounds,self.vMax[i]) #new method spaces bins uniformly, then makes vSlices center of these bins in CDF space cdfSlices = np.diff(cdfBounds)/2.0 + cdfBounds[:-1] #vSlices are Maxwellian distribution sample locations (@ bin centers) self.vSlices[i,:] = inverseCDF(cdfSlices) vBounds = inverseCDF(cdfBounds) self.vBounds[i,:] = vBounds #print(cdfBounds) #print(cdfSlices) #print(self.vBounds) #print(self.vSlices) #Now find energies that correspond to these vSlices #we integrate: v2 f(v) #energy pdf (missing 1/2mass but that gets divided out later anyways ) #EofV = lambda x: x2 pdf(x) #EofV = lambda x: 4np.pi x*4 pdf(x) f_E = lambda x: 2 * np.sqrt(x / np.pi) * (self.T0[i])*(-3.0/2.0) np.exp(-x / self.T0[i]) #energy slices that correspond to velocity slices self.energySlices[i,:] = f_E(0.5 * (self.mass_eV/self.c*2) self.vSlices[i,:]*2) #energy integrals for j in range(self.N_vSlice): Elo = 0.5 (self.mass_eV/self.c*2) vBounds[j]*2 Ehi = 0.5 (self.mass_eV/self.c*2) vBounds[j+1]*2 self.energyIntegrals[i,j] = integrate.quad(f_E, Elo, Ehi)[0] energyTotal = self.energyIntegrals[i,:].sum() #for testing #if i==0: # print("Integral Test===") # print(energyTotal) # print(integrate.quad(f_E, 0.0, self.vMax[i])[0]) #energy fractions for j in range(self.N_vSlice): self.energyFracs[i,j] = self.energyIntegrals[i,j] / energyTotal print("Found N_vPhase velocities of equal probability") log.info("Found N_vPhase velocities of equal probability") return def uniformGyroPhaseAngle(self): """ Uniform sampling of a uniform distribution between 0 and 2pi returns angles in radians """ self.gyroPhases = np.linspace(0,2np.pi,self.N_gyroPhase+1)[:-1] return def uniformVelPhaseAngle(self): """ Sampling of a uniform distribution between 0 and pi/2 (only forward velocities) vPerp is x-axis of velocity space vParallel is y-axis of velocity space returns angles in radians """ self.vPhases = np.linspace(0.0,np.pi/2,self.N_vPhase+2)[1:-1] return def singleGyroTrace(self,vPerp,vParallel,gyroPhase,N_gyroSteps, BtraceXYZ,controlfilePath,TGyro,rGyro,omegaGyro, verbose=True): """ Calculates the gyro-Orbit path and saves to .csv and .vtk vPerp and vParallel [m/s] are in velocities gyroPhase [degrees] is initial orbit phase angle N_gyroSteps is number of discrete line segments per gyro period BtraceXYZ is the points of the Bfield trace that we will gyrate about """ print("Calculating gyro trace...") #Loop thru B field trace while tracing gyro orbit helixTrace = None for i in range(len(BtraceXYZ)-1): #points in this iteration p0 = BtraceXYZ[i,:] p1 = BtraceXYZ[i+1,:] #vector delP = p1 - p0 #magnitude or length of line segment magP = np.sqrt(delP[0]2 + delP[1]2 + delP[2]*2) #time it takes to transit line segment delta_t = magP / (vParallel) #Number of steps in line segment Tsample = self.TGyro / N_gyroSteps Nsteps = int(delta_t / Tsample) #length (in time) along guiding center t = np.linspace(0,delta_t,Nsteps+1) #guiding center location xGC = np.linspace(p0[0],p1[0],Nsteps+1) yGC = np.linspace(p0[1],p1[1],Nsteps+1) zGC = np.linspace(p0[2],p1[2],Nsteps+1) # construct orthogonal system for coordinate transformation w = delP if np.all(w==[0,0,1]): u = np.cross(w,[0,1,0]) #prevent failure if bhat = [0,0,1] else: u = np.cross(w,[0,0,1]) #this would fail if bhat = [0,0,1] (rare) v = np.cross(w,u) #normalize u = u / np.sqrt(u.dot(u)) v = v / np.sqrt(v.dot(v)) w = w / np.sqrt(w.dot(w)) xfm = np.vstack([u,v,w]).T #get helix path along (proxy) z axis reference frame x_helix = self.rGyronp.cos(self.omegaGyrot + gyroPhase) y_helix = self.diamagself.rGyronp.sin(self.omegaGyrot + gyroPhase) z_helix = np.zeros((len(t))) #perform rotation to field line reference frame helix = np.vstack([x_helix,y_helix,z_helix]).T helix_rot = np.zeros((len(helix),3)) for j,coord in enumerate(helix): helix_rot[j,:] = helix[j,0]u + helix[j,1]v + helix[j,2]w #perform translation to field line reference frame helix_rot[:,0] += xGC helix_rot[:,1] += yGC helix_rot[:,2] += zGC #update gyroPhase variable so next iteration starts here gyroPhase = self.omegaGyrot[-1] + gyroPhase #append to helix trace if helixTrace is None: helixTrace = helix_rot else: helixTrace = np.vstack([helixTrace,helix_rot]) helixTrace=1000.0 #scale for ParaView print("Saving data to CSV and VTK formats") #save data to csv format head = 'X[mm],Y[mm],Z[mm]' np.savetxt(controlfilePath+'helix.csv', helixTrace, delimiter=',', header=head) #save data to vtk format tools.createVTKOutput(controlfilePath+'helix.csv', 'trace', 'Gyro_trace') if verbose==True: print("V_perp = {:f} [m/s]".format(vPerp)) print("V_parallel = {:f} [m/s]".format(vParallel)) print("Cyclotron Freq = {:f} [rad/s]".format(self.omegaGyro[0])) print("Cyclotron Freq = {:f} [Hz]".format(self.fGyro[0])) print("Gyro Radius = {:f} [m]".format(self.rGyro[0][0])) print("Number of gyro points = {:f}".format(len(helixTrace))) print("Longitudinal dist between gyro points = {:f} [m]".format(magP/float(Nsteps))) print("Each line segment length ~ {:f} [m]".format(magP)) return def gyroTraceParallel(self, i, mode='MT'): """ parallelized gyro trace. called by multiprocessing.pool.map() i is index of parallel run from multiprocessing, corresponds to a mesh face we are tracing in the ROI writes helical trace to self.helixTrace[i] in 2D matrix format: columns = X,Y,Z rows = steps up helical trace also updates self.lastPhase for use in next iteration step mode options are: -Signed Volume Loop: 'SigVolLoop' -Signed Volume Matrix: 'SigVolMat' -Moller-Trumbore Algorithm: 'MT' """ #vector delP = self.p1[i] - self.p0[i] #magnitude magP = np.sqrt(delP[0]2 + delP[1]2 + delP[2]2) #time it takes to transit line segment delta_t = magP / (self.vParallelMC[self.GYRO_HLXmap][i]) #Number of steps in line segment Tsample = self.TGyro[self.GYRO_HLXmap][i] / self.N_gyroSteps Nsteps = int(delta_t / Tsample) #length (in time) along guiding center t = np.linspace(0,delta_t,Nsteps+1) #guiding center location xGC = np.linspace(self.p0[i,0],self.p1[i,0],Nsteps+1) yGC = np.linspace(self.p0[i,1],self.p1[i,1],Nsteps+1) zGC = np.linspace(self.p0[i,2],self.p1[i,2],Nsteps+1) arrGC = np.vstack([xGC,yGC,zGC]).T # construct orthogonal system for coordinate transformation w = delP if np.all(w==[0,0,1]): u = np.cross(w,[0,1,0]) #prevent failure if bhat = [0,0,1] else: u = np.cross(w,[0,0,1]) #this would fail if bhat = [0,0,1] (rare) v = np.cross(w,u) #normalize u = u / np.sqrt(u.dot(u)) v = v / np.sqrt(v.dot(v)) w = w / np.sqrt(w.dot(w)) xfm = np.vstack([u,v,w]).T #get helix path along (proxy) z axis reference frame rGyro = self.rGyroMC[self.GYRO_HLXmap][i] omega = self.omegaGyro[self.GYRO_HLXmap][i] theta = self.lastPhase[self.GYRO_HLXmap][i] x_helix = rGyronp.cos(omegat + theta) y_helix = self.diamagrGyro*	np.sin(omega*t + theta)	numpy.sin
""" This module contains the BinMapper class. BinMapper is used for mapping a real-valued dataset into integer-valued bins. Bin thresholds are computed with the quantiles so that each bin contains approximately the same number of samples. """ # Author: <NAME> import numpy as np from ...utils import check_random_state, check_array from ...base import BaseEstimator, TransformerMixin from ...utils.validation import check_is_fitted from ._binning import _map_to_bins from .types import X_DTYPE, X_BINNED_DTYPE def _find_binning_thresholds(data, max_bins, subsample, random_state): """Extract feature-wise quantiles from numerical data. Parameters ---------- data : array-like, shape (n_samples, n_features) The data to bin. max_bins : int The maximum number of bins to use. If for a given feature the number of unique values is less than ``max_bins``, then those unique values will be used to compute the bin thresholds, instead of the quantiles. subsample : int or None If ``n_samples > subsample``, then ``sub_samples`` samples will be randomly choosen to compute the quantiles. If ``None``, the whole data is used. random_state: int or numpy.random.RandomState or None Pseudo-random number generator to control the random sub-sampling. See :term:`random_state`. Return ------ binning_thresholds: list of arrays For each feature, stores the increasing numeric values that can be used to separate the bins. Thus ``len(binning_thresholds) == n_features``. """ if not (2 <= max_bins <= 256): raise ValueError('max_bins={} should be no smaller than 2 ' 'and no larger than 256.'.format(max_bins)) rng = check_random_state(random_state) if subsample is not None and data.shape[0] > subsample: subset = rng.choice(	np.arange(data.shape[0])	numpy.arange
import os import tempfile import numpy as np import scipy.ndimage.measurements as meas from functools import reduce import warnings import sys sys.path.append(os.path.abspath(r'../lib')) import NumCppPy as NumCpp # noqa E402 #################################################################################### def factors(n): return set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))) #################################################################################### def test_seed():	np.random.seed(1)	numpy.random.seed
# This module has been generated automatically from space group information # obtained from the Computational Crystallography Toolbox # """ Space groups This module contains a list of all the 230 space groups that can occur in a crystal. The variable space_groups contains a dictionary that maps space group numbers and space group names to the corresponding space group objects. .. moduleauthor:: <NAME> <<EMAIL>> """ #----------------------------------------------------------------------------- # Copyright (C) 2013 The Mosaic Development Team # # Distributed under the terms of the BSD License. The full license is in # the file LICENSE.txt, distributed as part of this software. #----------------------------------------------------------------------------- import numpy as N class SpaceGroup(object): """ Space group All possible space group objects are created in this module. Other modules should access these objects through the dictionary space_groups rather than create their own space group objects. """ def __init__(self, number, symbol, transformations): """ :param number: the number assigned to the space group by international convention :type number: int :param symbol: the Hermann-Mauguin space-group symbol as used in PDB and mmCIF files :type symbol: str :param transformations: a list of space group transformations, each consisting of a tuple of three integer arrays (rot, tn, td), where rot is the rotation matrix and tn/td are the numerator and denominator of the translation vector. The transformations are defined in fractional coordinates. :type transformations: list """ self.number = number self.symbol = symbol self.transformations = transformations self.transposed_rotations = N.array([N.transpose(t[0]) for t in transformations]) self.phase_factors = N.exp(N.array([(-2jN.pit[1])/t[2] for t in transformations])) def __repr__(self): return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol)) def __len__(self): """ :return: the number of space group transformations :rtype: int """ return len(self.transformations) def symmetryEquivalentMillerIndices(self, hkl): """ :param hkl: a set of Miller indices :type hkl: Scientific.N.array_type :return: a tuple (miller_indices, phase_factor) of two arrays of length equal to the number of space group transformations. miller_indices contains the Miller indices of each reflection equivalent by symmetry to the reflection hkl (including hkl itself as the first element). phase_factor contains the phase factors that must be applied to the structure factor of reflection hkl to obtain the structure factor of the symmetry equivalent reflection. :rtype: tuple """ hkls = N.dot(self.transposed_rotations, hkl) p = N.multiply.reduce(self.phase_factors**hkl, -1) return hkls, p space_groups = {} transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(1, 'P 1', transformations) space_groups[1] = sg space_groups['P 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(2, 'P -1', transformations) space_groups[2] = sg space_groups['P -1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(3, 'P 1 2 1', transformations) space_groups[3] = sg space_groups['P 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(4, 'P 1 21 1', transformations) space_groups[4] = sg space_groups['P 1 21 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(5, 'C 1 2 1', transformations) space_groups[5] = sg space_groups['C 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(6, 'P 1 m 1', transformations) space_groups[6] = sg space_groups['P 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(7, 'P 1 c 1', transformations) space_groups[7] = sg space_groups['P 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(8, 'C 1 m 1', transformations) space_groups[8] = sg space_groups['C 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(9, 'C 1 c 1', transformations) space_groups[9] = sg space_groups['C 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(10, 'P 1 2/m 1', transformations) space_groups[10] = sg space_groups['P 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(11, 'P 1 21/m 1', transformations) space_groups[11] = sg space_groups['P 1 21/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(12, 'C 1 2/m 1', transformations) space_groups[12] = sg space_groups['C 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(13, 'P 1 2/c 1', transformations) space_groups[13] = sg space_groups['P 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(14, 'P 1 21/c 1', transformations) space_groups[14] = sg space_groups['P 1 21/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(15, 'C 1 2/c 1', transformations) space_groups[15] = sg space_groups['C 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(16, 'P 2 2 2', transformations) space_groups[16] = sg space_groups['P 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(17, 'P 2 2 21', transformations) space_groups[17] = sg space_groups['P 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(18, 'P 21 21 2', transformations) space_groups[18] = sg space_groups['P 21 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(19, 'P 21 21 21', transformations) space_groups[19] = sg space_groups['P 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(20, 'C 2 2 21', transformations) space_groups[20] = sg space_groups['C 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(21, 'C 2 2 2', transformations) space_groups[21] = sg space_groups['C 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(22, 'F 2 2 2', transformations) space_groups[22] = sg space_groups['F 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(23, 'I 2 2 2', transformations) space_groups[23] = sg space_groups['I 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(24, 'I 21 21 21', transformations) space_groups[24] = sg space_groups['I 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(25, 'P m m 2', transformations) space_groups[25] = sg space_groups['P m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(26, 'P m c 21', transformations) space_groups[26] = sg space_groups['P m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(27, 'P c c 2', transformations) space_groups[27] = sg space_groups['P c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(28, 'P m a 2', transformations) space_groups[28] = sg space_groups['P m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(29, 'P c a 21', transformations) space_groups[29] = sg space_groups['P c a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(30, 'P n c 2', transformations) space_groups[30] = sg space_groups['P n c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(31, 'P m n 21', transformations) space_groups[31] = sg space_groups['P m n 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(32, 'P b a 2', transformations) space_groups[32] = sg space_groups['P b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(33, 'P n a 21', transformations) space_groups[33] = sg space_groups['P n a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(34, 'P n n 2', transformations) space_groups[34] = sg space_groups['P n n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(35, 'C m m 2', transformations) space_groups[35] = sg space_groups['C m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(36, 'C m c 21', transformations) space_groups[36] = sg space_groups['C m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(37, 'C c c 2', transformations) space_groups[37] = sg space_groups['C c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(38, 'A m m 2', transformations) space_groups[38] = sg space_groups['A m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(39, 'A b m 2', transformations) space_groups[39] = sg space_groups['A b m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(40, 'A m a 2', transformations) space_groups[40] = sg space_groups['A m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(41, 'A b a 2', transformations) space_groups[41] = sg space_groups['A b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(42, 'F m m 2', transformations) space_groups[42] = sg space_groups['F m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(43, 'F d d 2', transformations) space_groups[43] = sg space_groups['F d d 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(44, 'I m m 2', transformations) space_groups[44] = sg space_groups['I m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(45, 'I b a 2', transformations) space_groups[45] = sg space_groups['I b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(46, 'I m a 2', transformations) space_groups[46] = sg space_groups['I m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(47, 'P m m m', transformations) space_groups[47] = sg space_groups['P m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(48, 'P n n n :2', transformations) space_groups[48] = sg space_groups['P n n n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(49, 'P c c m', transformations) space_groups[49] = sg space_groups['P c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(50, 'P b a n :2', transformations) space_groups[50] = sg space_groups['P b a n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(51, 'P m m a', transformations) space_groups[51] = sg space_groups['P m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(52, 'P n n a', transformations) space_groups[52] = sg space_groups['P n n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(53, 'P m n a', transformations) space_groups[53] = sg space_groups['P m n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(54, 'P c c a', transformations) space_groups[54] = sg space_groups['P c c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(55, 'P b a m', transformations) space_groups[55] = sg space_groups['P b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(56, 'P c c n', transformations) space_groups[56] = sg space_groups['P c c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(57, 'P b c m', transformations) space_groups[57] = sg space_groups['P b c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(58, 'P n n m', transformations) space_groups[58] = sg space_groups['P n n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(59, 'P m m n :2', transformations) space_groups[59] = sg space_groups['P m m n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(60, 'P b c n', transformations) space_groups[60] = sg space_groups['P b c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(61, 'P b c a', transformations) space_groups[61] = sg space_groups['P b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(62, 'P n m a', transformations) space_groups[62] = sg space_groups['P n m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(63, 'C m c m', transformations) space_groups[63] = sg space_groups['C m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(64, 'C m c a', transformations) space_groups[64] = sg space_groups['C m c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(65, 'C m m m', transformations) space_groups[65] = sg space_groups['C m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(66, 'C c c m', transformations) space_groups[66] = sg space_groups['C c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(67, 'C m m a', transformations) space_groups[67] = sg space_groups['C m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(68, 'C c c a :2', transformations) space_groups[68] = sg space_groups['C c c a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(69, 'F m m m', transformations) space_groups[69] = sg space_groups['F m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(70, 'F d d d :2', transformations) space_groups[70] = sg space_groups['F d d d :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(71, 'I m m m', transformations) space_groups[71] = sg space_groups['I m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(72, 'I b a m', transformations) space_groups[72] = sg space_groups['I b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(73, 'I b c a', transformations) space_groups[73] = sg space_groups['I b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(74, 'I m m a', transformations) space_groups[74] = sg space_groups['I m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(75, 'P 4', transformations) space_groups[75] = sg space_groups['P 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(76, 'P 41', transformations) space_groups[76] = sg space_groups['P 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(77, 'P 42', transformations) space_groups[77] = sg space_groups['P 42'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(78, 'P 43', transformations) space_groups[78] = sg space_groups['P 43'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(79, 'I 4', transformations) space_groups[79] = sg space_groups['I 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(80, 'I 41', transformations) space_groups[80] = sg space_groups['I 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(81, 'P -4', transformations) space_groups[81] = sg space_groups['P -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(82, 'I -4', transformations) space_groups[82] = sg space_groups['I -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(83, 'P 4/m', transformations) space_groups[83] = sg space_groups['P 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(84, 'P 42/m', transformations) space_groups[84] = sg space_groups['P 42/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(85, 'P 4/n :2', transformations) space_groups[85] = sg space_groups['P 4/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(86, 'P 42/n :2', transformations) space_groups[86] = sg space_groups['P 42/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(87, 'I 4/m', transformations) space_groups[87] = sg space_groups['I 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(88, 'I 41/a :2', transformations) space_groups[88] = sg space_groups['I 41/a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(89, 'P 4 2 2', transformations) space_groups[89] = sg space_groups['P 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(90, 'P 4 21 2', transformations) space_groups[90] = sg space_groups['P 4 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(91, 'P 41 2 2', transformations) space_groups[91] = sg space_groups['P 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(92, 'P 41 21 2', transformations) space_groups[92] = sg space_groups['P 41 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(93, 'P 42 2 2', transformations) space_groups[93] = sg space_groups['P 42 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(94, 'P 42 21 2', transformations) space_groups[94] = sg space_groups['P 42 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(95, 'P 43 2 2', transformations) space_groups[95] = sg space_groups['P 43 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(96, 'P 43 21 2', transformations) space_groups[96] = sg space_groups['P 43 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(97, 'I 4 2 2', transformations) space_groups[97] = sg space_groups['I 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(98, 'I 41 2 2', transformations) space_groups[98] = sg space_groups['I 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(99, 'P 4 m m', transformations) space_groups[99] = sg space_groups['P 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(100, 'P 4 b m', transformations) space_groups[100] = sg space_groups['P 4 b m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(101, 'P 42 c m', transformations) space_groups[101] = sg space_groups['P 42 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(102, 'P 42 n m', transformations) space_groups[102] = sg space_groups['P 42 n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(103, 'P 4 c c', transformations) space_groups[103] = sg space_groups['P 4 c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(104, 'P 4 n c', transformations) space_groups[104] = sg space_groups['P 4 n c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(105, 'P 42 m c', transformations) space_groups[105] = sg space_groups['P 42 m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(106, 'P 42 b c', transformations) space_groups[106] = sg space_groups['P 42 b c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(107, 'I 4 m m', transformations) space_groups[107] = sg space_groups['I 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(108, 'I 4 c m', transformations) space_groups[108] = sg space_groups['I 4 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(109, 'I 41 m d', transformations) space_groups[109] = sg space_groups['I 41 m d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(110, 'I 41 c d', transformations) space_groups[110] = sg space_groups['I 41 c d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(111, 'P -4 2 m', transformations) space_groups[111] = sg space_groups['P -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(112, 'P -4 2 c', transformations) space_groups[112] = sg space_groups['P -4 2 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(113, 'P -4 21 m', transformations) space_groups[113] = sg space_groups['P -4 21 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(114, 'P -4 21 c', transformations) space_groups[114] = sg space_groups['P -4 21 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(115, 'P -4 m 2', transformations) space_groups[115] = sg space_groups['P -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(116, 'P -4 c 2', transformations) space_groups[116] = sg space_groups['P -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(117, 'P -4 b 2', transformations) space_groups[117] = sg space_groups['P -4 b 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(118, 'P -4 n 2', transformations) space_groups[118] = sg space_groups['P -4 n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(119, 'I -4 m 2', transformations) space_groups[119] = sg space_groups['I -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(120, 'I -4 c 2', transformations) space_groups[120] = sg space_groups['I -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(121, 'I -4 2 m', transformations) space_groups[121] = sg space_groups['I -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(122, 'I -4 2 d', transformations) space_groups[122] = sg space_groups['I -4 2 d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(123, 'P 4/m m m', transformations) space_groups[123] = sg space_groups['P 4/m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(124, 'P 4/m c c', transformations) space_groups[124] = sg space_groups['P 4/m c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(125, 'P 4/n b m :2', transformations) space_groups[125] = sg space_groups['P 4/n b m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(126, 'P 4/n n c :2', transformations) space_groups[126] = sg space_groups['P 4/n n c :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(127, 'P 4/m b m', transformations) space_groups[127] = sg space_groups['P 4/m b m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(128, 'P 4/m n c', transformations) space_groups[128] = sg space_groups['P 4/m n c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(129, 'P 4/n m m :2', transformations) space_groups[129] = sg space_groups['P 4/n m m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(130, 'P 4/n c c :2', transformations) space_groups[130] = sg space_groups['P 4/n c c :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(131, 'P 42/m m c', transformations) space_groups[131] = sg space_groups['P 42/m m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(132, 'P 42/m c m', transformations) space_groups[132] = sg space_groups['P 42/m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(133, 'P 42/n b c :2', transformations) space_groups[133] = sg space_groups['P 42/n b c :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(134, 'P 42/n n m :2', transformations) space_groups[134] = sg space_groups['P 42/n n m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(135, 'P 42/m b c', transformations) space_groups[135] = sg space_groups['P 42/m b c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(136, 'P 42/m n m', transformations) space_groups[136] = sg space_groups['P 42/m n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(137, 'P 42/n m c :2', transformations) space_groups[137] = sg space_groups['P 42/n m c :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(138, 'P 42/n c m :2', transformations) space_groups[138] = sg space_groups['P 42/n c m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(139, 'I 4/m m m', transformations) space_groups[139] = sg space_groups['I 4/m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(140, 'I 4/m c m', transformations) space_groups[140] = sg space_groups['I 4/m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(141, 'I 41/a m d :2', transformations) space_groups[141] = sg space_groups['I 41/a m d :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(142, 'I 41/a c d :2', transformations) space_groups[142] = sg space_groups['I 41/a c d :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(143, 'P 3', transformations) space_groups[143] = sg space_groups['P 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(144, 'P 31', transformations) space_groups[144] = sg space_groups['P 31'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(145, 'P 32', transformations) space_groups[145] = sg space_groups['P 32'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(146, 'R 3 :H', transformations) space_groups[146] = sg space_groups['R 3 :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(147, 'P -3', transformations) space_groups[147] = sg space_groups['P -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(148, 'R -3 :H', transformations) space_groups[148] = sg space_groups['R -3 :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(149, 'P 3 1 2', transformations) space_groups[149] = sg space_groups['P 3 1 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(150, 'P 3 2 1', transformations) space_groups[150] = sg space_groups['P 3 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(151, 'P 31 1 2', transformations) space_groups[151] = sg space_groups['P 31 1 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(152, 'P 31 2 1', transformations) space_groups[152] = sg space_groups['P 31 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(153, 'P 32 1 2', transformations) space_groups[153] = sg space_groups['P 32 1 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(154, 'P 32 2 1', transformations) space_groups[154] = sg space_groups['P 32 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(155, 'R 3 2 :H', transformations) space_groups[155] = sg space_groups['R 3 2 :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(156, 'P 3 m 1', transformations) space_groups[156] = sg space_groups['P 3 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(157, 'P 3 1 m', transformations) space_groups[157] = sg space_groups['P 3 1 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(158, 'P 3 c 1', transformations) space_groups[158] = sg space_groups['P 3 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(159, 'P 3 1 c', transformations) space_groups[159] = sg space_groups['P 3 1 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(160, 'R 3 m :H', transformations) space_groups[160] = sg space_groups['R 3 m :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(161, 'R 3 c :H', transformations) space_groups[161] = sg space_groups['R 3 c :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(162, 'P -3 1 m', transformations) space_groups[162] = sg space_groups['P -3 1 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(163, 'P -3 1 c', transformations) space_groups[163] = sg space_groups['P -3 1 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(164, 'P -3 m 1', transformations) space_groups[164] = sg space_groups['P -3 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(165, 'P -3 c 1', transformations) space_groups[165] = sg space_groups['P -3 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(166, 'R -3 m :H', transformations) space_groups[166] = sg space_groups['R -3 m :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,-1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,-1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,-1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(167, 'R -3 c :H', transformations) space_groups[167] = sg space_groups['R -3 c :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(168, 'P 6', transformations) space_groups[168] = sg space_groups['P 6'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(169, 'P 61', transformations) space_groups[169] = sg space_groups['P 61'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(170, 'P 65', transformations) space_groups[170] = sg space_groups['P 65'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(171, 'P 62', transformations) space_groups[171] = sg space_groups['P 62'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(172, 'P 64', transformations) space_groups[172] = sg space_groups['P 64'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(173, 'P 63', transformations) space_groups[173] = sg space_groups['P 63'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(174, 'P -6', transformations) space_groups[174] = sg space_groups['P -6'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(175, 'P 6/m', transformations) space_groups[175] = sg space_groups['P 6/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(176, 'P 63/m', transformations) space_groups[176] = sg space_groups['P 63/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(177, 'P 6 2 2', transformations) space_groups[177] = sg space_groups['P 6 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(178, 'P 61 2 2', transformations) space_groups[178] = sg space_groups['P 61 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(179, 'P 65 2 2', transformations) space_groups[179] = sg space_groups['P 65 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(180, 'P 62 2 2', transformations) space_groups[180] = sg space_groups['P 62 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(181, 'P 64 2 2', transformations) space_groups[181] = sg space_groups['P 64 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(182, 'P 63 2 2', transformations) space_groups[182] = sg space_groups['P 63 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(183, 'P 6 m m', transformations) space_groups[183] = sg space_groups['P 6 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(184, 'P 6 c c', transformations) space_groups[184] = sg space_groups['P 6 c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(185, 'P 63 c m', transformations) space_groups[185] = sg space_groups['P 63 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(186, 'P 63 m c', transformations) space_groups[186] = sg space_groups['P 63 m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(187, 'P -6 m 2', transformations) space_groups[187] = sg space_groups['P -6 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(188, 'P -6 c 2', transformations) space_groups[188] = sg space_groups['P -6 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(189, 'P -6 2 m', transformations) space_groups[189] = sg space_groups['P -6 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(190, 'P -6 2 c', transformations) space_groups[190] = sg space_groups['P -6 2 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(191, 'P 6/m m m', transformations) space_groups[191] = sg space_groups['P 6/m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(192, 'P 6/m c c', transformations) space_groups[192] = sg space_groups['P 6/m c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(193, 'P 63/m c m', transformations) space_groups[193] = sg space_groups['P 63/m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(194, 'P 63/m m c', transformations) space_groups[194] = sg space_groups['P 63/m m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(195, 'P 2 3', transformations) space_groups[195] = sg space_groups['P 2 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(196, 'F 2 3', transformations) space_groups[196] = sg space_groups['F 2 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(197, 'I 2 3', transformations) space_groups[197] = sg space_groups['I 2 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(198, 'P 21 3', transformations) space_groups[198] = sg space_groups['P 21 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(199, 'I 21 3', transformations) space_groups[199] = sg space_groups['I 21 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(200, 'P m -3', transformations) space_groups[200] = sg space_groups['P m -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(201, 'P n -3 :2', transformations) space_groups[201] = sg space_groups['P n -3 :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(202, 'F m -3', transformations) space_groups[202] = sg space_groups['F m -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(203, 'F d -3 :2', transformations) space_groups[203] = sg space_groups['F d -3 :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(204, 'I m -3', transformations) space_groups[204] = sg space_groups['I m -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(205, 'P a -3', transformations) space_groups[205] = sg space_groups['P a -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(206, 'I a -3', transformations) space_groups[206] = sg space_groups['I a -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(207, 'P 4 3 2', transformations) space_groups[207] = sg space_groups['P 4 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(208, 'P 42 3 2', transformations) space_groups[208] = sg space_groups['P 42 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(209, 'F 4 3 2', transformations) space_groups[209] = sg space_groups['F 4 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(210, 'F 41 3 2', transformations) space_groups[210] = sg space_groups['F 41 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(211, 'I 4 3 2', transformations) space_groups[211] = sg space_groups['I 4 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(212, 'P 43 3 2', transformations) space_groups[212] = sg space_groups['P 43 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(213, 'P 41 3 2', transformations) space_groups[213] = sg space_groups['P 41 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(214, 'I 41 3 2', transformations) space_groups[214] = sg space_groups['I 41 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(215, 'P -4 3 m', transformations) space_groups[215] = sg space_groups['P -4 3 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(216, 'F -4 3 m', transformations) space_groups[216] = sg space_groups['F -4 3 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(217, 'I -4 3 m', transformations) space_groups[217] = sg space_groups['I -4 3 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(218, 'P -4 3 n', transformations) space_groups[218] = sg space_groups['P -4 3 n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(219, 'F -4 3 c', transformations) space_groups[219] = sg space_groups['F -4 3 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(220, 'I -4 3 d', transformations) space_groups[220] = sg space_groups['I -4 3 d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(221, 'P m -3 m', transformations) space_groups[221] = sg space_groups['P m -3 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(222, 'P n -3 n :2', transformations) space_groups[222] = sg space_groups['P n -3 n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(223, 'P m -3 n', transformations) space_groups[223] = sg space_groups['P m -3 n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(224, 'P n -3 m :2', transformations) space_groups[224] = sg space_groups['P n -3 m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(225, 'F m -3 m', transformations) space_groups[225] = sg space_groups['F m -3 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(226, 'F m -3 c', transformations) space_groups[226] = sg space_groups['F m -3 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(227, 'F d -3 m :2', transformations) space_groups[227] = sg space_groups['F d -3 m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,5,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,5,1]) trans_den =	N.array([4,4,2])	numpy.array
import numpy as np import pytest from plaguepy import bereken def test_perc_overlap(): """Test de functie perc_overlap in bereken.py.""" assert bereken.perc_overlap(0, 0, 1) == 1.0 assert bereken.perc_overlap(0, 1, 1) == 1.0 assert bereken.perc_overlap(1, 0, 1) == pytest.approx(0.3173105) assert bereken.perc_overlap(1, 1, 1) == pytest.approx(0.3173105) with pytest.raises(ValueError): assert bereken.perc_overlap(0, 1, 0) == ValueError assert bereken.perc_overlap(1, 0, 0) == ValueError assert bereken.perc_overlap(0, 0, 0) == ValueError assert bereken.perc_overlap(1, 1, 0) == ValueError def test_grens(): """Test de functie grens in bereken.py.""" assert bereken.grens(0.025, 0, 1) == pytest.approx(-1.95996398) # -2 SD assert bereken.grens(0.16, 0, 1) == pytest.approx(-0.99445788) # -1 SD assert bereken.grens(0.5, 0, 1) == 0.0 # 50% dus nog op gemiddelde assert bereken.grens(0.84, 0, 1) == pytest.approx(0.99445788) # 1 SD assert bereken.grens(0.975, 0, 1) == pytest.approx(1.95996398) # 2 SD with pytest.raises(ValueError): assert bereken.grens(-0.5, 0, 1) == ValueError assert bereken.grens(0, 0, 1) == ValueError assert bereken.grens(1, 0, 1) == ValueError assert bereken.grens(1.5, 0, 1) == ValueError def test_helling(): """Test de functie helling in bereken.py.""" assert bereken.helling(np.array([0, 0]), np.array([1, 0])) == 0.0 assert bereken.helling(np.array([0, 0]), np.array([1, 1])) == 45.0 assert bereken.helling(np.array([0, 0]), np.array([-1, -1])) == 45.0 assert bereken.helling(np.array([0, 0]), np.array([-1, 1])) == -45.0 assert bereken.helling(np.array([0, 0]), np.array([1, -1])) == -45.0 assert bereken.helling(np.array([0, 0]),	np.array([0, 0])	numpy.array
# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 =	np.linspace(maxima_y[-1], minima_y[-1], 101)	numpy.linspace
import os import json import numpy as np import torch from gym import spaces from omegaconf import OmegaConf def available_device() -> torch.device: if torch.cuda.is_available(): return torch.device('cuda') return torch.device('cpu') def format_number(num): return '{:,}'.format(num) def count_parameters(model): return sum(p.numel() for p in model.parameters() if p.requires_grad) def soft_update(target, source, polyak): for target_param, param in zip(target.parameters(), source.parameters()): target_param.data.copy_((1 - polyak) * param.data + polyak * target_param.data) def hard_update(target, source): for target_param, param in zip(target.parameters(), source.parameters()): target_param.data.copy_(param.data) class NumpyArrayEncoder(json.JSONEncoder): def default(self, obj): if isinstance(obj, np.integer): return int(obj) elif isinstance(obj, np.floating): return float(obj) elif isinstance(obj, np.ndarray): return obj.tolist() elif isinstance(obj, object): # NOTE: Ignore classes for now return None else: return super(NumpyArrayEncoder, self).default(obj) def init_storage(cfg): logdir = os.getcwd() model_path = os.path.join(logdir, 'models') if not os.path.exists(model_path): os.mkdir(model_path) video_path = os.path.join(logdir, 'videos') if cfg.log_video and not os.path.exists(video_path): os.mkdir(video_path) with open(os.path.join(logdir, 'omega_config.yaml'), 'w') as file: OmegaConf.save(config=cfg, f=file) return logdir, model_path def is_image_observation(observation_space): if isinstance(observation_space, spaces.Box) and len(observation_space.shape) == 3: # Check the type if observation_space.dtype == np.uint8: return True # Check the value range elif np.any(observation_space.low == 0) or	np.any(observation_space.high == 255)	numpy.any
import numpy as np from joblib import Memory from scipy.optimize import fmin_l_bfgs_b location = './cachedir' memory = Memory(location, verbose=0) def x_to_params(x, p, q, n): A = x[:p * q].reshape(p, q) P = x[p * q: p * q + q * n].reshape(n, q) return A, P def params_to_x(A, P): p, q = A.shape n, _ = P.shape x = np.zeros(p * q + n * q) x[:p * q] = A.ravel() x[p * q: p * q + q * n] = P.ravel() return x def kl(A, B): p, _ = A.shape C = np.dot(A,	np.linalg.inv(B)	numpy.linalg.inv
import numpy from radiomics import base, cMatrices class RadiomicsGLRLM(base.RadiomicsFeaturesBase): r""" A Gray Level Run Length Matrix (GLRLM) quantifies gray level runs, which are defined as the length in number of pixels, of consecutive pixels that have the same gray level value. In a gray level run length matrix :math:`\textbf{P}(i,j\|\theta)`, the :math:`(i,j)^{\text{th}}` element describes the number of runs with gray level :math:`i` and length :math:`j` occur in the image (ROI) along angle :math:`\theta`. As a two dimensional example, consider the following 5x5 image, with 5 discrete gray levels: .. math:: \textbf{I} = \begin{bmatrix} 5 & 2 & 5 & 4 & 4\\ 3 & 3 & 3 & 1 & 3\\ 2 & 1 & 1 & 1 & 3\\ 4 & 2 & 2 & 2 & 3\\ 3 & 5 & 3 & 3 & 2 \end{bmatrix} The GLRLM for :math:`\theta = 0`, where 0 degrees is the horizontal direction, then becomes: .. math:: \textbf{P} = \begin{bmatrix} 1 & 0 & 1 & 0 & 0\\ 3 & 0 & 1 & 0 & 0\\ 4 & 1 & 1 & 0 & 0\\ 1 & 1 & 0 & 0 & 0\\ 3 & 0 & 0 & 0 & 0 \end{bmatrix} Let: - :math:`N_g` be the number of discreet intensity values in the image - :math:`N_r` be the number of discreet run lengths in the image - :math:`N_p` be the number of voxels in the image - :math:`N_r(\theta)` be the number of runs in the image along angle :math:`\theta`, which is equal to :math:`\sum^{N_g}_{i=1}\sum^{N_r}_{j=1}{\textbf{P}(i,j\|\theta)}` and :math:`1 \leq N_r(\theta) \leq N_p` - :math:`\textbf{P}(i,j\|\theta)` be the run length matrix for an arbitrary direction :math:`\theta` - :math:`p(i,j\|\theta)` be the normalized run length matrix, defined as :math:`p(i,j\|\theta) = \frac{\textbf{P}(i,j\|\theta)}{N_r(\theta)}` By default, the value of a feature is calculated on the GLRLM for each angle separately, after which the mean of these values is returned. If distance weighting is enabled, GLRLMs are weighted by the distance between neighbouring voxels and then summed and normalised. Features are then calculated on the resultant matrix. The distance between neighbouring voxels is calculated for each angle using the norm specified in 'weightingNorm'. The following class specific settings are possible: - weightingNorm [None]: string, indicates which norm should be used when applying distance weighting. Enumerated setting, possible values: - 'manhattan': first order norm - 'euclidean': second order norm - 'infinity': infinity norm. - 'no_weighting': GLCMs are weighted by factor 1 and summed - None: Applies no weighting, mean of values calculated on separate matrices is returned. In case of other values, an warning is logged and option 'no_weighting' is used. References - <NAME>. 1975. Texture analysis using gray level run lengths. Computer Graphics and Image Processing, 4(2):172-179. - <NAME>., <NAME>., <NAME>. 1990. Use of gray value distribution of run length for texture analysis. Pattern Recognition Letters, 11(6):415-419 - <NAME>., <NAME>., <NAME>., <NAME>. 2004. Run-Length Encoding For Volumetric Texture. International Conference on Visualization, Imaging and Image Processing (VIIP), p. 452-458 - <NAME>. 1998. Texture information in run-length matrices. IEEE Transactions on Image Processing 7(11):1602-1609. - `<NAME>., <NAME>. Run-Length Matrices For Texture Analysis. Insight Journal 2008 January - June. <http://www.insight-journal.org/browse/publication/231>`_ """ def __init__(self, inputImage, inputMask, kwargs): super(RadiomicsGLRLM, self).__init__(inputImage, inputMask, kwargs) self.weightingNorm = kwargs.get('weightingNorm', None) # manhattan, euclidean, infinity self.P_glrlm = None self.imageArray = self._applyBinning(self.imageArray) def _initCalculation(self, voxelCoordinates=None): self.P_glrlm = self._calculateMatrix(voxelCoordinates) self._calculateCoefficients() self.logger.debug('GLRLM feature class initialized, calculated GLRLM with shape %s', self.P_glrlm.shape) def _calculateMatrix(self, voxelCoordinates=None): self.logger.debug('Calculating GLRLM matrix in C') Ng = self.coefficients['Ng'] Nr = numpy.max(self.imageArray.shape) matrix_args = [ self.imageArray, self.maskArray, Ng, Nr, self.settings.get('force2D', False), self.settings.get('force2Ddimension', 0) ] if self.voxelBased: matrix_args += [self.settings.get('kernelRadius', 1), voxelCoordinates] P_glrlm, angles = cMatrices.calculate_glrlm(matrix_args) # shape (Nvox, Ng, Nr, Na) self.logger.debug('Process calculated matrix') # Delete rows that specify gray levels not present in the ROI NgVector = range(1, Ng + 1) # All possible gray values GrayLevels = self.coefficients['grayLevels'] # Gray values present in ROI emptyGrayLevels = numpy.array(list(set(NgVector) - set(GrayLevels)), dtype=int) # Gray values NOT present in ROI P_glrlm = numpy.delete(P_glrlm, emptyGrayLevels - 1, 1) # Optionally apply a weighting factor if self.weightingNorm is not None: self.logger.debug('Applying weighting (%s)', self.weightingNorm) pixelSpacing = self.inputImage.GetSpacing()[::-1] weights = numpy.empty(len(angles)) for a_idx, a in enumerate(angles): if self.weightingNorm == 'infinity': weights[a_idx] = max(numpy.abs(a) pixelSpacing) elif self.weightingNorm == 'euclidean': weights[a_idx] = numpy.sqrt(numpy.sum((numpy.abs(a) * pixelSpacing) ** 2)) elif self.weightingNorm == 'manhattan': weights[a_idx] = numpy.sum(numpy.abs(a) * pixelSpacing) elif self.weightingNorm == 'no_weighting': weights[a_idx] = 1 else: self.logger.warning('weigthing norm "%s" is unknown, weighting factor is set to 1', self.weightingNorm) weights[a_idx] = 1 P_glrlm = numpy.sum(P_glrlm * weights[None, None, None, :], 3, keepdims=True) Nr = numpy.sum(P_glrlm, (1, 2)) # Delete empty angles if no weighting is applied if P_glrlm.shape[3] > 1: emptyAngles = numpy.where(numpy.sum(Nr, 0) == 0) if len(emptyAngles[0]) > 0: # One or more angles are 'empty' self.logger.debug('Deleting %d empty angles:\n%s', len(emptyAngles[0]), angles[emptyAngles]) P_glrlm = numpy.delete(P_glrlm, emptyAngles, 3) Nr = numpy.delete(Nr, emptyAngles, 1) else: self.logger.debug('No empty angles') Nr[Nr == 0] = numpy.nan # set sum to numpy.spacing(1) if sum is 0? self.coefficients['Nr'] = Nr return P_glrlm def _calculateCoefficients(self): self.logger.debug('Calculating GLRLM coefficients') pr = numpy.sum(self.P_glrlm, 1) # shape (Nvox, Nr, Na) pg = numpy.sum(self.P_glrlm, 2) # shape (Nvox, Ng, Na) ivector = self.coefficients['grayLevels'].astype(float) # shape (Ng,) jvector = numpy.arange(1, self.P_glrlm.shape[2] + 1, dtype=numpy.float64) # shape (Nr,) # Delete columns that run lengths not present in the ROI emptyRunLenghts = numpy.where(numpy.sum(pr, (0, 2)) == 0) self.P_glrlm = numpy.delete(self.P_glrlm, emptyRunLenghts, 2) jvector = numpy.delete(jvector, emptyRunLenghts) pr = numpy.delete(pr, emptyRunLenghts, 1) self.coefficients['pr'] = pr self.coefficients['pg'] = pg self.coefficients['ivector'] = ivector self.coefficients['jvector'] = jvector def getShortRunEmphasisFeatureValue(self): r""" 1. Short Run Emphasis (SRE) .. math:: \textit{SRE} = \frac{\sum^{N_g}_{i=1}\sum^{N_r}_{j=1}{\frac{\textbf{P}(i,j\|\theta)}{j^2}}}{N_r(\theta)} SRE is a measure of the distribution of short run lengths, with a greater value indicative of shorter run lengths and more fine textural textures. """ pr = self.coefficients['pr'] jvector = self.coefficients['jvector'] Nr = self.coefficients['Nr'] sre = numpy.sum((pr / (jvector[None, :, None] 2)), 1) / Nr return numpy.nanmean(sre, 1) def getLongRunEmphasisFeatureValue(self): r""" 2. Long Run Emphasis (LRE)** .. math:: \textit{LRE} = \frac{\sum^{N_g}_{i=1}\sum^{N_r}_{j=1}{\textbf{P}(i,j\|\theta)j^2}}{N_r(\theta)} LRE is a measure of the distribution of long run lengths, with a greater value indicative of longer run lengths and more coarse structural textures. """ pr = self.coefficients['pr'] jvector = self.coefficients['jvector'] Nr = self.coefficients['Nr'] lre = numpy.sum((pr * (jvector[None, :, None] 2)), 1) / Nr return numpy.nanmean(lre, 1) def getGrayLevelNonUniformityFeatureValue(self): r""" 3. Gray Level Non-Uniformity (GLN) .. math:: \textit{GLN} = \frac{\sum^{N_g}_{i=1}\left(\sum^{N_r}_{j=1}{\textbf{P}(i,j\|\theta)}\right)^2}{N_r(\theta)} GLN measures the similarity of gray-level intensity values in the image, where a lower GLN value correlates with a greater similarity in intensity values. """ pg = self.coefficients['pg'] Nr = self.coefficients['Nr'] gln = numpy.sum((pg 2), 1) / Nr return numpy.nanmean(gln, 1) def getGrayLevelNonUniformityNormalizedFeatureValue(self): r""" 4. Gray Level Non-Uniformity Normalized (GLNN) .. math:: \textit{GLNN} = \frac{\sum^{N_g}_{i=1}\left(\sum^{N_r}_{j=1}{\textbf{P}(i,j\|\theta)}\right)^2}{N_r(\theta)^2} GLNN measures the similarity of gray-level intensity values in the image, where a lower GLNN value correlates with a greater similarity in intensity values. This is the normalized version of the GLN formula. """ pg = self.coefficients['pg'] Nr = self.coefficients['Nr'] glnn = numpy.sum(pg 2, 1) / (Nr 2) return numpy.nanmean(glnn, 1) def getRunLengthNonUniformityFeatureValue(self): r""" 5. Run Length Non-Uniformity (RLN) .. math:: \textit{RLN} = \frac{\sum^{N_r}_{j=1}\left(\sum^{N_g}_{i=1}{\textbf{P}(i,j\|\theta)}\right)^2}{N_r(\theta)} RLN measures the similarity of run lengths throughout the image, with a lower value indicating more homogeneity among run lengths in the image. """ pr = self.coefficients['pr'] Nr = self.coefficients['Nr'] rln = numpy.sum((pr 2), 1) / Nr return numpy.nanmean(rln, 1) def getRunLengthNonUniformityNormalizedFeatureValue(self): r""" 6. Run Length Non-Uniformity Normalized (RLNN) .. math:: \textit{RLNN} = \frac{\sum^{N_r}_{j=1}\left(\sum^{N_g}_{i=1}{\textbf{P}(i,j\|\theta)}\right)^2}{N_r(\theta)^2} RLNN measures the similarity of run lengths throughout the image, with a lower value indicating more homogeneity among run lengths in the image. This is the normalized version of the RLN formula. """ pr = self.coefficients['pr'] Nr = self.coefficients['Nr'] rlnn = numpy.sum((pr 2), 1) / Nr 2 return numpy.nanmean(rlnn, 1) def getRunPercentageFeatureValue(self): r""" 7. Run Percentage (RP)** .. math:: \textit{RP} = {\frac{N_r(\theta)}{N_p}} RP measures the coarseness of the texture by taking the ratio of number of runs and number of voxels in the ROI. Values are in range :math:`\frac{1}{N_p} \leq RP \leq 1`, with higher values indicating a larger portion of the ROI consists of short runs (indicates a more fine texture). .. note:: Note that when weighting is applied and matrices are merged before calculation, :math:`N_p` is multiplied by :math:`n` number of matrices merged to ensure correct normalization (as each voxel is considered :math:`n` times) """ pr = self.coefficients['pr'] jvector = self.coefficients['jvector'] Nr = self.coefficients['Nr'] Np = numpy.sum(pr * jvector[None, :, None], 1) # shape (Nvox, Na) rp = Nr / Np return numpy.nanmean(rp, 1) def getGrayLevelVarianceFeatureValue(self): r""" 8. Gray Level Variance (GLV) .. math:: \textit{GLV} = \displaystyle\sum^{N_g}_{i=1}\displaystyle\sum^{N_r}_{j=1}{p(i,j\|\theta)(i - \mu)^2} Here, :math:`\mu = \displaystyle\sum^{N_g}_{i=1}\displaystyle\sum^{N_r}_{j=1}{p(i,j\|\theta)i}` GLV measures the variance in gray level intensity for the runs. """ ivector = self.coefficients['ivector'] Nr = self.coefficients['Nr'] pg = self.coefficients['pg'] / Nr[:, None, :] # divide by Nr to get the normalized matrix u_i = numpy.sum(pg * ivector[None, :, None], 1, keepdims=True) glv = numpy.sum(pg * (ivector[None, :, None] - u_i) 2, 1) return numpy.nanmean(glv, 1) def getRunVarianceFeatureValue(self): r""" 9. Run Variance (RV)** .. math:: \textit{RV} = \displaystyle\sum^{N_g}_{i=1}\displaystyle\sum^{N_r}_{j=1}{p(i,j\|\theta)(j - \mu)^2} Here, :math:`\mu = \displaystyle\sum^{N_g}_{i=1}\displaystyle\sum^{N_r}_{j=1}{p(i,j\|\theta)j}` RV is a measure of the variance in runs for the run lengths. """ jvector = self.coefficients['jvector'] Nr = self.coefficients['Nr'] pr = self.coefficients['pr'] / Nr[:, None, :] # divide by Nr to get the normalized matrix u_j = numpy.sum(pr * jvector[None, :, None], 1, keepdims=True) rv = numpy.sum(pr * (jvector[None, :, None] - u_j) 2, 1) return numpy.nanmean(rv, 1) def getRunEntropyFeatureValue(self): r""" 10. Run Entropy (RE)** .. math:: \textit{RE} = -\displaystyle\sum^{N_g}_{i=1}\displaystyle\sum^{N_r}_{j=1} {p(i,j\|\theta)\log_{2}(p(i,j\|\theta)+\epsilon)} Here, :math:`\epsilon` is an arbitrarily small positive number (:math:`\approx 2.2\times10^{-16}`). RE measures the uncertainty/randomness in the distribution of run lengths and gray levels. A higher value indicates more heterogeneity in the texture patterns. """ eps = numpy.spacing(1) Nr = self.coefficients['Nr'] p_glrlm = self.P_glrlm / Nr[:, None, None, :] # divide by Nr to get the normalized matrix re = -numpy.sum(p_glrlm * numpy.log2(p_glrlm + eps), (1, 2)) return numpy.nanmean(re, 1) def getLowGrayLevelRunEmphasisFeatureValue(self): r""" 11. Low Gray Level Run Emphasis (LGLRE) .. math:: \textit{LGLRE} = \frac{\sum^{N_g}_{i=1}\sum^{N_r}_{j=1}{\frac{\textbf{P}(i,j\|\theta)}{i^2}}}{N_r(\theta)} LGLRE measures the distribution of low gray-level values, with a higher value indicating a greater concentration of low gray-level values in the image. """ pg = self.coefficients['pg'] ivector = self.coefficients['ivector'] Nr = self.coefficients['Nr'] lglre = numpy.sum((pg / (ivector[None, :, None] ** 2)), 1) / Nr return	numpy.nanmean(lglre, 1)	numpy.nanmean
# -- coding: utf-8 -- import unittest import os import numpy as np try: from karta import Point from karta.crs import LonLatWGS84 except ImportError: from narwhal.geo import Point, LonLatWGS84 import narwhal from narwhal import gsw from narwhal.cast import Cast, CTDCast, XBTCast, LADCP from narwhal.cast import CastCollection from narwhal.bathymetry import Bathymetry from narwhal.util import force_monotonic, diff2, uintegrate, diff2_inner from narwhal import util directory = os.path.dirname(__file__) DATADIR = os.path.join(directory, "data") if not os.path.exists(DATADIR): os.mkdir(DATADIR) class CastTests(unittest.TestCase): def setUp(self): p = np.arange(1, 1001, 2) temp = 10. * np.exp(-.008p) - 15. np.exp(-0.005(p+100)) + 2. sal = -14. np.exp(-.01p) + 34. self.p = p self.temp = temp self.sal = sal self.cast = CTDCast(p, sal, temp) return def test_numerical_indexing(self): r = self.cast[40] self.assertTrue(r["pressure"] == 81) self.assertTrue(r["salinity"] == 27.771987072878822) self.assertTrue(r["temperature"] == 1.1627808544797258) r = self.cast[100] self.assertTrue(r["pressure"] == 201) self.assertTrue(r["salinity"] == 32.124158554636729) self.assertTrue(r["temperature"] == 0.67261848597249019) r = self.cast[400] self.assertTrue(r["pressure"] == 801) self.assertTrue(r["salinity"] == 33.995350253934227) self.assertTrue(r["temperature"] == 1.8506793256302907) return def test_kw_indexing(self): self.assertTrue(np.all(self.cast["pressure"] == self.p)) self.assertTrue(np.all(self.cast["salinity"] == self.sal)) self.assertTrue(np.all(self.cast["temperature"] == self.temp)) return def test_kw_property_indexing(self): cast = Cast(pressure=self.p, temp=self.temp, sal=self.sal, name="Cruise station 7") self.assertEqual(cast.p["name"], "Cruise station 7") return def test_concatenation(self): p = np.arange(1, 1001, 2) temp = 12. np.exp(-.007p) - 14. np.exp(-0.005(p+100)) + 1.8 sal = -13. np.exp(-.01p) + 34.5 cast2 = Cast(pres=p, temp=temp, sal=sal) cc = self.cast + cast2 self.assertTrue(isinstance(cc, CastCollection)) self.assertEqual(len(cc), 2) return def test_interpolate(self): self.assertEqual(np.round(self.cast.interpolate("temperature", "pressure", 4.0), 8), 2.76745605) self.assertEqual(np.round(self.cast.interpolate("temperature", "salinity", 33.0), 8), 0.77935861) # temp not monotonic, which screws up the simple interpolation scheme #self.assertEqual(np.round(self.cast.interpolate("pres", "temp", 1.5), 8), # 2.7674560521632685) return def test_add_property_using_alias(self): cast = Cast(pres=self.p, temp=self.temp, sal=self.sal) cast.p["comment"] = "performed bottle cast #23" self.assertEqual(cast.properties["comment"][-2:], "23") return def test_read_property_using_alias(self): cast = Cast(pressure=self.p, temp=self.temp, sal=self.sal, time="late") self.assertEqual(cast.p["time"], "late") return def test_add_density(self): p = np.arange(10) t = 20.0 0.2 * p s = 30.0 * 0.25 * p x = [-20.0 for _ in p] y = [50.0 for _ in p] sa = gsw.sa_from_sp(s, p, x, y) ct = gsw.ct_from_t(sa, t, p) rho = gsw.rho(sa, ct, p) cast = CTDCast(p, s, t, coordinates=(-20, 50)) cast.add_density() self.assertTrue(np.allclose(rho, cast["density"])) return def test_add_buoyancy_freq_squared(self): # This is a fairly lousy test, merely ensuring that an N^2 field was # calculated, and that it's not wildly different than the direct # calculation. p = np.arange(10) t = 20.0 * 0.2 * p s = 30.0 * 0.25 * p x = [-20.0 for _ in p] y = [50.0 for _ in p] sa = gsw.sa_from_sp(s, p, x, y) ct = gsw.ct_from_t(sa, t, p) rho = np.asarray(gsw.rho(sa, ct, p)) cast = CTDCast(p, s, t, coordinates=(-20, 50), density=rho) cast.add_depth() cast.add_Nsquared(depthkey="depth") # Calculate the buoyancy frequency directly z = cast["depth"].values drhodz = -np.r_[rho[1]-rho[0], rho[2:]-rho[:-2], rho[-1]-rho[-2]] / \ np.r_[z[1]-z[0], z[2:]-z[:-2], z[-1]-z[-2]] N2_direct = -9.81 / rho * drhodz self.assertTrue(np.mean(np.abs(cast["N2"][1:] - N2_direct[1:])) < 0.0004) return def test_LADCP_shear(self): z = np.arange(0, 300) u = z1.01 - z v = z1.005 - z u_ans = 1.01 * z*0.01 - 1 v_ans = 1.005 z*0.005 - 1 lad = narwhal.LADCP(z, u, v) lad.add_shear() self.assertTrue(np.max(abs(lad["dudz"][1:-1] - u_ans[1:-1])) < 0.005) self.assertTrue(np.max(abs(lad["dvdz"][1:-1] - v_ans[1:-1])) < 0.005) return #def test_projectother(self): # pass #def test_calculate_sigma(self): # pass #def test_calculate_theta(self): # pass class CastCollectionTests(unittest.TestCase): def setUp(self): p = np.linspace(1, 999, 500) casts = [] for i in range(10): cast = Cast(pres=p, temp=2np.ones_like(p), sal=30np.ones_like(p), station=i, val=abs(i-5), uniq_val=-i2) casts.append(cast) self.cc = CastCollection(casts) return def test_iteration1(self): for cast in self.cc: self.assertTrue(isinstance(cast, Cast)) return def test_iteration2(self): for i, cast in enumerate(self.cc): pass self.assertEqual(i, 9) return def test_len(self): self.assertEqual(len(self.cc), 10) return def test_slicing(self): subcc = self.cc[2:7] self.assertTrue(isinstance(subcc, CastCollection)) return def test_get_properties(self): self.assertEqual(self.cc["station"], [c.properties["station"] for c in self.cc]) return def test_castwhere(self): cc = self.cc self.assertEqual(cc.castwhere("station", 5), cc[5]) return def test_castswhere(self): cc = self.cc self.assertEqual(cc.castswhere("station", (3,5,6,7)), cc[3]+cc[5:8]) return def test_castswhere_onearg(self): cc = self.cc self.assertEqual(cc.castswhere("station", 5), CastCollection(cc[5])) return def test_castswhere_multiple_results(self): cc = self.cc self.assertEqual(cc.castswhere("val", (1, 2)), cc[3:5] + cc[6:8]) return def test_castswhere_function(self): cc = self.cc casts = cc.castswhere("val", lambda x: x <=3) self.assertEqual(casts, cc[2:-1]) return def test_select(self): cc = self.cc casts = cc.select("uniq_val", (-36, -49, -16)) self.assertEqual(casts, cc[6:8] + cc[4]) return def test_nearest_to(self): casts = [] for i in range(10): casts.append(Cast(pressure=[1, 2, 3], temperature=[5, 6, 7], coordinates=(-30.0 + i, 10.0 - 2i))) cc = CastCollection(casts) pt = Point((-26.2, 2.1), crs=LonLatWGS84) nearest, dist = cc.nearest_to_point(pt) self.assertEqual(nearest.coordinates.vertex, (-26.0, 2.0)) self.assertAlmostEqual(dist, 24845.9422, places=4) return def test_defray(self): lengths = np.arange(50, 71) casts = [] for n in lengths: p = np.r_[np.arange(0, 250, 5), np.arange(250, 250 + 5(n-50), 5)] t = np.ones(n) 10.0 s = np.ones(n) * 34.0 cast = Cast(pres=p, temp=t, sal=s) casts.append(cast) defrayed_casts = CastCollection(casts).defray() for cast in defrayed_casts: self.assertEqual(len(cast), 70) return class MiscTests(unittest.TestCase): def test_force_monotonic(self): s = np.array([1, 3, 5, 6, 7, 9, 13, 14, 15]) sm = force_monotonic(s) self.assertTrue(np.all(sm == s)) s = np.array([1, 3, 5, 4, 7, 9, 13, 11, 15]) sm = force_monotonic(s) self.assertTrue(np.all(sm == np.array([1, 3, 5, 5+1e-16, 7, 9, 13, 13+1e-16, 15]))) return def test_diff2(self): x = np.atleast_2d(np.linspace(-1, 1, 100)) A = x2 - (x + x.T)3 ans = 2x - 3(x + x.T)2 # true answer # add holes A[30:40,1] = np.nan A[15,35] = np.nan A[30:50,50:55] = np.nan A[60:65,60] = np.nan A[60:70,-2] = np.nan D = diff2(A, x.ravel()) self.assertTrue(np.max(abs(ans[~np.isnan(D)] - D[~np.isnan(D)])) < 0.15) return def test_diff2_inner(self): x = np.atleast_2d(np.linspace(-1, 1, 100)) A = x2 - (x + x.T)*3 xinner = np.atleast_2d(0.5 (x[0,1:] + x[0,:-1])) ans = 2xinner - 3(xinner + x.T)**2 # true answer # add holes A[30:40,1] = np.nan A[15,35] = np.nan A[30:50,50:55] = np.nan A[60:65,60] = np.nan A[60:70,-2] = np.nan D = diff2_inner(A, x.ravel()) self.assertTrue(np.max(abs(ans[~np.isnan(D)] - D[~np.isnan(D)])) < 0.0002) return def test_diff2_dinterp(self): x = np.atleast_2d(	np.linspace(-1, 1, 100)	numpy.linspace
# -- coding: utf-8 -- """ Created on Fri Oct 5 10:40:35 2018 @author: hamed """ try: import torch from torch.utils import data except: pass import numpy as np from sklearn import datasets #%% class kk_mimic_dataset(data.Dataset): def __init__(self, phase="train", seq_len=10, data_norm=True, test=False): percent = 20 n_valid = percent/20 * 328 ind_valid = np.ones(n_valid) ind_valid = np.concatenate((ind_valid, np.zeros(6564-n_valid))) ind_valid = np.random.permutation(ind_valid) ind_test = 1 - ind_valid self.ind_valid = np.greater(ind_valid, 0) self.ind_test = np.greater(ind_test, 0) super(kk_mimic_dataset, self).__init__() if phase == "train": if test: data_path = "../../mimic-libsvm/" + "PATIENTS_SPLIT_XGB_TRAIN" else: data_path = "../mimic-libsvm/" + "PATIENTS_SPLIT_XGB_TRAIN" data = datasets.load_svmlight_file(data_path) else: if test: data_path = "../../mimic-libsvm/" + "PATIENTS_SPLIT_XGB_VALID" else: data_path = "../mimic-libsvm/" + "PATIENTS_SPLIT_XGB_VALID" data = np.array(datasets.load_svmlight_file(data_path)) if phase == "valid":# # data = [ data[0][:data[1].shape[0]//percent], data[1][:data[1].shape[0]//percent] ] data = [ data[0][self.ind_valid], data[1][self.ind_valid] ] else: # data = [ data[0][data[1].shape[0]//percent:], data[1][data[1].shape[0]//percent:] ] data = [ data[0][self.ind_test], data[1][self.ind_test] ] # # TODO: ONLY for fast debugging ## factor = 10 # data = [ data[0][:data[1].shape[0]//factor], data[1][:data[1].shape[0]//factor] ] #Random selection factor = 20 n_data = data[1].shape[0] ind_ =	np.ones(n_data//factor)	numpy.ones
import isopy import numpy as np import pytest # calculate_mass_fractionation_factor, remove_mass_fractionation, add_mass_fractionation def test_mass_fractionation1(): # Testing with input as isotope array # Using default reference values mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 unfractionated = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed = 46) unfractionated = unfractionated * fraction_ref unfractionated['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated['105pd'] mf_factor = isopy.random(100, (0, 2), seed=47) c_fractionated1 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor, '105pd') c_fractionated2 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor) assert c_fractionated1.keys == unfractionated.keys assert c_fractionated1.size == unfractionated.size assert c_fractionated2.keys == unfractionated.keys assert c_fractionated2.size == unfractionated.size c_unfractionated1 = isopy.tb.remove_mass_fractionation(c_fractionated1, mf_factor, '105pd') c_unfractionated2 = isopy.tb.remove_mass_fractionation(c_fractionated2, mf_factor) assert c_unfractionated1.keys == unfractionated.keys assert c_unfractionated1.size == unfractionated.size assert c_unfractionated2.keys == unfractionated.keys assert c_unfractionated2.size == unfractionated.size c_mf_factor2 = isopy.tb.calculate_mass_fractionation_factor(c_fractionated1, '108pd/105pd') np.testing.assert_allclose(c_mf_factor2, mf_factor) for key in unfractionated.keys: mass_diff = mass_ref.get(key/'105pd') fractionated = unfractionated[key] * (mass_diff ** mf_factor) np.testing.assert_allclose(c_fractionated1[key], fractionated) np.testing.assert_allclose(c_unfractionated1[key], unfractionated[key]) np.testing.assert_allclose(c_unfractionated2[key], unfractionated[key]) #Changing reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 unfractionated = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed=46) unfractionated = unfractionated * fraction_ref unfractionated['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated['105pd'] unfractionated2 = unfractionated.ratio('105pd') mf_factor = isopy.random(100, (0, 2), seed=47) c_fractionated1 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor, '105pd', isotope_masses=mass_ref) c_fractionated2 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor, isotope_masses=mass_ref) assert c_fractionated1.keys == unfractionated.keys assert c_fractionated1.size == unfractionated.size assert c_fractionated2.keys == unfractionated.keys assert c_fractionated2.size == unfractionated.size c_unfractionated1 = isopy.tb.remove_mass_fractionation(c_fractionated1, mf_factor, '105pd', isotope_masses=mass_ref) c_unfractionated2 = isopy.tb.remove_mass_fractionation(c_fractionated2, mf_factor, isotope_masses=mass_ref) assert c_unfractionated1.keys == unfractionated.keys assert c_unfractionated1.size == unfractionated.size assert c_unfractionated2.keys == unfractionated.keys assert c_unfractionated2.size == unfractionated.size c_mf_factor2 = isopy.tb.calculate_mass_fractionation_factor(c_fractionated1, '108pd/105pd', isotope_masses=mass_ref, isotope_fractions=fraction_ref) np.testing.assert_allclose(c_mf_factor2, mf_factor) for key in unfractionated.keys: mass_diff = mass_ref.get(key / '105pd') fractionated = unfractionated[key] * (mass_diff ** mf_factor) np.testing.assert_allclose(c_fractionated1[key], fractionated) np.testing.assert_allclose(c_unfractionated1[key], unfractionated[key]) np.testing.assert_allclose(c_unfractionated2[key], unfractionated[key]) # calculate_mass_fractionation_factor, remove_mass_fractionation, add_mass_fractionation def test_mass_fractionation2(): # Testing with input as ratio array # Using default reference values mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 unfractionated = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed=46) unfractionated = unfractionated * fraction_ref unfractionated['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated['105pd'] unfractionated = unfractionated.ratio('105pd') mf_factor = isopy.random(100, (0, 2), seed=47) c_fractionated2 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor) assert c_fractionated2.keys == unfractionated.keys assert c_fractionated2.size == unfractionated.size c_unfractionated2 = isopy.tb.remove_mass_fractionation(c_fractionated2, mf_factor) assert c_unfractionated2.keys == unfractionated.keys assert c_unfractionated2.size == unfractionated.size c_mf_factor2 = isopy.tb.calculate_mass_fractionation_factor(c_fractionated2, '108pd/105pd') np.testing.assert_allclose(c_mf_factor2, mf_factor) for key in unfractionated.keys: mass_diff = mass_ref.get(key) fractionated = unfractionated[key] * (mass_diff ** mf_factor) np.testing.assert_allclose(c_fractionated2[key], fractionated) np.testing.assert_allclose(c_unfractionated2[key], unfractionated[key]) # Changing reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 unfractionated = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed=46) unfractionated = unfractionated * fraction_ref unfractionated['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated['105pd'] unfractionated = unfractionated.ratio('105pd') mf_factor = isopy.random(100, (0, 2), seed=47) c_fractionated2 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor, isotope_masses=mass_ref) assert c_fractionated2.keys == unfractionated.keys assert c_fractionated2.size == unfractionated.size c_unfractionated2 = isopy.tb.remove_mass_fractionation(c_fractionated2, mf_factor, isotope_masses=mass_ref) assert c_unfractionated2.keys == unfractionated.keys assert c_unfractionated2.size == unfractionated.size c_mf_factor2 = isopy.tb.calculate_mass_fractionation_factor(c_fractionated2, '108pd/105pd', isotope_masses=mass_ref, isotope_fractions=fraction_ref) np.testing.assert_allclose(c_mf_factor2, mf_factor) for key in unfractionated.keys: mass_diff = mass_ref.get(key) fractionated = unfractionated[key] * (mass_diff ** mf_factor) np.testing.assert_allclose(c_fractionated2[key], fractionated) np.testing.assert_allclose(c_unfractionated2[key], unfractionated[key]) class Test_MassIndependentCorrection: def test_one(self): # Default reference values mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 unfractionated1 = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed=46) unfractionated1 = unfractionated1 * fraction_ref unfractionated1['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated1['105pd'] unfractionated2 = unfractionated1.ratio('105pd') n_unfractionated2 = (unfractionated2 / fraction_ref - 1) * 10000 mf_factor = isopy.random(100, (0, 2), seed=47) fractionated1 = isopy.tb.add_mass_fractionation(unfractionated2, mf_factor) fractionated2 = fractionated1.deratio(unfractionated1['105pd']) self.run(fractionated1, unfractionated2, '108pd/105pd') self.run(fractionated2, unfractionated2, '108pd/105pd') self.run(fractionated1, n_unfractionated2, '108pd/105pd', factor=10_000) self.run(fractionated2, n_unfractionated2, '108pd/105pd', factor=10_000) self.run(fractionated1, n_unfractionated2, '108pd/105pd', factor='epsilon') self.run(fractionated2, n_unfractionated2, '108pd/105pd', factor='epsilon') # Different reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 unfractionated1 = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed=46) unfractionated1 = unfractionated1 * fraction_ref unfractionated1['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated1['105pd'] unfractionated2 = unfractionated1.ratio('105pd') n_unfractionated2 = (unfractionated2 / fraction_ref - 1) * 10000 mf_factor = isopy.random(100, (0, 2), seed=47) fractionated1 = isopy.tb.add_mass_fractionation(unfractionated2, mf_factor, isotope_masses=mass_ref) fractionated2 = fractionated1.deratio(unfractionated1['105pd']) self.run(fractionated1, unfractionated2, '108pd/105pd', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated2, unfractionated2, '108pd/105pd', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated1, n_unfractionated2, '108pd/105pd', factor=10_000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated2, n_unfractionated2, '108pd/105pd', factor=10_000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated1, n_unfractionated2, '108pd/105pd', factor='epsilon', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated2, n_unfractionated2, '108pd/105pd', factor='epsilon', mass_ref=mass_ref, fraction_ref=fraction_ref) def test_two(self): # With interference correctionn # We wont get an exact match here so we have to lower the tolerance. # Default reference values mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 mf_factor = isopy.random(100, (0, 2), seed=47) data = isopy.random(100, (1, 0.1), keys='101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd'.split(), seed=46) data = data * fraction_ref data['108pd'] = fraction_ref.get('108pd/105pd') * data['105pd'] fractionated = data.copy() fractionated = isopy.tb.add_mass_fractionation(fractionated, mf_factor) for key in fractionated.keys.filter(element_symbol='pd'): if (ru:=fraction_ref.get(f'ru{key.mass_number}/ru101', 0)) > 0: ru = fractionated['101ru'] (mass_ref.get(f'ru{key.mass_number}/ru101', 0) ** mf_factor) fractionated[key] += ru if (cd:=fraction_ref.get(f'cd{key.mass_number}/cd111', 0)) > 0: cd = fractionated['111cd'] (mass_ref.get(f'cd{key.mass_number}/cd111', 0) ** mf_factor) fractionated[key] += cd correct1 = data.copy(element_symbol = 'pd').ratio('105pd') correct2 = (correct1 / fraction_ref - 1) correct3 = (correct1 / fraction_ref - 1) * 10_000 self.run(fractionated, correct1, '108pd/105pd') self.run(fractionated, correct2, '108pd/105pd', factor=1) self.run(fractionated, correct3, '108pd/105pd', factor=10_000) self.run(fractionated, correct3, '108pd/105pd', factor='epsilon') # Different reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 mf_factor = isopy.random(100, (0, 2), seed=47) data = isopy.random(100, (1, 0.1), keys='101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd'.split(), seed=46) data = data * fraction_ref data['108pd'] = fraction_ref.get('108pd/105pd') * data['105pd'] fractionated = data.copy() fractionated = isopy.tb.add_mass_fractionation(fractionated, mf_factor, isotope_masses=mass_ref) for key in fractionated.keys.filter(element_symbol='pd'): if (ru := fraction_ref.get(f'ru{key.mass_number}/ru101', 0)) > 0: ru = fractionated['101ru'] ( mass_ref.get(f'ru{key.mass_number}/ru101', 0) ** mf_factor) fractionated[key] += ru if (cd := fraction_ref.get(f'cd{key.mass_number}/cd111', 0)) > 0: cd = fractionated['111cd'] ( mass_ref.get(f'cd{key.mass_number}/cd111', 0) ** mf_factor) fractionated[key] += cd correct1 = data.copy(element_symbol='pd').ratio('105pd') correct2 = (correct1 / fraction_ref - 1) correct3 = (correct1 / fraction_ref - 1) * 10_000 self.run(fractionated, correct1, '108pd/105pd', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct2, '108pd/105pd', factor=1, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct3, '108pd/105pd', factor=10_000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct3, '108pd/105pd', factor='epsilon', mass_ref=mass_ref, fraction_ref=fraction_ref) def test_three(self): # Normalisations # Default reference values mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 mf_factor = isopy.random(100, (0, 2), seed=47) data = isopy.random(100, (1, 0.1), keys='102pd 104pd 105pd 106pd 108pd 110pd'.split(), seed=46) data = data * fraction_ref data['108pd'] = fraction_ref.get('108pd/105pd') * data['105pd'] fractionated = data.copy() fractionated = isopy.tb.add_mass_fractionation(fractionated, mf_factor) correct1 = data.copy(element_symbol='pd').ratio('105pd') correct2 = (correct1 / fraction_ref - 1) correct3 = correct2 * 1000 correct4 = correct2 * 10_000 correct5 = correct2 * 1_000_000 self.run(fractionated, correct1, '108pd/105pd') self.run(fractionated, correct2, '108pd/105pd', factor=1) self.run(fractionated, correct3, '108pd/105pd', factor=1000) self.run(fractionated, correct3, '108pd/105pd', factor='ppt') self.run(fractionated, correct3, '108pd/105pd', factor='permil') self.run(fractionated, correct4, '108pd/105pd', factor=10_000) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon') self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000) self.run(fractionated, correct5, '108pd/105pd', factor='mu') self.run(fractionated, correct5, '108pd/105pd', factor='ppm') # Single value std1 = isopy.random(100, (1, 0.1), keys='102pd 104pd 105pd 106pd 108pd 110pd'.split(), seed=48) std1 = std1 * fraction_ref rstd1 = std1.ratio('pd105') correct1 = data.copy(element_symbol='pd').ratio('105pd') correct2 = (correct1 / np.mean(rstd1) - 1) correct3 = correct2 * 1000 correct4 = correct2 * 10_000 correct5 = correct2 * 1_000_000 self.run(fractionated, correct2, '108pd/105pd', norm_val=rstd1) self.run(fractionated, correct2, '108pd/105pd', factor=1, norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor=1000, norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor='permil', norm_val=rstd1) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, norm_val=rstd1) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor='mu', norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', norm_val=rstd1) std1 = np.mean(std1) rstd1 = np.mean(rstd1) self.run(fractionated, correct2, '108pd/105pd', norm_val=rstd1) self.run(fractionated, correct2, '108pd/105pd', factor=1, norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor=1000, norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor='permil', norm_val=rstd1) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, norm_val=rstd1) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor='mu', norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', norm_val=rstd1) # Multiple std1 = isopy.random(100, (1, 0.1), keys='102pd 104pd 105pd 106pd 108pd 110pd'.split(), seed=48) std1 = std1 * fraction_ref rstd1 = std1.ratio('pd105') std2 = isopy.random(50, (1, 0.1), keys='102pd 104pd 105pd 106pd 108pd 110pd'.split(), seed=49) std2 = std2 * fraction_ref rstd2 = std2.ratio('pd105') correct1 = data.copy(element_symbol='pd').ratio('105pd') correct2 = (correct1 / (np.mean(rstd1)/2 + np.mean(rstd2)/2) - 1) correct3 = correct2 * 1000 correct4 = correct2 * 10_000 correct5 = correct2 * 1_000_000 self.run(fractionated, correct2, '108pd/105pd', norm_val=(rstd1, rstd2)) self.run(fractionated, correct2, '108pd/105pd', factor=1, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor=1000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='permil', norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='mu', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', norm_val=(rstd1, rstd2)) std1 = np.mean(std1) rstd1 = np.mean(rstd1) self.run(fractionated, correct2, '108pd/105pd', norm_val=(rstd1, rstd2)) self.run(fractionated, correct2, '108pd/105pd', factor=1, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor=1000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='permil', norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='mu', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', norm_val=(rstd1, rstd2)) std2 = np.mean(std2) rstd2 = np.mean(rstd2) self.run(fractionated, correct2, '108pd/105pd', norm_val=(rstd1, rstd2)) self.run(fractionated, correct2, '108pd/105pd', factor=1, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor=1000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='permil', norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='mu', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', norm_val=(rstd1, rstd2)) # Different reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 mf_factor = isopy.random(100, (0, 2), seed=47) data = isopy.random(100, (1, 0.1), keys='102pd 104pd 105pd 106pd 108pd 110pd'.split(), seed=46) data = data * fraction_ref data['108pd'] = fraction_ref.get('108pd/105pd') * data['105pd'] fractionated = data.copy() fractionated = isopy.tb.add_mass_fractionation(fractionated, mf_factor, isotope_masses=mass_ref) correct1 = data.copy(element_symbol='pd').ratio('105pd') correct2 = (correct1 / fraction_ref - 1) correct3 = correct2 * 1000 correct4 = correct2 * 10_000 correct5 = correct2 * 1_000_000 self.run(fractionated, correct1, '108pd/105pd', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct2, '108pd/105pd', factor=1, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct3, '108pd/105pd', factor=1000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct3, '108pd/105pd', factor='permil', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct5, '108pd/105pd', factor='mu', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', mass_ref=mass_ref, fraction_ref=fraction_ref) def run(self, data, correct, mb_ratio, factor = None, mass_ref = None, fraction_ref=None, norm_val = None): if type(factor) is str: func = getattr(isopy.tb.internal_normalisation, factor) factor2 = None else: factor2 = factor func = isopy.tb.internal_normalisation kwargs = {} if factor2 is not None: kwargs['extnorm_factor'] = factor2 if mass_ref is not None: kwargs['isotope_masses'] = mass_ref if fraction_ref is not None: kwargs['isotope_fractions'] = fraction_ref if norm_val is not None: kwargs['extnorm_value'] = norm_val corrected = func(data, mb_ratio, kwargs) assert corrected.keys == correct.keys - mb_ratio assert corrected.size == correct.size assert corrected.ndim == correct.ndim for key in corrected.keys: np.testing.assert_allclose(corrected[key], correct[key]) # mass independent correction if type(factor) is str: func = getattr(isopy.tb.mass_independent_correction, factor) factor2 = None else: factor2 = factor func = isopy.tb.mass_independent_correction kwargs = {} if factor2 is not None: kwargs['normalisation_factor'] = factor2 if mass_ref is not None: kwargs['isotope_masses'] = mass_ref if fraction_ref is not None: kwargs['isotope_fractions'] = fraction_ref if norm_val is not None: kwargs['normalisation_value'] = norm_val corrected = func(data, mb_ratio, kwargs) assert corrected.keys == correct.keys - mb_ratio assert corrected.size == correct.size assert corrected.ndim == correct.ndim for key in corrected.keys: np.testing.assert_allclose(corrected[key], correct[key]) class Test_IsobaricInterferences: def test_one(self): # No mass fractionation factor # Single interference isotope # Default reference values fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 base_data = isopy.random(100, (1, 0.01), keys='101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd'.split()) base_data = base_data * fraction_ref data = base_data.copy() for key in data.keys.filter(element_symbol='pd'): data[key] += fraction_ref.get(f'ru{key.mass_number}/ru101', 0) * data['101ru'] data[key] += fraction_ref.get(f'cd{key.mass_number}/cd111', 0) * data['111cd'] interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '111cd'] = 0 interferences2 = {'ru': ('104pd',), 'cd': ('106pd', '108pd')} correct2 = base_data.copy() correct2['101ru', '111cd'] = 0 correct2['102pd'] = data['102pd'] correct2['110pd'] = data['110pd'] self.run(data, data, correct1, correct2, interferences1, interferences2, '105pd') # Different reference values fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 base_data = isopy.random(100, (1, 0.01), keys='101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd'.split()) base_data = base_data * fraction_ref data = base_data.copy() for key in data.keys.filter(element_symbol='pd'): data[key] += fraction_ref.get(f'ru{key.mass_number}/ru101', 0) * data['101ru'] data[key] += fraction_ref.get(f'cd{key.mass_number}/cd111', 0) * data['111cd'] interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '111cd'] = 0 interferences2 = {'ru': ('104pd',), 'cd': ('106pd', '108pd')} correct2 = base_data.copy() correct2['101ru', '111cd'] = 0 correct2['102pd'] = data['102pd'] correct2['110pd'] = data['110pd'] self.run(data, data, correct1, correct2, interferences1, interferences2, '105pd', fraction_ref=fraction_ref) def test_two(self): # No mass fractionation factor # Multiple interference isotopes # Default reference values fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 base_data = isopy.random(100, (1, 0.01), keys='99ru 101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd 112cd'.split()) # 112cd > 111cd, 101ru > 99ru base_data = base_data * fraction_ref data1 = base_data.copy() data1['99ru', '111cd'] = -1 # so that we dont accidentally make this the largest isotope for key in data1.keys.filter(key_neq = '<KEY>'.split()): data1[key] += fraction_ref.get(f'ru{key.mass_number}/ru101', 0) * data1['101ru'] data1[key] += fraction_ref.get(f'cd{key.mass_number}/cd112', 0) * data1['112cd'] interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '112cd'] = 0 correct1['99ru', '111cd'] = -1 interferences2 = {'ru99': ('104pd',), 'cd111': ('106pd', '108pd')} data2 = base_data.copy() data2['ru101', 'cd112'] = -1 # so that we dont accidentally make this the largest isotope for key in data2.keys.filter(key_neq='ru99 cd111 102pd 110pd'.split()): data2[key] += fraction_ref.get(f'ru{key.mass_number}/ru99', 0) * data2['99ru'] data2[key] += fraction_ref.get(f'cd{key.mass_number}/cd111', 0) * data2['111cd'] correct2 = base_data.copy() correct2['99ru', '111cd'] = 0 correct2['101ru', '112cd'] = -1 self.run(data1, data2, correct1, correct2, interferences1, interferences2, '105pd') # Different reference values fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 base_data = isopy.random(100, (1, 0.01), keys='99ru 101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd 112cd'.split()) # 112cd > 111cd, 101ru > 99ru base_data = base_data * fraction_ref data1 = base_data.copy() data1['99ru', '111cd'] = -1 # so that we dont accidentally make this the largest isotope for key in data1.keys.filter(key_neq='<KEY>'.split()): data1[key] += fraction_ref.get(f'ru{key.mass_number}/ru101', 0) * data1['101ru'] data1[key] += fraction_ref.get(f'cd{key.mass_number}/cd112', 0) * data1['112cd'] interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '112cd'] = 0 correct1['99ru', '111cd'] = -1 interferences2 = {'ru99': ('104pd',), 'cd111': ('106pd', '108pd')} data2 = base_data.copy() data2['ru101', 'cd112'] = -1 # so that we dont accidentally make this the largest isotope for key in data2.keys.filter(key_neq='<KEY>'.split()): data2[key] += fraction_ref.get(f'ru{key.mass_number}/ru99', 0) * data2['99ru'] data2[key] += fraction_ref.get(f'cd{key.mass_number}/cd111', 0) * data2['111cd'] correct2 = base_data.copy() correct2['99ru', '111cd'] = 0 correct2['101ru', '112cd'] = -1 self.run(data1, data2, correct1, correct2, interferences1, interferences2, '105pd', fraction_ref=fraction_ref) def test_three(self): #Mass fractionation #Single interference isotope mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 base_data = isopy.random(100, (1, 0.01), keys='<KEY>'.split()) mf_factor = isopy.random(100, (0,2)) base_data = base_data * fraction_ref data = base_data.copy() for key in data.keys.filter(element_symbol='pd'): if (ru:=fraction_ref.get(f'ru{key.mass_number}/ru101', 0)) > 0: ru = data['101ru'] (mass_ref.get(f'ru{key.mass_number}/ru101', 0) ** mf_factor) data[key] += ru if (cd:=fraction_ref.get(f'cd{key.mass_number}/cd111', 0)) > 0: cd = data['111cd'] (mass_ref.get(f'cd{key.mass_number}/cd111', 0) ** mf_factor) data[key] += cd interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '111cd'] = 0 interferences2 = {'ru': ('104pd',), 'cd': ('106pd', '108pd')} correct2 = base_data.copy() correct2['101ru', '111cd'] = 0 correct2['102pd'] = data['102pd'] correct2['110pd'] = data['110pd'] self.run(data, data, correct1, correct2, interferences1, interferences2, '105pd', mf_factor=mf_factor) #M Multiple interference isotopes # Different reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 base_data = isopy.random(100, (1, 0.01), keys='99ru 101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd 112cd'.split()) # 112cd > 111cd, 101ru > 99ru base_data = base_data * fraction_ref data1 = base_data.copy() data1['99ru', '111cd'] = -1 # so that we dont accidentally make this the largest isotope for key in data1.keys.filter(key_neq='<KEY>'.split()): if (ru:=fraction_ref.get(f'ru{key.mass_number}/ru101', 0)) > 0: ru = data1['101ru'] (mass_ref.get(f'ru{key.mass_number}/ru101', 0) ** mf_factor) data1[key] += ru if (cd:=fraction_ref.get(f'cd{key.mass_number}/cd112', 0)) > 0: cd = data1['cd112'] (mass_ref.get(f'cd{key.mass_number}/cd112', 0) ** mf_factor) data1[key] += cd interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '112cd'] = 0 correct1['99ru', '111cd'] = -1 interferences2 = {'ru99': ('104pd',), 'cd111': ('106pd', '108pd')} data2 = base_data.copy() data2['ru101', 'cd112'] = -1 # so that we dont accidentally make this the largest isotope for key in data2.keys.filter(key_neq='ru99 cd111 102pd 110pd'.split()): if (ru:=fraction_ref.get(f'ru{key.mass_number}/ru99', 0)) > 0: ru = data2['ru99'] (mass_ref.get(f'ru{key.mass_number}/ru99', 0) ** mf_factor) data2[key] += ru if (cd:=fraction_ref.get(f'cd{key.mass_number}/cd111', 0)) > 0: cd = data2['111cd'] (mass_ref.get(f'cd{key.mass_number}/cd111', 0) ** mf_factor) data2[key] += cd correct2 = base_data.copy() correct2['99ru', '111cd'] = 0 correct2['101ru', '112cd'] = -1 self.run(data1, data2, correct1, correct2, interferences1, interferences2, '105pd', fraction_ref=fraction_ref, mass_ref=mass_ref, mf_factor=mf_factor) def run(self, data1, data2, correct1, correct2, interferences1, interferences2, denom=None, mf_factor=None, fraction_ref=None, mass_ref=None): interferences = isopy.tb.find_isobaric_interferences('pd', data1) assert len(interferences) == len(interferences) for key in interferences1: assert key in interferences assert interferences[key] == interferences1[key] corrected1 = isopy.tb.remove_isobaric_interferences(data1, interferences, mf_factor=mf_factor, isotope_fractions=fraction_ref, isotope_masses=mass_ref) assert corrected1.keys == correct1.keys assert corrected1.size == correct1.size for key in corrected1.keys: np.testing.assert_allclose(corrected1[key], correct1[key]) corrected2 = isopy.tb.remove_isobaric_interferences(data2, interferences2, mf_factor=mf_factor, isotope_fractions=fraction_ref, isotope_masses=mass_ref) assert corrected2.keys == correct2.keys assert corrected2.size == correct2.size for key in corrected2.keys: np.testing.assert_allclose(corrected2[key], correct2[key]) #Ratio test data if denom is not None: data1 = data1.ratio(denom) data2 = data2.ratio(denom) correct1 = correct1.ratio(denom) correct2 = correct2.ratio(denom) interferences = isopy.tb.find_isobaric_interferences('pd', data1) assert len(interferences) == len(interferences) for key in interferences1: assert key in interferences assert interferences[key] == interferences1[key] corrected1 = isopy.tb.remove_isobaric_interferences(data1, interferences, mf_factor=mf_factor, isotope_fractions=fraction_ref, isotope_masses=mass_ref) assert corrected1.keys == correct1.keys assert corrected1.size == correct1.size for key in corrected1.keys: np.testing.assert_allclose(corrected1[key], correct1[key]) corrected2 = isopy.tb.remove_isobaric_interferences(data2, interferences2, mf_factor=mf_factor, isotope_fractions=fraction_ref, isotope_masses=mass_ref) assert corrected2.keys == correct2.keys assert corrected2.size == correct2.size for key in corrected2.keys: np.testing.assert_allclose(corrected2[key], correct2[key]) def test_find(self): interferences = isopy.tb.find_isobaric_interferences('pd', ('ru', 'cd')) assert len(interferences) == 2 assert 'ru' in interferences assert interferences['ru'] == ('102Pd', '104Pd') assert 'cd' in interferences assert interferences['cd'] == ('106Pd', '108Pd', '110Pd') interferences = isopy.tb.find_isobaric_interferences('pd', ('ru', 'rh', 'ag', 'cd')) assert len(interferences) == 2 assert 'ru' in interferences assert interferences['ru'] == ('102Pd', '104Pd') assert 'cd' in interferences assert interferences['cd'] == ('106Pd', '108Pd', '110Pd') interferences = isopy.tb.find_isobaric_interferences('ce') assert len(interferences) == 4 assert 'xe' in interferences assert interferences['xe'] == ('136Ce',) assert 'ba' in interferences assert interferences['ba'] == ('136Ce', '138Ce') assert 'la' in interferences assert interferences['la'] == ('138Ce', ) assert 'nd' in interferences assert interferences['nd'] == ('142Ce',) interferences = isopy.tb.find_isobaric_interferences('138ce') assert len(interferences) == 2 assert 'ba' in interferences assert interferences['ba'] == ('138Ce',) assert 'la' in interferences assert interferences['la'] == ('138Ce',) interferences = isopy.tb.find_isobaric_interferences('zn', ('ni', 'ge', 'ba++')) assert len(interferences) == 3 assert 'ni' in interferences assert interferences['ni'] == ('64Zn',) assert 'ge' in interferences assert interferences['ge'] == ('70Zn',) assert 'ba++' in interferences assert interferences['ba++'] == ('66Zn', '67Zn', '68Zn') class Test_rDelta(): def test_rDelta1(self): # Data is a single value data = isopy.refval.isotope.fraction.to_array(element_symbol='pd') # Dict reference = isopy.refval.isotope.fraction correct1 = isopy.zeros(None, data.keys) correct2 = isopy.ones(None, data.keys) self.run(data, data, reference, correct1, correct2) # Single array reference = isopy.random(100, keys=data.keys) correct1 = data / np.mean(reference) - 1 correct2 = data / np.mean(reference) self.run(data, data, reference, correct1, correct2) self.run(data, data, np.mean(reference), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data, reference, correct1, correct2, 10_000) self.run(data, data, np.mean(reference), correct1, correct2, 10_000) # Multiple values reference1 = isopy.random(100, keys=data.keys) reference2 = isopy.random(100, keys=data.keys) meanmean = np.mean(reference1)/2 + np.mean(reference2)/2 correct1 = data / meanmean - 1 correct2 = data / meanmean self.run(data, data, (reference1, reference2), correct1, correct2) self.run(data, data, (np.mean(reference1), reference2), correct1, correct2) self.run(data, data, (np.mean(reference1), np.mean(reference2)), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data, (reference1, reference2), correct1, correct2, 10_000) self.run(data, data, (np.mean(reference1), reference2), correct1, correct2, 10_000) self.run(data, data, (np.mean(reference1), np.mean(reference2)), correct1, correct2, 10_000) # Keys that do not match data2 = data.copy() data2['105pd', '106pd'] = np.nan reference1 = isopy.random(100, keys='101ru 102pd 104pd 105pd 108pd 110pd 111cd'.split()) reference2 = isopy.random(100, keys='101ru 102pd 104pd 106pd 108pd 110pd 111cd'.split()) meanmean = np.mean(reference1) / 2 + np.mean(reference2) / 2 correct1 = data / meanmean - 1 correct2 = data / meanmean self.run(data, data2, (reference1, reference2), correct1, correct2) self.run(data, data2, (np.mean(reference1), reference2), correct1, correct2) self.run(data, data2, (np.mean(reference1), np.mean(reference2)), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data2, (reference1, reference2), correct1, correct2, 10_000) self.run(data, data2, (np.mean(reference1), reference2), correct1, correct2, 10_000) self.run(data, data2, (np.mean(reference1), np.mean(reference2)), correct1, correct2, 10_000) def test_rDelta2(self): data = isopy.random(100, keys=isopy.refval.element.isotopes['pd']) data = data * isopy.refval.isotope.fraction # Dict reference = isopy.refval.isotope.fraction correct1 = data / reference - 1 correct2 = data / reference self.run(data, data, reference, correct1, correct2) # Single array reference = isopy.random(100, keys=data.keys) correct1 = data / np.mean(reference) - 1 correct2 = data / np.mean(reference) self.run(data, data, reference, correct1, correct2) self.run(data, data, np.mean(reference), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data, reference, correct1, correct2, 10_000) self.run(data, data, np.mean(reference), correct1, correct2, 10_000) # Multiple values reference1 = isopy.random(100, keys=data.keys) reference2 = isopy.random(100, keys=data.keys) meanmean = np.mean(reference1)/2 + np.mean(reference2)/2 correct1 = data / meanmean - 1 correct2 = data / meanmean self.run(data, data, (reference1, reference2), correct1, correct2) self.run(data, data, (np.mean(reference1), reference2), correct1, correct2) self.run(data, data, (np.mean(reference1), np.mean(reference2)), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data, (reference1, reference2), correct1, correct2, 10_000) self.run(data, data, (np.mean(reference1), reference2), correct1, correct2, 10_000) self.run(data, data, (np.mean(reference1), np.mean(reference2)), correct1, correct2, 10_000) # Keys that do not match data2 = data.copy() data2['105pd', '106pd'] = np.nan reference1 = isopy.random(100, keys='101ru 102pd 104pd 105pd 108pd 110pd 111cd'.split()) reference2 = isopy.random(100, keys='101ru 102pd 104pd 106pd 108pd 110pd 111cd'.split()) meanmean = np.mean(reference1) / 2 + np.mean(reference2) / 2 correct1 = data / meanmean - 1 correct2 = data / meanmean self.run(data, data2, (reference1, reference2), correct1, correct2) self.run(data, data2, (np.mean(reference1), reference2), correct1, correct2) self.run(data, data2, (np.mean(reference1), np.mean(reference2)), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data2, (reference1, reference2), correct1, correct2, 10_000) self.run(data, data2, (np.mean(reference1), reference2), correct1, correct2, 10_000) self.run(data, data2, (np.mean(reference1), np.mean(reference2)), correct1, correct2, 10_000) def test_presets(self): data = isopy.random(100, keys=isopy.refval.element.isotopes['pd']) data = data * isopy.refval.isotope.fraction reference = isopy.refval.isotope.fraction correct = (data / reference - 1) * 1000 normalised = isopy.tb.rDelta.ppt(data, reference) denormalised = isopy.tb.inverse_rDelta.ppt(normalised, reference) self.compare(correct, normalised) self.compare(data, denormalised) correct = (data / reference - 1) * 1000 normalised = isopy.tb.rDelta.permil(data, reference) denormalised = isopy.tb.inverse_rDelta.permil(normalised, reference) self.compare(correct, normalised) self.compare(data, denormalised) correct = (data / reference - 1) * 10_000 normalised = isopy.tb.rDelta.epsilon(data, reference) denormalised = isopy.tb.inverse_rDelta.epsilon(normalised, reference) self.compare(correct, normalised) self.compare(data, denormalised) correct = (data / reference - 1) * 1_000_000 normalised = isopy.tb.rDelta.mu(data, reference) denormalised = isopy.tb.inverse_rDelta.mu(normalised, reference) self.compare(correct, normalised) self.compare(data, denormalised) correct = (data / reference - 1) * 1_000_000 normalised = isopy.tb.rDelta.ppm(data, reference) denormalised = isopy.tb.inverse_rDelta.ppm(normalised, reference) self.compare(correct, normalised) self.compare(data, denormalised) def run(self, data1, data2, reference_value, correct1, correct2, factor=1): normalised = isopy.tb.rDelta(data1, reference_value, factor=factor) assert normalised.keys == data1.keys assert normalised.size == data1.size assert normalised.ndim == data1.ndim for key in normalised.keys: np.testing.assert_allclose(normalised[key], correct1[key]) denormalised = isopy.tb.inverse_rDelta(normalised, reference_value, factor=factor) assert denormalised.keys == data1.keys assert denormalised.size == data1.size assert denormalised.ndim == data1.ndim for key in denormalised.keys: np.testing.assert_allclose(denormalised[key], data2[key]) normalised = isopy.tb.rDelta(data1, reference_value, factor=factor, deviations=0) assert normalised.keys == data1.keys assert normalised.size == data1.size assert normalised.ndim == data1.ndim for key in normalised.keys: np.testing.assert_allclose(normalised[key], correct2[key]) denormalised = isopy.tb.inverse_rDelta(normalised, reference_value, factor=factor, deviations=0) assert denormalised.keys == data1.keys assert denormalised.size == data1.size assert denormalised.ndim == data1.ndim for key in denormalised.keys: np.testing.assert_allclose(denormalised[key], data2[key]) def compare(self, correct, calculated): assert calculated.keys == correct.keys assert calculated.size == correct.size assert calculated.ndim == correct.ndim for key in calculated.keys: np.testing.assert_allclose(calculated[key], correct[key]) class Test_OutliersLimits: def test_limits(self): data = isopy.random(100, (1,1), keys=isopy.refval.element.isotopes['pd']) median = np.median(data) mean = np.mean(data) mad3 = isopy.mad3(data) sd2 = isopy.sd2(data) upper = isopy.tb.upper_limit(data) assert upper == median + mad3 upper = isopy.tb.upper_limit(data, np.mean, isopy.sd2) assert upper == mean + sd2 upper = isopy.tb.upper_limit.sd2(data) assert upper == mean + sd2 upper = isopy.tb.upper_limit(data, 1, isopy.sd2) assert upper == 1 + sd2 upper = isopy.tb.upper_limit(data, np.mean, 1) assert upper == mean + 1 upper = isopy.tb.upper_limit(data, 1, 1) assert upper == 2 lower = isopy.tb.lower_limit(data) assert lower == median - mad3 lower = isopy.tb.lower_limit.sd2(data) assert lower == mean - sd2 lower = isopy.tb.lower_limit(data, np.mean, isopy.sd2) assert lower == mean - sd2 lower = isopy.tb.lower_limit(data, 1, isopy.sd2) assert lower == 1 - sd2 lower = isopy.tb.lower_limit(data, np.mean, 1) assert lower == mean - 1 lower = isopy.tb.lower_limit(data, 1, 1) assert lower == 0 def test_find_outliers1(self): #axis = 0 data = isopy.random(100, (1, 1), keys=isopy.refval.element.isotopes['pd']) median = np.median(data) mean = np.mean(data) mad3 = isopy.mad3(data) sd = isopy.sd(data) median_outliers = (data > (median + mad3)) + (data < (median - mad3)) mean_outliers = (data > (mean + sd)) + (data < (mean - sd)) mean_outliers1 = (data > (1 + sd)) + (data < (1 - sd)) mean_outliers2 = (data > (mean + 1)) + (data < (mean - 1)) mean_outliers3 = (data > (1 + 1)) + (data < (1 - 1)) outliers = isopy.tb.find_outliers(data) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], median_outliers[key]) outliers = isopy.tb.find_outliers(data, np.mean, isopy.sd) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], mean_outliers[key]) outliers = isopy.tb.find_outliers.sd(data) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], mean_outliers[key]) outliers = isopy.tb.find_outliers(data, 1, isopy.sd) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], mean_outliers1[key]) outliers = isopy.tb.find_outliers(data, np.mean, 1) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], mean_outliers2[key]) outliers = isopy.tb.find_outliers(data, 1, 1) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], mean_outliers3[key]) # invert median_outliers = np.invert(median_outliers) mean_outliers = np.invert(mean_outliers) mean_outliers1 = np.invert(mean_outliers1) mean_outliers2 = np.invert(mean_outliers2) mean_outliers3 = np.invert(mean_outliers3) outliers = isopy.tb.find_outliers(data, invert=True) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys:	np.testing.assert_allclose(outliers[key], median_outliers[key])	numpy.testing.assert_allclose
import numpy as np from pype3 import pypeify,pypeify_namespace,p,_,_0,_1,_2,ep,tup,db,a,iff,d from pype3.helpers import * from pype3 import ep # from numba import njit,jit from functools import reduce ''' This is a series of operations for numpy. Will document later. ''' def agg_sum(m): indices=m[:,0].argsort() m[:,0]=m[indices,0] m[:,1:]=m[indices,1:] uniqueKeys=np.unique(m[:,0],return_counts=True) cumSum=np.cumsum(uniqueKeys[1])[:-1] splitValues=np.split(m[:,1:],cumSum) sm=np.array([np.sum(l,axis=0) for l in splitValues]) return sm,uniqueKeys[0],uniqueKeys[1] def build_mat(y,X): m=np.zeros([y.shape[0],X.shape[1]+1]) m[:,0]=y m[:,1:]=X return m # @njit def shuffle(m): np.random.shuffle(m) return m def aggregate_by_first_column(m): indices=m[:,0].argsort() m[:,0]=m[indices,0] m[:,1:]=m[indices,1:] uniqueKeys=np.unique(m[:,0],return_counts=True) cumSum=np.cumsum(uniqueKeys[1])[:-1] splitValues=np.split(m[:,1:],cumSum) return splitValues,uniqueKeys[0],uniqueKeys[1] # @njit def vectors_to_column_matrix(vecs,m): for (i,vec) in enumerate(vecs): m[:vec.shape[0],i]=vec return m # @njit def sizes(vecs,s): for (i,vec) in enumerate(vecs): s[i]=vec.shape[0] return s def np_tile_cols(vec,numCols): return np.tile(vec,(numCols,1)).T def np_tile_rows(vec,numCols): return np.tile(vec,(numCols,1)) def np_zero_array(rows): return np.zeros([rows]) def np_zeros(rows,cols): return np.zeros([rows,cols]) def square_zeros(ln): return np.zeros([ln,ln]) def aggregate_by_key(m,padVal=0,pad=True): ''' This is a helper which takes an array with two columns. It is the numpy equivalent of grouping represented by tup_ls_dct in pype. The first column is the key, and the second column is the value. We perform the following operations on this: 1) Sort the keys of m, getting their indices. 2) Reorder the keys and values of m accordingly. 3) Find the unique keys and their counts, stored in uniqueKeys[1]. 4) The np.split function takes an array, and splits it according to the counts of the unique elements. So, take the first x elements, put it in one part of the list, then take the next y elements, append it to the list, etc. 5) In the resulting list of arrays, we find the maximum length. 6) We pad these arrays with zeros if they're shorter than the maximum length. 7) Then, we convert this into a matrix, whose i-th row represents the i-th key, and whose j-th column represents the j-th value with that key. 8) We return the matrix and the unique keys. We do this rather than json-style grouping for performance reasons, as many people have complained about using pure json-style aggregation. Thanks to: https://stackoverflow.com/questions/38013778/is-there-any-numpy-group-by-function ''' indices=m[:,0].argsort() m[:,0]=m[indices,0] m[:,1]=m[indices,1] uniqueKeys=np.unique(m[:,0],return_counts=True) splitValues=np.split(m[:, 1], np.cumsum(uniqueKeys[1])[:-1]) if pad: maxLen=np.max([a.shape[0] for a in splitValues]) aggregatedValues=[np.lib.pad(a, (0,maxLen-a.shape[0]), 'constant', constant_values=(padVal,padVal))\ for a in splitValues] aggregatedValues=np.array(aggregatedValues) else: aggregatedValues=splitValues return aggregatedValues,uniqueKeys[0],uniqueKeys[1] def sorted_aggregate_by_key(m,padVal=0,pad=True): aggregatedValues,uniqueKeys,uniqueCounts=aggregate_by_key(m,padVal,pad) aggregatedValues.sort(axis=1) return aggregatedValues,uniqueKeys,uniqueCounts def aggregate_jsons_by_key(ls,key): uniqueVals=np.unique([js[key] for js in ls]) indexToKeyMap={k:i for (i,k) in enumerate(uniqueVals)} m=np.array([(indexToKeyMap(js[key]),i) for (i,js) in enumerate(ls)]) aggregatedValues,keys,uniqueKeys=aggregate_by_key(m,False) return {k:[ls[index] for index in l] \ for (k,l) in zip(uniqueVals,aggregatedValues)} def np_int_array(x): return np.array(x,dtype=np.int32) def sum_by_row(x): return np.sum(x,axis=1) def sum_by_column(x): return np.sum(x,axis=0) def vector_copy_matrix(shape,vector): z=	np.zeros(shape)	numpy.zeros
################################################################################# ### ### ### Date created - Monday, Nov 11, 2019 ### ### Author - <NAME> <<EMAIL>, <EMAIL> > ### ### ### ################################################################################# """ * This library is only made to work for binary images. The goal was to detect outer boundary and loops in handwritten word images. Using this library, all edges, outer boundary and loops can be quickly detected in a binary image. * The input is binary image. * The output is a list of loops, edges, outer boundary in the same order as mentioned. Each of the return value is an image with the same size as input image with relevant points marked as foreground. """ import cv2, sys import numpy as np from scipy.ndimage import convolve # Find 8 connected neighbors of a point def GetNeighbors(row, col, x, y) : """ This function gives 8 connected neighbors of a pixel.""" neighbors = [ [x-1,y-1], [x-1,y], [x-1, y+1], [x, y-1], [x, y+1], [x+1, y-1], [x+1, y], [x+1, y+1] ] neighbors = [[p,q] for p,q in neighbors if p>=0 and p<row and q >=0 and q<col ] return neighbors # Find 8 connected neighbors of a point which are foreground pixels def GetForegroundNeighbors(Im, x, y) : """ This function gives 8 connected neighbors of a pixel which are foreground pixels.""" row, col = Im.shape neighbors = GetNeighbors(row, col, x, y) FG = [[p,q] for p,q in neighbors if Im[p][q] == 0 ] return FG # Check if image is valid def CheckImage(Im) : """ This function asserts if the image is valid or not.""" if type(Im) is not np.ndarray : if not Im : print("Error! NoneType object") sys.exit(1) print("Error! Input is not ndarray") sys.exit(1) shape = Im.shape if len(shape) <=1 : print("Error! Input is a 1D array, expected 2D or 3D np.ndarray") sys.exit(1) elif len(shape) == 3 : if shape[0] == 0 : print("Error! Image width is zero") sys.exit(1) if shape[1] == 0 : print("Error! Image height is zero") sys.exit(1) gray = cv2.cvtColor(Im, cv2.COLOR_BGR2GRAY) # Convert Image to Binary (thresh, Im) = cv2.threshold(gray, 128, 255, cv2.THRESH_BINARY \| cv2.THRESH_OTSU) elif len(shape) == 2 : if shape[0] == 0 : print("Error! Image width is zero") sys.exit(1) if shape[1] == 0 : print("Error! Image height is zero") sys.exit(1) # If image is not binary if len(np.unique(Im)) > 2 : # Convert Image to Binary (thresh, Im) = cv2.threshold(gray, 128, 255, cv2.THRESH_BINARY \| cv2.THRESH_OTSU) return Im # Detect edges in binary images def DetectLoopsEdges(Im) : """ This function detects loops, edges and outer boundary in binary image in order [loops, edges, outer_boundary].""" Im = CheckImage(Im) # Pad image with background pixels from all sides(top, bottom, left and right) Im = 1 - Im/255 Im =	np.pad(Im, ((1, 1), (1, 1)), 'constant')	numpy.pad
# execfile("read.py") import numpy as np import pandas as pd def get_data(limit=None): print("Reading data...") df = pd.read_csv('train.csv') data = df.as_matrix() np.random.shuffle(data) X = data[:, 1:] / 255.0 # data is from 0..255 Y = data[:, 0] if limit is not None: X, Y = X[:limit], Y[:limit] return X, Y def get_xor(): X = np.zeros((200, 2)) X[:50] = np.random.random((50, 2)) / 2 + 0.5 # (0.5-1, 0.5-1) X[50:100] = np.random.random((50, 2)) / 2 # (0-0.5, 0-0.5) X[100:150] = np.random.random((50, 2)) / 2 + np.array([[0, 0.5]]) # (0-0.5, 0.5-1) X[150:] = np.random.random((50, 2)) / 2 + np.array([[0.5, 0]]) # (0.5-1, 0-0.5) Y =	np.array([0]100 + [1]100)	numpy.array
""" A pytest module to test Galois field polynomial alternate constructors. """ import numpy as np import pytest import galois FIELDS = [ galois.GF2, # GF(2) galois.GF(31), # GF(p) with np.int dtypes galois.GF(36893488147419103183), # GF(p) with object dtype galois.GF(28), # GF(2^m) with np.int dtypes galois.GF(2100), # GF(2^m) with object dtype galois.GF(73), # GF(p^m) with np.int dtypes galois.GF(1099874), # GF(p^m) with object dtypes ] @pytest.mark.parametrize("field", FIELDS) def test_zero(field): p = galois.Poly.Zero(field) assert isinstance(p, galois.Poly) assert p.field is field assert p.degree == 0 assert np.array_equal(p.nonzero_degrees, []) assert np.array_equal(p.nonzero_coeffs, []) assert np.array_equal(p.degrees, [0]) assert np.array_equal(p.coeffs, [0]) assert p.integer == 0 @pytest.mark.parametrize("field", FIELDS) def test_one(field): p = galois.Poly.One(field) assert isinstance(p, galois.Poly) assert p.field is field assert p.degree == 0 assert np.array_equal(p.nonzero_degrees, [0]) assert np.array_equal(p.nonzero_coeffs, [1]) assert	np.array_equal(p.degrees, [0])	numpy.array_equal
# stdlib imports import re # third party imports import numpy as np import logging from strec.subtype import SubductionSelector def get_weights(origin, config): """Get list of GMPEs and their weights for a given earthquake. Args: origin (Origin object): ShakeMap Origin object, containing earthquake info. config (dict-like): Configuration information regarding earthquake type. Returns: tuple: Tuple with elements that are: - list of strings indicating the GMPEs selected for this earthquake. - ndarray (float) of GMPE weights. - Pandas series containing STREC output. """ tprobs, strec_results = get_probs(origin, config) gmpelist = [] weightlist = [] # remove all probabilities that are == 0 probs = {} for key, value in tprobs.items(): if value > 0.0: probs[key] = value all_keylist = list(probs.keys()) # let's have the code default to use the slab data if config["tectonic_regions"]["subduction"]: use_slab = config["tectonic_regions"]["subduction"]["use_slab"] else: use_slab = True for region, rdict in config["tectonic_regions"].items(): if (region == "subduction") and use_slab: if "crustal" in probs or "subduction_0" in probs: if "crustal" in probs: topkey = "crustal" else: topkey = "subduction_0" gmpelist += rdict["crustal"]["gmpe"] weightlist.append(probs[topkey]) if "interface" in probs or "subduction_1" in probs: if "interface" in probs: midkey = "interface" else: midkey = "subduction_1" gmpelist += rdict["interface"]["gmpe"] weightlist.append(probs[midkey]) if "intraslab" in probs or "subduction_2" in probs: if "intraslab" in probs: botkey = "intraslab" else: botkey = "subduction_2" gmpelist += rdict["intraslab"]["gmpe"] weightlist.append(probs[botkey]) else: pat = re.compile(region + "_") keylist = sorted(list(filter(pat.search, all_keylist))) if len(keylist): for key in keylist: weightlist.append(probs[key]) idx = int(key.split("_")[1]) gmpelist.append(rdict["gmpe"][idx]) weightlist = np.array(weightlist) logging.debug(f"gmpelist: {gmpelist}") logging.debug(f"weightlist: {weightlist}") gmmdict = {"gmpelist": gmpelist, "weightlist": weightlist} # # Here we get the region-specific ipe, gmice, and ccf. If they are # not specified in the config, we use None, and let the value # fall back to whatever is specified in the system config. # if strec_results["TectonicRegion"] == "Active": gmmdict["ipe"] = config["tectonic_regions"]["acr"].get("ipe", None) gmmdict["gmice"] = config["tectonic_regions"]["acr"].get("gmice", None) gmmdict["ccf"] = config["tectonic_regions"]["acr"].get("ccf", None) elif strec_results["TectonicRegion"] == "Stable": gmmdict["ipe"] = config["tectonic_regions"]["scr"].get("ipe", None) gmmdict["gmice"] = config["tectonic_regions"]["scr"].get("gmice", None) gmmdict["ccf"] = config["tectonic_regions"]["scr"].get("ccf", None) elif strec_results["TectonicRegion"] == "Subduction": gmmdict["ipe"] = config["tectonic_regions"]["subduction"].get("ipe", None) gmmdict["gmice"] = config["tectonic_regions"]["subduction"].get("gmice", None) gmmdict["ccf"] = config["tectonic_regions"]["subduction"].get("ccf", None) elif strec_results["TectonicRegion"] == "Volcanic": gmmdict["ipe"] = config["tectonic_regions"]["volcanic"].get("ipe", None) gmmdict["gmice"] = config["tectonic_regions"]["volcanic"].get("gmice", None) gmmdict["ccf"] = config["tectonic_regions"]["volcanic"].get("ccf", None) return gmmdict, strec_results def get_probs(origin, config): """Calculate probabilities for each earthquake type. The results here contain probabilities that can be rolled up in many ways: - The probabilities of acr, scr, volcanic, and subduction should sum to one. - The probabilities of acr_X,scr_X,volcanic_X, crustal, interface and intraslab should sum to 1. - The probabilities of acr_X should sum to acr, and so on. Args: origin (Origin object): ShakeMap Origin object, containing earthquake info. config (dict-like): Configuration information regarding earthquake type. Returns: (dict, dict): Probabilities for each earthquake type, with fields: - acr Probability that the earthquake is in an active region. - acr_X Probability that the earthquake is in a depth layer of ACR, starting from the top. - scr Probability that the earthquake is in a stable region. - scr_X Probability that the earthquake is in a depth layer of SCR, starting from the top. - volcanic Probability that the earthquake is in a volcanic region. - volcanic_X Probability that the earthquake is in a depth layer of Volcanic, starting from the top. - subduction Probability that the earthquake is in a subduction zone. - crustal Probability that the earthquake is in the crust above an interface. - interface Probability that the earthquake is on the interface. - intraslab Probability that the earthquake is in the slab below interface. STREC results """ selector = SubductionSelector() lat, lon, depth, mag = origin.lat, origin.lon, origin.depth, origin.mag if origin.id is not None and not origin.id.startswith(origin.netid): eid = origin.netid + origin.id else: eid = origin.id tensor_params = None if hasattr(origin, "moment"): tensor_params = origin.moment strec_results = selector.getSubductionType( lat, lon, depth, eid, tensor_params=tensor_params ) region_probs = get_region_probs(eid, depth, strec_results, config) in_subduction = strec_results["TectonicRegion"] == "Subduction" above_slab = not	np.isnan(strec_results["SlabModelDepth"])	numpy.isnan
# -- coding: utf-8 -- # @Author: <NAME> # @Email: <EMAIL> # @Date: 2016-09-19 22:30:46 # @Last Modified by: <NAME> # @Last Modified time: 2021-05-15 11:04:35 ''' Definition of generic utility functions used in other modules ''' import sys import itertools import csv from functools import wraps import operator import time from inspect import signature import os from shutil import get_terminal_size import lockfile import math import pickle import json from tqdm import tqdm import logging import tkinter as tk from tkinter import filedialog import base64 import datetime import numpy as np from scipy.optimize import brentq from scipy import linalg import colorlog from pushbullet import Pushbullet # Package logger my_log_formatter = colorlog.ColoredFormatter( '%(log_color)s %(asctime)s %(message)s', datefmt='%d/%m/%Y %H:%M:%S:', reset=True, log_colors={ 'DEBUG': 'green', 'INFO': 'white', 'WARNING': 'yellow', 'ERROR': 'red', 'CRITICAL': 'red,bg_white', }, style='%') def setHandler(logger, handler): for h in logger.handlers: logger.removeHandler(h) logger.addHandler(handler) return logger def setLogger(name, formatter): handler = colorlog.StreamHandler() handler.setFormatter(formatter) handler.stream = sys.stdout logger = colorlog.getLogger(name) logger.addHandler(handler) return logger class TqdmHandler(logging.StreamHandler): def __init__(self, formatter): logging.StreamHandler.__init__(self) self.setFormatter(formatter) def emit(self, record): msg = self.format(record) tqdm.write(msg) logger = setLogger('PySONIC', my_log_formatter) LOOKUP_DIR = os.path.abspath(os.path.split(__file__)[0] + "/lookups/") def fillLine(text, char='-', totlength=None): ''' Surround a text with repetitions of a specific character in order to fill a line to a given total length. :param text: text to be surrounded :param char: surrounding character :param totlength: target number of characters in filled text line :return: filled text line ''' if totlength is None: totlength = get_terminal_size().columns - 1 ndashes = totlength - len(text) - 2 if ndashes < 2: return text else: nside = ndashes // 2 nleft, nright = nside, nside if ndashes % 2 == 1: nright += 1 return f'{char * nleft} {text} {char * nright}' # SI units prefixes si_prefixes = { 'y': 1e-24, # yocto 'z': 1e-21, # zepto 'a': 1e-18, # atto 'f': 1e-15, # femto 'p': 1e-12, # pico 'n': 1e-9, # nano 'u': 1e-6, # micro 'm': 1e-3, # mili '': 1e0, # None 'k': 1e3, # kilo 'M': 1e6, # mega 'G': 1e9, # giga 'T': 1e12, # tera 'P': 1e15, # peta 'E': 1e18, # exa 'Z': 1e21, # zetta 'Y': 1e24, # yotta } sorted_si_prefixes = sorted(si_prefixes.items(), key=operator.itemgetter(1)) def getSIpair(x, scale='lin'): ''' Get the correct SI factor and prefix for a floating point number. ''' if isIterable(x): # If iterable, get a representative number of the distribution x = np.asarray(x) x = x.prod()**(1.0 / x.size) if scale == 'log' else np.mean(x) if x == 0: return 1e0, '' else: vals = [tmp[1] for tmp in sorted_si_prefixes] ix = np.searchsorted(vals, np.abs(x)) - 1 if	np.abs(x)	numpy.abs
#!/usr/bin/env python """SPECFIT.PY - Generic stellar abundance determination software """ from __future__ import print_function __authors__ = '<NAME> <<EMAIL>>' __version__ = '20200711' # yyyymmdd import os import shutil import contextlib, io, sys import numpy as np import warnings from astropy.io import fits from astropy.table import Table from dlnpyutils.minpack import curve_fit from dlnpyutils.least_squares import least_squares from scipy.interpolate import interp1d from dlnpyutils import utils as dln, bindata, astro import doppler from doppler.spec1d import Spec1D from doppler import (cannon,utils,reader) import copy import logging import time import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt from matplotlib.legend import Legend import tempfile from . import models from synple import synple # Ignore these warnings, it's a bug warnings.filterwarnings("ignore", message="numpy.dtype size changed") warnings.filterwarnings("ignore", message="numpy.ufunc size changed") cspeed = 2.99792458e5 # speed of light in km/s def synmodel(spec,params,alinefile=None,mlinefile=None,verbose=False,normalize=True): """ Synthetic spectrum model. Parameters ---------- spec : Spec1D object or str The observed Spec1D spectrum to match or the name of a spectrum file. params : dict Dictionary of initial values to use or parameters/elements to hold fixed. normalize : bool, optional Renormalize the model spectrum using the observed spectrum's continuum function. The synthetic spectrum will already have been normalized using the "true" continuum. This step is to simulate any systematic effects of the spectrum normalization algorithm that the observed spectrum undergoes. Default is True. verbose : int, optional Verbosity level (0, 1, or 2). The default is 0 and verbose=2 is for debugging. alinefile : str, optional The atomic linelist to use. Default is None which means the default synple linelist is used. mlinefile : str, optional The molecular linelist to use. Default is None which means the default synple linelist is used. Returns ------- model : Spec1D object The synthetic spectrum. The "true" continuum is in model.cont. Example ------- .. code-block:: python model = synmodel(spec,params) """ # Read in the spectrum if type(spec) is str: filename = spec spec = doppler.read(filename) if spec is None: print('Problem loading '+filename) return params = dict((key.upper(), value) for (key, value) in params.items()) # all CAPS # Initialize the fitter fitparams = ['TEFF'] # "dummy" fitting variable spfitter = SpecFitter(spec,params,fitparams=fitparams,verbose=(verbose>=2), alinefile=alinefile,mlinefile=mlinefile) spfitter.norm = normalize # normalize the synthetic spectrum model = spfitter.model(spec.wave.flatten(),params['TEFF'],retobj=True) model.instrument = 'Model' return model class SpecFitter: def __init__ (self,spec,params,fitparams=None,norm=True,verbose=False, alinefile=None,mlinefile=None): # Parameters self.params = params if fitparams is not None: self.fitparams = fitparams else: self.fitparams = list(params.keys()) # by default fit all parameters self.nsynfev = 0 # number of synthetic spectra made self.njac = 0 # number of times jacobian called # Save spectrum information self.spec = spec.copy() self.flux = spec.flux.flatten() self.err = spec.err.flatten() self.wave = spec.wave.flatten() self.lsf = spec.lsf.copy() self.lsf.wavevac = spec.wavevac # need this later for synspec prep self.wavevac = spec.wavevac self.verbose = verbose self.norm = norm # normalize self.continuum_func = spec.continuum_func self.alinefile = alinefile self.mlinefile = mlinefile # Convert vacuum to air wavelengths # synspec uses air wavelengths if spec.wavevac is True: wave = astro.vactoair(spec.wave.copy().flatten()).reshape(spec.wave.shape) else: wave = spec.wave.copy() if wave.ndim==1: wave = np.atleast_2d(wave).T # Figure out the wavelength parameters npix = spec.npix norder = spec.norder xp = np.arange(npix//20)20 wr = np.zeros((spec.lsf.norder,2),np.float64) dw = np.zeros(spec.lsf.norder,np.float64) mindw = np.zeros(norder,np.float64) for o in range(spec.norder): dw[o] = np.median(dln.slope(wave[:,o])) wr[o,0] = np.min(wave[:,o]) wr[o,1] = np.max(wave[:,o]) fwhm = spec.lsf.fwhm(wave[xp,o],xtype='Wave',order=o) # FWHM is in units of lsf.xtype, convert to wavelength/angstroms, if necessary if spec.lsf.xtype.lower().find('pix')>-1: fwhm = np.abs(dw[o]) # need at least ~4 pixels per LSF FWHM across the spectrum # using 3 affects the final profile shape mindw[o] = np.min(fwhm/4) self._dwair = np.min(mindw) # IN AIR WAVELENGTHS!! self._w0air = np.min(wave) self._w1air = np.max(wave) # parameters to save self._all_pars = [] self._all_model = [] self._all_chisq = [] self._jac_array = None @property def params(self): return self._params @params.setter def params(self,params): """ Dictionary, keys must be all CAPS.""" self._params = dict((key.upper(), value) for (key, value) in params.items()) # all CAPS @property def fitparams(self): return self._fitparams @fitparams.setter def fitparams(self,fitparams): """ list, keys must be all CAPS.""" self._fitparams = [v.upper() for v in fitparams] # all CAPS def mkinputs(self,args): """ Make INPUTS dictionary.""" # Create INPUTS with all arguments needed to make the spectrum inputs = self.params.copy() # initialize with initial/fixed values for k in range(len(self.fitparams)): # this overwrites the values for the fitted values inputs[self.fitparams[k]] = args[k] inputs['DW'] = self._dwair # add in wavelength parameters inputs['W0'] = self._w0air inputs['W1'] = self._w1air return inputs def chisq(self,model): return np.sqrt( np.sum( (self.flux-model)2/self.err2 )/len(self.flux) ) def model(self, xx, args, retobj=False): """ Return a model spectrum flux with the given input arguments.""" # The input arguments correspond to FITPARAMS # This corrects for air/vacuum wavelength differences if self.verbose: print(args) # The arguments correspond to the fitting parameters inputs = self.mkinputs(args) if self.verbose: print(inputs) # Create the synthetic spectrum synspec = model_spectrum(inputs,verbose=self.verbose, # always returns air wavelengths alinefile=self.alinefile,mlinefile=self.mlinefile) self.nsynfev += 1 # Convolve with the LSF and do air/vacuum wave conversion pspec = prepare_synthspec(synspec,self.lsf,norm=self.norm, continuum_func=self.continuum_func) # Save models/pars/chisq self._all_pars.append(list(args).copy()) self._all_model.append(pspec.flux.flatten().copy()) self._all_chisq.append(self.chisq(pspec.flux.flatten())) # Return flattened spectrum if retobj: return pspec else: return pspec.flux.flatten() def getstep(self,name,val,relstep=0.02): """ Calculate step for a parameter.""" # It mainly deals with edge cases #if val != 0.0: # step = relstepval #else: # if name=='RV': # step = 1.0 # elif name=='VROT': # step = 0.5 # elif name=='VMICRO': # step = 0.5 # elif name.endswith('_H'): # step = 0.02 # else: # step = 0.02 if name=='TEFF': step = 5.0 elif name=='RV': step = 0.1 elif name=='VROT': step = 0.5 elif name=='VMICRO': step = 0.5 elif name.endswith('_H'): step = 0.01 else: step = 0.01 return step return step def jac(self,x,args): """ Compute the Jacobian matrix (an m-by-n matrix, where element (i, j) is the partial derivative of f[i] with respect to x[j]). """ if hasattr(self,'logger') is False: logger = dln.basiclogger() else: logger = self.logger logger.info(args) if self.verbose: logger.info(' ') logger.info('##### Calculating Jacobian Matrix #####') logger.info(' ') # A new synthetic spectrum does not need to be generated RV, vmicro or vsini. # Some time can be saved by not remaking those. # Use a one-sided derivative. # Boundaries lbounds,ubounds = mkbounds(self.fitparams) relstep = 0.02 npix = len(x) npar = len(args) # Get INPUTS dictionary and make keys all CAPS inputs = self.mkinputs(args) inputs = dict((key.upper(), value) for (key, value) in inputs.items()) # Some important parameters w0 = inputs['W0'] w1 = inputs['W1'] dw = inputs['DW'] rv = inputs.get('RV') vrot = inputs.get('VROT') vmicro = inputs.get('VMICRO') # Create synthetic spectrum at current values # set vrot=vmicro=rv=0, will modify later if necessary if self.verbose: logger.info('--- Current values ---') logger.info(args) tinputs = inputs.copy() tinputs['VMICRO'] = 0 tinputs['VROT'] = 0 tinputs['RV'] = 0 origspec = model_spectrum(tinputs,keepextend=True, # always are wavelengths alinefile=self.alinefile,mlinefile=self.mlinefile) self.nsynfev += 1 # Smooth and shift smorigspec = smoothshift_spectrum(origspec,vrot=vrot,vmicro=vmicro,rv=rv) # Trim to final wavelengths smorigspec = trim_spectrum(smorigspec,w0,w1) # Convolve with the LSF and do air/vacuum wave conversion pspec = prepare_synthspec(smorigspec,self.lsf,norm=self.norm, continuum_func=self.continuum_func) # Flatten the spectrum f0 = pspec.flux.flatten() # Save models/pars/chisq self._all_pars.append(list(args).copy()) self._all_model.append(f0.copy()) self._all_chisq.append(self.chisq(f0)) chisq = np.sqrt( np.sum( (self.flux-f0)2/self.err2 )/len(self.flux) ) self if self.verbose: logger.info('chisq = '+str(chisq)) # MASK PIXELS!? # Initialize jacobian matrix jac = np.zeros((npix,npar),np.float64) # Loop over parameters for i in range(npar): pars = np.array(copy.deepcopy(args)) step = self.getstep(self.fitparams[i],pars[i],relstep) # Check boundaries, if above upper boundary # go the opposite way if pars[i]>ubounds[i]: step = -1 pars[i] += step tinputs = self.mkinputs(pars) if self.verbose: logger.info(' ') logger.info('--- '+str(i+1)+' '+self.fitparams[i]+' '+str(pars[i])+' ---') logger.info(pars) # VROT/VMICRO/RV, just shift/smooth original spectrum if self.fitparams[i]=='VROT' or self.fitparams[i]=='VMICRO' or self.fitparams[i]=='RV': tvrot = tinputs.get('VROT') tvmicro = tinputs.get('VMICRO') trv = tinputs.get('RV') #import pdb; pdb.set_trace() # Smooth and shift synspec = smoothshift_spectrum(origspec,vrot=tvrot,vmicro=tvmicro,rv=trv) # Trim to final wavelengths synspec = trim_spectrum(synspec,w0,w1) else: synspec = model_spectrum(tinputs,alinefile=self.alinefile, mlinefile=self.mlinefile) # always returns air wavelengths self.nsynfev += 1 # Convert to vacuum wavelengths if necessary if self.wavevac: synspec.wave = astro.airtovac(synspec.wave) synspec.wavevac = True # Convolve with the LSF and do air/vacuum wave conversion pspec = prepare_synthspec(synspec,self.lsf,norm=self.norm, continuum_func=self.continuum_func) # Flatten the spectrum f1 = pspec.flux.flatten() # Save models/pars/chisq self._all_pars.append(list(pars).copy()) self._all_model.append(f1.copy()) self._all_chisq.append(self.chisq(f1)) if np.sum(~np.isfinite(f1))>0: print('some nans/infs') import pdb; pdb.set_trace() jac[:,i] = (f1-f0)/step if np.sum(~np.isfinite(jac))>0: print('some nans/infs') import pdb; pdb.set_trace() self._jac_array = jac.copy() # keep a copy self.njac += 1 return jac def trim_spectrum(spec,w0,w1): """ Trim a synthetic spectrum to [w0,w1].""" # This assumes that the spectrum has a single order wv1, ind1 = dln.closest(spec.wave,w0) wv2, ind2 = dln.closest(spec.wave,w1) # Nothing to do if ind1==0 and ind2==(spec.npix-1): return spec outspec = spec.copy() outspec.flux = outspec.flux[ind1:ind2+1] outspec.wave = outspec.wave[ind1:ind2+1] if outspec.err is not None: outspec.err = outspec.err[ind1:ind2+1] if outspec.mask is not None: outspec.mask = outspec.mask[ind1:ind2+1] if hasattr(outspec,'cont'): if outspec.cont is not None: outspec.cont = outspec.cont[ind1:ind2+1] outspec.npix = len(outspec.flux) return outspec def getabund(inputs,verbose=False): """ Grab the abundances out of the input file and return array of abundances.""" # Create the input 99-element abundance array codedir = os.path.dirname(os.path.abspath(__file__)) pertab = Table.read(codedir+'/data/periodic_table.txt',format='ascii') feh = inputs.get('FEH') if feh is None: feh = inputs.get('FE_H') if feh is None: raise ValueError('FE_H missing from inputs') # Read model atmosphere modelfile = inputs.get('modelfile') if modelfile is None: raise ValueError('modelfile missing from inputs') atmostype, teff, logg, vmicro2, mabu, nd, atmos = synple.read_model(modelfile,verbose=verbose) mlines = dln.readlines(modelfile) # solar abundances # first two are Teff and logg # last two are Hydrogen and Helium solar_abund = np.array([ 4750., 2.5, -10.99, -10.66, -9.34, -3.61, -4.21, -3.35, -7.48, -4.11, -5.80, -4.44, -5.59, -4.53, -6.63, -4.92, -6.54, -5.64, -7.01, -5.70, -8.89, -7.09, -8.11, -6.40, -6.61, -4.54, -7.05, -5.82, -7.85, -7.48, -9.00, -8.39, -9.74, -8.70, -9.50, -8.79, -9.52, -9.17, -9.83, -9.46, -10.58, -10.16, -20.00, -10.29, -11.13, -10.47, -11.10, -10.33, -11.24, -10.00, -11.03, -9.86, -10.49, -9.80, -10.96, -9.86, -10.94, -10.46, -11.32, -10.62, -20.00, -11.08, -11.52, -10.97, -11.74, -10.94, -11.56, -11.12, -11.94, -11.20, -11.94, -11.19, -12.16, -11.19, -11.78, -10.64, -10.66, -10.42, -11.12, -10.87, -11.14, -10.29, -11.39, -20.00, -20.00, -20.00, -20.00, -20.00, -20.00, -12.02, -20.00, -12.58, -20.00, -20.00, -20.00, -20.00, -20.00, -20.00, -20.00]) # Deal with alpha abundances # only add the individual alpha abundance if it's not already there # sometimes we might fit a single alpha element but want to use # ALPHA_H to set the rest of them if inputs.get('ALPHA_H') is not None: alpha = inputs['ALPHA_H'] elem = ['O','MG','SI','S','CA','TI'] for k in range(len(elem)): if inputs.get(elem[k]+'_H') is None: inputs[elem[k]+'_H'] = alpha # Scale global metallicity abu = solar_abund.copy() abu[2:] += feh # Now offset the elements with [X/Fe], [X/Fe]=[X/H]-[Fe/H] g, = np.where( (np.char.array(list(inputs.keys())).find('_H') != -1) & (np.char.array(list(inputs.keys())) != 'FE_H') ) if len(g)>0: ind1,ind2 = dln.match(np.char.array(list(inputs.keys()))[g],np.char.array(pertab['symbol']).upper()+'_H') for k in range(len(ind1)): key1 = np.char.array(list(inputs.keys()))[g[ind1[k]]] abu[ind2[k]] += float(inputs[key1]) - feh if verbose: print('%s %f' % (key1,float(inputs[key1]))) # convert to linear abu[2:] = 10*abu[2:] # Divide by N(H) g, = np.where(np.char.array(mlines).find('ABUNDANCE SCALE') != -1) nhtot = np.float64(mlines[g[0]].split()[6]) abu[2:] /= nhtot # use model values for H and He abu[0:2] = mabu[0:2] return abu def synple_wrapper(inputs,verbose=False,tmpbase='/tmp',alinefile=None,mlinefile=None): """ This is a wrapper around synple to generate a new synthetic spectrum.""" # Wavelengths are all AIR!! # inputs is a dictionary with all of the inputs # Teff, logg, [Fe/H], some [X/Fe], and the wavelength parameters (w0, w1, dw). # Make temporary directory for synple to work in curdir = os.path.abspath(os.curdir) tdir = os.path.abspath(tempfile.mkdtemp(prefix="syn",dir=tmpbase)) os.chdir(tdir) # Linelists to use linelist = ['gfallx3_bpo.19','kmol3_0.01_30.20'] # default values if alinefile is not None: # atomic linelist input linelist[0] = alinefile if mlinefile is not None: # molecular linelist input linelist[1] = mlinefile if verbose: print('Using linelist: ',linelist) # Make key names all CAPS inputs = dict((key.upper(), value) for (key, value) in inputs.items()) # Make the model atmosphere file teff = inputs['TEFF'] logg = inputs['LOGG'] metal = inputs['FE_H'] tid,modelfile = tempfile.mkstemp(prefix="mod",dir=".") os.close(tid) # close the open file # Limit values # of course the logg/feh ranges vary with Teff mteff = dln.limit(teff,3500.0,60000.0) mlogg = dln.limit(logg,0.0,5.0) mmetal = dln.limit(metal,-2.5,0.5) model, header, tail = models.mkmodel(mteff,mlogg,mmetal,modelfile) inputs['modelfile'] = modelfile if os.path.exists(modelfile) is False or os.stat(modelfile).st_size==0: print('model atmosphere file does NOT exist') import pdb; pdb.set_trace() # Create the synspec synthetic spectrum w0 = inputs['W0'] w1 = inputs['W1'] dw = inputs['DW'] vmicro = inputs.get('VMICRO') vrot = inputs.get('VROT') if vrot is None: vrot = 0.0 # Get the abundances abu = getabund(inputs,verbose=verbose) wave,flux,cont = synple.syn(modelfile,(w0,w1),dw,vmicro=vmicro,vrot=vrot, abu=list(abu),verbose=verbose,linelist=linelist) # Delete temporary files shutil.rmtree(tdir) os.chdir(curdir) return (wave,flux,cont) def smoothshift_spectrum(inpspec,vmicro=None,vrot=None,rv=None): """ This smoothes the spectrum by Vrot+Vmicro and shifts it by RV.""" #vmicro = inputs.get('VMICRO') #vrot = inputs.get('VROT') #rv = inputs.get('RV') # Nothing to do if vmicro is None and vrot is None and rv is None: return inpspec.copy() # Initialize output spectrum spec = inpspec.copy() # Some broadening if vmicro is not None or vrot is not None: flux = utils.broaden(spec.wave,spec.flux,vgauss=vmicro,vsini=vrot) spec.flux = flux ## Vrot/Vsini (km/s) and Vmicro (in km/s) #if vrot is not None or vmicro is not None: # wave, flux = synple.call_rotin(wave, flux, vrot, fwhm, space, steprot, stepfwhm, clean=False, reuseinputfiles=True) # Doppler shift only (in km/s) if rv is not None: if rv != 0.0: shiftwave = spec.wave(1+rv/cspeed) gd,ngd,bd,nbd = dln.where( (spec.wave >= np.min(shiftwave)) & (spec.wave <= np.max(shiftwave)), comp=True) # Doppler shift and interpolate onto wavelength array if hasattr(spec,'cont'): cont = synple.interp_spl(spec.wave[gd], shiftwave, spec.cont) spec.cont = 0 spec.cont[gd] = cont # interpolate the continuing to the missing pixels if nbd>0: contmissing = dln.interp(spec.wave[gd],spec.cont[gd],spec.wave[bd],kind='linear',assume_sorted=False) spec.cont[bd] = contmissing flux = synple.interp_spl(spec.wave[gd], shiftwave, spec.flux) spec.flux = 0 spec.flux[gd] = flux if nbd>0: # Fill in missing values with interpolated values if np.sum(np.isfinite(spec.flux[gd]))>0: coef = dln.poly_fit(spec.wave[gd],spec.flux[gd],2) fluxmissing = dln.poly(spec.wave[bd],coef) spec.flux[bd] = fluxmissing # Mask these pixels if spec.mask is None: spec.mask = np.zeros(len(spec.flux),bool) spec.mask[bd] = True return spec def model_spectrum(inputs,verbose=False,keepextend=False,alinefile=None,mlinefile=None): """ This creates a model spectrum given the inputs: RV, Teff, logg, vmicro, vsini, [Fe/H], [X/Fe], w0, w1, dw. This creates the new synthetic spectrum and then convolves with vmicro, vsini and shifts to velocity RV. The returned spectrum always uses AIR wavelengths!!! Parameters ---------- inputs : dictionary Input parameters, stellar parameters, abundances. keepextend : bool, optional Keep the extensions on the ends. Default is False. alinefile : str, optional Atomic linelist filename. Default is None (use synple's default one). mlinefile : str, optional Molecular linelist filename. Default is None (use synple's default one). verbose : bool, optional Verbose output. Default is False. Returns ------- synspec : Spec1D The synthetic spectrum as Spec1D object. """ # Make key names all CAPS inputs = dict((key.upper(), value) for (key, value) in inputs.items()) # Extend on the ends for RV/convolution purposes w0 = inputs['W0'] w1 = inputs['W1'] dw = inputs['DW'] rv = inputs.get('RV') vrot = inputs.get('VROT') vmicro = inputs.get('VMICRO') inputsext = inputs.copy() if rv is not None or vrot is not None or vmicro is not None: numext = int(np.ceil(w1(1.0+1500/cspeed)-w1)) inputsext['W0'] = w0-numextdw inputsext['W1'] = w1+numextdw if verbose: print('Extending wavelength by '+str(numext)+' pixels on each end') # Create the synthetic spectrum # set vrot=vmicro=0, will convolve later if necessary inputsext['VMICRO'] = 0 inputsext['VROT'] = 0 wave1,flux1,cont1 = synple_wrapper(inputsext,verbose=verbose,alinefile=alinefile, mlinefile=mlinefile) # Get final wavelength array wv1, ind1 = dln.closest(wave1,w0) wv2, ind2 = dln.closest(wave1,w1) synspec = Spec1D(flux1/cont1,err=flux10,wave=wave1,lsfpars=np.array(0.0)) synspec.cont = cont1 synspec.wavevac = False # Smooth and shift if rv is not None or vrot is not None or vmicro is not None: synspec = smoothshift_spectrum(synspec,vrot=vrot,vmicro=vmicro,rv=rv) # Trim to final wavelengths if keepextend is False: synspec = trim_spectrum(synspec,w0,w1) return synspec def prepare_synthspec(synspec,lsf,norm=True,continuum_func=None): """ Prepare a synthetic spectrum to be compared to an observed spectrum.""" # Convolve with LSF and do air<->vacuum wavelength conversion # Convert wavelength from air->vacuum or vice versa if synspec.wavevac != lsf.wavevac: # Air -> Vacuum if synspec.wavevac is False: synspec.wave = astro.airtovac(synspec.wave) synspec.wavevac = True # Vacuum -> Air else: synspec.dispersion = astro.vactoair(synspec.wave) synspec.wavevac = False # Initialize the output spectrum if lsf.wave.ndim==2: npix,norder = lsf.wave.shape else: npix = len(lsf.wave) norder = 1 pspec = Spec1D(np.zeros((npix,norder),np.float32),err=np.zeros((npix,norder),np.float32), wave=lsf.wave,lsfpars=lsf.pars,lsftype=lsf.lsftype,lsfxtype=lsf.xtype) pspec.cont = np.zeros((npix,norder),np.float32) if continuum_func is not None: pspec.continuum_func = continuum_func # Loop over orders if lsf.wave.ndim==1: wave = np.atleast_2d(lsf.wave.copy()).T else: wave = lsf.wave.copy() for o in range(lsf.norder): wobs = wave[:,o] dw = np.median(dln.slope(wobs)) wv1,ind1 = dln.closest(synspec.wave,np.min(wobs)-2np.abs(dw)) wv2,ind2 = dln.closest(synspec.wave,np.max(wobs)+2np.abs(dw)) modelflux = synspec.flux[ind1:ind2+1] modelwave = synspec.wave[ind1:ind2+1] modelcont = synspec.cont[ind1:ind2+1] # Rebin, if necessary # get LSF FWHM (A) for a handful of positions across the spectrum xp = np.arange(npix//20)20 fwhm = lsf.fwhm(wobs[xp],xtype='Wave',order=o) # FWHM is in units of lsf.xtype, convert to wavelength/angstroms, if necessary if lsf.xtype.lower().find('pix')>-1: fwhm = np.abs(dw) # convert FWHM (A) in number of model pixels at those positions dwmod = dln.slope(modelwave) dwmod = np.hstack((dwmod,dwmod[-1])) xpmod = dln.interp(modelwave,np.arange(len(modelwave)),wobs[xp],kind='cubic',assume_sorted=False,extrapolate=True) xpmod = np.round(xpmod).astype(int) fwhmpix = np.abs(fwhm/dwmod[xpmod]) # need at least ~4 pixels per LSF FWHM across the spectrum # using 3 affects the final profile shape nbin = np.round(np.min(fwhmpix)//4).astype(int) if np.min(fwhmpix) < 3.7: warnings.warn('Model has lower resolution than the observed spectrum. Only '+str(np.min(fwhmpix))+' model pixels per resolution element') if np.min(fwhmpix) < 2.8: raise Exception('Model has lower resolution than the observed spectrum. Only '+str(np.min(fwhmpix))+' model pixels per resolution element') if nbin>1: npix2 = np.round(len(synspec.flux) // nbin).astype(int) modelflux = dln.rebin(modelflux[0:npix2nbin],npix2) modelwave = dln.rebin(modelwave[0:npix2nbin],npix2) modelcont = dln.rebin(modelcont[0:npix2nbin],npix2) # Convolve lsf2d = lsf.anyarray(modelwave,xtype='Wave',order=o,original=False) cflux = utils.convolve_sparse(modelflux,lsf2d) # Interpolate onto final wavelength array flux = synple.interp_spl(wobs, modelwave, cflux) cont = synple.interp_spl(wobs, modelwave, modelcont) pspec.flux[:,o] = flux pspec.cont[:,o] = cont pspec.normalized = True # Normalize if norm is True: newcont = pspec.continuum_func(pspec) pspec.flux /= newcont pspec.cont = newcont return pspec def mkbounds(params,paramlims=None): """ Make lower and upper boundaries for parameters """ params = np.char.array(params).upper() if paramlims is not None: limkeys = np.char.array(list(paramlims.keys())).upper() n = len(params) lbounds = np.zeros(n,np.float64) ubounds = np.zeros(n,np.float64) # Teff g, = np.where(params=='TEFF') if len(g)>0: lbounds[g[0]] = 3500 ubounds[g[0]] = 60000 # logg g, = np.where(params=='LOGG') if len(g)>0: lbounds[g[0]] = 0 ubounds[g[0]] = 5 # fe_h g, = np.where(params=='FE_H') if len(g)>0: lbounds[g[0]] = -3 ubounds[g[0]] = 1 # Vmicro g, = np.where(params=='VMICRO') if len(g)>0: lbounds[g[0]] = 0 ubounds[g[0]] = 5 # Vsini/vrot g, = np.where(params=='VROT') if len(g)>0: lbounds[g[0]] = 0 ubounds[g[0]] = 500 # RV g, = np.where(params=='RV') if len(g)>0: lbounds[g[0]] = -1500 ubounds[g[0]] = 1500 # abundances g, = np.where( (params.find('_H') != -1) & (params != 'FE_H') ) if len(g)>0: lbounds[g] = -3 ubounds[g] = 10 # Use input parameter limits if paramlims is not None: for i,f in enumerate(params): g, = np.where(limkeys==f) if len(g)>0: lbounds[i] = paramlims[limkeys[g[0]]][0] ubounds[i] = paramlims[limkeys[g[0]]][1] bounds = (lbounds,ubounds) return bounds def mkdxlim(fitparams): """ Make array of parameter changes at which curve_fit should finish.""" npar = len(fitparams) dx_lim = np.zeros(npar,float) for k in range(npar): if fitparams[k]=='TEFF': dx_lim[k] = 1.0 elif fitparams[k]=='LOGG': dx_lim[k] = 0.005 elif fitparams[k]=='VMICRO': dx_lim[k] = 0.1 elif fitparams[k]=='VROT': dx_lim[k] = 0.1 elif fitparams[k]=='RV': dx_lim[k] = 0.01 elif fitparams[k].endswith('_H'): dx_lim[k] = 0.005 else: dx_lim[k] = 0.01 return dx_lim def initpars(params,fitparams,bounds=None): """ Make initial set of parameters given PARAMS and FITPARAMS.""" params = dict((key.upper(), value) for (key, value) in params.items()) # all CAPS fitparams = [v.upper() for v in fitparams] # all CAPS npars = len(fitparams) pinit = np.zeros(npars,np.float64) # Loop over parameters for k in range(npars): ind, = np.where(np.char.array(list(params.keys()))==fitparams[k]) # This parameter is in PARAMS if len(ind)>0: pinit[k] = params[fitparams[k]] # Not in PARAMS else: if fitparams[k]=='RV': pinit[k] = 0.0 elif fitparams[k]=='VMICRO': pinit[k] = 2.0 elif fitparams[k]=='VROT': pinit[k] = 0.0 elif fitparams[k]=='TEFF': pinit[k] = 5000.0 elif fitparams[k]=='LOGG': pinit[k] = 3.0 elif fitparams[k].endswith('_H'): # Abundances, use FE_H if possible if 'FE_H' in params.keys(): pinit[k] = params['FE_H'] else: pinit[k] = 0.0 else: pinit[k] = 0.0 # Make sure inital parameters are within the boundary limits if bounds is not None: for k in range(npars): pinit[k] = dln.limit(pinit[k],bounds[0][k],bounds[1][k]) return pinit def specfigure(figfile,spec,fmodel,out,original=None,verbose=True,figsize=10): """ Make diagnostic figure.""" #import matplotlib matplotlib.use('Agg') #import matplotlib.pyplot as plt if os.path.exists(figfile): os.remove(figfile) norder = spec.norder nlegcol = 2 if original is not None: nlegcol=3 # Single-order plot if norder==1: fig,ax = plt.subplots() fig.set_figheight(figsize0.5) fig.set_figwidth(figsize) if original is not None: plt.plot(original.wave,original.flux,color='green',label='Original',linewidth=1) plt.plot(spec.wave,spec.flux,'b',label='Masked Data',linewidth=0.5) plt.plot(fmodel.wave,fmodel.flux,'r',label='Model',linewidth=0.5,alpha=0.8) leg = ax.legend(loc='upper left', frameon=True, framealpha=0.8, ncol=nlegcol) plt.xlabel('Wavelength (Angstroms)') plt.ylabel('Normalized Flux') xr = dln.minmax(spec.wave) yr = [np.min([spec.flux,fmodel.flux]), np.max([spec.flux,fmodel.flux])] if original is not None: yr = [np.min([original.flux,spec.flux,fmodel.flux]), np.max([spec.flux,fmodel.flux])] yr = [yr[0]-dln.valrange(yr)0.15,yr[1]+dln.valrange(yr)0.005] yr = [np.max([yr[0],-0.2]), np.min([yr[1],2.0])] plt.xlim(xr) plt.ylim(yr) snr = np.nanmedian(spec.flux/spec.err) plt.title(spec.filename) #ax.annotate(r'S/N=%5.1f Teff=%5.1f$\pm$%5.1f logg=%5.2f$\pm$%5.2f [Fe/H]=%5.2f$\pm$%5.2f Vrel=%5.2f$\pm$%5.2f chisq=%5.2f' % # (snr, out['TEFF'], out['tefferr'], out['LOGG'], out['loggerr'], out['FE_H'], out['feherr'], out['RV'], out['vrelerr'], out['chisq']), # xy=(np.mean(xr), yr[0]+dln.valrange(yr)0.05),ha='center') # Multi-order plot else: fig,ax = plt.subplots(norder) fig.set_figheight(figsize) fig.set_figwidth(figsize) for i in range(norder): if original is not None: ax[i].plot(original.wave[:,i],original.flux[:,i],color='green',label='Original',linewidth=1) ax[i].plot(spec.wave[:,i],spec.flux[:,i],'b',label='Masked Data',linewidth=0.5) ax[i].plot(fmodel.wave[:,i],fmodel.flux[:,i],'r',label='Model',linewidth=0.5,alpha=0.8) if i==0: leg = ax[i].legend(loc='upper left', frameon=True, framealpha=0.8, ncol=nlegcol) ax[i].set_xlabel('Wavelength (Angstroms)') ax[i].set_ylabel('Normalized Flux') xr = dln.minmax(spec.wave[:,i]) yr = [np.min([spec.flux[:,i],fmodel.flux[:,i]]), np.max([spec.flux[:,i],fmodel.flux[:,i]])] if original is not None: yr = [np.min([original.flux[:,i],spec.flux[:,i],fmodel.flux[:,i]]), np.max([spec.flux[:,i],fmodel.flux[:,i]])] yr = [yr[0]-dln.valrange(yr)0.05,yr[1]+dln.valrange(yr)0.05] if i==0: yr = [yr[0]-dln.valrange(yr)0.15,yr[1]+dln.valrange(yr)0.05] yr = [np.max([yr[0],-0.2]), np.min([yr[1],2.0])] ax[i].set_xlim(xr) ax[i].set_ylim(yr) # legend if i==0: snr = np.nanmedian(spec.flux/spec.err) ax[i].set_title(spec.filename) #ax[i].annotate(r'S/N=%5.1f Teff=%5.1f$\pm$%5.1f logg=%5.2f$\pm$%5.2f [Fe/H]=%5.2f$\pm$%5.2f Vrel=%5.2f$\pm$%5.2f chisq=%5.2f' % # (snr,out['teff'],out['tefferr'],out['logg'],out['loggerr'],out['feh'],out['feherr'],out['vrel'],out['vrelerr'],out['chisq']), # xy=(np.mean(xr), yr[0]+dln.valrange(yr)*0.05),ha='center') plt.savefig(figfile,bbox_inches='tight') plt.close(fig) if verbose is True: print('Figure saved to '+figfile) def dopvrot_lsq(spec,models=None,initpar=None,verbose=False,logger=None): """ Least Squares fitting with forward modeling of the spectrum. Parameters ---------- spec : Spec1D object The observed spectrum to match. models : list of Cannon models, optional A list of Cannon models to use. The default is to load all of the Cannon models in the data/ directory and use those. initpar : numpy array, optional Initial estimate for [teff, logg, feh, RV, vsini], optional. verbose : bool, optional Verbose output of the various steps. This is False by default. Returns ------- out : numpy structured array The output structured array of the final derived RVs, stellar parameters and errors. bmodel : Spec1D object The best-fitting Cannon model spectrum (as Spec1D object). Example ------- .. code-block:: python out, bmodel = fit_lsq(spec) """ if logger is None: logger = dln.basiclogger() # Load and prepare the Cannon models #------------------------------------------- if models is None: models = cannon.models.copy() models.prepare(spec) # Get initial estimates if initpar is None: initpar = np.array([6000.0, 2.5, -0.5, 0.0, 0.0]) initpar =	np.array(initpar)	numpy.array
# Licensed under a 3-clause BSD style license - see LICENSE.rst """ Utilities to generate toymodel (fake) reconstruction inputs for testing purposes. Examples: .. code-block:: python >>> from ctapipe.instrument import CameraGeometry >>> geom = CameraGeometry.make_rectangular(20, 20) >>> showermodel = Gaussian(x=0.25 * u.m, y=0.0 * u.m, length=0.1 * u.m, width=0.02 * u.m, psi='40d') >>> image, signal, noise = showermodel.generate_image(geom, intensity=1000) >>> print(image.shape) (400,) """ import numpy as np from ctapipe.utils import linalg from ctapipe.image.hillas import camera_to_shower_coordinates import astropy.units as u from astropy.coordinates import Angle from scipy.stats import multivariate_normal, skewnorm, norm from scipy.ndimage import convolve1d from abc import ABCMeta, abstractmethod __all__ = [ "WaveformModel", "Gaussian", "SkewedGaussian", "ImageModel", "obtain_time_image", ] @u.quantity_input( x=u.m, y=u.m, centroid_x=u.m, centroid_y=u.m, psi=u.deg, time_gradient=u.ns / u.m, time_intercept=u.ns, ) def obtain_time_image(x, y, centroid_x, centroid_y, psi, time_gradient, time_intercept): """Create a pulse time image for a toymodel shower. Assumes the time development occurs only along the longitudinal (major) axis of the shower, and scales linearly with distance along the axis. Parameters ---------- x : u.Quantity[length] X camera coordinate to evaluate the time at. Usually the array of pixel X positions y : u.Quantity[length] Y camera coordinate to evaluate the time at. Usually the array of pixel Y positions centroid_x : u.Quantity[length] X camera coordinate for the centroid of the shower centroid_y : u.Quantity[length] Y camera coordinate for the centroid of the shower psi : convertible to `astropy.coordinates.Angle` rotation angle about the centroid (0=x-axis) time_gradient : u.Quantity[time/length] Rate at which the time changes with distance along the shower axis time_intercept : u.Quantity[time] Pulse time at the shower centroid Returns ------- float or ndarray Pulse time in nanoseconds at (x, y) """ longitudinal, _ = camera_to_shower_coordinates(x, y, centroid_x, centroid_y, psi) longitudinal_m = longitudinal.to_value(u.m) time_gradient_ns_m = time_gradient.to_value(u.ns / u.m) time_intercept_ns = time_intercept.to_value(u.ns) return longitudinal_m * time_gradient_ns_m + time_intercept_ns class WaveformModel: @u.quantity_input(reference_pulse_sample_width=u.ns, sample_width=u.ns) def __init__(self, reference_pulse, reference_pulse_sample_width, sample_width): """Generate a toy model waveform using the reference pulse shape of a camera. Useful for testing image extraction algorithms. Does not include the electronic noise and the Excess Noise Factor of the photosensor, and therefore should not be used to make charge resolution conclusions about a camera. Parameters ---------- reference_pulse_sample_width : u.Quantity[time] Sample width of the reference pulse shape reference_pulse : ndarray Reference pulse shape sample_width : u.Quantity[time] Sample width of the waveform """ self.upsampling = 10 reference_pulse_sample_width = reference_pulse_sample_width.to_value(u.ns) sample_width_ns = sample_width.to_value(u.ns) ref_max_sample = reference_pulse.size * reference_pulse_sample_width reference_pulse_x = np.arange(0, ref_max_sample, reference_pulse_sample_width) self.ref_width_ns = sample_width_ns / self.upsampling self.ref_interp_x = np.arange(0, reference_pulse_x.max(), self.ref_width_ns) self.ref_interp_y = np.interp( self.ref_interp_x, reference_pulse_x, reference_pulse ) self.ref_interp_y /= self.ref_interp_y.sum() * self.ref_width_ns self.origin = self.ref_interp_y.argmax() - self.ref_interp_y.size // 2 def get_waveform(self, charge, time, n_samples): """Obtain the waveform toy model. Parameters ---------- charge : ndarray Amount of charge in each pixel Shape: (n_pixels) time : ndarray The signal time in the waveform in nanoseconds Shape: (n_pixels) n_samples : int Number of samples in the waveform Returns ------- waveform : ndarray Toy model waveform Shape (n_pixels, n_samples) """ n_pixels = charge.size n_upsampled_samples = n_samples * self.upsampling readout = np.zeros((n_pixels, n_upsampled_samples)) sample = (time / self.ref_width_ns).astype(np.int) outofrange = (sample < 0) \| (sample >= n_upsampled_samples) sample[outofrange] = 0 charge[outofrange] = 0 readout[np.arange(n_pixels), sample] = charge convolved = convolve1d( readout, self.ref_interp_y, mode="constant", origin=self.origin ) sampled = ( convolved.reshape( (n_pixels, convolved.shape[-1] // self.upsampling, self.upsampling) ).sum(-1) * self.ref_width_ns # Waveform units: p.e. ) return sampled @classmethod def from_camera_readout(cls, readout, gain_channel=0): """Create class from a `ctapipe.instrument.CameraReadout`. Parameters ---------- readout : `ctapipe.instrument.CameraReadout` gain_channel : int The reference pulse gain channel to use Returns ------- WaveformModel """ return cls( readout.reference_pulse_shape[gain_channel], readout.reference_pulse_sample_width, (1 / readout.sampling_rate).to(u.ns), ) class ImageModel(metaclass=ABCMeta): @u.quantity_input(x=u.m, y=u.m) @abstractmethod def pdf(self, x, y): """Probability density function. """ def generate_image(self, camera, intensity=50, nsb_level_pe=20): """Generate a randomized DL1 shower image. For the signal, poisson random numbers are drawn from the expected signal distribution for each pixel. For the background, for each pixel a poisson random number if drawn with mean `nsb_level_pe`. Parameters ---------- camera : `ctapipe.instrument.CameraGeometry` camera geometry object intensity : int Total number of photo electrons to generate nsb_level_pe : type level of NSB/pedestal in photo-electrons Returns ------- image: array with length n_pixels containing the image signal: only the signal part of image noise: only the noise part of image """ expected_signal = self.expected_signal(camera, intensity) signal = np.random.poisson(expected_signal) noise = np.random.poisson(nsb_level_pe, size=signal.shape) image = (signal + noise) - np.mean(noise) return image, signal, noise def expected_signal(self, camera, intensity): """Expected signal in each pixel for the given camera and total intensity. Parameters ---------- camera: `ctapipe.instrument.CameraGeometry` camera geometry object intensity: int Total number of expected photo electrons Returns ------- image: array with length n_pixels containing the image """ pdf = self.pdf(camera.pix_x, camera.pix_y) return pdf * intensity * camera.pix_area.value class Gaussian(ImageModel): @u.quantity_input(x=u.m, y=u.m, length=u.m, width=u.m) def __init__(self, x, y, length, width, psi): """Create 2D Gaussian model for a shower image in a camera. Parameters ---------- centroid : u.Quantity[length, shape=(2, )] position of the centroid of the shower in camera coordinates width: u.Quantity[length] width of shower (minor axis) length: u.Quantity[length] length of shower (major axis) psi : convertable to `astropy.coordinates.Angle` rotation angle about the centroid (0=x-axis) Returns ------- a `scipy.stats` object """ self.x = x self.y = y self.width = width self.length = length self.psi = psi @u.quantity_input(x=u.m, y=u.m) def pdf(self, x, y): """2d probability for photon electrons in the camera plane""" aligned_covariance = np.array( [[self.length.to_value(u.m) 2, 0], [0, self.width.to_value(u.m) 2]] ) # rotate by psi angle: C' = R C R+ rotation = linalg.rotation_matrix_2d(self.psi) rotated_covariance = rotation @ aligned_covariance @ rotation.T return multivariate_normal( mean=[self.x.to_value(u.m), self.y.to_value(u.m)], cov=rotated_covariance, ).pdf(np.column_stack([x.to_value(u.m), y.to_value(u.m)])) class SkewedGaussian(ImageModel): """A shower image that has a skewness along the major axis. """ @u.quantity_input(x=u.m, y=u.m, length=u.m, width=u.m) def __init__(self, x, y, length, width, psi, skewness): """Create 2D skewed Gaussian model for a shower image in a camera. Skewness is only applied along the main shower axis. See https://en.wikipedia.org/wiki/Skew_normal_distribution and https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skewnorm.html for details. Parameters ---------- centroid : u.Quantity[length, shape=(2, )] position of the centroid of the shower in camera coordinates width: u.Quantity[length] width of shower (minor axis) length: u.Quantity[length] length of shower (major axis) psi : convertable to `astropy.coordinates.Angle` rotation angle about the centroid (0=x-axis) Returns ------- a `scipy.stats` object """ self.x = x self.y = y self.width = width self.length = length self.psi = psi self.skewness = skewness def _moments_to_parameters(self): """Returns loc and scale from mean, std and skewnewss.""" # see https://en.wikipedia.org/wiki/Skew_normal_distribution#Estimation skew23 =	np.abs(self.skewness)	numpy.abs
# Note that we test the main astropy.wcs.WCS class directly rather than testing # the mix-in class on its own (since it's not functional without being used as # a mix-in) import warnings from packaging.version import Version import numpy as np import pytest from numpy.testing import assert_equal, assert_allclose from itertools import product from astropy import units as u from astropy.time import Time from astropy.tests.helper import assert_quantity_allclose from astropy.units import Quantity from astropy.coordinates import ICRS, FK5, Galactic, SkyCoord, SpectralCoord, ITRS, EarthLocation from astropy.io.fits import Header from astropy.io.fits.verify import VerifyWarning from astropy.units.core import UnitsWarning from astropy.utils.data import get_pkg_data_filename from astropy.wcs.wcs import WCS, FITSFixedWarning, Sip, NoConvergence from astropy.wcs.wcsapi.fitswcs import custom_ctype_to_ucd_mapping, VELOCITY_FRAMES from astropy.wcs._wcs import __version__ as wcsver from astropy.utils import iers from astropy.utils.exceptions import AstropyUserWarning ############################################################################### # The following example is the simplest WCS with default values ############################################################################### WCS_EMPTY = WCS(naxis=1) WCS_EMPTY.wcs.crpix = [1] def test_empty(): wcs = WCS_EMPTY # Low-level API assert wcs.pixel_n_dim == 1 assert wcs.world_n_dim == 1 assert wcs.array_shape is None assert wcs.pixel_shape is None assert wcs.world_axis_physical_types == [None] assert wcs.world_axis_units == [''] assert wcs.pixel_axis_names == [''] assert wcs.world_axis_names == [''] assert_equal(wcs.axis_correlation_matrix, True) assert wcs.world_axis_object_components == [('world', 0, 'value')] assert wcs.world_axis_object_classes['world'][0] is Quantity assert wcs.world_axis_object_classes['world'][1] == () assert wcs.world_axis_object_classes['world'][2]['unit'] is u.one assert_allclose(wcs.pixel_to_world_values(29), 29) assert_allclose(wcs.array_index_to_world_values(29), 29) assert np.ndim(wcs.pixel_to_world_values(29)) == 0 assert np.ndim(wcs.array_index_to_world_values(29)) == 0 assert_allclose(wcs.world_to_pixel_values(29), 29) assert_equal(wcs.world_to_array_index_values(29), (29,)) assert np.ndim(wcs.world_to_pixel_values(29)) == 0 assert np.ndim(wcs.world_to_array_index_values(29)) == 0 # High-level API coord = wcs.pixel_to_world(29) assert_quantity_allclose(coord, 29 * u.one) assert np.ndim(coord) == 0 coord = wcs.array_index_to_world(29) assert_quantity_allclose(coord, 29 * u.one) assert np.ndim(coord) == 0 coord = 15 * u.one x = wcs.world_to_pixel(coord) assert_allclose(x, 15.) assert np.ndim(x) == 0 i = wcs.world_to_array_index(coord) assert_equal(i, 15) assert np.ndim(i) == 0 ############################################################################### # The following example is a simple 2D image with celestial coordinates ############################################################################### HEADER_SIMPLE_CELESTIAL = """ WCSAXES = 2 CTYPE1 = RA---TAN CTYPE2 = DEC--TAN CRVAL1 = 10 CRVAL2 = 20 CRPIX1 = 30 CRPIX2 = 40 CDELT1 = -0.1 CDELT2 = 0.1 CROTA2 = 0. CUNIT1 = deg CUNIT2 = deg """ with warnings.catch_warnings(): warnings.simplefilter('ignore', VerifyWarning) WCS_SIMPLE_CELESTIAL = WCS(Header.fromstring( HEADER_SIMPLE_CELESTIAL, sep='\n')) def test_simple_celestial(): wcs = WCS_SIMPLE_CELESTIAL # Low-level API assert wcs.pixel_n_dim == 2 assert wcs.world_n_dim == 2 assert wcs.array_shape is None assert wcs.pixel_shape is None assert wcs.world_axis_physical_types == ['pos.eq.ra', 'pos.eq.dec'] assert wcs.world_axis_units == ['deg', 'deg'] assert wcs.pixel_axis_names == ['', ''] assert wcs.world_axis_names == ['', ''] assert_equal(wcs.axis_correlation_matrix, True) assert wcs.world_axis_object_components == [('celestial', 0, 'spherical.lon.degree'), ('celestial', 1, 'spherical.lat.degree')] assert wcs.world_axis_object_classes['celestial'][0] is SkyCoord assert wcs.world_axis_object_classes['celestial'][1] == () assert isinstance(wcs.world_axis_object_classes['celestial'][2]['frame'], ICRS) assert wcs.world_axis_object_classes['celestial'][2]['unit'] is u.deg assert_allclose(wcs.pixel_to_world_values(29, 39), (10, 20)) assert_allclose(wcs.array_index_to_world_values(39, 29), (10, 20)) assert_allclose(wcs.world_to_pixel_values(10, 20), (29., 39.)) assert_equal(wcs.world_to_array_index_values(10, 20), (39, 29)) # High-level API coord = wcs.pixel_to_world(29, 39) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, ICRS) assert_allclose(coord.ra.deg, 10) assert_allclose(coord.dec.deg, 20) coord = wcs.array_index_to_world(39, 29) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, ICRS) assert_allclose(coord.ra.deg, 10) assert_allclose(coord.dec.deg, 20) coord = SkyCoord(10, 20, unit='deg', frame='icrs') x, y = wcs.world_to_pixel(coord) assert_allclose(x, 29.) assert_allclose(y, 39.) i, j = wcs.world_to_array_index(coord) assert_equal(i, 39) assert_equal(j, 29) # Check that if the coordinates are passed in a different frame things still # work properly coord_galactic = coord.galactic x, y = wcs.world_to_pixel(coord_galactic) assert_allclose(x, 29.) assert_allclose(y, 39.) i, j = wcs.world_to_array_index(coord_galactic) assert_equal(i, 39) assert_equal(j, 29) # Check that we can actually index the array data = np.arange(3600).reshape((60, 60)) coord = SkyCoord(10, 20, unit='deg', frame='icrs') index = wcs.world_to_array_index(coord) assert_equal(data[index], 2369) coord = SkyCoord([10, 12], [20, 22], unit='deg', frame='icrs') index = wcs.world_to_array_index(coord) assert_equal(data[index], [2369, 3550]) ############################################################################### # The following example is a spectral cube with axes in an unusual order ############################################################################### HEADER_SPECTRAL_CUBE = """ WCSAXES = 3 CTYPE1 = GLAT-CAR CTYPE2 = FREQ CTYPE3 = GLON-CAR CNAME1 = Latitude CNAME2 = Frequency CNAME3 = Longitude CRVAL1 = 10 CRVAL2 = 20 CRVAL3 = 25 CRPIX1 = 30 CRPIX2 = 40 CRPIX3 = 45 CDELT1 = -0.1 CDELT2 = 0.5 CDELT3 = 0.1 CUNIT1 = deg CUNIT2 = Hz CUNIT3 = deg """ with warnings.catch_warnings(): warnings.simplefilter('ignore', VerifyWarning) WCS_SPECTRAL_CUBE = WCS(Header.fromstring(HEADER_SPECTRAL_CUBE, sep='\n')) def test_spectral_cube(): # Spectral cube with a weird axis ordering wcs = WCS_SPECTRAL_CUBE # Low-level API assert wcs.pixel_n_dim == 3 assert wcs.world_n_dim == 3 assert wcs.array_shape is None assert wcs.pixel_shape is None assert wcs.world_axis_physical_types == ['pos.galactic.lat', 'em.freq', 'pos.galactic.lon'] assert wcs.world_axis_units == ['deg', 'Hz', 'deg'] assert wcs.pixel_axis_names == ['', '', ''] assert wcs.world_axis_names == ['Latitude', 'Frequency', 'Longitude'] assert_equal(wcs.axis_correlation_matrix, [[True, False, True], [False, True, False], [True, False, True]]) assert len(wcs.world_axis_object_components) == 3 assert wcs.world_axis_object_components[0] == ('celestial', 1, 'spherical.lat.degree') assert wcs.world_axis_object_components[1][:2] == ('spectral', 0) assert wcs.world_axis_object_components[2] == ('celestial', 0, 'spherical.lon.degree') assert wcs.world_axis_object_classes['celestial'][0] is SkyCoord assert wcs.world_axis_object_classes['celestial'][1] == () assert isinstance(wcs.world_axis_object_classes['celestial'][2]['frame'], Galactic) assert wcs.world_axis_object_classes['celestial'][2]['unit'] is u.deg assert wcs.world_axis_object_classes['spectral'][0] is Quantity assert wcs.world_axis_object_classes['spectral'][1] == () assert wcs.world_axis_object_classes['spectral'][2] == {} assert_allclose(wcs.pixel_to_world_values(29, 39, 44), (10, 20, 25)) assert_allclose(wcs.array_index_to_world_values(44, 39, 29), (10, 20, 25)) assert_allclose(wcs.world_to_pixel_values(10, 20, 25), (29., 39., 44.)) assert_equal(wcs.world_to_array_index_values(10, 20, 25), (44, 39, 29)) # High-level API coord, spec = wcs.pixel_to_world(29, 39, 44) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, Galactic) assert_allclose(coord.l.deg, 25) assert_allclose(coord.b.deg, 10) assert isinstance(spec, SpectralCoord) assert_allclose(spec.to_value(u.Hz), 20) coord, spec = wcs.array_index_to_world(44, 39, 29) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, Galactic) assert_allclose(coord.l.deg, 25) assert_allclose(coord.b.deg, 10) assert isinstance(spec, SpectralCoord) assert_allclose(spec.to_value(u.Hz), 20) coord = SkyCoord(25, 10, unit='deg', frame='galactic') spec = 20 * u.Hz with pytest.warns(AstropyUserWarning, match='No observer defined on WCS'): x, y, z = wcs.world_to_pixel(coord, spec) assert_allclose(x, 29.) assert_allclose(y, 39.) assert_allclose(z, 44.) # Order of world coordinates shouldn't matter with pytest.warns(AstropyUserWarning, match='No observer defined on WCS'): x, y, z = wcs.world_to_pixel(spec, coord) assert_allclose(x, 29.) assert_allclose(y, 39.) assert_allclose(z, 44.) with pytest.warns(AstropyUserWarning, match='No observer defined on WCS'): i, j, k = wcs.world_to_array_index(coord, spec) assert_equal(i, 44) assert_equal(j, 39) assert_equal(k, 29) # Order of world coordinates shouldn't matter with pytest.warns(AstropyUserWarning, match='No observer defined on WCS'): i, j, k = wcs.world_to_array_index(spec, coord) assert_equal(i, 44) assert_equal(j, 39) assert_equal(k, 29) HEADER_SPECTRAL_CUBE_NONALIGNED = HEADER_SPECTRAL_CUBE.strip() + '\n' + """ PC2_3 = -0.5 PC3_2 = +0.5 """ with warnings.catch_warnings(): warnings.simplefilter('ignore', VerifyWarning) WCS_SPECTRAL_CUBE_NONALIGNED = WCS(Header.fromstring( HEADER_SPECTRAL_CUBE_NONALIGNED, sep='\n')) def test_spectral_cube_nonaligned(): # Make sure that correlation matrix gets adjusted if there are non-identity # CD matrix terms. wcs = WCS_SPECTRAL_CUBE_NONALIGNED assert wcs.world_axis_physical_types == ['pos.galactic.lat', 'em.freq', 'pos.galactic.lon'] assert wcs.world_axis_units == ['deg', 'Hz', 'deg'] assert wcs.pixel_axis_names == ['', '', ''] assert wcs.world_axis_names == ['Latitude', 'Frequency', 'Longitude'] assert_equal(wcs.axis_correlation_matrix, [[True, True, True], [False, True, True], [True, True, True]]) # NOTE: we check world_axis_object_components and world_axis_object_classes # again here because in the past this failed when non-aligned axes were # present, so this serves as a regression test. assert len(wcs.world_axis_object_components) == 3 assert wcs.world_axis_object_components[0] == ('celestial', 1, 'spherical.lat.degree') assert wcs.world_axis_object_components[1][:2] == ('spectral', 0) assert wcs.world_axis_object_components[2] == ('celestial', 0, 'spherical.lon.degree') assert wcs.world_axis_object_classes['celestial'][0] is SkyCoord assert wcs.world_axis_object_classes['celestial'][1] == () assert isinstance(wcs.world_axis_object_classes['celestial'][2]['frame'], Galactic) assert wcs.world_axis_object_classes['celestial'][2]['unit'] is u.deg assert wcs.world_axis_object_classes['spectral'][0] is Quantity assert wcs.world_axis_object_classes['spectral'][1] == () assert wcs.world_axis_object_classes['spectral'][2] == {} ############################################################################### # The following example is from Rots et al (2015), Table 5. It represents a # cube with two spatial dimensions and one time dimension ############################################################################### HEADER_TIME_CUBE = """ SIMPLE = T / Fits standard BITPIX = -32 / Bits per pixel NAXIS = 3 / Number of axes NAXIS1 = 2048 / Axis length NAXIS2 = 2048 / Axis length NAXIS3 = 11 / Axis length DATE = '2008-10-28T14:39:06' / Date FITS file was generated OBJECT = '2008 TC3' / Name of the object observed EXPTIME = 1.0011 / Integration time MJD-OBS = 54746.02749237 / Obs start DATE-OBS= '2008-10-07T00:39:35.3342' / Observing date TELESCOP= 'VISTA' / ESO Telescope Name INSTRUME= 'VIRCAM' / Instrument used. TIMESYS = 'UTC' / From Observatory Time System TREFPOS = 'TOPOCENT' / Topocentric MJDREF = 54746.0 / Time reference point in MJD RADESYS = 'ICRS' / Not equinoctal CTYPE2 = 'RA---ZPN' / Zenithal Polynomial Projection CRVAL2 = 2.01824372640628 / RA at ref pixel CUNIT2 = 'deg' / Angles are degrees always CRPIX2 = 2956.6 / Pixel coordinate at ref point CTYPE1 = 'DEC--ZPN' / Zenithal Polynomial Projection CRVAL1 = 14.8289418840003 / Dec at ref pixel CUNIT1 = 'deg' / Angles are degrees always CRPIX1 = -448.2 / Pixel coordinate at ref point CTYPE3 = 'UTC' / linear time (UTC) CRVAL3 = 2375.341 / Relative time of first frame CUNIT3 = 's' / Time unit CRPIX3 = 1.0 / Pixel coordinate at ref point CTYPE3A = 'TT' / alternative linear time (TT) CRVAL3A = 2440.525 / Relative time of first frame CUNIT3A = 's' / Time unit CRPIX3A = 1.0 / Pixel coordinate at ref point OBSGEO-B= -24.6157 / [deg] Tel geodetic latitute (=North)+ OBSGEO-L= -70.3976 / [deg] Tel geodetic longitude (=East)+ OBSGEO-H= 2530.0000 / [m] Tel height above reference ellipsoid CRDER3 = 0.0819 / random error in timings from fit CSYER3 = 0.0100 / absolute time error PC1_1 = 0.999999971570892 / WCS transform matrix element PC1_2 = 0.000238449608932 / WCS transform matrix element PC2_1 = -0.000621542859395 / WCS transform matrix element PC2_2 = 0.999999806842218 / WCS transform matrix element CDELT1 = -9.48575432499806E-5 / Axis scale at reference point CDELT2 = 9.48683176211164E-5 / Axis scale at reference point CDELT3 = 13.3629 / Axis scale at reference point PV1_1 = 1. / ZPN linear term PV1_3 = 42. / ZPN cubic term """ with warnings.catch_warnings(): warnings.simplefilter('ignore', (VerifyWarning, FITSFixedWarning)) WCS_TIME_CUBE = WCS(Header.fromstring(HEADER_TIME_CUBE, sep='\n')) def test_time_cube(): # Spectral cube with a weird axis ordering wcs = WCS_TIME_CUBE assert wcs.pixel_n_dim == 3 assert wcs.world_n_dim == 3 assert wcs.array_shape == (11, 2048, 2048) assert wcs.pixel_shape == (2048, 2048, 11) assert wcs.world_axis_physical_types == ['pos.eq.dec', 'pos.eq.ra', 'time'] assert wcs.world_axis_units == ['deg', 'deg', 's'] assert wcs.pixel_axis_names == ['', '', ''] assert wcs.world_axis_names == ['', '', ''] assert_equal(wcs.axis_correlation_matrix, [[True, True, False], [True, True, False], [False, False, True]]) components = wcs.world_axis_object_components assert components[0] == ('celestial', 1, 'spherical.lat.degree') assert components[1] == ('celestial', 0, 'spherical.lon.degree') assert components[2][:2] == ('time', 0) assert callable(components[2][2]) assert wcs.world_axis_object_classes['celestial'][0] is SkyCoord assert wcs.world_axis_object_classes['celestial'][1] == () assert isinstance(wcs.world_axis_object_classes['celestial'][2]['frame'], ICRS) assert wcs.world_axis_object_classes['celestial'][2]['unit'] is u.deg assert wcs.world_axis_object_classes['time'][0] is Time assert wcs.world_axis_object_classes['time'][1] == () assert wcs.world_axis_object_classes['time'][2] == {} assert callable(wcs.world_axis_object_classes['time'][3]) assert_allclose(wcs.pixel_to_world_values(-449.2, 2955.6, 0), (14.8289418840003, 2.01824372640628, 2375.341)) assert_allclose(wcs.array_index_to_world_values(0, 2955.6, -449.2), (14.8289418840003, 2.01824372640628, 2375.341)) assert_allclose(wcs.world_to_pixel_values(14.8289418840003, 2.01824372640628, 2375.341), (-449.2, 2955.6, 0)) assert_equal(wcs.world_to_array_index_values(14.8289418840003, 2.01824372640628, 2375.341), (0, 2956, -449)) # High-level API coord, time = wcs.pixel_to_world(29, 39, 44) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, ICRS) assert_allclose(coord.ra.deg, 1.7323356692202325) assert_allclose(coord.dec.deg, 14.783516054817797) assert isinstance(time, Time) assert_allclose(time.mjd, 54746.03429755324) coord, time = wcs.array_index_to_world(44, 39, 29) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, ICRS) assert_allclose(coord.ra.deg, 1.7323356692202325)	assert_allclose(coord.dec.deg, 14.783516054817797)	numpy.testing.assert_allclose
""" Data preparation file """ import numpy as np import pandas as pd def clean_string(string): return ''.join(e for e in string if e.isalnum()) def reverse_dict(d): new_d = {} for k,i in d.items(): new_d[i] = k return new_d def mapping(files): """ Creates a unique index for ever entity and relation. """ E = set() R = set() for filename in files: with open(filename,'r') as f: for line in f: s,p,o = line.split() E.add(s) E.add(o) R.add(p) E_mapping = {e:i for i,e in enumerate(E)} R_mapping = {e:i for i,e in enumerate(R)} return E_mapping, R_mapping def prep_data(filename): """ Prep data without labels """ sub = [] obj = [] pred = [] with open(filename, 'r') as f: for l in f: s,p,o = l.split() sub.append(s.strip()) obj.append(o.strip()) pred.append(p.strip()) return sub, obj, pred def class_distribution(filename, R_mapping): """ Return the a priori probability for each class. """ _, _, pred = prep_data(filename) labels = np.asarray([R_mapping[i] for i in pred]) unique, counts =	np.unique(labels, return_counts=True)	numpy.unique
#!/opt/anaconda/bin/python # -- coding: utf-8 -- # Unfortunately the `which` way of calling python can't accept command-line arguments. """ Created on Mon Nov 03 16:13:48 2014 @author: <NAME> @email: <EMAIL> OR <EMAIL> A selection of alignment routines designed for registering and summing stacks of images or diffraction patterns in the field of electron microscopy. """ from __future__ import division, print_function, absolute_import, unicode_literals import numpy as np if np.version.version.split('.')[1] == 7: print( "WARNING: NUMPY VERSION 1.7 DETECTED, ZORRO IS DESIGNED FOR >1.10" ) print( "CHECK YOUR ENVIRONMENT VARIABLES TO SEE IF EMAN2 HAS HIJACKED YOUR PYTHON DISTRIBUTION" ) import numexprz as nz # Now see which numexpr we have, by the dtype of float (whether it casts or not) try: # Now see which numexpr we have, by the dtype of float (whether it casts or not) tdata = np.complex64( 1.0 + 2.0j ) fftw_dtype = nz.evaluate( 'tdata + tdata' ).dtype float_dtype = nz.evaluate( 'real(tdata+tdata)' ).dtype except: fftw_dtype = 'complex128' float_dtype = 'float64' import scipy.optimize import scipy.ndimage import scipy.stats import time try: import ConfigParser as configparser except: import configparser # Python 3 # Here we have to play some games depending on where the file was called from # with the use of absolute_import # print( "__name__ of zorro: " + str(__name__) ) try: import zorro_util as util import zorro_plotting as plot except ImportError: from . import zorro_util as util from . import zorro_plotting as plot import mrcz import os, os.path, tempfile, sys import subprocess # Should we disable Multiprocessing on Windows due to general bugginess in the module? import multiprocessing as mp try: import pyfftw except: print( "Zorro did not find pyFFTW package: get it at https://pypi.python.org/pypi/pyFFTW" ) try: import tables except: print( "Zorro did not find pyTables installation for HDF5 file support" ) import matplotlib.pyplot as plt # Numpy.pad is bad at dealing with interpreted strings if sys.version_info >= (3,0): symmetricPad = u'symmetric' constantPad = u'constant' else: symmetricPad = b'symmetric' constantPad = b'constant' #### OBJECT-ORIENTED INTERFACE #### class ImageRegistrator(object): # Should be able to handle differences in translation, rotation, and scaling # between images def __init__( self ): # Declare class members self.verbose = 0 self.umask = 2 # Meta-information for processing, not saved in configuration files. self.METApriority = 0.0 self.METAstatus = u'new' self.METAmtime = 0.0 self.METAsize = 0 self.xcorrMode = 'zorro' # 'zorro', 'unblur v1.02', 'motioncorr v2.1' # FFTW_PATIENT is bugged for powers of 2, so use FFTW_MEASURE as default self.fftw_effort = u"FFTW_MEASURE" # TODO: change this to drop into cachePath self.n_threads = nz.nthreads # Number of cores to limit FFTW to, if None uses all cores self.cachePath = tempfile.gettempdir() # CALIBRATIONS self.pixelsize = None # Typically we use nanometers, the same units as Digital Micrograph self.voltage = 300.0 # Accelerating voltage, kV self.C3 = 2.7 # Spherical aberration of objective, mm self.gain = None self.detectorPixelSize = None # Physical dimensions of detector pixel (5 um for K2) # Timings self.bench = {} # Dict holds various benchmark times for the code self.saveC = False # Save the cross-correlation within +/- maxShift # INFORMATION REDUCTION # The SNR at high spatial frequencies tends to be lower due to how information transfer works, so # removing/filtering those frequencies can improve stability of the registration. YMMV, IMHO, etc. self.Brad = 512 # Gaussian low-pass applied to data before registration, units are radius in Fourier space, or equivalent point-spread function in real-space self.Bmode = u'opti' # can be a real-space Gaussian convolution, 'conv' or Fourier filter, 'fourier', or 'opti' for automatic Brad # For Bmode = 'fourier', a range of available filters can be used: gaussian, gauss_trunc, butterworth.order (order is an int), hann, hamming self.BfiltType = u'gaussian' self.fouCrop = [3072,3072] # Size of FFT in frequency-space to crop to (e.g. [2048,2048]) self.reloadData = True # Data self.images = None self.imageSum = None self.filtSum = None # Dose-filtered, Wiener-filtered, etc. representations go here self.gainRef = None # For application of gain reference in Zorro rather than Digital Micrograph/TIA/etc. self.gainInfo = { "Horizontal": True, "Vertical": True, "Diagonal":False, "GammaParams": [ 0.12035633, -1.04171635, -0.03363192, 1.03902726], } # One of None, 'dose', 'dose,background', 'dosenorm', 'gaussLP', 'gaussLP,background' # also 'hot' can be in the comma-seperated list for pre-filtering of hot pixels self.filterMode = None # Dose filt param = [dosePerFrame, critDoseA, critDoseB, critDoseC, cutoffOrder, missingStartFrame] self.doseFiltParam = [None, 0.24499, -1.6649, 2.8141, 32, 0] # for 'hot' in filterMode self.hotpixInfo = { u"logisticK":6.0, u"relax":0.925, u"maxSigma":8.0, u"psf": u"K2", u"guessHotpix":0, u"guessDeadpix":0, u"decorrOutliers":False, u"cutoffLower":-4.0, u"cutoffUpper":3.25, u"neighborPix":0 } self.FFTSum = None # If you want to use one mask, it should have dims [1,N_Y,N_X]. This is # to ensure Cythonized code can interact safely with Numpy self.incohFouMag = None # Incoherent Fourier magnitude, for CTF determination, resolution checks self.masks = None self.maskSum = None self.C = None # Results self.translations = None self.transEven = None # For even-odd tiled FRC, the half-stack translations self.transOdd = None # For even-odd tiled FRC, the half-stack translations self.velocities = None # pixel velocity, in pix/frame, to find frames that suffer from excessive drift self.rotations = None # rotations, for polar-transformed data self.scales = None # scaling, for polar-transformed data self.errorDictList = [] # A list of dictionaries of errors and such from different runs on the same data. self.trackCorrStats = False self.corrStats = None self.doLazyFRC = True self.doEvenOddFRC = False self.FRC = None # A Fourier ring correlation # Filtering # TODO: add more fine control over filtering options # CTF currently supports CTFFIND4.1 or GCTF self.CTFProgram = None # None, "ctffind4.1", or "gctf", 'ctffind4.1,sum' works on (aligned) sum, same for 'gctf,sum' self.CTFInfo = { u'DefocusU':None, u'DefocusV': None, u'DefocusAngle':None, u'CtfFigureOfMerit':None, u'FinalResolution': None, u'AmplitudeContrast':0.07, u'AdditionalPhaseShift':None, } self.CTFDiag = None # Diagnostic image from CTFFIND4.1 or GCTF # DEPRICATED ctf stuff #self.doCTF = False #self.CTF4Results = None # Micrograph number, DF1, DF2, Azimuth, Additional Phase shift, CC, and max spacing fit-to #self.CTF4Diag = None # Registration parameters self.shapePadded = [4096,4096] self.shapeOriginal = None self.shapeBinned = None self.subPixReg = 16 # fraction of a pixel to REGISTER image shift to # Subpixel alignment method: None (shifts still registered subpixally), lanczos, or fourier # lanczos is cheaper computationally and has fewer edge artifacts self.shiftMethod = u'lanczos' self.maxShift = 100 # Generally should be 1/2 distance to next lattice spacing # Pre-shift every image by that of the previous frame, useful for high-resolution where one can jump a lattice # i.e. should be used with small values for maxShift self.preShift = False # Solver weighting can be raw max correlation coeffs (None), normalized to [0,1] by the # min and max correlations ('norm'), or 'logistic' function weighted which # requires corrThres to be set. self.peakLocMode = u'interpolated' # interpolated (oversampled), or a RMS-best fit like fitlaplacian self.weightMode = u'autologistic' # autologistic, normalized, unweighted, logistic, or corr self.peaksigThres = 6.0 self.logisticK = 5.0 self.logisticNu = 0.15 self.originMode = u'centroid' # 'centroid' or None self.suppressOrigin = True # Delete the XC pixel at (0,0). Only necessary if gain reference is bad, but defaults to on. # Triangle-matrix indexing parameters self.triMode = u'diag' # Can be: tri, diag, auto, first self.startFrame = 0 self.endFrame = 0 self.diagStart = 0 # XC to neighbour frame on 0, next-nearest neighbour on +1, etc. self.diagWidth = 5 self.autoMax = 10 self.corrThres = None # Use with 'auto' mode to stop doing cross-correlations if the values drop below the threshold self.velocityThres = None # Pixel velocity threshold (pix/frame), above which to throw-out frames with too much motion blur. #### INPUT/OUTPUT #### self.files = { u"config":None, u"stack":None, u"mask":None, u"sum":None, u"align":None, u"figurePath":None, u"xc":None, u"moveRawPath":None, u"original":None, u"gainRef":None, u"stdout": None, u"automatch":None, u"rejected":None, u"compressor": None, u"clevel": 1 } #self.savePDF = False self.savePNG = True self.saveMovie = True self.doCompression = False self.compress_ext = ".bz2" #### PLOTTING #### self.plotDict = { u"imageSum":True, u"imageFirst":False, u"FFTSum":True, u"polarFFTSum":True, u"filtSum":True, u'stats': False, u"corrTriMat":False, u"peaksigTriMat": True, u"translations":True, u"pixRegError":True, u"CTFDiag":True, u"logisticWeights": True, u"FRC": True, u'Transparent': True, u'plot_dpi':144, u'image_dpi':250, u'image_cmap':u'gray', u'graph_cmap':u'gnuplot', u'fontsize':12, u'fontstyle': u'serif', u'colorbar': True, u'backend': u'Qt4Agg', u'multiprocess':True, u'show':False } pass def initDefaultFiles( self, stackName ): self.files[u'stack'] = stackName self.files[u'config'] = stackName + u".zor" stackPath, stackFront = os.path.split( stackName ) stackFront = os.path.splitext( stackFront )[0] if not 'compressor' in self.files or not bool(self.files['compressor']): mrcExt = ".mrc" mrcsExt = ".mrcs" else: mrcExt = ".mrcz" mrcsExt = ".mrcsz" self.files[u'align'] = os.path.relpath( os.path.join( u"./align", "%s_zorro_movie%s" %(stackFront, mrcsExt) ), start=stackPath ) self.files[u'sum'] = os.path.relpath( stackPath, os.path.join( u"./sum", "%s_zorro%s" %(stackFront, mrcExt) ), start=stackPath ) self.files[u'figurePath'] = os.path.relpath( os.path.join(stackPath, u"./figs"), start=stackPath ) def xcorr2_mc2_1( self, gpu_id = 0, loadResult=True, clean=True ): """ This makes an external operating system call to the Cheng's lab GPU-based B-factor multireference executable. It and CUDA libraries must be on the system path and libary path respectively. NOTE: Spyder looks loads PATH and LD_LIBRARY_PATH from .profile, not .bashrc """ dosef_cmd = util.which("dosefgpu_driftcorr") if dosef_cmd is None: print( "Error: dosefgpu_driftcorr not found in system path." ) return #tempFileHash = str(uuid.uuid4() ) # Key let's us multiprocess safely stackBase = os.path.basename( os.path.splitext( self.files['stack'] )[0] ) if self.cachePath is None: self.cachePath = "." InName = os.path.join( self.cachePath, stackBase + u"_mcIn.mrc" ) # Unfortunately these files may as well be in the working directory. OutAvName = os.path.join( self.cachePath, stackBase + u"_mcOutAv.mrc" ) OutStackName = os.path.join( self.cachePath, stackBase + u"_mcOut.mrc" ) logName = os.path.join( self.cachePath, stackBase + u"_mc.zor" ) mrcz.writeMRC( self.images, InName ) # Force binning to 1, as performance with binning is poor binning = 1 if self.Brad is not None: # Li masking is in MkPosList() in cufunc.cu (line 413) # Their r2 is normalized and mine isn't # Li has mask = exp( -0.5 * bfactor * r_norm2 ) # r_norm2 = xx/NxNx + yy/NyNy = r2 / (Nx2 + Ny2) # For non-square arrays they have a non-square (but constant frequency) filter # RAM has mask = exp( -(r/brad)2 ) # We can only get Bfactor approximately then but it's close enough for 3710x3838 bfac = 2.0 * (self.images.shape[1]2 + self.images.shape[2]2) / (self.Brad*2) print( "Using B-factor of " + str(bfac) + " for dosefgpu_driftcorr" ) else: bfac = 1000 # dosef default 'safe' bfactor for mediocre gain reference # Consider: Dosef suffers at the ends of the sequence, so make the middle frame zero drift? # align_to = np.floor( self.images.shape[0]/2 ) # This seems to cause more problems then it's worth. align_to = 0 if self.diagWidth != None: fod = self.diagWidth else: fod = 0 # Dosef can limit search to a certain box size if self.maxShift == None: maxshift = 96 else: maxshift = self.maxShift 2 if self.startFrame == None: self.startFrame = 0 if self.endFrame == None: self.endFrame = 0 motion_flags = ( " " + InName + " -gpu " + str(gpu_id) + " -nss " + str(self.startFrame) + " -nes " + str(self.endFrame) + " -fod " + str(fod) + " -bin " + str(binning) + " -bft " + str(bfac) + " -atm -" + str(align_to) + " -pbx " + str(maxshift) + " -ssc 1 -fct " + OutStackName + " -fcs " + OutAvName + " -flg " + logName ) sub = subprocess.Popen( dosef_cmd + motion_flags, shell=True ) sub.wait() self.loadMCLog( logName ) time.sleep(0.5) if bool(clean): try: os.remove(InName) except: pass try: os.remove(OutStackName) except: pass try: os.remove(OutAvName) except: pass try: os.remove(logName) except: pass def loadMCLog( self, logName ): """ Load and part a MotionCorr log from disk using regular expressions. """ import re # Parse to get the translations fhMC = open( logName ) MClog = fhMC.readlines() fhMC.close() # Number of footer lines changes with the options you use. # I would rather find Sum Frame #000 for linenumber, line in enumerate(MClog): try: test = re.findall( "Sum Frame #000", line) if bool(test): frameCount = np.int( re.findall( "\d\d\d", line )[1] ) + 1 break except: pass MClog_crop = MClog[linenumber+1:linenumber+frameCount+1] MCdrifts = np.zeros( [frameCount,2] ) for J in np.arange(0,frameCount): MCdrifts[J,:] = re.findall( r"([+-]?\d+.\d+)", MClog_crop[J] )[1:] # Zorro saves translations, motioncorr saves shifts. self.translations = -np.fliplr( MCdrifts ) if self.originMode == u'centroid': centroid = np.mean( self.translations, axis=0 ) self.translations -= centroid def xcorr2_unblur1_02( self, dosePerFrame = None, minShift = 2.0, terminationThres = 0.1, maxIteration=10, verbose=False, loadResult=True, clean=True ): """ Calls UnBlur by <NAME> Rohou using the Zorro interface. """ self.bench['unblur0'] = time.time() unblur_exename = "unblur_openmp_7_17_15.exe" if util.which( unblur_exename ) is None: print( "UnBlur not found in system path" ) return print( "Calling UnBlur for " + self.files['stack'] ) print( " written by <NAME> and <NAME>: http://grigoriefflab.janelia.org/unblur" ) print( " http://grigoriefflab.janelia.org/node/4900" ) import os try: os.umask( self.umask ) # Why is Python not using default umask from OS? except: pass if self.cachePath is None: self.cachePath = "." # Force trailing slashes onto cachePatch stackBase = os.path.basename( os.path.splitext( self.files[u'stack'] )[0] ) frcOutName = os.path.join( self.cachePath, stackBase + u"_unblur_frc.txt" ) shiftsOutName = os.path.join( self.cachePath, stackBase + u"_unblur_shifts.txt" ) outputAvName = os.path.join( self.cachePath, stackBase + u"_unblur.mrc" ) outputStackName = os.path.join( self.cachePath, stackBase + u"_unblur_movie.mrc" ) ps = self.pixelsize * 10.0 if 'dose' in self.filterMode: doDoseFilter = True if dosePerFrame == None: # We have to guesstimate the dose per frame in e/A^2 if it's not provided dosePerFrame = np.mean( self.images ) / (psps) preExposure = 0.0 if 'dosenorm' in self.filterMode: restoreNoise=True else: restoreNoise=False else: doDoseFilter = False if self.Brad is not None: # Li masking is in MkPosList() in cufunc.cu (line 413) # Their r2 is normalized and mine isn't # Li has mask = exp( -0.5 bfactor * r_norm2 ) # r_norm2 = xx/NxNx + yy/NyNy = r2 / (Nx2 + Ny2) # For non-square arrays they have a non-square (but constant frequency) filter # RAM has mask = exp( -(r/brad)2 ) # We can only get Bfactor approximately then but it's close enough for 3710x3838 bfac = 2.0 * (self.images.shape[1]2 + self.images.shape[2]2) / (self.Brad*2) print( "Using B-factor of " + str(bfac) + " for UnBlur" ) else: bfac = 1500 # dosef default 'safe' bfactor for mediocre gain reference outerShift = self.maxShift ps # RAM: I see no reason to let people change the Fourier cross masking vertFouMaskHW = 1 horzFouMaskHW = 1 try: mrcName = os.path.join( self.cachePath, stackBase + "_unblurIN.mrc" ) mrcz.writeMRC( self.images, mrcName ) except: print( "Error in exporting MRC file to UnBlur" ) return # Are there flags for unblur? Check the source code. flags = "" # Not using any flags unblurexec = ( unblur_exename + " " + flags + " << STOP_PARSING \n" + mrcName ) unblurexec = (unblurexec + "\n" + str(self.images.shape[0]) + "\n" + outputAvName + "\n" + shiftsOutName + "\n" + str(ps) + "\n" + str(doDoseFilter) ) if bool(doDoseFilter): unblurexec += "\n" + str(dosePerFrame) + "\n" + str(self.voltage) + "\n" + str(preExposure) unblurexec += ("\n yes \n" + outputStackName + "\n yes \n" + frcOutName + "\n" + str(minShift) + "\n" + str(outerShift) + "\n" + str(bfac) + "\n" + str( np.int(vertFouMaskHW) ) + "\n" + str( np.int(horzFouMaskHW) ) + "\n" + str(terminationThres) + "\n" + str(maxIteration) ) if bool(doDoseFilter): unblurexec += "\n" + str(restoreNoise) unblurexec += "\n" + str(verbose) unblurexec = unblurexec + "\nSTOP_PARSING" print( unblurexec ) sub = subprocess.Popen( unblurexec, shell=True ) sub.wait() try: # Their FRC is significantly different from mine. self.FRC = np.loadtxt(frcOutName, comments='#', skiprows=0 ) self.translations = np.loadtxt( shiftsOutName, comments='#', skiprows=0 ).transpose() # UnBlur uses Fortran ordering, so we need to swap y and x for Zorro C-ordering self.translations = np.fliplr( self.translations ) # UnBlur returns drift in Angstroms self.translations /= ps # UnBlur registers to middle frame self.translations -= self.translations[0,:] if bool( loadResult ): print( "Loading UnBlur aligned frames into ImageRegistrator.images" ) if 'dose' in self.filterMode: # TODO: WHow to get both filtered images and unfiltered? self.imageSum = mrcz.readMRC( outputAvName )[0] else: self.imageSum = mrcz.readMRC( outputAvName )[0] # TODO: We have a bit of an issue, this UnBlur movie is dose filtered... self.images = mrcz.readMRC( outputStackName )[0] except IOError: print( "UnBlur likely core-dumped, try different input parameters?" ) finally: time.sleep(0.5) # DEBUG: try and see if temporary files are deleteable now. frcOutName = os.path.join( self.cachePath, stackBase + "_unblur_frc.txt" ) shiftsOutName = os.path.join( self.cachePath, stackBase + "_unblur_shifts.txt" ) outputAvName = os.path.join( self.cachePath, stackBase + "_unblur.mrc" ) outputStackName = os.path.join( self.cachePath, stackBase + "_unblur_movie.mrc" ) pass if self.originMode == 'centroid': centroid = np.mean( self.translations, axis=0 ) self.translations -= centroid time.sleep(0.5) if bool(clean): try: os.remove( mrcName ) except: print( "Could not remove Unblur MRC input file" ) try: os.remove( frcOutName ) except: print( "Could not remove Unblur FRC file" ) try: os.remove( shiftsOutName ) except: print( "Could not remove Unblur Shifts file" ) try: os.remove( outputAvName ) except: print( "Could not remove Unblur MRC average" ) try: os.remove( outputStackName ) except: print( "Could not remove Unblur MRC stack" ) self.bench['unblur1'] = time.time() def __init_xcorrnm2( self, triIndices=None ): """ """ self.bench['xcorr0'] = time.time() shapeImage = np.array( [self.images.shape[1], self.images.shape[2]] ) self.__N = np.asarray( self.images.shape )[0] if self.preShift: print( "Warning: Preshift will break if there are skipped frames in a triIndices row." ) # Test to see if triIndices is a np.array or use self.triMode if hasattr( triIndices, "__array__" ): # np.array # Ensure triIndices is a square array of the right size if triIndices.shape[0] != self.__N or triIndices.shape[1] != self.__N: raise IndexError("triIndices is wrong size, should be of length: " + str(self.__N) ) elif triIndices is None: [xmesh, ymesh] = np.meshgrid( np.arange(0,self.__N), np.arange(0,self.__N) ) trimesh = xmesh - ymesh # Build the triMat if it wasn't passed in as an array if( self.triMode == 'first' ): print( "Correlating in template mode to first image" ) triIndices = np.ones( [1,self.__N], dtype='bool' ) triIndices[0,0] = False # Don't autocorrelate the first frame. elif( self.triMode == u'diag' ): if (self.diagWidth is None) or (self.diagWidth < 0): # For negative numbers, align the entire triangular matrix self.diagWidth = self.__N triIndices = (trimesh <= self.diagWidth + self.diagStart ) * (trimesh > self.diagStart ) print( "Correlating in diagonal mode with width " + str(self.diagWidth) ) elif( self.triMode == u'autocorr' ): triIndices = (trimesh == 0) elif( self.triMode == u'refine' ): triIndices = trimesh == 0 else: # 'tri' or 'auto' ; default is an upper triangular matrix triIndices = trimesh >= 1 pass else: raise TypeError( "Error: triIndices not recognized as valid: " + str(triIndices) ) if self.masks is None or self.masks == []: print( "Warning: No mask not recommened with MNXC-style correlation" ) self.masks = np.ones( [1,shapeImage[0],shapeImage[1]], dtype = self.images.dtype ) if( self.masks.ndim == 2 ): self.masks = np.reshape( self.masks.astype(self.images.dtype), [1,shapeImage[0],shapeImage[1]] ) # Pre-loop allocation self.__shiftsTriMat = np.zeros( [self.__N,self.__N,2], dtype=float_dtype ) # Triagonal matrix of shifts in [I,J,(y,x)] self.__corrTriMat = np.zeros( [self.__N,self.__N], dtype=float_dtype ) # Triagonal matrix of maximum correlation coefficient in [I,J] self.__peaksigTriMat = np.zeros( [self.__N,self.__N], dtype=float_dtype ) # Triagonal matrix of correlation peak contrast level self.__originTriMat= np.zeros( [self.__N,self.__N], dtype=float_dtype ) # Triagonal matrix of origin correlation coefficient in [I,J] # Make pyFFTW objects if not bool( np.any( self.fouCrop ) ): self.__tempFullframe = np.empty( shapeImage, dtype=fftw_dtype ) self.__FFT2, self.__IFFT2 = util.pyFFTWPlanner( self.__tempFullframe, wisdomFile=os.path.join( self.cachePath, "fftw_wisdom.pkl" ), effort = self.fftw_effort, n_threads=self.n_threads ) self.__shapeCropped = shapeImage self.__tempComplex = np.empty( self.__shapeCropped, dtype=fftw_dtype ) else: self.__tempFullframe = np.empty( shapeImage, dtype=fftw_dtype ) self.__FFT2, _ = util.pyFFTWPlanner( self.__tempFullframe, wisdomFile=os.path.join( self.cachePath, "fftw_wisdom.pkl" ) , effort = self.fftw_effort, n_threads=self.n_threads, doReverse=False ) # Force fouCrop to multiple of 2 self.__shapeCropped = 2 * np.floor( np.array( self.fouCrop ) / 2.0 ).astype('int') self.__tempComplex = np.empty( self.__shapeCropped, dtype=fftw_dtype ) _, self.__IFFT2 = util.pyFFTWPlanner( self.__tempComplex, wisdomFile=os.path.join( self.cachePath, "fftw_wisdom.pkl" ) , effort = self.fftw_effort, n_threads=self.n_threads, doForward=False ) self.__shapeCropped2 = (np.array( self.__shapeCropped) / 2.0).astype('int') self.__templateImageFFT = np.empty( self.__shapeCropped, dtype=fftw_dtype ) self.__templateSquaredFFT = np.empty( self.__shapeCropped, dtype=fftw_dtype ) self.__templateMaskFFT = np.empty( self.__shapeCropped, dtype=fftw_dtype ) self.__tempComplex2 = np.empty( self.__shapeCropped, dtype=fftw_dtype ) # Subpixel initialization # Ideally subPix should be a power of 2 (i.e. 2,4,8,16,32) self.__subR = 8 # Sampling range around peak of +/- subR if self.subPixReg is None: self.subPixReg = 1; if self.subPixReg > 1.0: # hannfilt = np.fft.fftshift( ram.apodization( name='hann', size=[subR2,subR2], radius=[subR,subR] ) ).astype( fftw_dtype ) # Need a forward transform that is [subR2,subR2] self.__Csub = np.empty( [self.__subR2,self.__subR2], dtype=fftw_dtype ) self.__CsubFFT = np.empty( [self.__subR2,self.__subR2], dtype=fftw_dtype ) self.__subFFT2, _ = util.pyFFTWPlanner( self.__Csub, fouMage=self.__CsubFFT, wisdomFile=os.path.join( self.cachePath, "fftw_wisdom.pkl" ) , effort = self.fftw_effort, n_threads=self.n_threads, doReverse = False ) # and reverse transform that is [subR2subPix, subR2subPix] self.__CpadFFT = np.empty( [self.__subR2self.subPixReg,self.__subR2self.subPixReg], dtype=fftw_dtype ) self.__Csub_over = np.empty( [self.__subR2self.subPixReg,self.__subR2self.subPixReg], dtype=fftw_dtype ) _, self.__subIFFT2 = util.pyFFTWPlanner( self.__CpadFFT, fouMage=self.__Csub_over, wisdomFile=os.path.join( self.cachePath, "fftw_wisdom.pkl" ) , effort = self.fftw_effort, n_threads=self.n_threads, doForward = False ) self.__maskProduct = np.zeros( self.__shapeCropped, dtype=float_dtype ) self.__normConst2 = np.float32( 1.0 / ( np.float64(self.__shapeCropped[0])np.float64(self.__shapeCropped[1]))2.0 ) self.bench['xcorr1'] = time.time() return triIndices def xcorrnm2_speckle( self, triIndices=None ): """ <NAME> <EMAIL> October 1, 2016 With data recorded automatically from SerialEM, we no long have access to the gain reference normalization step provided by Gatan. With the K2 detector, gain normalization is no longer a simple multiplication. Therefore we see additional, multiplicative (or speckle) noise in the images compared to those recorded by Gatan Microscopy Suite. Here we want to use a different approach from the Padfield algorithm, which is useful for suppressing additive noise, and In general Poisson noise should be speckle noise, especially at the dose rates commonly seen in cryo-EM. """ triIndices = self.__init_xcorrnm2( triIndices = triIndices) # Pre-compute forward FFTs (template will just be copied conjugate Fourier spectra) self.__imageFFT = np.empty( [self.__N, self.shapePadded[0], self.shapePadded[1]], dtype=fftw_dtype ) self.__autocorrHalfs = np.empty( [self.__N, self.__shapeCropped[0], self.__shapeCropped[1]], dtype=float_dtype ) currIndex = 0 self.__originC = []; self.C = [] print( "Pre-computing forward Fourier transforms and autocorrelations" ) # For even-odd and noise estimates, we often skip many rows # precompIndices = np.unique( np.vstack( [np.argwhere( np.sum( triIndices, axis=1 ) > 0 ), np.argwhere( np.sum( triIndices, axis=0 ) > 0 ) ] ) ) precompIndices = np.unique( np.vstack( [np.argwhere( np.sum( triIndices, axis=1 ) >= 0 ), np.argwhere( np.sum( triIndices, axis=0 ) >= 0 ) ] ) ) for I in precompIndices: if self.verbose >= 2: print( "Precomputing forward FFT frame: " + str(I) ) # Apply masks to images if self.masks.shape[0] == 1: masks_block = self.masks[0,:,:] images_block = self.images[I,:,:] else: masks_block = self.masks[I,:,:] images_block = self.images[I,:,:] self.__tempComplex = nz.evaluate( "masks_block images_block" ).astype( fftw_dtype ) self.__FFT2.update_arrays( self.__tempComplex, self.__imageFFT[I,:,:]); self.__FFT2.execute() print( "TODO: FOURIER CROPPING" ) # Compute autocorrelation imageFFT = self.__imageFFT[I,:,:] # Not sure if numexpr is useful for such a simple operation? self.__tempComplex = nz.evaluate( "imageFFT * conj(imageFFT)" ) self.__IFFT2.update_arrays( self.__tempComplex, self.__tempComplex2 ) tempComplex2 = self.__tempComplex2 nz.evaluate( "0.5abs(tempComplex2)", out=self.__autocorrHalfs[I,:,:] ) self.bench['xcorr2'] = time.time() ########### COMPUTE PHASE CORRELATIONS ############# print( "Starting correlation calculations, mode: " + self.triMode ) if self.triMode == u'refine': # Find FFT sum (it must be reduced by the current frame later) # FIXME: Is there some reason this might not be linear after FFT? # FIXME: is it the complex conjugate operation below??? self.__sumFFT = np.sum( self.__baseImageFFT, axis = 0 ) self.__sumSquaredFFT = np.sum( self.__baseSquaredFFT, axis = 0 ) print( "In refine" ) for I in np.arange(self.images.shape[0] - 1): # In refine mode we have to build the template on the fly from imageSum - currentImage self.__templateImageFFT = np.conj( self.__sumFFT - self.__baseImageFFT[I,:,:] ) / self.images.shape[0] self.__templateSquaredFFT = np.conj( self.__sumSquaredFFT - self.__baseSquaredFFT[I,:,:] ) / self.images.shape[0] tempComplex2 = None self.mnxc2_SPECKLE( I, I, self.__shapeCropped, refine=True ) #### Find maximum positions #### self.locatePeak( I, I ) if self.verbose: print( "Refine # " + str(I) + " shift: [%.2f"%self.__shiftsTriMat[I,I,0] + ", %.2f"%self.__shiftsTriMat[I,I,1] + "], cc: %.6f"%self.__corrTriMat[I,I] + ", peak sig: %.3f"%self.__peaksigTriMat[I,I] ) else: # For even-odd and noise estimates, we often skip many rows rowIndices = np.unique( np.argwhere( np.sum( triIndices, axis=1 ) > 0 ) ) #print( "rowIndices: " + str(rowIndices) ) for I in rowIndices: # I is the index of the template image tempComplex = self.__baseImageFFT[I,:,:] self.__templateImageFFT = nz.evaluate( "conj(tempComplex)") # Now we can start looping through base images columnIndices = np.unique( np.argwhere( triIndices[I,:] ) ) #print( "columnIndices: " + str(columnIndices) ) for J in columnIndices: ####### MNXC2 revisement with private variable to make the code more manageable. self.mnxc2_speckle( I, J, self.__shapeCropped ) #### Find maximum positions #### self.locatePeak( I, J ) if self.verbose: print( "# " + str(I) + "->" + str(J) + " shift: [%.2f"%self.__shiftsTriMat[I,J,0] + ", %.2f"%self.__shiftsTriMat[I,J,1] + "], cc: %.6f"%self.__corrTriMat[I,J] + ", peak sig: %.3f"%self.__peaksigTriMat[I,J] ) # Correlation stats is for establishing correlation scores for fixed-pattern noise. if bool( self.trackCorrStats ): self.calcCorrStats( currIndex, triIndices ) # triMode 'auto' diagonal mode if self.triMode == u'auto' and (self.__peaksigTriMat[I,J] <= self.peaksigThres or J-I >= self.autoMax): if self.verbose: print( "triMode 'auto' stopping at frame: " + str(J) ) break currIndex += 1 pass # C max position location if bool( np.any( self.fouCrop ) ): self.__shiftsTriMat[:,:,0] = self.shapePadded[0] / self.__shapeCropped[0] self.__shiftsTriMat[:,:,1] = self.shapePadded[1] / self.__shapeCropped[1] self.bench['xcorr3'] = time.time() # Pointer reference house-keeping del images_block, masks_block, imageFFT, tempComplex2 def xcorrnm2_tri( self, triIndices=None ): """ <NAME> <EMAIL> April 16, 2015 triIndices is the index locations to correlate to. If None, self.triMode is used to build one. Normally you should use self.triMode for the first iteration, and pass in a triIndice from the errorDict if you want to repeat. returns : [shiftsTriMat, corrTriMat, peaksTriMat] This is an evolution of the Padfield cross-correlation algorithm to take advantage of the Cheng multi-reference approach for cross-correlation alignment of movies. Padfield, "Masked object registration in the Fourier domain," IEEE Transactions on Image Processing 21(5) (2012): 3706-2718. <NAME> al. Nature Methods, 10 (2013): 584-590. It cross-correlates every frame to every other frame to build a triangular matrix of shifts and then does a functional minimization over the set of equations. This means the computational cost grows with a power law with the number of frames but it is more noise resistant. triIndices can be an arbitrary boolean N x N matrix of frames to correlate Alternatively it can be a string which will generate an appropriate matrix: 'tri' (default) correlates all frames to eachother 'first' is correlate to the first frame as a template 'diag' correlates to the next frame (i.e. a diagonal ) 'auto' is like diag but automatically determines when to stop based on corrcoeffThes diagWidth is for 'diag' and the number of frames to correlate each frame to, default is None, which does the entire triangular matrix diagWidth = 1 correlates to each preceding frame NOTE: only calculates FFTs up to Nyquist/2. """ triIndices = self.__init_xcorrnm2( triIndices = triIndices) if self.masks.shape[0] == 1 : # tempComplex = self.masks[0,:,:].astype( fftw_dtype ) self.__baseMaskFFT = np.empty( self.__shapeCropped, dtype=fftw_dtype ) self.__FFT2.update_arrays( self.masks[0,:,:].squeeze().astype( fftw_dtype ), self.__tempFullframe ); self.__FFT2.execute() # FFTCrop sC2 = self.__shapeCropped2 self.__baseMaskFFT[0:sC2[0],0:sC2[1]] = self.__tempFullframe[0:sC2[0],0:sC2[1]] self.__baseMaskFFT[0:sC2[0],-sC2[1]:] = self.__tempFullframe[0:sC2[0],-sC2[1]:] self.__baseMaskFFT[-sC2[0]:,0:sC2[1]] = self.__tempFullframe[-sC2[0]:,0:sC2[1]] self.__baseMaskFFT[-sC2[0]:,-sC2[1]:] = self.__tempFullframe[-sC2[0]:,-sC2[1]:] self.__templateMaskFFT = np.conj( self.__baseMaskFFT ) # maskProduct term is M1^ .* M2 templateMaskFFT = self.__templateMaskFFT; baseMaskFFT = self.__baseMaskFFT # Pointer assignment self.__tempComplex2 = nz.evaluate( "templateMaskFFT * baseMaskFFT" ) self.__IFFT2.update_arrays( self.__tempComplex2, self.__tempComplex ); self.__IFFT2.execute() tempComplex = self.__tempComplex normConst2 = self.__normConst2 self.__maskProduct = nz.evaluate( "normConst2real(tempComplex)" ) else: # Pre-allocate only self.__baseMaskFFT = np.zeros( [self.__N, self.__shapeCropped[0], self.__shapeCropped[1]], dtype=fftw_dtype ) if bool( self.maxShift ) or self.Bmode is u'fourier': if self.maxShift is None or self.preShift is True: [xmesh,ymesh] = np.meshgrid( np.arange(-self.__shapeCropped2[0], self.__shapeCropped2[0]), np.arange(-self.__shapeCropped2[1], self.__shapeCropped2[1]) ) else: [xmesh,ymesh] = np.meshgrid( np.arange(-self.maxShift, self.maxShift), np.arange(-self.maxShift, self.maxShift) ) rmesh2 = nz.evaluate( "xmeshxmesh + ymeshymesh" ) # rmesh2 = xmeshxmesh + ymeshymesh if bool( self.maxShift ): self.__mask_maxShift = ( rmesh2 < self.maxShift*2.0 ) if self.Bmode is u'fourier': self.__Bfilter = np.fft.fftshift( util.apodization( name=self.BfiltType, size=self.__shapeCropped, radius=[self.Brad,self.Brad] ) ) self.bench['xcorr1'] = time.time() # Pre-compute forward FFTs (template will just be copied conjugate Fourier spectra) self.__imageFFT = np.empty( [self.__N, self.shapePadded[0], self.shapePadded[1]], dtype=fftw_dtype ) self.__baseImageFFT = np.empty( [self.__N, self.__shapeCropped[0], self.__shapeCropped[1]], dtype=fftw_dtype ) self.__baseSquaredFFT =	np.empty( [self.__N, self.__shapeCropped[0], self.__shapeCropped[1]], dtype=fftw_dtype )	numpy.empty
import xarray as xr import numpy as np import dask.bag as db import dask.array as da from time import time from scipy.interpolate import LinearNDInterpolator from ..core import Instrument, Model from .attenuation import calc_radar_atm_attenuation from .psd import calc_mu_lambda from ..core.instrument import ureg, quantity def calc_total_reflectivity(model, detect_mask=False): """ This method calculates the total (convective + stratiform) reflectivity (Ze). Parameters ---------- model: :func:`emc2.core.Model` class The model to calculate the parameters for. detect_mask: bool True - generating a mask determining signal below noise floor. Returns ------- model: :func:`emc2.core.Model` The xarray Dataset containing the calculated radar moments. """ Ze_tot = np.where(np.isfinite(model.ds["sub_col_Ze_tot_strat"].values), 10 (model.ds["sub_col_Ze_tot_strat"].values / 10.), 0) if model.process_conv: Ze_tot = np.where(np.isfinite(model.ds["sub_col_Ze_tot_conv"].values), Ze_tot + 10 (model.ds["sub_col_Ze_tot_conv"].values / 10.), Ze_tot) model.ds['sub_col_Ze_tot'] = xr.DataArray(10 * np.log10(Ze_tot), dims=model.ds["sub_col_Ze_tot_strat"].dims) model.ds['sub_col_Ze_tot'].values = np.where(np.isinf(model.ds['sub_col_Ze_tot'].values), np.nan, model.ds['sub_col_Ze_tot'].values) model.ds['sub_col_Ze_tot'].attrs["long_name"] = \ "Total (convective + stratiform) equivalent radar reflectivity factor" model.ds['sub_col_Ze_tot'].attrs["units"] = "dBZ" if model.process_conv: model.ds['sub_col_Ze_att_tot'] = 10 * np.log10(Ze_tot * model.ds['hyd_ext_conv'].fillna(1) * model.ds[ 'hyd_ext_strat'].fillna(1) * model.ds['atm_ext'].fillna(1)) else: model.ds['sub_col_Ze_att_tot'] = 10 * np.log10(Ze_tot * model.ds['hyd_ext_strat'].fillna(1) * model.ds['atm_ext'].fillna(1)) model.ds['sub_col_Ze_att_tot'].values = np.where(np.isinf(model.ds['sub_col_Ze_att_tot'].values), np.nan, model.ds['sub_col_Ze_att_tot'].values) model.ds['sub_col_Ze_att_tot'].attrs["long_name"] = \ "Total (convective + stratiform) attenuated (hydrometeor + gaseous) equivalent radar reflectivity factor" model.ds['sub_col_Ze_att_tot'].attrs["units"] = "dBZ" model.ds["sub_col_Ze_tot"] = model.ds["sub_col_Ze_tot"].where(np.isfinite(model.ds["sub_col_Ze_tot"])) model.ds["sub_col_Ze_att_tot"] = model.ds["sub_col_Ze_att_tot"].where( np.isfinite(model.ds["sub_col_Ze_att_tot"])) model.ds["detect_mask"] = model.ds["Ze_min"] >= model.ds["sub_col_Ze_att_tot"] model.ds["detect_mask"].attrs["long_name"] = "Radar detectability mask" model.ds["detect_mask"].attrs["units"] = ("1 = radar signal below noise floor, 0 = signal detected") return model def accumulate_attenuation(model, is_conv, z_values, hyd_ext, atm_ext, OD_from_sfc=True, use_empiric_calc=False, *kwargs): """ Accumulates atmospheric and condensate radar attenuation (linear units) from TOA or the surface. Output fields are condensate and atmospheric transmittance. Parameters ---------- model: Model The model to generate the parameters for. is_conv: bool True if the cell is convective z_values: ndarray model output height array in m. hyd_ext: ndarray fwd calculated extinction due to condensate per layer (empirical - dB km^-1, m^-1 otherwise). atm_ext: ndarray atmospheric attenuation per layer (dB/km). OD_from_sfc: bool If True, then calculate optical depth from the surface. use_empirical_calc: bool When True using empirical relations from literature for the fwd calculations (the cloud fraction still follows the scheme logic set by use_rad_logic). Returns ------- model: :func:`emc2.core.Model` The model with the added simulated lidar parameters. """ if is_conv: cloud_str = "conv" else: cloud_str = "strat" if not use_empiric_calc: hyd_ext = hyd_ext 1e3 if OD_from_sfc: OD_str = "model layer base" else: OD_str = "model layer top" n_subcolumns = model.num_subcolumns Dims = model.ds["%s_q_subcolumns_cl" % cloud_str].shape if OD_from_sfc: dz = np.diff(z_values / 1e3, axis=1, prepend=0.) hyd_ext = np.cumsum( np.tile(dz, (n_subcolumns, 1, 1)) * np.concatenate((np.zeros(Dims[:2] + (1,)), hyd_ext[:, :, :-1]), axis=2), axis=2) atm_ext = np.cumsum(dz * np.concatenate((np.zeros((Dims[1],) + (1,)), atm_ext[:, :-1]), axis=1), axis=1) else: dz = np.diff(z_values / 1e3, axis=1, append=0.) hyd_ext = np.flip( np.cumsum(np.flip(np.tile(dz, (n_subcolumns, 1, 1)) * np.concatenate((hyd_ext[:, :, 1:], np.zeros(Dims[:2] + (1,))), axis=2), axis=2), axis=2), axis=2) atm_ext = np.flip( np.cumsum(np.flip(dz * np.concatenate((atm_ext[:, 1:], np.zeros((Dims[1],) + (1,))), axis=1), axis=1), axis=1), axis=1) if use_empiric_calc: model.ds['hyd_ext_%s' % cloud_str] = xr.DataArray(10 ** (-2 * hyd_ext / 10.), dims=model.ds["%s_q_subcolumns_cl" % cloud_str].dims) else: model.ds['hyd_ext_%s' % cloud_str] = \ xr.DataArray(np.exp(-2 * hyd_ext), dims=model.ds["sub_col_Ze_tot_%s" % cloud_str].dims) model.ds['atm_ext'] = xr.DataArray(10 ** (-2 * atm_ext / 10), dims=model.ds[model.T_field].dims) model.ds['hyd_ext_%s' % cloud_str].attrs["long_name"] = \ "Two-way %s hydrometeor transmittance at %s" % (cloud_str, OD_str) model.ds['hyd_ext_%s' % cloud_str].attrs["units"] = "1" model.ds['atm_ext'].attrs["long_name"] = \ "Two-way atmospheric transmittance due to H2O and O2 at %s" % OD_str model.ds['atm_ext'].attrs["units"] = "1" return model def calc_radar_empirical(instrument, model, is_conv, p_values, t_values, z_values, atm_ext, OD_from_sfc=True, use_empiric_calc=False, hyd_types=None, *kwargs): """ Calculates the radar stratiform or convective reflectivity and attenuation in a sub-columns using empirical formulation from literature. Parameters ---------- instrument: :func:`emc2.core.Instrument` class The instrument to calculate the reflectivity parameters for. model: :func:`emc2.core.Model` class The model to calculate the parameters for. is_conv: bool True if the cell is convective p_values: ndarray model output pressure array in Pa. t_values: ndarray model output temperature array in C. z_values: ndarray model output height array in m. atm_ext: ndarray atmospheric attenuation per layer (dB/km). OD_from_sfc: bool If True, then calculate optical depth from the surface. hyd_types: list or None list of hydrometeor names to include in calcuation. using default Model subclass types if None. Additonal keyword arguments are passed into :py:func:`emc2.simulator.lidar_moments.accumulate_attenuation`. Returns ------- model: :func:`emc2.core.Model` The model with the added simulated lidar parameters. """ hyd_types = model.set_hyd_types(hyd_types) if is_conv: cloud_str = "conv" else: cloud_str = "strat" if not instrument.instrument_class.lower() == "radar": raise ValueError("Reflectivity can only be derived from a radar!") Dims = model.ds["%s_q_subcolumns_cl" % cloud_str].shape model.ds["sub_col_Ze_tot_%s" % cloud_str] = xr.DataArray( np.zeros(Dims), dims=model.ds["%s_q_subcolumns_cl" % cloud_str].dims) for hyd_type in hyd_types: q_field = "%s_q_subcolumns_%s" % (cloud_str, hyd_type) WC_tot = np.zeros(Dims) WC = model.ds["%s_q_subcolumns_%s" % (cloud_str, hyd_type)] p_values / \ (instrument.R_d * (t_values + 273.15)) * 1e3 # Fox and Illingworth (1997) if hyd_type.lower() == "cl": Ze_emp = 0.031 * WC ** 1.56 WC_tot += WC # Hagen and Yuter (2003) elif hyd_type.lower() == "pl": Ze_emp = ((WC * 1e3) / 3.4) 1.75 WC_tot += WC else: # Hogan et al. (2006) if 2e9 <= instrument.freq < 4e9: Ze_emp = 10 (((np.log10(WC) + 0.0197 * t_values + 1.7) / 0.060) / 10.) elif 27e9 <= instrument.freq < 40e9: Ze_emp = 10 ** (((np.log10(WC) + 0.0186 * t_values + 1.63) / (0.000242 * t_values + 0.0699)) / 10.) elif 75e9 <= instrument.freq < 110e9: Ze_emp = 10 ** (((np.log10(WC) + 0.00706 * t_values + 0.992) / (0.000580 * t_values + 0.0923)) / 10.) else: Ze_emp = 10 ** (((np.log10(WC) + 0.0186 * t_values + 1.63) / (0.000242 * t_values + 0.0699)) / 10.) var_name = "sub_col_Ze_%s_%s" % (hyd_type, cloud_str) model.ds[var_name] = xr.DataArray( Ze_emp.values, dims=model.ds[q_field].dims) model.ds["sub_col_Ze_tot_%s" % cloud_str] += Ze_emp.fillna(0) kappa_f = 6 * np.pi / (instrument.wavelength * model.Rho_hyd["cl"].magnitude) * \ ((instrument.eps_liq - 1) / (instrument.eps_liq + 2)).imag * 4.34e6 # dB m^3 g^-1 km^-1 model = accumulate_attenuation(model, is_conv, z_values, WC_tot * kappa_f, atm_ext, OD_from_sfc=OD_from_sfc, use_empiric_calc=True, kwargs) return model def calc_radar_bulk(instrument, model, is_conv, p_values, z_values, atm_ext, OD_from_sfc=True, hyd_types=None, mie_for_ice=False, kwargs): """ Calculates the radar stratiform or convective reflectivity and attenuation in a sub-columns using bulk scattering LUTs assuming geometric scatterers (radiation scheme logic). Effective radii for each hydrometeor class must be provided (in model.ds). Parameters ---------- instrument: Instrument The instrument to simulate. The instrument must be a lidar. model: Model The model to generate the parameters for. is_conv: bool True if the cell is convective p_values: ndarray model output pressure array in Pa. z_values: ndarray model output height array in m. atm_ext: ndarray atmospheric attenuation per layer (dB/km). OD_from_sfc: bool If True, then calculate optical depth from the surface. hyd_types: list or None list of hydrometeor names to include in calcuation. using default Model subclass types if None. mie_for_ice: bool If True, using bulk mie caculation LUTs. Otherwise, currently using the bulk C6 scattering LUTs for 8-column severly roughned aggregate. Additonal keyword arguments are passed into :py:func:`emc2.simulator.lidar_moments.accumulate_attenuation`. Returns ------- model: :func:`emc2.core.Model` The model with the added simulated lidar parameters. """ hyd_types = model.set_hyd_types(hyd_types) n_subcolumns = model.num_subcolumns if is_conv: cloud_str = "conv" re_fields = model.conv_re_fields else: cloud_str = "strat" re_fields = model.strat_re_fields if model.model_name in ["E3SM", "CESM2"]: bulk_ice_lut = "CESM_ice" bulk_mie_ice_lut = "mie_ice_CESM_PSD" bulk_liq_lut = "CESM_liq" else: bulk_ice_lut = "E3_ice" bulk_mie_ice_lut = "mie_ice_E3_PSD" bulk_liq_lut = "E3_liq" Dims = model.ds["%s_q_subcolumns_cl" % cloud_str].shape model.ds["sub_col_Ze_tot_%s" % cloud_str] = xr.DataArray( np.zeros(Dims), dims=model.ds["%s_q_subcolumns_cl" % cloud_str].dims) hyd_ext = np.zeros(Dims) rhoa_dz = np.tile( np.abs(np.diff(p_values, axis=1, append=0.)) / instrument.g, (n_subcolumns, 1, 1)) dz = np.tile( np.diff(z_values, axis=1, append=0.), (n_subcolumns, 1, 1)) for hyd_type in hyd_types: if hyd_type[-1] == 'l': rho_b = model.Rho_hyd[hyd_type] # bulk water re_array = np.tile(model.ds[re_fields[hyd_type]].values, (n_subcolumns, 1, 1)) if model.lambda_field is not None: # assuming my and lambda can be provided only for liq hydrometeors if not model.lambda_field[hyd_type] is None: lambda_array = model.ds[model.lambda_field[hyd_type]].values mu_array = model.ds[model.mu_field[hyd_type]].values else: rho_b = instrument.rho_i # bulk ice fi_factor = model.fluffy[hyd_type].magnitude * model.Rho_hyd[hyd_type] / rho_b + \ (1 - model.fluffy[hyd_type].magnitude) * (model.Rho_hyd[hyd_type] / rho_b) ** (1 / 3) re_array = np.tile(model.ds[re_fields[hyd_type]].values * fi_factor, (n_subcolumns, 1, 1)) tau_hyd = np.where(model.ds["%s_q_subcolumns_%s" % (cloud_str, hyd_type)] > 0, 3 * model.ds["%s_q_subcolumns_%s" % (cloud_str, hyd_type)] * rhoa_dz / (2 * rho_b * re_array * 1e-6), 0) A_hyd = tau_hyd / (2 * dz) # model assumes geometric scatterers if np.isin(hyd_type, ["ci", "pi"]): if mie_for_ice: r_eff_bulk = instrument.bulk_table[bulk_mie_ice_lut]["r_e"].values.copy() Qback_bulk = instrument.bulk_table[bulk_mie_ice_lut]["Q_back"].values Qext_bulk = instrument.bulk_table[bulk_mie_ice_lut]["Q_ext"].values else: r_eff_bulk = instrument.bulk_table[bulk_ice_lut]["r_e"].values.copy() Qback_bulk = instrument.bulk_table[bulk_ice_lut]["Q_back"].values Qext_bulk = instrument.bulk_table[bulk_ice_lut]["Q_ext"].values else: if model.model_name in ["E3SM", "CESM2"]: mu_b = np.tile(instrument.bulk_table[bulk_liq_lut]["mu"].values, (instrument.bulk_table[bulk_liq_lut]["lambdas"].size)).flatten() lambda_b = instrument.bulk_table[bulk_liq_lut]["lambda"].values.flatten() else: r_eff_bulk = instrument.bulk_table[bulk_liq_lut]["r_e"].values Qback_bulk = instrument.bulk_table[bulk_liq_lut]["Q_back"].values Qext_bulk = instrument.bulk_table[bulk_liq_lut]["Q_ext"].values if np.logical_and(np.isin(hyd_type, ["cl", "pl"]), model.model_name in ["E3SM", "CESM2"]): print("2-D interpolation of bulk liq radar backscattering using mu-lambda values") rel_locs = model.ds[model.q_names_stratiform[hyd_type]].values > 0. interpolator = LinearNDInterpolator(	np.stack((mu_b, lambda_b), axis=1)	numpy.stack
#!/usr/bin/env python # coding: utf-8 import h5py import numpy as np from functools import reduce from tqdm import tqdm import disk.funcs as dfn class binary_mbh(object): def __init__(self, filename): self.filename = filename with h5py.File(self.filename, 'r') as f: self.SubhaloMassInHalfRadType = np.array(f['meta/SubhaloMassInHalfRadType']) self.SubhaloSFRinHalfRad = np.array(f['meta/SubhaloSFRinHalfRad']) self.snapshot = np.array(f['meta/snapshot']) self.subhalo_id = np.array(f['meta/subhalo_id']) self.masses = np.array(f['evolution/masses']) #g self.mdot = np.array(f['evolution/mdot_eff']) #g/s self.sep = np.array(f['evolution/sep']) #cm self.dadt = np.array(f['evolution/dadt']) #cm/s self.dadt_df = np.array(f['evolution/dadt_df']) #cm/s self.dadt_gw = np.array(f['evolution/dadt_gw']) #cm/s self.dadt_lc = np.array(f['evolution/dadt_lc']) #cm/s self.dadt_vd = np.array(f['evolution/dadt_vd']) #cm/s self.scales = np.array(f['evolution/scales']) #NA self.times = np.array(f['evolution/times']) #s self.eccen = np.array(f['evolution/eccen']) #NA self.z = (1./self.scales)-1 #NA self.m1 = self.masses[:,0] self.m2 = self.masses[:,1] self.mtot = self.m1+self.m2 self.q = self.m2/self.m1 def find_Rlc(self): R_lc = np.zeros((self.sep.shape[0],3)) for i in range(len(self.sep)): try: idx = reduce(np.intersect1d,(np.where(np.abs(self.dadt_lc[i])>np.abs(self.dadt_df[i]))[0], np.where(np.abs(self.dadt_lc[i])>np.abs(self.dadt_vd[i]))[0], np.where(np.abs(self.dadt_lc[i])>np.abs(self.dadt_gw[i]))[0]))[0] R_lc[i]=[i,idx,self.sep[i][idx]] except: R_lc[i]=[i,np.nan,np.nan] return R_lc def find_Rvd(self): R_vd = np.zeros((self.sep.shape[0],3)) for i in range(len(self.sep)): try: idx = reduce(np.intersect1d,(np.where(np.abs(self.dadt_vd[i])>np.abs(self.dadt_df[i]))[0], np.where(np.abs(self.dadt_vd[i])>np.abs(self.dadt_lc[i]))[0], np.where(	np.abs(self.dadt_vd[i])	numpy.abs
import argparse import os import numpy as np import matplotlib.pyplot as plt from scipy.misc import imread from scipy.misc import imsave def blend(x, y, overlay): blended = x * (1 - overlay) + y * overlay blended = np.clip(blended, 0.0, 1.0) blended = np.where(y != 0, blended, x) return blended def is_mask(img): i = 0 for row in img: for col in row: for px in col: if px != 0.0 and px != 1.0: i = i + 1 f = np.vectorize(lambda x: x == 0.0 or x == 1.0) non_zero = np.count_nonzero(f(img)) / 3 total = np.shape(img)[0] *	np.shape(img)	numpy.shape
import os import pickle import warnings import platform import tempfile import numpy as np from pytransform3d.rotations import ( q_id, active_matrix_from_intrinsic_euler_xyz, random_quaternion) from pytransform3d.transformations import ( random_transform, invert_transform, concat, transform_from_pq, transform_from) from pytransform3d.transform_manager import TransformManager from pytransform3d import transform_manager from numpy.testing import assert_array_almost_equal from nose.tools import (assert_raises_regexp, assert_equal, assert_true, assert_false) from nose import SkipTest def test_request_added_transform(): """Request an added transform from the transform manager.""" random_state = np.random.RandomState(0) A2B = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) A2B_2 = tm.get_transform("A", "B") assert_array_almost_equal(A2B, A2B_2) def test_request_inverse_transform(): """Request an inverse transform from the transform manager.""" random_state = np.random.RandomState(0) A2B = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) A2B_2 = tm.get_transform("A", "B") assert_array_almost_equal(A2B, A2B_2) B2A = tm.get_transform("B", "A") B2A_2 = invert_transform(A2B) assert_array_almost_equal(B2A, B2A_2) def test_has_frame(): """Check if frames have been registered with transform.""" tm = TransformManager() tm.add_transform("A", "B", np.eye(4)) assert_true(tm.has_frame("A")) assert_true(tm.has_frame("B")) assert_false(tm.has_frame("C")) def test_transform_not_added(): """Test request for transforms that have not been added.""" random_state = np.random.RandomState(0) A2B = random_transform(random_state) C2D = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) tm.add_transform("C", "D", C2D) assert_raises_regexp(KeyError, "Unknown frame", tm.get_transform, "A", "G") assert_raises_regexp(KeyError, "Unknown frame", tm.get_transform, "G", "D") assert_raises_regexp(KeyError, "Cannot compute path", tm.get_transform, "A", "D") def test_request_concatenated_transform(): """Request a concatenated transform from the transform manager.""" random_state = np.random.RandomState(0) A2B = random_transform(random_state) B2C = random_transform(random_state) F2A = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) tm.add_transform("B", "C", B2C) tm.add_transform("D", "E", np.eye(4)) tm.add_transform("F", "A", F2A) A2C = tm.get_transform("A", "C") assert_array_almost_equal(A2C, concat(A2B, B2C)) C2A = tm.get_transform("C", "A") assert_array_almost_equal(C2A, concat(invert_transform(B2C), invert_transform(A2B))) F2B = tm.get_transform("F", "B") assert_array_almost_equal(F2B, concat(F2A, A2B)) def test_update_transform(): """Update an existing transform.""" random_state = np.random.RandomState(0) A2B1 = random_transform(random_state) A2B2 = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B1) tm.add_transform("A", "B", A2B2) A2B = tm.get_transform("A", "B") # Hack: test depends on internal member assert_array_almost_equal(A2B, A2B2) assert_equal(len(tm.i), 1) assert_equal(len(tm.j), 1) def test_pickle(): """Test if a transform manager can be pickled.""" random_state = np.random.RandomState(1) A2B = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) _, filename = tempfile.mkstemp(".pickle") try: pickle.dump(tm, open(filename, "wb")) tm2 = pickle.load(open(filename, "rb")) finally: if os.path.exists(filename): try: os.remove(filename) except WindowsError: pass # workaround for permission problem on Windows A2B2 = tm2.get_transform("A", "B") assert_array_almost_equal(A2B, A2B2) def test_whitelist(): """Test correct handling of whitelists for plotting.""" random_state = np.random.RandomState(2) A2B = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) nodes = tm._whitelisted_nodes(None) assert_equal({"A", "B"}, nodes) nodes = tm._whitelisted_nodes(["A"]) assert_equal({"A"}, nodes) assert_raises_regexp(KeyError, "unknown nodes", tm._whitelisted_nodes, "C") def test_check_consistency(): """Test correct detection of inconsistent graphs.""" random_state = np.random.RandomState(2) tm = TransformManager() A2B = random_transform(random_state) tm.add_transform("A", "B", A2B) B2A = random_transform(random_state) tm.add_transform("B", "A", B2A) assert_false(tm.check_consistency()) tm = TransformManager() A2B = random_transform(random_state) tm.add_transform("A", "B", A2B) assert_true(tm.check_consistency()) C2D = random_transform(random_state) tm.add_transform("C", "D", C2D) assert_true(tm.check_consistency()) B2C = random_transform(random_state) tm.add_transform("B", "C", B2C) assert_true(tm.check_consistency()) A2D_over_path = tm.get_transform("A", "D") A2D = random_transform(random_state) tm.add_transform("A", "D", A2D) assert_false(tm.check_consistency()) tm.add_transform("A", "D", A2D_over_path) assert_true(tm.check_consistency()) def test_connected_components(): """Test computation of connected components in the graph.""" tm = TransformManager() tm.add_transform("A", "B", np.eye(4)) assert_equal(tm.connected_components(), 1) tm.add_transform("D", "E", np.eye(4)) assert_equal(tm.connected_components(), 2) tm.add_transform("B", "C",	np.eye(4)	numpy.eye
import random from typing import List, Dict, Tuple import math import numpy as np from synthetic_data.observation import Observation import os import pickle import time from llr.llr import * # Created by <NAME> 29 November 2017 class Simulator: def __init__(self, n_users: int, user_features: List[int], n_items: int, item_features: int, bias: int, users_distribution: str = "zipf", items_distribution: str = "zipf", read_cache_dir: str = None, save_cache_dir: str = None, timestamp: bool=True, tout: bool=True) -> None: """Produce a list of observations --users who "buy" items. e.g. ``` s = Simulator(n_users=101, user_features=0, n_items=1500, item_features=10, bias=1.0) s.run() ``` :param int n_users: Number of users :param List[int] user_features: [feature1_n_values, feature2... ] :param int n_items: Number of items :param List[int] item_features: as for users :param int bias: how similarity influences. If 0, at all. If 1, p(item after an item sim=-1)=0 :param int timestamp: unix-like timestamp (in seconds) :return List[Tuple3]: list of observations (user_id, item_id, timestamp) """ self.user_buying_dict = {} # {user: [(item, timestamp), (), ...], ...} self.observations_list = [] self._user_features = user_features self._item_features = item_features self.n_users = n_users self.n_items = n_items self._reset_cooccurrences_matrices() self._reset_sequentials_matrices() self.tout = tout assert read_cache_dir is None or save_cache_dir is None, \ "saving and reading the cache at the same time does not make sense" self.read_cache_dir = read_cache_dir self.save_cache_dir = save_cache_dir if bias >= 0: self.bias =	np.float32(bias)	numpy.float32
import argparse import dill import jax import numpy as np import pomdp pomdp.horizon = 25 parser = argparse.ArgumentParser() parser.add_argument('--silent', action='store_true') parser.add_argument('--bias', action='store_true') args = parser.parse_args() with open('data/data{}-meta.obj'.format('-bias' if args.bias else ''), 'rb') as f: data_meta = dill.load(f) S = data_meta['S'] A = data_meta['A'] Z = data_meta['Z'] envr_b0 = data_meta['envr_b0'] envr_O = data_meta['envr_O'] plcy_b0 = data_meta['plcy_b0'] plcy_T = data_meta['plcy_T'] plcy_O = data_meta['plcy_O'] plcy_mu = data_meta['plcy_mu'] def log_pi_il(mu, eta, b): res = -eta * np.sum((mu - b[None,...])*2, axis=-1) return res - np.log(np.sum(np.exp(res))) def log_pi_irl(alp, bet, b): res = np.zeros(A) for a in range(A): if alp[a].size == 0: res[a] = -1e6 else: res[a] = bet np.amax(alp[a] @ b) return res - np.log(np.sum(np.exp(res))) algs = list() with open('res/res{}-interpole.obj'.format('-bias' if args.bias else ''), 'rb') as f: res = dill.load(f) algs.append(dict()) algs[-1]['name'] = 'interpole' algs[-1]['log_pi'] = log_pi_il algs[-1]['b0'] = res['b0'] algs[-1]['O'] = res['O'] algs[-1]['tht'] = res['mu'] with open('res/res{}-offpoirl.obj'.format('-bias' if args.bias else ''), 'rb') as f: res = dill.load(f) res = res['out'][500::10] algs.append(dict()) algs[-1]['name'] = 'offpoirl' algs[-1]['log_pi'] = log_pi_irl algs[-1]['b0'] = np.zeros(S) algs[-1]['O'] = np.zeros((A,S,Z)) algs[-1]['R'] = np.zeros((S,A)) for b0, _, O, R in res: algs[-1]['b0'] += b0 algs[-1]['O'] += O algs[-1]['R'] += R algs[-1]['b0'] /= len(res) algs[-1]['O'] /= len(res) algs[-1]['R'] /= len(res) algs[-1]['tht'] = pomdp.solve(S, A, Z, algs[-1]['b0'], plcy_T, algs[-1]['O'], algs[-1]['R']) with open('res/res{}-poirl.obj'.format('-bias' if args.bias else ''), 'rb') as f: res = dill.load(f) res = res['out'][500::10] algs.append(dict()) algs[-1]['name'] = 'poirl' algs[-1]['log_pi'] = log_pi_irl algs[-1]['b0'] = np.zeros(S) algs[-1]['O'] = np.zeros((A,S,Z)) algs[-1]['R'] = np.zeros((S,A)) for b0, _, O, R in res: algs[-1]['b0'] += b0 algs[-1]['O'] += O algs[-1]['R'] += R algs[-1]['b0'] /= len(res) algs[-1]['O'] /= len(res) algs[-1]['R'] /= len(res) algs[-1]['tht'] = pomdp.solve(S, A, Z, algs[-1]['b0'], plcy_T, algs[-1]['O'], algs[-1]['R']) with open('res/res{}-pombil.obj'.format('-bias' if args.bias else ''), 'rb') as f: res = dill.load(f) algs.append(dict()) algs[-1]['name'] = 'pombil' algs[-1]['log_pi'] = log_pi_il algs[-1]['b0'] = res['b0'] algs[-1]['O'] = res['O'] algs[-1]['tht'] = res['mu'] with open('res/res{}-rbc.obj'.format('-bias' if args.bias else ''), 'rb') as f: alg_rbc = dill.load(f) for alg in algs: alg['e1'] = list() alg['e2'] = list() alg['e3'] = list() e1_rbc = list() e2_rbc = list() for i in range(500): if not args.silent: if i % 100 == 0: print('i = {}'.format(i)) s = np.random.choice(range(S), p=envr_b0) b = plcy_b0 tau = None for alg in algs: alg['b'] = alg['b0'] alg['tau'] = None h_rbc = np.zeros(alg_rbc['H']) c_rbc = np.zeros(alg_rbc['H']) tau_rbc = None t = 0 while True: t += 1 pi = np.exp(log_pi_il(plcy_mu, 10, b)) for alg in algs: alg['pi'] = np.exp(alg['log_pi'](alg['tht'], 10, alg['b'])) if t > 1: pi_rbc = np.array(jax.nn.softmax(alg_rbc['W_y'] @ l_rbc + alg_rbc['b_y'])) if tau is None: for alg in algs: alg['e2'].append(np.sum(pi * np.log(pi / alg['pi']))) alg['e3'].append(np.sum(b * np.log(b / alg['b']))) if t > 1: e2_rbc.append(np.sum(pi * np.log(pi / pi_rbc))) a = np.random.choice(range(A), p=pi) for alg in algs: alg['a'] = np.random.choice(range(A), p=alg['pi']) if t > 1: a_rbc = np.random.choice(range(A), p=pi_rbc) z = np.random.choice(range(Z), p=envr_O[2,s,:]) b = plcy_O[2,:,z] * b b /= b.sum() for alg in algs: alg['b'] = alg['O'][2,:,z] * alg['b'] alg['b'] /= alg['b'].sum() x = np.concatenate((np.array([0, 0, 1]), jax.nn.one_hot(z, Z))) f = jax.nn.sigmoid(alg_rbc['W_f'] @ x + alg_rbc['U_f'] @ h_rbc + alg_rbc['b_f']) i = jax.nn.sigmoid(alg_rbc['W_i'] @ x + alg_rbc['U_i'] @ h_rbc + alg_rbc['b_i']) o = jax.nn.sigmoid(alg_rbc['W_o'] @ x + alg_rbc['U_o'] @ h_rbc + alg_rbc['b_o']) c_rbc = f * c_rbc + i * np.tanh(alg_rbc['W_c'] @ x + alg_rbc['U_c'] @ h_rbc + alg_rbc['b_c']) h_rbc = o * np.tanh(c_rbc) l_rbc = np.tanh(alg_rbc['W_l'] @ h_rbc + alg_rbc['b_l']) if tau is None and a != 2: tau = t for alg in algs: if alg['tau'] is None and alg['a'] != 2: alg['tau'] = t if t > 1: if tau_rbc is None and a_rbc != 2: tau_rbc = t brk = tau is not None for alg in algs: brk = brk and alg['tau'] is not None brk = brk and tau_rbc is not None if brk: break for alg in algs: alg['e1'].append(np.abs(alg['tau'] - tau)) e1_rbc.append(	np.abs(tau_rbc - tau)	numpy.abs
import pytest import numpy as np import sys if (sys.version_info > (3, 0)): from io import StringIO else: from StringIO import StringIO from keras_contrib import callbacks from keras.models import Sequential, Model from keras.layers import Input, Dense, Conv2D, Flatten, Activation from keras import backend as K n_out = 11 # with 1 neuron dead, 1/11 is just below the threshold of 10% with verbose = False def check_print(do_train, expected_warnings, nr_dead=None, perc_dead=None): """ Receive stdout to check if correct warning message is delivered :param nr_dead: int :param perc_dead: float, 10% should be written as 0.1 """ saved_stdout = sys.stdout out = StringIO() out.flush() sys.stdout = out # overwrite current stdout do_train() stdoutput = out.getvalue().strip() # get prints, can be something like: "Layer dense (#0) has 2 dead neurons (20.00%)!" str_to_count = "dead neurons" count = stdoutput.count(str_to_count) sys.stdout = saved_stdout # restore stdout out.close() assert expected_warnings == count if expected_warnings and (nr_dead is not None): str_to_check = 'has {} dead'.format(nr_dead) assert str_to_check in stdoutput, '"{}" not in "{}"'.format(str_to_check, stdoutput) if expected_warnings and (perc_dead is not None): str_to_check = 'neurons ({:.2%})!'.format(perc_dead) assert str_to_check in stdoutput, '"{}" not in "{}"'.format(str_to_check, stdoutput) def test_DeadDeadReluDetector(): n_samples = 9 input_shape = (n_samples, 3, 4) # 4 input features shape_out = (n_samples, 3, n_out) # 11 output features shape_weights = (4, n_out) # ignore batch size input_shape_dense = tuple(input_shape[1:]) def do_test(weights, expected_warnings, verbose, nr_dead=None, perc_dead=None): def do_train(): dataset = np.ones(input_shape) # data to be fed as training model = Sequential() model.add(Dense(n_out, activation='relu', input_shape=input_shape_dense, use_bias=False, weights=[weights], name='dense')) model.compile(optimizer='sgd', loss='categorical_crossentropy') model.fit( dataset, np.ones(shape_out), batch_size=1, epochs=1, callbacks=[callbacks.DeadReluDetector(dataset, verbose=verbose)], verbose=False ) check_print(do_train, expected_warnings, nr_dead, perc_dead) weights_1_dead = np.ones(shape_weights) # weights that correspond to NN with 1/11 neurons dead weights_2_dead = np.ones(shape_weights) # weights that correspond to NN with 2/11 neurons dead weights_all_dead = np.zeros(shape_weights) # weights that correspond to all neurons dead weights_1_dead[:, 0] = 0 weights_2_dead[:, 0:2] = 0 do_test(weights_1_dead, verbose=True, expected_warnings=1, nr_dead=1, perc_dead=1. / n_out) do_test(weights_1_dead, verbose=False, expected_warnings=0) do_test(weights_2_dead, verbose=True, expected_warnings=1, nr_dead=2, perc_dead=2. / n_out) # do_test(weights_all_dead, verbose=True, expected_warnings=1, nr_dead=n_out, perc_dead=1.) def test_DeadDeadReluDetector_bias(): n_samples = 9 input_shape = (n_samples, 4) # 4 input features shape_weights = (4, n_out) shape_bias = (n_out, ) shape_out = (n_samples, n_out) # 11 output features # ignore batch size input_shape_dense = tuple(input_shape[1:]) def do_test(weights, bias, expected_warnings, verbose, nr_dead=None, perc_dead=None): def do_train(): dataset = np.ones(input_shape) # data to be fed as training model = Sequential() model.add(Dense(n_out, activation='relu', input_shape=input_shape_dense, use_bias=True, weights=[weights, bias], name='dense')) model.compile(optimizer='sgd', loss='categorical_crossentropy') model.fit( dataset, np.ones(shape_out), batch_size=1, epochs=1, callbacks=[callbacks.DeadReluDetector(dataset, verbose=verbose)], verbose=False ) check_print(do_train, expected_warnings, nr_dead, perc_dead) weights_1_dead = np.ones(shape_weights) # weights that correspond to NN with 1/11 neurons dead weights_2_dead = np.ones(shape_weights) # weights that correspond to NN with 2/11 neurons dead weights_all_dead = np.zeros(shape_weights) # weights that correspond to all neurons dead weights_1_dead[:, 0] = 0 weights_2_dead[:, 0:2] = 0 bias =	np.zeros(shape_bias)	numpy.zeros
from __future__ import absolute_import, division, print_function import six import logging import os import json import numpy as np import torch from madminer.utils.ml import ratio_losses, flow_losses from madminer.utils.ml.models.maf import ConditionalMaskedAutoregressiveFlow from madminer.utils.ml.models.maf_mog import ConditionalMixtureMaskedAutoregressiveFlow from madminer.utils.ml.models.ratio import ParameterizedRatioEstimator, DoublyParameterizedRatioEstimator from madminer.utils.ml.models.score import LocalScoreEstimator from madminer.utils.ml.flow_trainer import train_flow_model, evaluate_flow_model from madminer.utils.ml.ratio_trainer import train_ratio_model, evaluate_ratio_model from madminer.utils.ml.score_trainer import train_local_score_model, evaluate_local_score_model from madminer.utils.various import create_missing_folders, load_and_check, shuffle logger = logging.getLogger(__name__) class MLForge: """ Estimating likelihood ratios and scores with machine learning. Each instance of this class represents one neural estimator. The most important functions are: * `MLForge.train()` to train an estimator. The keyword `method` determines the inference technique and whether a class instance represents a single-parameterized likelihood ratio estimator, a doubly-parameterized likelihood ratio estimator, or a local score estimator. * `MLForge.evaluate()` to evaluate the estimator. * `MLForge.save()` to save the trained model to files. * `MLForge.load()` to load the trained model from files. Please see the tutorial for a detailed walk-through. """ def __init__(self): self.method_type = None self.model = None self.method = None self.nde_type = None self.n_observables = None self.n_parameters = None self.n_hidden = None self.activation = None self.maf_n_mades = None self.maf_batch_norm = None self.maf_batch_norm_alpha = None self.features = None self.x_scaling_means = None self.x_scaling_stds = None def train( self, method, x_filename, y_filename=None, theta0_filename=None, theta1_filename=None, r_xz_filename=None, t_xz0_filename=None, t_xz1_filename=None, features=None, nde_type="mafmog", n_hidden=(100, 100), activation="tanh", maf_n_mades=3, maf_batch_norm=False, maf_batch_norm_alpha=0.1, maf_mog_n_components=10, alpha=1.0, trainer="amsgrad", n_epochs=50, batch_size=128, initial_lr=0.001, final_lr=0.0001, nesterov_momentum=None, validation_split=None, early_stopping=True, scale_inputs=True, shuffle_labels=False, grad_x_regularization=None, limit_samplesize=None, return_first_loss=False, verbose=False, ): """ Trains a neural network to estimate either the likelihood ratio or, if method is 'sally' or 'sallino', the score. The keyword method determines the structure of the estimator that an instance of this class represents: * For 'alice', 'alices', 'carl', 'nde', 'rascal', 'rolr', and 'scandal', the neural network models the likelihood ratio as a function of the observables `x` and the numerator hypothesis `theta0`, while the denominator hypothesis is kept at a fixed reference value ("single-parameterized likelihood ratio estimator"). In addition to the likelihood ratio, the estimator allows to estimate the score at `theta0`. * For 'alice2', 'alices2', 'carl2', 'rascal2', and 'rolr2', the neural network models the likelihood ratio as a function of the observables `x`, the numerator hypothesis `theta0`, and the denominator hypothesis `theta1` ("doubly parameterized likelihood ratio estimator"). The score at `theta0` and `theta1` can also be evaluated. * For 'sally' and 'sallino', the neural networks models the score evaluated at some reference hypothesis ("local score regression"). The likelihood ratio cannot be estimated directly from the neural network, but can be estimated in a second step through density estimation in the estimated score space. Parameters ---------- method : str The inference method used. Allows values are 'alice', 'alices', 'carl', 'nde', 'rascal', 'rolr', and 'scandal' for a single-parameterized likelihood ratio estimator; 'alice2', 'alices2', 'carl2', 'rascal2', and 'rolr2' for a doubly-parameterized likelihood ratio estimator; and 'sally' and 'sallino' for local score regression. x_filename : str Path to an unweighted sample of observations, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for all inference methods. y_filename : str or None, optional Path to an unweighted sample of class labels, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'alice', 'alice2', 'alices', 'alices2', 'carl', 'carl2', 'rascal', 'rascal2', 'rolr', and 'rolr2' methods. Default value: None. theta0_filename : str or None, optional Path to an unweighted sample of numerator parameters, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'alice', 'alice2', 'alices', 'alices2', 'carl', 'carl2', 'nde', 'rascal', 'rascal2', 'rolr', 'rolr2', and 'scandal' methods. Default value: None. theta1_filename : str or None, optional Path to an unweighted sample of denominator parameters, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'alice2', 'alices2', 'carl2', 'rascal2', and 'rolr2' methods. Default value: None. r_xz_filename : str or None, optional Path to an unweighted sample of joint likelihood ratios, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'alice', 'alice2', 'alices', 'alices2', 'rascal', 'rascal2', 'rolr', and 'rolr2' methods. Default value: None. t_xz0_filename : str or None, optional Path to an unweighted sample of joint scores at theta0, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'alices', 'alices2', 'rascal', 'rascal2', 'sallino', 'sally', and 'scandal' methods. Default value: None. t_xz1_filename : str or None, optional Path to an unweighted sample of joint scores at theta1, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'rascal2' and 'alices2' methods. Default value: None. features : list of int or None, optional Indices of observables (features) that are used as input to the neural networks. If None, all observables are used. Default value: None. nde_type : {'maf', 'mafmog'}, optional If the method is 'nde' or 'scandal', nde_type determines the architecture used in the neural density estimator. Currently supported are 'maf' for a Masked Autoregressive Flow with a Gaussian base density, or 'mafmog' for a Masked Autoregressive Flow with a mixture of Gaussian base densities. Default value: 'mafmog'. n_hidden : tuple of int, optional Units in each hidden layer in the neural networks. If method is 'nde' or 'scandal', this refers to the setup of each individual MADE layer. Default value: (100, 100). activation : {'tanh', 'sigmoid', 'relu'}, optional Activation function. Default value: 'tanh'. maf_n_mades : int, optional If method is 'nde' or 'scandal', this sets the number of MADE layers. Default value: 3. maf_batch_norm : bool, optional If method is 'nde' or 'scandal', switches batch normalization layers after each MADE layer on or off. Default: False. maf_batch_norm_alpha : float, optional If method is 'nde' or 'scandal' and maf_batch_norm is True, this sets the alpha parameter in the calculation of the running average of the mean and variance. Default value: 0.1. maf_mog_n_components : int, optional If method is 'nde' or 'scandal' and nde_type is 'mafmog', this sets the number of Gaussian base components. Default value: 10. alpha : float, optional Hyperparameter weighting the score error in the loss function of the 'alices', 'alices2', 'rascal', 'rascal2', and 'scandal' methods. Default value: 1. trainer : {"adam", "amsgrad", "sgd"}, optional Optimization algorithm. Default value: "amsgrad". n_epochs : int, optional Number of epochs. Default value: 50. batch_size : int, optional Batch size. Default value: 128. initial_lr : float, optional Learning rate during the first epoch, after which it exponentially decays to final_lr. Default value: 0.001. final_lr : float, optional Learning rate during the last epoch. Default value: 0.0001. nesterov_momentum : float or None, optional If trainer is "sgd", sets the Nesterov momentum. Default value: None. validation_split : float or None, optional Fraction of samples used for validation and early stopping (if early_stopping is True). If None, the entire sample is used for training and early stopping is deactivated. Default value: None. early_stopping : bool, optional Activates early stopping based on the validation loss (only if validation_split is not None). Default value: True. scale_inputs : bool, optional Scale the observables to zero mean and unit variance. Default value: True. shuffle_labels : bool, optional If True, the labels (`y`, `r_xz`, `t_xz`) are shuffled, while the observations (`x`) remain in their normal order. This serves as a closure test, in particular as cross-check against overfitting: an estimator trained with shuffle_labels=True should predict to likelihood ratios around 1 and scores around 0. grad_x_regularization : float or None, optional If not None, a term of the form `grad_x_regularization * \|grad_x f(x)\|^2` is added to the loss, where `f(x)` is the neural network output (the estimated log likelihood ratio or score). Default value: None. limit_samplesize : int or None, optional If not None, only this number of samples (events) is used to train the estimator. Default value: None. return_first_loss : bool, optional If True, the training routine only proceeds until the loss is calculated for the first time, at which point the loss tensor is returned. This can be useful for debugging or visualization purposes (but of course not for training a model). verbose : bool, optional If True, prints loss updates after every epoch. Returns ------- None """ logger.info("Starting training") logger.info(" Method: %s", method) logger.info(" Training data: x at %s", x_filename) if theta0_filename is not None: logger.info(" theta0 at %s", theta0_filename) if theta1_filename is not None: logger.info(" theta1 at %s", theta1_filename) if y_filename is not None: logger.info(" y at %s", y_filename) if r_xz_filename is not None: logger.info(" r_xz at %s", r_xz_filename) if t_xz0_filename is not None: logger.info(" t_xz (theta0) at %s", t_xz0_filename) if t_xz1_filename is not None: logger.info(" t_xz (theta1) at %s", t_xz1_filename) if features is None: logger.info(" Features: all") else: logger.info(" Features: %s", features) logger.info(" Method: %s", method) if method in ["nde", "scandal"]: logger.info(" Neural density est.: %s", nde_type) if method not in ["nde", "scandal"]: logger.info(" Hidden layers: %s", n_hidden) if method in ["nde", "scandal"]: logger.info(" MAF, number MADEs: %s", maf_n_mades) logger.info(" MAF, batch norm: %s", maf_batch_norm) logger.info(" MAF, BN alpha: %s", maf_batch_norm_alpha) logger.info(" MAF MoG, components: %s", maf_mog_n_components) logger.info(" Activation function: %s", activation) if method in ["cascal", "cascal2", "rascal", "rascal2", "scandal", "alices"]: logger.info(" alpha: %s", alpha) logger.info(" Batch size: %s", batch_size) logger.info(" Trainer: %s", trainer) logger.info(" Epochs: %s", n_epochs) logger.info(" Learning rate: %s initially, decaying to %s", initial_lr, final_lr) if trainer == "sgd": logger.info(" Nesterov momentum: %s", nesterov_momentum) logger.info(" Validation split: %s", validation_split) logger.info(" Early stopping: %s", early_stopping) logger.info(" Scale inputs: %s", scale_inputs) logger.info(" Shuffle labels %s", shuffle_labels) if grad_x_regularization is None: logger.info(" Regularization: None") else: logger.info(" Regularization: %s * \|grad_x f(x)\|^2", grad_x_regularization) if limit_samplesize is None: logger.info(" Samples: all") else: logger.info(" Samples: %s", limit_samplesize) # Load training data logger.info("Loading training data") theta0 = load_and_check(theta0_filename) theta1 = load_and_check(theta1_filename) x = load_and_check(x_filename) y = load_and_check(y_filename) r_xz = load_and_check(r_xz_filename) t_xz0 = load_and_check(t_xz0_filename) t_xz1 = load_and_check(t_xz1_filename) if y is not None: y = y.reshape((-1, 1)) # Check necessary information is theere assert x is not None if method in [ "carl", "carl2", "nde", "scandal", "rolr", "alice", "rascal", "alices", "rolr2", "alice2", "rascal2", "alices2", ]: assert theta0 is not None if method in ["rolr", "alice", "rascal", "alices", "rolr2", "alice2", "rascal2", "alices2"]: assert r_xz is not None if method in ["carl", "carl2", "rolr", "alice", "rascal", "alices", "rolr2", "alice2", "rascal2", "alices2"]: assert y is not None if method in ["scandal", "rascal", "alices", "rascal2", "alices2", "sally", "sallino"]: assert t_xz0 is not None if method in ["carl2", "rolr2", "alice2", "rascal2", "alices2"]: assert theta1 is not None if method in ["rascal2", "alices2"]: assert t_xz1 is not None if method in ["nde", "scandal"]: assert nde_type in ["maf", "mafmog"] calculate_model_score = method in ["rascal", "cascal", "alices", "scandal", "rascal2", "cascal2", "alices2"] # Infer dimensions of problem n_samples = x.shape[0] n_observables = x.shape[1] if theta0 is not None: n_parameters = theta0.shape[1] else: n_parameters = t_xz0.shape[1] logger.info("Found %s samples with %s parameters and %s observables", n_samples, n_parameters, n_observables) # Limit sample size if limit_samplesize is not None and limit_samplesize < n_samples: logger.info("Only using %s of %s training samples", limit_samplesize, n_samples) x = x[:limit_samplesize] if theta0 is not None: theta0 = theta0[:limit_samplesize] if theta1 is not None: theta1 = theta1[:limit_samplesize] if y is not None: y = y[:limit_samplesize] if r_xz is not None: r_xz = r_xz[:limit_samplesize] if t_xz0 is not None: t_xz0 = t_xz0[:limit_samplesize] if t_xz1 is not None: t_xz1 = t_xz1[:limit_samplesize] # Scale features if scale_inputs: logger.info("Rescaling inputs") self.x_scaling_means = np.mean(x, axis=0) self.x_scaling_stds = np.maximum(np.std(x, axis=0), 1.0e-6) x[:] -= self.x_scaling_means x[:] /= self.x_scaling_stds else: self.x_scaling_means = np.zeros(n_parameters) self.x_scaling_stds = np.ones(n_parameters) logger.debug("Observable ranges:") for i in range(n_observables): logger.debug( " x_%s: mean %s, std %s, range %s ... %s", i + 1, np.mean(x[:, i]), np.std(x[:, i]), np.min(x[:, i]),	np.max(x[:, i])	numpy.max
import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt import matplotlib.colors as colors import astropy.units as u from astropy.cosmology import z_at_value from astropy.cosmology import WMAP9 as cosmo def Plot_SNR( var_x, sample_x, var_y, sample_y, SNRMatrix, fig=None, ax=None, display=True, return_plt=False, dl_axis=False, lb_axis=False, smooth_contours=True, cfill=True, display_cbar=True, x_axis_label=True, y_axis_label=True, x_axis_line=None, y_axis_line=None, logLevels_min=-1.0, logLevels_max=0.0, hspace=0.15, wspace=0.1, contour_kwargs={}, contourf_kwargs={}, xticklabels_kwargs={}, xlabels_kwargs={}, xline_kwargs={}, yticklabels_kwargs={}, ylabels_kwargs={}, yline_kwargs={}, ): """Plots the SNR contours from calcSNR Parameters ---------- var_x: str x-axis variable sample_x: array samples at which ``SNRMatrix`` was calculated corresponding to the x-axis variable var_y: str y-axis variable sample_y: array samples at which ``SNRMatrix`` was calculated corresponding to the y-axis variable SNRMatrix: array-like the matrix at which the SNR was calculated corresponding to the particular x and y-axis variable choices fig: object, optional matplotlib figure object on which to collate the individual plots ax: object, optional matplotlib axes object on which to plot the individual plot display: bool, optional Option to turn off display if saving multiple plots to a file return_plt: bool, optional Option to return ``fig`` and ``ax`` dl_axis: bool, optional Option to turn on the right hand side labels of luminosity distance lb_axis: bool, optional Option to turn on the right hand side labels of lookback time smooth_contours: bool, optional Option to have contours appear smooth instead of tiered (depending on sample size the edges appear boxey). cfill: bool, optional Option to use filled contours or not, default is ``True`` display_cbar: bool, optional Option to display the colorbar on the axes object x_axis_label: bool, optional Option to display the x axis label y_axis_label: bool, optional Option to display the y axis label x_axis_line: int,float, optional Option to display a line on the x axis if not None y_axis_line: int,float, optional Option to display a line on the y axis if not None logLevels_min: float, optional Sets the minimum log level of the colorbar, default is -1.0 which set the minimum to the log minimum of the given ``SNRMatrix`` logLevels_max: float, optional Sets the maximum log level of the colorbar, default is 0.0, which sets the maximum to the log maximum value of the given ``SNRMatrix`` hspace: float, optional Sets the vertical space between axes objects, default is 0.15 wspace: float, optional Sets the horizontal space between axes objects, default is 0.1 contour_kwargs: dict, optional Sets additional kwargs taken by contour in matplotlib contourf_kwargs: dict, optional Sets additional kwargs taken by contourf in matplotlib xticklabels_kwargs: dict, optional Sets additional kwargs taken by xticklabel in matplotlib xlabels_kwargs=: dict, optional Sets additional kwargs taken by xlabel in matplotlib xline_kwargs: dict, optional Sets additional kwargs taken by ax.axvline in matplotlib yticklabels_kwargs: dict, optional Sets additional kwargs taken by yticklabel in matplotlib ylabels_kwargs: dict, optional Sets additional kwargs taken by ylabel in matplotlib yline_kwargs: dict, optional Sets additional kwargs taken by ax.axhline in matplotlib """ if fig is not None: if ax is not None: pass else: fig, ax = plt.subplots() else: fig, ax = plt.subplots() if "colors" not in contour_kwargs.keys() and "cmap" not in contour_kwargs.keys(): contour_kwargs["colors"] = "k" if "linewidths" not in contour_kwargs.keys(): contour_kwargs["linewidths"] = 2.0 if "cmap" not in contourf_kwargs.keys(): contourf_kwargs["cmap"] = "viridis" logSNR = np.log10(SNRMatrix) if logLevels_min == -1.0: logLevels_min = np.log10(np.array([1.0])) if logLevels_max == 0.0: logLevels_max = np.ceil(np.amax(logSNR)) if logLevels_max < logLevels_min: raise ValueError("All SNRs are lower than 5.") logLevels_add = np.log10(np.array([3.0, 10.0, 31.0])) print_logLevels = np.concatenate( (logLevels_min, logLevels_add, np.arange(2.0, logLevels_max + 1.0)) ) logLevels = print_logLevels ylabel_min = min(sample_y) ylabel_max = max(sample_y) xlabel_min = min(sample_x) xlabel_max = max(sample_x) # Set whether log or linearly spaced axes if xlabel_max < 0.0 or xlabel_min < 0.0 or var_x in ["n_p", "T_obs"]: xaxis_type = "lin" step_size = int(xlabel_max - xlabel_min + 1) x_labels = np.linspace(xlabel_min, xlabel_max, step_size) else: x_log_range = np.log10(xlabel_max) - np.log10(xlabel_min) if x_log_range >= 2.0: xaxis_type = "log" step_size = int(np.log10(xlabel_max) - np.log10(xlabel_min) + 1) x_labels = np.logspace( np.log10(xlabel_min), np.log10(xlabel_max), step_size ) else: xaxis_type = "lin" x_scale = 10 ** round(np.log10(xlabel_min)) x_labels = ( np.arange( round(xlabel_min / x_scale), round(xlabel_max / x_scale) + 1, 1 ) * x_scale ) if x_labels[0] < xlabel_min: x_labels[0] = xlabel_min if x_labels[-1] > xlabel_max: x_labels[-1] = xlabel_max if ylabel_max < 0.0 or ylabel_min < 0.0 or var_y in ["n_p", "T_obs"]: yaxis_type = "lin" step_size = int(ylabel_max - ylabel_min + 1) y_labels = np.linspace(ylabel_min, ylabel_max, step_size) else: y_log_range = np.log10(ylabel_max) - np.log10(ylabel_min) if y_log_range >= 2.0: yaxis_type = "log" step_size = int(np.log10(ylabel_max) - np.log10(ylabel_min) + 1) y_labels = np.logspace( np.log10(ylabel_min), np.log10(ylabel_max), step_size ) else: yaxis_type = "lin" y_scale = 10 ** round(np.log10(ylabel_min)) y_labels = ( np.arange( round(ylabel_min / y_scale), round(ylabel_max / y_scale) + 1, 1 ) * y_scale ) if y_labels[0] < ylabel_min: y_labels[0] = ylabel_min if y_labels[-1] > ylabel_max: y_labels[-1] = ylabel_max # Set axis scales based on what data sampling we used if yaxis_type == "lin" and xaxis_type == "log": if not cfill: CS1 = ax.contour( np.log10(sample_x), sample_y, logSNR, print_logLevels, contour_kwargs ) else: if smooth_contours: cmap = mpl.cm.get_cmap(name=contourf_kwargs["cmap"]) cmap.set_under(color="white") CS1 = ax.imshow( logSNR, extent=[ np.log10(xlabel_min), np.log10(xlabel_max), ylabel_min, ylabel_max, ], vmin=logLevels_min, vmax=logLevels_max, origin="lower", aspect="auto", cmap=cmap, ) else: CS1 = ax.contourf( np.log10(sample_x), sample_y, logSNR, logLevels, contourf_kwargs ) ax.contour( np.log10(sample_x), sample_y, logSNR, print_logLevels, contour_kwargs ) ax.set_xlim(np.log10(xlabel_min), np.log10(xlabel_max)) ax.set_ylim(ylabel_min, ylabel_max) elif yaxis_type == "log" and xaxis_type == "lin": if not cfill: CS1 = ax.contour( sample_x, np.log10(sample_y), logSNR, print_logLevels, contour_kwargs ) else: if smooth_contours: cmap = mpl.cm.get_cmap(name=contourf_kwargs["cmap"]) cmap.set_under(color="white") CS1 = ax.imshow( logSNR, extent=[ xlabel_min, xlabel_max, np.log10(ylabel_min), np.log10(ylabel_max), ], vmin=logLevels_min, vmax=logLevels_max, origin="lower", aspect="auto", cmap=cmap, ) else: CS1 = ax.contourf( sample_x, np.log10(sample_y), logSNR, logLevels, contourf_kwargs ) ax.contour( sample_x, np.log10(sample_y), logSNR, print_logLevels, contour_kwargs ) ax.set_xlim(xlabel_min, xlabel_max) ax.set_ylim(np.log10(ylabel_min), np.log10(ylabel_max)) elif yaxis_type == "lin" and xaxis_type == "lin": if not cfill: CS1 = ax.contour( sample_x, sample_y, logSNR, print_logLevels, contour_kwargs ) else: if smooth_contours: cmap = mpl.cm.get_cmap(name=contourf_kwargs["cmap"]) cmap.set_under(color="white") CS1 = ax.imshow( logSNR, extent=[xlabel_min, xlabel_max, ylabel_min, ylabel_max], vmin=logLevels_min, vmax=logLevels_max, origin="lower", aspect="auto", cmap=cmap, ) else: CS1 = ax.contourf( sample_x, sample_y, logSNR, logLevels, contourf_kwargs ) ax.contour(sample_x, sample_y, logSNR, print_logLevels, contour_kwargs) ax.set_xlim(xlabel_min, xlabel_max) ax.set_ylim(ylabel_min, ylabel_max) else: if not cfill: CS1 = ax.contour( np.log10(sample_x), np.log10(sample_y), logSNR, print_logLevels, contour_kwargs ) else: if smooth_contours: cmap = mpl.cm.get_cmap(name=contourf_kwargs["cmap"]) cmap.set_under(color="white") CS1 = ax.imshow( logSNR, extent=[	np.log10(xlabel_min)	numpy.log10
# This file is part of QuTiP: Quantum Toolbox in Python. # # Copyright (c) 2011 and later, <NAME> and <NAME>. # All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions are # met: # # 1. Redistributions of source code must retain the above copyright notice, # this list of conditions and the following disclaimer. # # 2. Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in the # documentation and/or other materials provided with the distribution. # # 3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names # of its contributors may be used to endorse or promote products derived # from this software without specific prior written permission. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS # "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT # LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A # PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT # HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, # SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT # LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, # DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY # THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT # (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE # OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ############################################################################### import numpy as np from numpy.testing import run_module_suite, assert_equal, assert_almost_equal import scipy.sparse as sp from qutip.random_objects import (rand_dm, rand_herm, rand_ket) from qutip.states import coherent from qutip.sparse import (sp_bandwidth, sp_permute, sp_reverse_permute, sp_profile, sp_one_norm, sp_inf_norm) from qutip.cy.spmath import zcsr_kron def _permutateIndexes(array, row_perm, col_perm): return array[np.ix_(row_perm, col_perm)] def _dense_profile(B): row_pro = 0 for i in range(B.shape[0]): j = np.where(B[i, :] != 0)[0] if np.any(j): if j[-1] > i: row_pro += (j[-1]-i) col_pro = 0 for j in range(B.shape[0]): i = np.where(B[:, j] != 0)[0] if np.any(i): if i[-1] > j: col_pro += i[-1]-j ans = (row_pro+col_pro, col_pro, row_pro) return ans def test_sparse_symmetric_permute(): "Sparse: Symmetric Permute" # CSR version A = rand_dm(25, 0.5) perm = np.random.permutation(25) x = sp_permute(A.data, perm, perm).toarray() z = _permutateIndexes(A.full(), perm, perm) assert_equal((x - z).all(), 0) # CSC version B = A.data.tocsc() y = sp_permute(B, perm, perm).toarray() assert_equal((y - z).all(), 0) def test_sparse_nonsymmetric_permute(): "Sparse: Nonsymmetric Permute" # CSR version A = rand_dm(25, 0.5) rperm = np.random.permutation(25) cperm = np.random.permutation(25) x = sp_permute(A.data, rperm, cperm).toarray() z = _permutateIndexes(A.full(), rperm, cperm) assert_equal((x - z).all(), 0) # CSC version B = A.data.tocsc() y = sp_permute(B, rperm, cperm).toarray() assert_equal((y - z).all(), 0) def test_sparse_symmetric_reverse_permute(): "Sparse: Symmetric Reverse Permute" # CSR version A = rand_dm(25, 0.5) perm = np.random.permutation(25) x = sp_permute(A.data, perm, perm) B = sp_reverse_permute(x, perm, perm) assert_equal((A.full() - B.toarray()).all(), 0) # CSC version B = A.data.tocsc() perm = np.random.permutation(25) x = sp_permute(B, perm, perm) B = sp_reverse_permute(x, perm, perm) assert_equal((A.full() - B.toarray()).all(), 0) def test_sparse_nonsymmetric_reverse_permute(): "Sparse: Nonsymmetric Reverse Permute" # CSR square array check A = rand_dm(25, 0.5) rperm = np.random.permutation(25) cperm = np.random.permutation(25) x = sp_permute(A.data, rperm, cperm) B = sp_reverse_permute(x, rperm, cperm) assert_equal((A.full() - B.toarray()).all(), 0) # CSC square array check A = rand_dm(25, 0.5) rperm = np.random.permutation(25) cperm = np.random.permutation(25) B = A.data.tocsc() x = sp_permute(B, rperm, cperm) B = sp_reverse_permute(x, rperm, cperm) assert_equal((A.full() - B.toarray()).all(), 0) # CSR column vector check A = coherent(25, 1) rperm = np.random.permutation(25) x = sp_permute(A.data, rperm, []) B = sp_reverse_permute(x, rperm, []) assert_equal((A.full() - B.toarray()).all(), 0) # CSC column vector check A = coherent(25, 1) rperm = np.random.permutation(25) B = A.data.tocsc() x = sp_permute(B, rperm, []) B = sp_reverse_permute(x, rperm, []) assert_equal((A.full() - B.toarray()).all(), 0) # CSR row vector check A = coherent(25, 1).dag() cperm =	np.random.permutation(25)	numpy.random.permutation
#!/usr/bin/env python """ A TensorFlow-based 2D Cardiac Electrophysiology Modeler Copyright 2017-2018 <NAME> (<EMAIL>) Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. """ import tensorflow as tf import numpy as np from screen import Screen from ionic import IonicModel from functools import partial class Courtemanche(IonicModel): """ The modified Courtemanche atrial model """ def __init__(self, props): super().__init__(props) self.min_v = -100.0 # mV self.max_v = 50.0 # mV self.depol = -81.0 # mV self.chronic = True self.fast_states = ['V', '_Na_i_', '_m_', '_h_'] def init_state_variable(self, state, name, value): if name in state: print('Warning! The state variable arlready exists') state[name] = np.full([self.height, self.width], value, dtype=np.float32) def define(self, s1=True, state=None): """ Defines the tensorflow model It sets ode_op, s2_op and V used by other methods """ super().define() if state is None: state = {} self.init_state_variable(state, 'V', -81.18) self.init_state_variable(state, '_Na_i_', 1.117e+01) # self.init_state_variable(state, '_Na_i_', 1.3e+01) self.init_state_variable(state, '_m_', 2.98e-3) self.init_state_variable(state, '_h_', 9.649e-1) self.init_state_variable(state, '_j_', 9.775e-1) self.init_state_variable(state, '_K_i_', 1.39e+02) self.init_state_variable(state, '_oa_', 3.043e-2) self.init_state_variable(state, '_oi_', 9.992e-1) self.init_state_variable(state, '_ua_', 4.966e-3) self.init_state_variable(state, '_ui_', 9.986e-1) self.init_state_variable(state, '_xr_', 3.296e-5) self.init_state_variable(state, '_xs_', 1.869e-2) self.init_state_variable(state, '_Ca_i_', 1.013e-4) self.init_state_variable(state, '_d_', 1.367e-4) self.init_state_variable(state, '_f_', 9.996e-1) self.init_state_variable(state, '_f_Ca_', 7.755e-1) self.init_state_variable(state, '_Ca_rel_', 1.488) self.init_state_variable(state, '_u_', 0.0) self.init_state_variable(state, '_v_', 1.0) self.init_state_variable(state, '_w_', 0.9992) self.init_state_variable(state, '_Ca_up_', 1.488) if self.ultra_slow: self.init_state_variable(state, '_us_', 0.72) # steady-state at 500 ms # S1 stimulation: vertical along the left side if s1: state['V'][:,:25] = 20.0 # define the graph... with tf.device('/device:GPU:0'): # Create variables for simulation state State = {} for s in state: State[s] = tf.Variable(state[s]) State1, inter = self.solve(State) self.dt_per_step = 1 fasts = [] slows = [] # for s in State: # if s in self.fast_states: # fasts.append(tf.assign(State[s], State1[s])) # else: # slows.append(tf.assign(State[s], State1[s])) for s in State: fasts.append(tf.assign(State[s], State1[s])) self._ode_op = tf.group(fasts) self._ops['slow'] = tf.group(slows) self._V = State['V'] # V is needed by self.image() self._State = State self._Inter = inter Trend = tf.Variable(np.zeros([2], dtype=np.float32)) self._ops['trend'] = tf.group( tf.assign(Trend[0], self._V[self.width//2,self.height//8]) # tf.assign(Trend[1], State['_us_'][self.width//2,self.height//8]) ) self._Trend = Trend def euler(self, g, Rate, dt): return g + Rate * dt def δt(self, name): return self.dt # if name in self.fast_states: # return self.dt # else: # return self.dt * 10 def solve(self, State): """ Explicit Euler ODE solver """ V0 = State['V'] V = self.enforce_boundary(V0) R = 8.3143 # (joule/mole_kelvin). T = 310; # (kelvin). F = 96.4867 # (coulomb/millimole). Cm = 100 # Cm is Cm in membrane (picoF). g_Na = 7.8 # fast_sodium_current (nanoS/picoF). Na_o = 140 # (millimolar). K_o = 5.4 # (millimolar). g_to = 0.1652 # transient_outward_K_current (nanoS/picoF). g_Ks = 0.12941176 # slow_delayed_rectifier_K_current (nanoS/picoF). g_Ca_L = 0.12375 # L_type_Ca_channel (nanoS/picoF). Km_Na_i = 10 # sodium_potassium_pump (millimolar). Km_K_o = 1.5 # sodium_potassium_pump (millimolar). i_NaK_max = 0.59933874 # sodium_potassium_pump (picoA/picoF). i_CaP_max = 0.275 # sarcolemmal_calcium_pump_current (picoA/picoF). g_B_Na = 0.0006744375 # background_currents (nanoS/picoF). g_B_Ca = 0.001131 # background_currents (nanoS/picoF). g_B_K = 0 # background_currents (nanoS/picoF). Ca_o = 1.8 # (millimolar). K_rel = 30 # Ca_release_current_from_JSR (per_millisecond). tau_tr = 180 # transfer_current_from_NSR_to_JSR (millisecond). I_up_max = 0.005 # Ca_uptake_current_by_the_NSR (millimolar/millisecond). K_up = 0.00092 # Ca_uptake_current_by_the_NSR (millimolar). Ca_up_max = 15 # Ca_leak_current_by_the_NSR (millimolar). CMDN_max = 0.05 # CMDN_max is CMDN_max in Ca_buffers (millimolar). TRPN_max = 0.07 # TRPN_max is TRPN_max in Ca_buffers (millimolar). CSQN_max = 10 # CSQN_max is CSQN_max in Ca_buffers (millimolar). Km_CMDN = 0.00238 # Km_CMDN is Km_CMDN in Ca_buffers (millimolar). Km_TRPN = 0.0005 # Km_TRPN is Km_TRPN in Ca_buffers (millimolar). Km_CSQN = 0.8 # Km_CSQN is Km_CSQN in Ca_buffers (millimolar). V_cell = 20100 # intracellular_ion_concentrations (micrometre_3). V_i = V_cell * 0.68 # intracellular_ion_concentrations (micrometre_3). tau_f_Ca = 2.0 # L_type_Ca_channel_f_Ca_gate (millisecond). tau_u = 8.0 # Ca_release_current_from_JSR_u_gate (millisecond). V_rel = 0.0048 * V_cell # intracellular_ion_concentrations (micrometre_3). V_up = 0.0552 * V_cell # intracellular_ion_concentrations (micrometre_3). State1 = {} if self.chronic: chronic = 1.0 else: chronic = 0.0 with self.jit_scope(): inter = self.calc_inter(V, tf) State1['_d_'] = self.rush_larsen(State['_d_'], inter['d_infinity'], inter['tau_d'], self.δt('_d_')) State1['_f_'] = self.rush_larsen(State['_f_'], inter['f_infinity'], inter['tau_f'], self.δt('_f_')) State1['_w_'] = self.rush_larsen(State['_w_'], inter['w_infinity'], inter['tau_w'], self.δt('_d_')) State1['_m_'] = self.rush_larsen(State['_m_'], inter['m_inf'], inter['tau_m'], self.δt('_m_')) State1['_h_'] = self.rush_larsen(State['_h_'], inter['h_inf'], inter['tau_h'], self.δt('_h_')) State1['_j_'] = self.rush_larsen(State['_j_'], inter['j_inf'], inter['tau_j'], self.δt('_j_')) State1['_oa_'] = self.rush_larsen(State['_oa_'], inter['oa_infinity'], inter['tau_oa'], self.δt('_oa_')) State1['_oi_'] = self.rush_larsen(State['_oi_'], inter['oi_infinity'], inter['tau_oi'], self.δt('_oi_')) State1['_ua_'] = self.rush_larsen(State['_ua_'], inter['ua_infinity'], inter['tau_ua'], self.δt('_ua_')) State1['_ui_'] = self.rush_larsen(State['_ui_'], inter['ui_infinity'], inter['tau_ui'], self.δt('_ui_')) State1['_xr_'] = self.rush_larsen(State['_xr_'], inter['xr_infinity'], inter['tau_xr'], self.δt('_xr_')) State1['_xs_'] = self.rush_larsen(State['_xs_'], inter['xs_infinity'], inter['tau_xs'], self.δt('_xs_')) if self.ultra_slow: State1['_us_'] = self.rush_larsen(State['_us_'], inter['us_infinity'], inter['tau_us'], self.δt('_us_')) f_Ca_infinity = tf.reciprocal(1.0 + State['_Ca_i_'] / 0.00035) State1['_f_Ca_'] = self.rush_larsen(State['_f_Ca_'], f_Ca_infinity, tau_f_Ca, self.δt('_f_Ca_')) E_K = ((R * T) / F) * tf.log(K_o / State['_K_i_']) i_K1 = inter['i_K1a'] * (V - E_K) i_to = (1.0-0.5chronic) Cm * g_to * tf.pow(State['_oa_'], 3) * State['_oi_'] * (V - E_K) i_Kur = (1.0-0.5chronic) Cm * inter['g_Kur'] * tf.pow(State['_ua_'], 3) * State['_ui_'] * (V - E_K) i_Kr = inter['i_Kra'] * State['_xr_'] * (V - E_K) i_Ks = Cm * g_Ks * tf.square(State['_xs_']) * (V - E_K) i_NaK = ((Cm * i_NaK_max * inter['f_NaK']) / (1.0 + tf.sqrt(tf.pow(Km_Na_i / State['_Na_i_'], 3.0)))) * (K_o / (K_o + Km_K_o)) i_B_K = Cm * g_B_K * (V - E_K) State1['_K_i_'] = self.euler( State['_K_i_'], (2.0 * i_NaK - (i_K1 + i_to + i_Kur + i_Kr + i_Ks + i_B_K)) / (V_i * F), self.δt('_K_i_') ) E_Na = ((R * T) / F) * tf.log(Na_o / State['_Na_i_']) i_Na = Cm * g_Na * tf.pow(State['_m_'], 3) * State['_h_'] * State['_j_'] * (V - E_Na) if self.ultra_slow: i_Na = State['_us_'] i_NaCa = inter['i_NaCaa'] tf.pow(State['_Na_i_'], 3) - inter['i_NaCab'] * State['_Ca_i_'] i_B_Na = Cm * g_B_Na * (V - E_Na) State1['_Na_i_'] = self.euler( State['_Na_i_'], (-3.0 * i_NaK - (3.0 * i_NaCa + i_B_Na + i_Na)) / (V_i * F), self.δt('_Na_i_') ) i_st = 0.0 i_Ca_L = (1.0-0.7chronic) Cm * g_Ca_L * State['_d_'] * State['_f_'] * State['_f_Ca_'] * (V - 65.0) i_CaP = (Cm * i_CaP_max * State['_Ca_i_']) / (0.0005 + State['_Ca_i_']) E_Ca = ((R * T) / (2.0 * F)) * tf.log(Ca_o / State['_Ca_i_']) i_B_Ca = Cm * g_B_Ca * (V - E_Ca) DV = self.euler( V, -(i_Na + i_K1 + i_to + i_Kur + i_Kr + i_Ks + i_B_Na + i_B_Ca + i_NaK + i_CaP + i_NaCa + i_Ca_L + i_st) / Cm, self.δt('V') ) State1['V'] = DV + self.diff * self.δt('V') * self.laplace(V) i_rel = K_rel * tf.square(State['_u_']) * State['_v_'] * State['_w_'] * (State['_Ca_rel_'] - State['_Ca_i_']) i_tr = (State['_Ca_up_'] - State['_Ca_rel_']) / tau_tr State1['_Ca_rel_'] = self.euler( State['_Ca_rel_'], (i_tr - i_rel) * tf.reciprocal(1.0 + (CSQN_max * Km_CSQN) / tf.square(State['_Ca_rel_'] + Km_CSQN)), self.δt('_Ca_rel_') ) Fn = 1000.0 * (1.0e-15 * V_rel * i_rel - (1.0e-15 / (2.0 * F)) * (0.5 * i_Ca_L - 0.2 * i_NaCa)) u_infinity = tf.reciprocal(1.0 + tf.exp(-(Fn - 3.4175e-13) / 1.367e-15)) State1['_u_'] = self.rush_larsen(State['_u_'], u_infinity, tau_u, self.δt('_u_')) tau_v = 1.91 + 2.09 * u_infinity v_infinity = 1.0 - tf.reciprocal(1.0 + tf.exp(-(Fn - 6.835e-14) / 1.367e-15)) State1['_v_'] = self.rush_larsen(State['_v_'], v_infinity, tau_v, self.δt('_v_')) i_up = I_up_max / (1.0 + K_up / State['_Ca_i_']) i_up_leak = (I_up_max * State['_Ca_up_']) / Ca_up_max State1['_Ca_up_'] = self.euler( State['_Ca_up_'], i_up - (i_up_leak + (i_tr * V_rel) / V_up), self.δt('_Ca_up_') ) B1 = (2.0 * i_NaCa - (i_CaP + i_Ca_L + i_B_Ca)) / (2.0 * V_i * F) + (V_up * (i_up_leak - i_up) + i_rel * V_rel) / V_i B2 = 1.0 + (TRPN_max * Km_TRPN) / tf.square(State['_Ca_i_'] + Km_TRPN) + (CMDN_max * Km_CMDN) / tf.square(State['_Ca_i_'] + Km_CMDN) State1['_Ca_i_'] = self.euler( State['_Ca_i_'], B1 / B2, self.δt('_Ca_i_') ) for s in State: if not s in State1: print('Warning! Missing New State: %s' % s) return State1, inter def calc_inter(self, V, mod=np): R = 8.3143 # R in membrane (joule/mole_kelvin). T = 310 # T in (kelvin). F = 96.4867 # F in membrane (coulomb/millimole). Cm = 100 # Cm in membrane (picoF). Na_o = 140 # Na_o (millimolar). g_K1 = 0.09 # g_K1 (nanoS/picoF). K_Q10 = 3 # transient_outward_K_current (dimensionless). g_Kr = 0.029411765 # rapid_delayed_rectifier_K_current (nanoS/picoF). Ca_o = 1.8 # (millimolar). I_NaCa_max = 1600 # Na_Ca_exchanger_current(picoA/picoF). K_mNa = 87.5 # Na_Ca_exchanger_current (millimolar). K_mCa = 1.38 # Na_Ca_exchanger_current (millimolar). K_sat = 0.1 # Na_Ca_exchanger_current (dimensionless). gamma_ = 0.35 # Na_Ca_exchanger_current (dimensionless). sigma = 1.0 # sodium_potassium_pump (dimensionless). def where(cond, x, y): ret = mod.where(cond, x, y) if type(ret) is np.ndarray and ret.shape == (): ret = float(ret) return ret inter = {} ϵ = V * 1e-20 inter['d_infinity'] = mod.reciprocal(1.0 + mod.exp((V + 10.0) / -8.0)) # note: V + 10 is changed to V + 10.0001 to suppress a warning passing V = -10 inter['tau_d'] = where( mod.abs(V + 10.0001) < 1.0e-10, 4.579 / (1.0 + mod.exp((V + 10.0) / -6.24)), (1.0 - mod.exp((V + 10.0001) / -6.24)) / (0.0350000 * (V + 10.0001) * (1.0 + mod.exp((V + 10.0001) / -6.24))) ) inter['f_infinity'] = mod.exp(-(V + 28.0) / 6.9) / (1.0 + mod.exp(-(V + 28.0) / 6.9)) inter['tau_f'] = 9.0 * mod.reciprocal(0.0197000 * mod.exp(-mod.square(0.0337) * mod.square(V + 10.0)) + 0.02) inter['tau_w'] = where( mod.abs(V - 7.9) < 1.0e-10, ϵ + ((6.0 * 0.2) / 1.3), (6.0 * (1.0 - mod.exp(-(V - 7.9) / 5.0))) / ((1.0 + 0.3 * mod.exp(-(V - 7.9) / 5.0)) * 1.0 * (V - 7.9)) ) inter['w_infinity'] = 1.0 - mod.reciprocal(1.0 + mod.exp(-(V - 40.0) / 17.0)) alpha_m = where( mod.abs(V - -47.13) < 0.001, ϵ + 3.2, (0.32 * (V + 47.13)) / (1.0 - mod.exp(-0.1 * (V + 47.13))) ) beta_m = 0.08 * mod.exp(-V / 11.0) inter['m_inf'] = alpha_m / (alpha_m + beta_m) inter['tau_m'] = mod.reciprocal(alpha_m + beta_m) alpha_h = where( V < -40.0, 0.135 * mod.exp((V + 80.0) / -6.8), ϵ ) beta_h = where( V < -40.0, 3.56 * mod.exp(0.079 * V) + 310000. * mod.exp(0.35 * V), mod.reciprocal(0.13 * (1.0 + mod.exp((V + 10.66) / -11.1))) ) inter['h_inf'] = alpha_h / (alpha_h + beta_h) inter['tau_h'] = mod.reciprocal(alpha_h + beta_h) alpha_j = where( V < -40.0, ((-127140. * mod.exp(0.2444 * V) - 3.474e-05 * mod.exp(-0.04391 * V)) * (V + 37.78)) / (1.0 + mod.exp(0.311 * (V + 79.23))), ϵ ) beta_j = where( V < -40.0, (0.1212 * mod.exp(-0.01052 * V)) / (1.0 + mod.exp(-0.1378 * (V + 40.14))), (0.3 * mod.exp(-2.535e-07 * V)) / (1.0 + mod.exp(-0.1 * (V + 32.0))) ) inter['j_inf'] = alpha_j / (alpha_j + beta_j) inter['tau_j'] = mod.reciprocal(alpha_j + beta_j) alpha_oa = 0.65 * mod.reciprocal(mod.exp((V - -10.0) / -8.5) + mod.exp(((V - -10.0) - 40.0) / -59.0)) beta_oa = 0.65 * mod.reciprocal(2.5 + mod.exp(((V - -10.0) + 72.0) / 17.0)) inter['tau_oa'] = mod.reciprocal(alpha_oa + beta_oa) / K_Q10 inter['oa_infinity'] = mod.reciprocal(1.0 + mod.exp(((V - -10.0) + 10.47) / -17.54)) alpha_oi = mod.reciprocal(18.53 + 1.0 * mod.exp(((V - -10.0) + 103.7) / 10.95)) beta_oi = mod.reciprocal(35.56 + 1.0 * mod.exp(((V - -10.0) - 8.74) / -7.44)) inter['tau_oi'] = mod.reciprocal(alpha_oi + beta_oi) / K_Q10 inter['oi_infinity'] = mod.reciprocal(1.0 + mod.exp(((V - -10.0) + 33.1) / 5.3)) alpha_ua = 0.65 * mod.reciprocal(mod.exp((V - -10.0) / -8.5) + mod.exp(((V - -10.0) - 40.0) / -59.0)) beta_ua = 0.65 * mod.reciprocal(2.5 + mod.exp(((V - -10.0) + 72.0) / 17.0)) inter['tau_ua'] = mod.reciprocal(alpha_ua + beta_ua) / K_Q10 inter['ua_infinity'] = mod.reciprocal(1.0 + mod.exp(((V - -10.0) + 20.3) / -9.6)) alpha_ui = mod.reciprocal(21.0 + 1.0 * mod.exp(((V - -10.0) - 195.000) / -28.0)) beta_ui = mod.reciprocal(mod.exp(((V - -10.0) - 168.0) / -16.0)) inter['tau_ui'] = mod.reciprocal(alpha_ui + beta_ui) / K_Q10 inter['ui_infinity'] = mod.reciprocal(1.0 + mod.exp(((V - -10.0) - 109.45) / 27.48)) alpha_xr = where( mod.abs(V + 14.1) < 1.0e-10, ϵ + 0.0015, (0.0003 * (V + 14.1)) / (1.0 - mod.exp((V + 14.1) / -5.0)) ) beta_xr = where( mod.abs(V - 3.3328) < 1.0e-10, ϵ + 0.000378361, (7.3898e-05 * (V - 3.3328)) / (mod.exp((V - 3.3328) / 5.1237) - 1.0) ) inter['tau_xr'] = mod.reciprocal(alpha_xr + beta_xr); inter['xr_infinity'] = mod.reciprocal(1.0 + mod.exp((V + 14.1) / -6.5)) alpha_xs = where( mod.abs(V - 19.9) < 1.0e-10, ϵ + 0.00068, (4.0e-05 * (V - 19.9)) / (1.0 - mod.exp((V - 19.9) / -17.0)) ) beta_xs = where( mod.abs(V - 19.9) < 1.0e-10, ϵ + 0.000315, (3.5e-05 * (V - 19.9)) / (mod.exp((V - 19.9) / 9.0) - 1.0) ) inter['tau_xs'] = 0.5 * mod.reciprocal(alpha_xs + beta_xs) inter['xs_infinity'] = mod.sqrt(mod.reciprocal(1.0 + mod.exp((V - 19.9) / -12.7))) inter['g_Kur'] = 0.005 + 0.05 / (1.0 + mod.exp((V - 15.0) / -13.0)) inter['f_NaK'] = mod.reciprocal(1.0 + 0.1245 * mod.exp((-0.1 * F * V) / (R * T)) + 0.0365 * sigma * mod.exp((-F * V) / (R * T))) i_NaCad = (K_mNaK_mNaK_mNa + Na_oNa_oNa_o) * (K_mCa + Ca_o) * (1.0 + K_sat * mod.exp(((gamma_ - 1.0) * V * F) / (R * T))) inter['i_NaCaa'] = (Cm * I_NaCa_max * (mod.exp((gamma_ * F * V) / (R * T)) * Ca_o)) / i_NaCad inter['i_NaCab'] = (Cm * I_NaCa_max * (mod.exp(((gamma_ - 1.0) * F * V) / (R * T)) * (Na_oNa_oNa_o))) / i_NaCad inter['i_K1a'] = (Cm * g_K1) / (1.0 + mod.exp(0.07 * (V + 80.0))) # * (V - E_K) inter['i_Kra'] = (Cm * g_Kr) / (1.0 + mod.exp((V + 15.0) / 22.4)) # * state[_xr_] * (V - E_K) V_us = -83.0 K_us = 23.0 alpha_us = 3e-5 * (0.5 * (1 - mod.tanh((V - V_us) / K_us))) beta_us = 1e-5 * (0.5 * (1 + mod.tanh((V - (V_us + 30)) / K_us))) inter['us_infinity'] = alpha_us / (alpha_us + beta_us) inter['tau_us'] = mod.reciprocal(alpha_us + beta_us) return inter def pot(self): return self._V def image(self): """ Returns a [height x width] float ndarray in the range 0 to 1 that encodes V in grayscale """ v = self._V.eval() return (v - self.min_v) / (self.max_v - self.min_v) def cl_observer(m, cyclelengths, i0, i, cl): na = m._State['_Na_i_'].eval() mean_na =	np.average(na, weights=m.phase)	numpy.average
from datetime import datetime from dateutil.tz import tzlocal, tzutc import pandas as pd import numpy as np from hdmf.backends.hdf5 import HDF5IO from hdmf.common import DynamicTable from pynwb import NWBFile, TimeSeries, NWBHDF5IO, get_manager from pynwb.file import Subject from pynwb.epoch import TimeIntervals from pynwb.ecephys import ElectricalSeries from pynwb.testing import NWBH5IOMixin, TestCase, remove_test_file class TestNWBFileHDF5IO(TestCase): """ Test reading/writing an NWBFile using HDF5IO """ def setUp(self): """ Set up an NWBFile object with an acquisition TimeSeries, analysis TimeSeries, and a processing module """ self.start_time = datetime(1970, 1, 1, 12, tzinfo=tzutc()) self.ref_time = datetime(1979, 1, 1, 0, tzinfo=tzutc()) self.create_date = datetime(2017, 4, 15, 12, tzinfo=tzlocal()) self.manager = get_manager() self.filename = 'test_nwbfileio.h5' self.nwbfile = NWBFile(session_description='a test NWB File', identifier='TEST123', session_start_time=self.start_time, timestamps_reference_time=self.ref_time, file_create_date=self.create_date, experimenter='test experimenter', stimulus_notes='test stimulus notes', data_collection='test data collection notes', experiment_description='test experiment description', institution='nomad', lab='nolab', notes='nonotes', pharmacology='nopharmacology', protocol='noprotocol', related_publications='nopubs', session_id='007', slices='noslices', source_script='nosources', surgery='nosurgery', virus='novirus', source_script_file_name='nofilename') self.ts = TimeSeries(name='test_timeseries', data=list(range(100, 200, 10)), unit='SIunit', timestamps=np.arange(10.), resolution=0.1) self.nwbfile.add_acquisition(self.ts) self.ts2 = TimeSeries(name='test_timeseries2', data=list(range(200, 300, 10)), unit='SIunit', timestamps=np.arange(10.), resolution=0.1) self.nwbfile.add_analysis(self.ts2) self.mod = self.nwbfile.create_processing_module('test_module', 'a test module') self.ts3 = TimeSeries(name='test_timeseries2', data=list(range(100, 200, 10)), unit='SIunit', timestamps=np.arange(10.), resolution=0.1) self.mod.add(self.ts3) def tearDown(self): """ Delete the created test file """ remove_test_file(self.filename) def test_children(self): """ Test that the TimeSeries and processing module are children of their respective parents """ self.assertIn(self.ts, self.nwbfile.children) self.assertIn(self.ts2, self.nwbfile.children) self.assertIn(self.mod, self.nwbfile.children) self.assertIn(self.ts3, self.mod.children) def test_write(self): """ Test writing the NWBFile using HDF5IO """ hdf5io = HDF5IO(self.filename, manager=self.manager, mode='a') hdf5io.write(self.nwbfile) hdf5io.close() # TODO add some asserts def test_read(self): """ Test reading the NWBFile using HDF5IO """ hdf5io = HDF5IO(self.filename, manager=self.manager, mode='w') hdf5io.write(self.nwbfile) hdf5io.close() hdf5io = HDF5IO(self.filename, manager=self.manager, mode='r') container = hdf5io.read() self.assertIsInstance(container, NWBFile) self.assertEqual(len(container.acquisition), 1) self.assertEqual(len(container.analysis), 1) for v in container.acquisition.values(): self.assertIsInstance(v, TimeSeries) self.assertContainerEqual(container, self.nwbfile) hdf5io.close() class TestNWBFileIO(NWBH5IOMixin, TestCase): """ Test writing an NWBFile to disk and reading back the file """ # this uses methods tearDown, test_roundtrip, and validate from NWBH5IOMixin. the rest are overridden def setUp(self): super().setUp() self.start_time = datetime(1970, 1, 1, 12, tzinfo=tzutc()) self.ref_time = datetime(1979, 1, 1, 0, tzinfo=tzutc()) self.create_dates = [datetime(2017, 5, 1, 12, tzinfo=tzlocal()), datetime(2017, 5, 2, 13, 0, 0, 1, tzinfo=tzutc()), datetime(2017, 5, 2, 14, tzinfo=tzutc())] def setUpContainer(self): """ Return a placeholder NWBFile """ return NWBFile('placeholder', 'placeholder', datetime(1970, 1, 1, 12, tzinfo=tzutc())) def build_nwbfile(self): """ Create an NWB file """ self.container = NWBFile(session_description='a test session description for a test NWBFile', identifier='FILE123', session_start_time=self.start_time, file_create_date=self.create_dates, timestamps_reference_time=self.ref_time, experimenter='A test experimenter', lab='a test lab', institution='a test institution', experiment_description='a test experiment description', session_id='test1', notes='my notes', pharmacology='drugs', protocol='protocol', related_publications='my pubs', slices='my slices', surgery='surgery', virus='a virus', source_script='noscript', source_script_file_name='nofilename', stimulus_notes='test stimulus notes', data_collection='test data collection notes', keywords=('these', 'are', 'keywords')) def roundtripContainer(self, cache_spec=False): """ Build and write an NWBFile to disk, read the file, and return the NWBFile """ self.build_nwbfile() self.writer = NWBHDF5IO(self.filename, mode='w') self.writer.write(self.container, cache_spec=cache_spec) self.writer.close() self.reader = NWBHDF5IO(self.filename, mode='r') self.read_nwbfile = self.reader.read() return self.read_nwbfile def addContainer(self, nwbfile): """ No-op. roundtripContainer is overridden and no longer uses addContainer """ pass def getContainer(self, nwbfile): """ Get the NWBFile object from the given NWBFile """ return nwbfile class TestExperimentersConstructorRoundtrip(TestNWBFileIO): """ Test that a list of multiple experimenters in a constructor is written to and read from file """ def build_nwbfile(self): description = 'test nwbfile experimenter' identifier = 'TEST_experimenter' self.nwbfile = NWBFile(session_description=description, identifier=identifier, session_start_time=self.start_time, experimenter=('experimenter1', 'experimenter2')) class TestExperimentersSetterRoundtrip(TestNWBFileIO): """ Test that a list of multiple experimenters in a setter is written to and read from file """ def build_nwbfile(self): description = 'test nwbfile experimenter' identifier = 'TEST_experimenter' self.nwbfile = NWBFile(session_description=description, identifier=identifier, session_start_time=self.start_time) self.nwbfile.experimenter = ('experimenter1', 'experimenter2') class TestPublicationsConstructorRoundtrip(TestNWBFileIO): """ Test that a list of multiple publications in a constructor is written to and read from file """ def build_nwbfile(self): description = 'test nwbfile publications' identifier = 'TEST_publications' self.nwbfile = NWBFile(session_description=description, identifier=identifier, session_start_time=self.start_time, related_publications=('pub1', 'pub2')) class TestPublicationsSetterRoundtrip(TestNWBFileIO): """ Test that a list of multiple publications in a setter is written to and read from file """ def build_nwbfile(self): description = 'test nwbfile publications' identifier = 'TEST_publications' self.nwbfile = NWBFile(session_description=description, identifier=identifier, session_start_time=self.start_time) self.nwbfile.related_publications = ('pub1', 'pub2') class TestSubjectIO(NWBH5IOMixin, TestCase): def setUpContainer(self): """ Return the test Subject """ return Subject(age='P90D', description='An unfortunate rat', genotype='WT', sex='M', species='Rattus norvegicus', subject_id='RAT123', weight='2 kg', date_of_birth=datetime(1970, 1, 1, 12, tzinfo=tzutc()), strain='my_strain') def addContainer(self, nwbfile): """ Add the test Subject to the given NWBFile """ nwbfile.subject = self.container def getContainer(self, nwbfile): """ Return the test Subject from the given NWBFile """ return nwbfile.subject class TestEmptySubjectIO(TestSubjectIO): def setUpContainer(self): return Subject() class TestEpochsIO(NWBH5IOMixin, TestCase): def setUpContainer(self): """ Return placeholder epochs object. Tested epochs are added directly to the NWBFile in addContainer """ return TimeIntervals('epochs') def addContainer(self, nwbfile): """ Add the test epochs to the given NWBFile """ nwbfile.add_epoch_column( name='temperature', description='average temperture (c) during epoch' ) nwbfile.add_epoch( start_time=5.3, stop_time=6.1, timeseries=[], tags='ambient', temperature=26.4, ) # reset the thing self.container = nwbfile.epochs def getContainer(self, nwbfile): """ Return the test epochs from the given NWBFile """ return nwbfile.epochs class TestEpochsIODf(TestEpochsIO): def addContainer(self, nwbfile): """ Add the test epochs with TimeSeries objects to the given NWBFile """ tsa, tsb = [ TimeSeries(name='a', data=np.arange(11), unit='flubs', timestamps=np.linspace(0, 1, 11)), TimeSeries(name='b', data=np.arange(13), unit='flubs', timestamps=	np.linspace(0.1, 5, 13)	numpy.linspace
from Bio import pairwise2 from Bio.SubsMat.MatrixInfo import blosum62 import numpy as np import scipy import pandas as pd import regex as re import pickle def sub_pivot_df(pps, sdf, group=True): """function takes a long form datatable of extracts and peaks (input sdf), filters for peptide plasmids of interest (input pps) and outputs a datatable with one row per extract, with columns for 'unmod' and 'mod' (or any other peak type) with the respective peak area. group option specifies if replicates should be grouped (by peptide sequence), with""" #filter for a sub-dataframe that includes just the peptide plasmids of interest sub_df = sdf[sdf['pep_plasmid'].isin(pps)] #Grab the set of sequences of interest (set to make non-redundant) sequences = set(sub_df['sequence']) #grab just the modification information (%mod fractions) for each extract stats_df = sub_df.pivot_table(index='extract', columns='peak_type', values='mod_area', fill_value=0).reset_index() #metadata for all of the extracts meta_df = sub_df.groupby('extract', group_keys=False).first().reset_index().sort_values('extract') #merge metadata with stats data based on extract extract_df = meta_df.merge(stats_df, on='extract', how='inner') #if include_other: # sub_data['mod'] = sub_data['mod'] + sub_data['other'] if group: extract_df['replicate'] = 1 return extract_df.groupby( ['sequence', 'mod_plasmid', 'modification description'], group_keys=False).agg( {'media':'first','ms':'first', 'pep_plasmid':'first', 'replicate':'sum', 'total_area':'mean', 'mod':'mean','unmod':'mean', 'extract':'first'}).reset_index().sort_values('mod', ascending=False) else: return extract_df def seq_alignment(wt_sequence, sdf, score='ddg', penalties=(-15, -2)): """Function takes a wild-type sequence and a dataframe of extracts of sequence variants to align to. Returns four lists, each list having one element per row of the input dataframe: seq_alignments - a list of tuples. Each tuple is the variant sequence, it's alignment to the wild-type sequence, and it's modification score (the type of score specified in 'score' input). labels_sparse - the variant sequence aligned to the wild-type sequence, positions that match wild-type are blank (space), positions that are mutated are the mutant amino acid (or '-' for gap). Note that for the wild-type sequence, the full sequence is here, no spaces, as a reference. labels - the variant sequence, unchanged/unaligned. labels_aligned - the variant sequence, aligned (with gaps) """ seq_alignments = [] labels = [wt_sequence] labels_sparse = [wt_sequence] labels_aligned = [wt_sequence] for ind, row in enumerate(sdf.iterrows()): #get rid of the index row = row[1] seq = row['sequence'] mod_efficiency = row[score] #align the sequences, this will be a list of alignments, we just take the first one, since they are all # functionally equivalent for our purposes alignments = pairwise2.align.globalds(wt_sequence, seq.split("*")[0], blosum62, penalties[0], penalties[1])[0] #skip the wt sequence for the labels/order, so we added it at the beginning if alignments[1] == wt_sequence: seq_alignments.append((seq, alignments[1], mod_efficiency)) else: seq_alignments.append((seq, alignments[1], mod_efficiency)) labels_sparse.append("".join([i if i != w else " " for i, w in zip(alignments[1], wt_sequence)])) labels.append(seq) labels_aligned.append(alignments[1]) return seq_alignments, labels_sparse, labels, labels_aligned def aln2binary_df(wt_sequence, seq_alignments, invert=False): """function takes a wild-type sequence, and a list of sequence alignments from the seq_alignment function (list should be a list of tuples, one tuple per variant: (variant sequence, it's alignment to the wild-type sequence, and it's modification score) Returns a new dataframe that is one row per variant, and one column per amino acid position. At each position, the number 1 means that the variant sequence matches wild-type, 0 means the variant sequence does not match wild-type If invert, then the 1/0 assignment is switched. DOES NOT WORK IF THERE ARE GAPS (or rather, it just assumes that a gap is not a match, it is not recorded specially) """ #Making a new dataframe (seq_df) that has a column for each amino acid indexes = [i for i in range(len(wt_sequence))] #temporary list, 1 element for each variant new_form = [] mod_scores = [] for variant_seq, aligned_seq, mod_eff in seq_alignments: binary_seq = [] for s,w in zip(aligned_seq, wt_sequence): if s == w: binary_seq.append(0 if invert else 1) else: binary_seq.append(1 if invert else 0) new_form.append(binary_seq) mod_scores.append(mod_eff) binary_df = pd.DataFrame(new_form, columns = indexes) #convert modification scores into a numpy array and then into delta delta G for each variant mod_scores =	np.array(mod_scores)	numpy.array
""" qgs tensor module ================= This module computes and holds the tensor representing the tendencies of the model's equations. Notes ----- These are computed using the analytical expressions from: * <NAME>., <NAME>. and <NAME>.: The Modular Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0, Geosci. Model Dev., 9, 2793-2808, `doi:10.5194/gmd-9-2793-2016 <http://dx.doi.org/10.5194/gmd-9-2793-2016>`_, 2016. * <NAME>., & <NAME>. (1987). Theories of multiple equilibria and weather regimes—A critical reexamination. Part II: Baroclinic two-layer models. Journal of the atmospheric sciences, 44 (21), 3282-3303. `link <https://journals.ametsoc.org/doi/abs/10.1175/1520-0469(1987)044%3C3282%3ATOMEAW%3E2.0.CO%3B2>`_ """ import numpy as np import sparse as sp class QgsTensor(object): """qgs tendencies tensor class. Parameters ---------- atmospheric_innner_product: AtmosphericInnerProducts or None The inner products of the atmospheric basis functions on which the model's PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. oceanic_innner_product: OceanicInnerProducts or None The inner products of the atmospheric basis functions on which the model's PDE oceanic equations are projected. If None, disable the oceanic tendencies. Attributes ---------- atmospheric_innner_product: AtmosphericInnerProducts or None The inner products of the atmospheric basis functions on which the model's PDE equations are projected. If None, the atmospheric tendencies are disabled. oceanic_innner_product: OceanicInnerProducts or None The inner products of the atmospheric basis functions on which the model's PDE equations are projected. If None, the oceanic tendencies are disabled. params: QgParams The models parameters. tensor: sparse.COO(float) The tensor :math:`\mathcal{T}_{i,j,k}` :math:`i`-th components. jacobian_tensor: sparse.COO(float) The jacobian tensor :math:`\mathcal{T}_{i,j,k} + \mathcal{T}_{i,k,j}` :math:`i`-th components. """ def __init__(self, atmospheric_inner_products=None, oceanic_inner_products=None): self.atmospheric_inner_products = atmospheric_inner_products self.oceanic_inner_products = oceanic_inner_products if self.atmospheric_inner_products is not None: self.params = self.atmospheric_inner_products.params if self.oceanic_inner_products is not None: self.params = self.oceanic_inner_products.params self.tensor = None self.jacobian_tensor = None self.compute_tensor() def _psi_a(self, i): """Transform the :math:`\psi_{\mathrm a}` :math:`i`-th coefficient into the effective model's variable. Parameters ---------- i: int The :math:`i`-th coefficients of :math:`\psi_{\mathrm a}` Returns ------- int The effective model's variable. """ return i def _theta_a(self, i): """Transform the :math:`\\theta_{\mathrm a}` :math:`i`-th coefficient into the effective model's variable. Parameters ---------- i: int The :math:`i`-th coefficients of :math:`\\theta_{\mathrm a}` Returns ------- int The effective model's variable. """ return i + self.params.nmod[0] def _psi_o(self, i): """Transform the :math:`\psi_{\mathrm o}` :math:`i`-th coefficient into the effective model's variable. Parameters ---------- i: int The :math:`i`-th coefficients of :math:`\psi_{\mathrm o}` Returns ------- int The effective model's variable. """ return i + 2 * self.params.nmod[0] def _deltaT_o(self, i): """Transform the :math:`\delta T_{\mathrm o}` :math:`i`-th coefficient into the effective model's variable. Parameters ---------- i: int The :math:`i`-th coefficients of :math:`\delta T_{\mathrm o}` Returns ------- int The effective model's variable. """ return i + 2 * self.params.nmod[0] + self.params.nmod[1] def _deltaT_g(self, i): """Transform the :math:`\delta T_{\mathrm o}` :math:`i`-th coefficient into the effective model's variable. Parameters ---------- i: int The :math:`i`-th coefficients of :math:`\delta T_{\mathrm o}` Returns ------- int The effective model's variable. """ return i + 2 * self.params.nmod[0] def compute_tensor(self): """Routine to compute the tensor.""" aips = self.atmospheric_inner_products oips = self.oceanic_inner_products par = self.params atp = par.atemperature_params ap = par.atmospheric_params op = par.oceanic_params scp = par.scale_params gp = par.ground_params namod = par.nmod[0] ngomod = par.nmod[1] ndim = par.ndim if par.gotemperature_params is not None: ocean = par.gotemperature_params._name == "Oceanic Temperature" ground_temp = par.gotemperature_params._name == "Ground Temperature" else: ocean = False ground_temp = False # 0-th tensor component is an empty matrix tensor = sp.zeros((ndim+1, ndim + 1, ndim + 1), dtype=np.float64, format='dok') jacobian_tensor = sp.zeros((ndim+1, ndim + 1, ndim + 1), dtype=np.float64, format='dok') ## Problem with matmul with object and DOK archi : Temporary fix until a better solution is found hk = np.array(gp.hk, dtype=np.float) g = aips.g.to_coo() ################# # psi_a part for i in range(1, namod + 1): t = np.zeros((ndim + 1, ndim + 1), dtype=np.float64) for j in range(1, namod + 1): t[self._psi_a(j), 0] = -((aips.c[(i - 1), (j - 1)] * scp.beta) / aips.a[(i - 1), (i - 1)]) \ - (ap.kd * _kronecker_delta((i - 1), (j - 1))) / 2 t[self._theta_a(j), 0] = (ap.kd * _kronecker_delta((i - 1), (j - 1))) / 2 if gp.hk is not None: oro = (g[(i - 1), (j - 1), :] @ hk) / (2 * aips.a[(i - 1), (i - 1)]) t[self._psi_a(j), 0] -= oro t[self._theta_a(j), 0] += oro for k in range(1, namod + 1): t[self._psi_a(j), self._psi_a(k)] = - aips.b[(i - 1), (j - 1), (k - 1)] \ / aips.a[(i - 1), (i - 1)] t[self._theta_a(j), self._theta_a(k)] = - aips.b[(i - 1), (j - 1), (k - 1)] \ / aips.a[(i - 1), (i - 1)] if ocean: for j in range(1, ngomod + 1): t[self._psi_o(j), 0] = ap.kd * aips.d[(i - 1), (j - 1)] / \ (2 * aips.a[(i - 1), (i - 1)]) t = self.simplify_matrix(t) tensor[self._psi_a(i)] = t jacobian_tensor[self._psi_a(i)] = t + t.T # theta_a part for i in range(1, namod + 1): t = np.zeros((ndim + 1, ndim + 1), dtype=np.float64) if par.Cpa is not None: t[0, 0] = par.Cpa[i - 1] / (1 - aips.a[0, 0] * ap.sig0) if atp.hd is not None and atp.thetas is not None: t[0, 0] += atp.hd * atp.thetas[(i - 1)] / (1. - ap.sig0 * aips.a[(i - 1), (i - 1)]) for j in range(1, namod + 1): t[self._psi_a(j), 0] = (aips.a[(i - 1), (j - 1)] * ap.kd * ap.sig0) \ / (-2 + 2 * aips.a[(i - 1), (i - 1)] * ap.sig0) if par.LSBpa is not None and par.Lpa is not None: heat = 2. * (par.LSBpa + atp.sc * par.Lpa) * _kronecker_delta((i - 1), (j - 1)) else: heat = 0 t[self._theta_a(j), 0] = (-((ap.sig0 * (2. * aips.c[(i - 1), (j - 1)] * scp.beta + aips.a[(i - 1), (j - 1)] * (ap.kd + 4. * ap.kdp)))) + heat) / (-2. + 2. * aips.a[(i - 1), (i - 1)] * ap.sig0) if atp.hd is not None: t[self._theta_a(j), 0] += (atp.hd * _kronecker_delta((i - 1), (j - 1))) / (ap.sig0 * aips.a[(i - 1), (i - 1)] - 1.) if gp.hk is not None: oro = (ap.sig0 * g[(i - 1), (j - 1), :] @ hk) / (2 * aips.a[(i - 1), (i - 1)] * ap.sig0 - 2.) t[self._theta_a(j), 0] -= oro t[self._psi_a(j), 0] += oro for k in range(1, namod + 1): t[self._psi_a(j), self._theta_a(k)] = (aips.g[(i - 1), (j - 1), (k - 1)] - aips.b[(i - 1), (j - 1), (k - 1)] * ap.sig0) / \ (-1 + aips.a[(i - 1), (i - 1)] * ap.sig0) t[self._theta_a(j), self._psi_a(k)] = (aips.b[(i - 1), (j - 1), (k - 1)] * ap.sig0) \ / (1 - aips.a[(i - 1), (i - 1)] * ap.sig0) if ocean: for j in range(1, ngomod + 1): t[self._psi_o(j), 0] = ap.kd * (aips.d[(i - 1), (j - 1)] * ap.sig0) \ / (2 - 2 * aips.a[(i - 1), (i - 1)] * ap.sig0) if par.LSBpgo is not None and par.Lpa is not None: t[self._deltaT_o(j), 0] = aips.s[(i - 1), (j - 1)] * (2 * par.LSBpgo + par.Lpa) \ / (2 - 2 * aips.a[(i - 1), (i - 1)] * ap.sig0) if ground_temp and i <= ngomod: t[self._deltaT_g(i), 0] = (2 * par.LSBpgo + par.Lpa) / (2 - 2 * aips.a[(i - 1), (i - 1)] * ap.sig0) t = self.simplify_matrix(t) tensor[self._theta_a(i)] = t jacobian_tensor[self._theta_a(i)] = t + t.T if ocean: # psi_o part for i in range(1, ngomod + 1): t =	np.zeros((ndim + 1, ndim + 1), dtype=np.float64)	numpy.zeros
''' Author: <NAME>, <NAME> Acknowledgment: Derived some functions from <NAME>'s work Description: This script is used to train the dual neural network for tool substitution with material properties. ''' import os, sys import numpy as np import cPickle as pickle import csv import keras from keras.models import Sequential, Model from keras.layers import Dense, Input, Lambda, Dropout, merge, MaxPooling1D, Flatten, Conv1D import keras.backend as K from keras import optimizers from keras import regularizers from keras.utils import plot_model from keras.utils.np_utils import to_categorical from sklearn.preprocessing import Normalizer, StandardScaler from sklearn.model_selection import train_test_split from sklearn.metrics import classification_report, confusion_matrix from sklearn.utils import shuffle from sklearn.externals import joblib from sklearn.metrics import accuracy_score import random def sigmoid(z): return 1/(1+np.exp(-z)) def features_scio(csv_file): # Take csv file and retrieve scio_processed_data corresponding to input features = {} obj_materials = {} wavelengthCount = 331 with open(csv_file) as f: reader = csv.reader(f) for idx, row in enumerate(reader): if idx == 10: wavelengths = [float(r.strip().split('_')[-1].split()[0]) + 740.0 for r in row[10:wavelengthCount+10]] try: int(row[0]) # To skip first few rows until first integer encountered if '.ply' not in row[3]: obj_name = row[3] + '.ply' else: obj_name = row[3] features_list = [float(elt) for elt in row[10:wavelengthCount+10]] features_list = firstDeriv(features_list, wavelengths) features[obj_name] = features_list material_name = row[4] obj_materials[obj_name] = row[4] except: pass return features, obj_materials def loadScioDataset(pklFile, csvFile, materialNames=[], objectNames=[]): saveFilename = pklFile + '.pkl' if os.path.isfile(saveFilename): with open(saveFilename, 'rb') as f: X, y_materials, y_objects, wavelengths = pickle.load(f) else: X = [] y_materials = [] y_objects = [] filename = csvFile + '.csv' print(filename) wavelengthCount = 331 with open(filename, 'rb') as f: reader = csv.reader(f) for i, row in enumerate(reader): if i < 10 or i == 11: continue if i == 10: # Header row wavelengths = [float(r.strip().split('_')[-1].split()[0]) + 740.0 for r in row[10:wavelengthCount+10]] continue obj = row[3].strip() material = row[4].strip() if material not in materialNames: continue index = materialNames.index(material) if objectNames is not None and obj not in objectNames[index]: continue values = [float(v) for v in row[10:wavelengthCount+10]] X.append(values) y_materials.append(index) y_objects.append(obj) with open(saveFilename, 'wb') as f: pickle.dump([X, y_materials, y_objects, wavelengths], f, protocol=pickle.HIGHEST_PROTOCOL) return X, y_materials, y_objects, wavelengths def firstDeriv(x, wavelengths): # First derivative of measurements with respect to wavelength x = np.copy(x) for i, xx in enumerate(x): dx = np.zeros(xx.shape, np.float) dx[0:-1] =	np.diff(xx)	numpy.diff
# from __future__ import print_function, absolute_import, division import multiprocessing import re import shutil import types from pathlib import Path import allesfitter import numpy as np import yaml from argparse import ArgumentParser from sherlockpipe.star.HabitabilityCalculator import HabitabilityCalculator import pandas as pd import os from os import path resources_dir = path.join(path.dirname(__file__)) class Fitter: def __init__(self, object_dir, only_initial, mcmc = False, detrend = False): self.args = types.SimpleNamespace() self.args.noshow = True self.args.north = False self.args.o = True self.args.auto = True self.args.save = True self.args.nickname = "" # TODO do we set the sherlock id? self.args.FFI = False # TODO get this from input self.args.targetlist = "best_signal_latte_input.csv" self.args.new_path = "" # TODO check what to do with this self.object_dir = os.getcwd() if object_dir is None else object_dir self.latte_dir = str(Path.home()) + "/.sherlockpipe/latte/" if not os.path.exists(self.latte_dir): os.mkdir(self.latte_dir) self.data_dir = self.object_dir self.only_initial = only_initial self.mcmc = mcmc self.detrend = detrend def fit(self, candidate_df, star_df, cpus, allesfit_dir): candidate_row = candidate_df.iloc[0] sherlock_star_file = self.object_dir + "/params_star.csv" star_file = allesfit_dir + "/params_star.csv" params_file = allesfit_dir + "/params.csv" settings_file = allesfit_dir + "/settings.csv" if candidate_row["number"] is None or	np.isnan(candidate_row["number"])	numpy.isnan
import sys import numpy as np import pandas as pd import openmdao.api as om from wisdem.commonse import gravity eps = 1e-3 # Convenience functions for computing McDonald's C and F parameters def chsMshc(x): return np.cosh(x) * np.sin(x) - np.sinh(x) * np.cos(x) def chsPshc(x): return np.cosh(x) * np.sin(x) + np.sinh(x) * np.cos(x) def carterFactor(airGap, slotOpening, slotPitch): """Return Carter factor (based on Langsdorff's empirical expression) See page 3-13 Boldea Induction machines Chapter 3 """ gma = (2 * slotOpening / airGap) ** 2 / (5 + 2 * slotOpening / airGap) return slotPitch / (slotPitch - airGap * gma * 0.5) # --------------- def carterFactorMcDonald(airGap, h_m, slotOpening, slotPitch): """Return Carter factor using Carter's equation (based on Schwartz-Christoffel's conformal mapping on simplified slot geometry) This code is based on Eq. B.3-5 in Appendix B of McDonald's thesis. It is used by PMSG_arms and PMSG_disc. h_m : magnet height (m) b_so : stator slot opening (m) tau_s : Stator slot pitch (m) """ mu_r = 1.06 # relative permeability (probably for neodymium magnets, often given as 1.05 - GNS) g_1 = airGap + h_m / mu_r # g b_over_a = slotOpening / (2 * g_1) gamma = 4 / np.pi * (b_over_a * np.arctan(b_over_a) - np.log(np.sqrt(1 + b_over_a ** 2))) return slotPitch / (slotPitch - gamma * g_1) # --------------- def carterFactorEmpirical(airGap, slotOpening, slotPitch): """Return Carter factor using Langsdorff's empirical expression""" sigma = (slotOpening / airGap) / (5 + slotOpening / airGap) return slotPitch / (slotPitch - sigma * slotOpening) # --------------- def carterFactorSalientPole(airGap, slotWidth, slotPitch): """Return Carter factor for salient pole rotor Where does this equation come from? It's different from other approximations above. Original code: tau_s = np.pi * dia / S # slot pitch b_s = tau_s * b_s_tau_s # slot width b_t = tau_s - b_s # tooth width K_C1 = (tau_s + 10 * g_a) / (tau_s - b_s + 10 * g_a) # salient pole rotor slotPitch - slotWidth == toothWidth """ return (slotPitch + 10 * airGap) / (slotPitch - slotWidth + 10 * airGap) # salient pole rotor # --------------------------------- def array_seq(q1, b, c, Total_number): Seq = np.array([1, 0, 0, 1, 0]) diff = Total_number * 5 / 6 G = np.prod(Seq.shape) return Seq, diff, G # --------------------------------- def winding_factor(Sin, b, c, p, m): S = int(Sin) # Step 1 Writing q1 as a fraction q1 = b / c # Step 2: Writing a binary sequence of b-c zeros and b ones Total_number = int(S / b) L = array_seq(q1, b, c, Total_number) # STep 3 : Repeat binary sequence Q_s/b times New_seq = np.tile(L[0], Total_number) Actual_seq1 = pd.DataFrame(New_seq[:, None].T) Winding_sequence = ["A", "C1", "B", "A1", "C", "B1"] New_seq2 = np.tile(Winding_sequence, int(L[1])) Actual_seq2 = pd.DataFrame(New_seq2[:, None].T) Seq_f = pd.concat([Actual_seq1, Actual_seq2], ignore_index=True) Seq_f.reset_index(drop=True) Slots = S R = S if S % 2 == 0 else S + 1 Windings_arrange = (pd.DataFrame(index=Seq_f.index, columns=Seq_f.columns[1:R])).fillna(0) counter = 1 # Step #4 Arranging winding in Slots for i in range(0, len(New_seq)): if Seq_f.loc[0, i] == 1: Windings_arrange.loc[0, counter] = Seq_f.loc[1, i] counter = counter + 1 Windings_arrange.loc[1, 1] = "C1" for k in range(1, R): if Windings_arrange.loc[0, k] == "A": Windings_arrange.loc[1, k + 1] = "A1" elif Windings_arrange.loc[0, k] == "B": Windings_arrange.loc[1, k + 1] = "B1" elif Windings_arrange.loc[0, k] == "C": Windings_arrange.loc[1, k + 1] = "C1" elif Windings_arrange.loc[0, k] == "A1": Windings_arrange.loc[1, k + 1] = "A" elif Windings_arrange.loc[0, k] == "B1": Windings_arrange.loc[1, k + 1] = "B" elif Windings_arrange.loc[0, k] == "C1": Windings_arrange.loc[1, k + 1] = "C" Phase_A = np.zeros((1000, 1), dtype=float) counter_A = 0 # Windings_arrange.to_excel('test.xlsx') # Winding vector, W_A for Phase A for l in range(1, R): if Windings_arrange.loc[0, l] == "A" and Windings_arrange.loc[1, l] == "A": Phase_A[counter_A, 0] = l Phase_A[counter_A + 1, 0] = l counter_A = counter_A + 2 elif Windings_arrange.loc[0, l] == "A1" and Windings_arrange.loc[1, l] == "A1": Phase_A[counter_A, 0] = -1 * l Phase_A[counter_A + 1, 0] = -1 * l counter_A = counter_A + 2 elif Windings_arrange.loc[0, l] == "A" or Windings_arrange.loc[1, l] == "A": Phase_A[counter_A, 0] = l counter_A = counter_A + 1 elif Windings_arrange.loc[0, l] == "A1" or Windings_arrange.loc[1, l] == "A1": Phase_A[counter_A, 0] = -1 * l counter_A = counter_A + 1 W_A = (np.trim_zeros(Phase_A)).T # Calculate winding factor K_w = 0 for r in range(0, int(2 * (S) / 3)): Gamma = 2 * np.pi * p * np.abs(W_A[0, r]) / S K_w += np.sign(W_A[0, r]) * (np.exp(Gamma * 1j)) K_w = np.abs(K_w) / (2 * S / 3) CPMR = np.lcm(S, int(2 * p)) N_cog_s = CPMR / S N_cog_p = CPMR / p N_cog_t = CPMR * 0.5 / p A = np.lcm(S, int(2 * p)) b_p_tau_p = 2 * 1 * p / S - 0 b_t_tau_s = (2) * S * 0.5 / p - 2 return K_w # --------------------------------- def shell_constant(R, t, l, x, E, v): Lambda = (3 * (1 - v 2) / (R 2 * t 2)) 0.25 D = E * t ** 3 / (12 * (1 - v ** 2)) C_14 = (np.sinh(Lambda * l)) ** 2 + (np.sin(Lambda * l)) ** 2 C_11 = (np.sinh(Lambda * l)) ** 2 - (np.sin(Lambda * l)) ** 2 F_2 = np.cosh(Lambda * x) * np.sin(Lambda * x) + np.sinh(Lambda * x) * np.cos(Lambda * x) C_13 = np.cosh(Lambda * l) * np.sinh(Lambda * l) - np.cos(Lambda * l) * np.sin(Lambda * l) F_1 = np.cosh(Lambda * x) * np.cos(Lambda * x) F_4 = np.cosh(Lambda * x) * np.sin(Lambda * x) - np.sinh(Lambda * x) * np.cos(Lambda * x) return D, Lambda, C_14, C_11, F_2, C_13, F_1, F_4 # --------------------------------- def plate_constant(a, b, E, v, r_o, t): D = E * t ** 3 / (12 * (1 - v ** 2)) C_2 = 0.25 * (1 - (b / a) ** 2 * (1 + 2 * np.log(a / b))) C_3 = 0.25 * (b / a) * (((b / a) ** 2 + 1) * np.log(a / b) + (b / a) ** 2 - 1) C_5 = 0.5 * (1 - (b / a) ** 2) C_6 = 0.25 * (b / a) * ((b / a) ** 2 - 1 + 2 * np.log(a / b)) C_8 = 0.5 * (1 + v + (1 - v) * (b / a) ** 2) C_9 = (b / a) * (0.5 * (1 + v) * np.log(a / b) + 0.25 * (1 - v) * (1 - (b / a) ** 2)) L_11 = (1 / 64) * ( 1 + 4 * (r_o / a) ** 2 - 5 * (r_o / a) ** 4 - 4 * (r_o / a) ** 2 * (2 + (r_o / a) ** 2) * np.log(a / r_o) ) L_17 = 0.25 * (1 - 0.25 * (1 - v) * ((1 - (r_o / a) 4) - (r_o / a) 2 * (1 + (1 + v) * np.log(a / r_o)))) return D, C_2, C_3, C_5, C_6, C_8, C_9, L_11, L_17 # --------------------------------- debug = False # --------------------------------- class GeneratorBase(om.ExplicitComponent): """ Base class for generators Parameters ---------- B_r : float, [T] Remnant flux density E : float, [Pa] youngs modulus G : float, [Pa] Shear modulus P_Fe0e : float, [W/kg] specific eddy losses @ 1.5T, 50Hz P_Fe0h : float, [W/kg] specific hysteresis losses W / kg @ 1.5 T @50 Hz S_N : float Slip alpha_p : float b_r_tau_r : float Rotor Slot width / Slot pitch ratio b_ro : float, [m] Rotor slot opening width b_s_tau_s : float Stator Slot width/Slot pitch ratio b_so : float, [m] Stator slot opening width cofi : float power factor freq : float, [Hz] grid frequency h_i : float, [m] coil insulation thickness h_sy0 : float h_w : float, [m] Slot wedge height k_fes : float Stator iron fill factor per Grauers k_fillr : float Rotor slot fill factor k_fills : float Stator Slot fill factor k_s : float magnetic saturation factor for iron m : int Number of phases mu_0 : float, [mkg/s2/A2] permeability of free space mu_r : float, [mkg/s2/A2] relative permeability (neodymium) p : float number of pole pairs (taken as int within code) phi : numpy array[90], [rad] tilt angle (during transportation) q1 : int Stator slots per pole per phase q2 : int Rotor slots per pole per phase ratio_mw2pp : float ratio of magnet width to pole pitch(bm / self.tau_p) resist_Cu : float, [ohm/m] Copper resistivity sigma : float, [Pa] assumed max shear stress v : float poisson ratio y_tau_p : float Stator coil span to pole pitch y_tau_pr : float Rotor coil span to pole pitch I_0 : float, [A] no-load excitation current T_rated : float, [Nm] Rated torque d_r : float, [m] arm depth d_r h_m : float, [m] magnet height h_0 : float, [m] Slot height h_s : float, [m] Yoke height h_s len_s : float, [m] Stator core length machine_rating : float, [W] Machine rating shaft_rpm : numpy array[n_pc], [rpm] rated speed of input shaft (lss for direct, hss for geared) n_r : float number of arms n rad_ag : float, [m] airgap radius t_wr : float, [m] arm depth thickness n_s : float number of stator arms n_s b_st : float, [m] arm width b_st d_s : float, [m] arm depth d_s t_ws : float, [m] arm depth thickness D_shaft : float, [m] Shaft diameter rho_Copper : float, [kgm*-3] Copper density rho_Fe : float, [kgm*-3] Magnetic Steel density rho_Fes : float, [kgm*-3] Structural Steel density rho_PM : float, [kgm-3] Magnet density Returns ------- B_rymax : float, [T] Peak Rotor yoke flux density B_trmax : float, [T] maximum tooth flux density in rotor B_tsmax : float, [T] maximum tooth flux density in stator B_g : float, [T] Peak air gap flux density B_g B_g1 : float, [T] air gap flux density fundamental B_pm1 : float Fundamental component of peak air gap flux density N_s : float Number of turns in the stator winding b_s : float, [m] slot width b_t : float, [m] tooth width A_Curcalc : float, [mm2] Conductor cross-section mm^2 A_Cuscalc : float, [mm*2] Stator Conductor cross-section mm^2 b_m : float magnet width mass_PM : float, [kg] Magnet mass Copper : float, [kg] Copper Mass Iron : float, [kg] Electrical Steel Mass Structural_mass : float, [kg] Structural Mass generator_mass : float, [kg] Actual mass f : float Generator output frequency I_s : float, [A] Generator output phase current R_s : float, [ohm] Stator resistance L_s : float Stator synchronising inductance J_s : float, [Am-2] Stator winding current density A_1 : float Specific current loading K_rad : float Stack length ratio Losses : numpy array[n_pc], [W] Total loss generator_efficiency : numpy array[n_pc] Generator electromagnetic efficiency values (<1) u_ar : float, [m] Rotor radial deflection u_as : float, [m] Stator radial deflection u_allow_r : float, [m] Allowable radial rotor u_allow_s : float, [m] Allowable radial stator y_ar : float, [m] Rotor axial deflection y_as : float, [m] Stator axial deflection y_allow_r : float, [m] Allowable axial y_allow_s : float, [m] Allowable axial z_ar : float, [m] Rotor circumferential deflection z_as : float, [m] Stator circumferential deflection z_allow_r : float, [m] Allowable circum rotor z_allow_s : float, [m] Allowable circum stator b_allow_r : float, [m] Allowable arm dimensions b_allow_s : float, [m] Allowable arm TC1 : float, [m3] Torque constraint TC2r : float, [m3] Torque constraint-rotor TC2s : float, [m3] Torque constraint-stator R_out : float, [m] Outer radius S : float Stator slots Slot_aspect_ratio : float Slot aspect ratio Slot_aspect_ratio1 : float Stator slot aspect ratio Slot_aspect_ratio2 : float Rotor slot aspect ratio D_ratio : float Stator diameter ratio J_r : float Rotor winding Current density L_sm : float mutual inductance Q_r : float Rotor slots R_R : float Rotor resistance b_r : float rotor slot width b_tr : float rotor tooth width b_trmin : float minimum tooth width """ def initialize(self): self.options.declare("n_pc", default=20) def setup(self): n_pc = self.options["n_pc"] # Constants and parameters self.add_input("B_r", val=1.2, units="T") self.add_input("E", val=0.0, units="Pa") self.add_input("G", val=0.0, units="Pa") self.add_input("P_Fe0e", val=1.0, units="W/kg") self.add_input("P_Fe0h", val=4.0, units="W/kg") self.add_input("S_N", val=-0.002) self.add_input("alpha_p", val=0.5 * np.pi * 0.7) self.add_input("b_r_tau_r", val=0.45) self.add_input("b_ro", val=0.004, units="m") self.add_input("b_s_tau_s", val=0.45) self.add_input("b_so", val=0.004, units="m") self.add_input("cofi", val=0.85) self.add_input("freq", val=60, units="Hz") self.add_input("h_i", val=0.001, units="m") self.add_input("h_sy0", val=0.0) self.add_input("h_w", val=0.005, units="m") self.add_input("k_fes", val=0.9) self.add_input("k_fillr", val=0.7) self.add_input("k_fills", val=0.65) self.add_input("k_s", val=0.2) self.add_discrete_input("m", val=3) self.add_input("mu_0", val=np.pi * 4e-7, units="mkg/s2/A2") self.add_input("mu_r", val=1.06, units="mkg/s2/A2") self.add_input("p", val=3.0) self.add_input("phi", val=np.deg2rad(90), units="rad") self.add_discrete_input("q1", val=6) self.add_discrete_input("q2", val=4) self.add_input("ratio_mw2pp", val=0.7) self.add_input("resist_Cu", val=1.8e-8 * 1.4, units="ohm/m") self.add_input("sigma", val=40e3, units="Pa") self.add_input("v", val=0.3) self.add_input("y_tau_p", val=1.0) self.add_input("y_tau_pr", val=10.0 / 12) # General inputs # self.add_input('r_s', val=0.0, units='m', desc='airgap radius r_s') self.add_input("I_0", val=0.0, units="A") self.add_input("rated_torque", val=0.0, units="Nm") self.add_input("d_r", val=0.0, units="m") self.add_input("h_m", val=0.0, units="m") self.add_input("h_0", val=0.0, units="m") self.add_input("h_s", val=0.0, units="m") self.add_input("len_s", val=0.0, units="m") self.add_input("machine_rating", val=0.0, units="W") self.add_input("shaft_rpm", val=np.zeros(n_pc), units="rpm") self.add_input("n_r", val=0.0) self.add_input("rad_ag", val=0.0, units="m") self.add_input("t_wr", val=0.0, units="m") # Structural design variables self.add_input("n_s", val=0.0) self.add_input("b_st", val=0.0, units="m") self.add_input("d_s", val=0.0, units="m") self.add_input("t_ws", val=0.0, units="m") self.add_input("D_shaft", val=0.0, units="m") # Material properties self.add_input("rho_Copper", val=8900.0, units="kgm*-3") self.add_input("rho_Fe", val=7700.0, units="kgm*-3") self.add_input("rho_Fes", val=7850.0, units="kgm*-3") self.add_input("rho_PM", val=7450.0, units="kgm-3") # Magnetic loading self.add_output("B_rymax", val=0.0, units="T") self.add_output("B_trmax", val=0.0, units="T") self.add_output("B_tsmax", val=0.0, units="T") self.add_output("B_g", val=0.0, units="T") self.add_output("B_g1", val=0.0, units="T") self.add_output("B_pm1", val=0.0) # Stator design self.add_output("N_s", val=0.0) self.add_output("b_s", val=0.0, units="m") self.add_output("b_t", val=0.0, units="m") self.add_output("A_Curcalc", val=0.0, units="mm2") self.add_output("A_Cuscalc", val=0.0, units="mm*2") # Rotor magnet dimension self.add_output("b_m", val=0.0) # Mass Outputs self.add_output("mass_PM", val=0.0, units="kg") self.add_output("Copper", val=0.0, units="kg") self.add_output("Iron", val=0.0, units="kg") self.add_output("Structural_mass", val=0.0, units="kg") self.add_output("generator_mass", val=0.0, units="kg") # Electrical performance self.add_output("f", val=np.zeros(n_pc)) self.add_output("I_s", val=np.zeros(n_pc), units="A") self.add_output("R_s", val=np.zeros(n_pc), units="ohm") self.add_output("L_s", val=0.0) self.add_output("J_s", val=np.zeros(n_pc), units="Am-2") self.add_output("A_1", val=np.zeros(n_pc)) # Objective functions self.add_output("K_rad", val=0.0) self.add_output("Losses", val=np.zeros(n_pc), units="W") self.add_output("eandm_efficiency", val=np.zeros(n_pc)) # Structural performance self.add_output("u_ar", val=0.0, units="m") self.add_output("u_as", val=0.0, units="m") self.add_output("u_allow_r", val=0.0, units="m") self.add_output("u_allow_s", val=0.0, units="m") self.add_output("y_ar", val=0.0, units="m") self.add_output("y_as", val=0.0, units="m") self.add_output("y_allow_r", val=0.0, units="m") self.add_output("y_allow_s", val=0.0, units="m") self.add_output("z_ar", val=0.0, units="m") self.add_output("z_as", val=0.0, units="m") self.add_output("z_allow_r", val=0.0, units="m") self.add_output("z_allow_s", val=0.0, units="m") self.add_output("b_allow_r", val=0.0, units="m") self.add_output("b_allow_s", val=0.0, units="m") self.add_output("TC1", val=0.0, units="m3") self.add_output("TC2r", val=0.0, units="m3") self.add_output("TC2s", val=0.0, units="m3") # Other parameters self.add_output("R_out", val=0.0, units="m") self.add_output("S", val=0.0) self.add_output("Slot_aspect_ratio", val=0.0) self.add_output("Slot_aspect_ratio1", val=0.0) self.add_output("Slot_aspect_ratio2", val=0.0) self.add_output("D_ratio", val=0.0) self.add_output("J_r", val=np.zeros(n_pc)) self.add_output("L_sm", val=0.0) self.add_output("Q_r", val=0.0) self.add_output("R_R", val=0.0) self.add_output("b_r", val=0.0) self.add_output("b_tr", val=0.0) self.add_output("b_trmin", val=0.0) # ---------------------------------------------------------------------------------------- class PMSG_Outer(GeneratorBase): """ Estimates overall electromagnetic dimensions and Efficiency of PMSG -arms generator. Parameters ---------- P_mech : float, [W] Shaft mechanical power N_c : float Number of turns per coil b : float Slot pole combination c : float Slot pole combination E_p : float, [V] Stator phase voltage h_yr : float, [m] rotor yoke height h_ys : float, [m] Yoke height h_sr : float, [m] Structural Mass h_ss : float, [m] Stator yoke height t_r : float, [m] Rotor disc thickness t_s : float, [m] Stator disc thickness y_sh : float, [m] Shaft deflection theta_sh : float, [rad] slope of shaft D_nose : float, [m] Nose outer diameter y_bd : float, [m] Deflection of the bedplate theta_bd : float, [rad] Slope at the bedplate u_allow_pcent : float Radial deflection as a percentage of air gap diameter y_allow_pcent : float Radial deflection as a percentage of air gap diameter z_allow_deg : float, [deg] Allowable torsional twist B_tmax : float, [T] Peak Teeth flux density Returns ------- B_smax : float, [T] Peak Stator flux density B_symax : float, [T] Peak Stator flux density tau_p : float, [m] Pole pitch q : float, [N/m2] Normal stress len_ag : float, [m] Air gap length h_t : float, [m] tooth height tau_s : float, [m] Slot pitch J_actual : float, [A/m2] Current density T_e : float, [Nm] Electromagnetic torque twist_r : float, [deg] torsional twist twist_s : float, [deg] Stator torsional twist Structural_mass_rotor : float, [kg] Rotor mass (kg) Structural_mass_stator : float, [kg] Stator mass (kg) Mass_tooth_stator : float, [kg] Teeth and copper mass Mass_yoke_rotor : float, [kg] Rotor yoke mass Mass_yoke_stator : float, [kg] Stator yoke mass rotor_mass : float, [kg] Total rotor mass stator_mass : float, [kg] Total stator mass """ def initialize(self): super(PMSG_Outer, self).initialize() def setup(self): super(PMSG_Outer, self).setup() n_pc = self.options["n_pc"] # PMSG_structrual inputs self.add_input("P_mech", units="W") self.add_input("N_c", 0.0) self.add_input("b", 0.0) self.add_input("c", 0.0) self.add_input("E_p", 0.0, units="V") self.add_input("h_yr", val=0.0, units="m") self.add_input("h_ys", val=0.0, units="m") self.add_input("h_sr", 0.0, units="m") self.add_input("h_ss", 0.0, units="m") self.add_input("t_r", 0.0, units="m") self.add_input("t_s", 0.0, units="m") self.add_input("y_sh", units="m") self.add_input("theta_sh", 0.0, units="rad") self.add_input("D_nose", 0.0, units="m") self.add_input("y_bd", units="m") self.add_input("theta_bd", 0.0, units="rad") self.add_input("u_allow_pcent", 0.0) self.add_input("y_allow_pcent", 0.0) self.add_input("z_allow_deg", 0.0, units="deg") # Magnetic loading self.add_input("B_tmax", 0.0, units="T") self.add_output("B_smax", val=0.0, units="T") self.add_output("B_symax", val=0.0, units="T") self.add_output("tau_p", 0.0, units="m") self.add_output("q", 0.0, units="N/m2") self.add_output("len_ag", 0.0, units="m") # Stator design self.add_output("h_t", 0.0, units="m") self.add_output("tau_s", 0.0, units="m") # Electrical performance self.add_output("J_actual", val=np.zeros(n_pc), units="A/m2") self.add_output("T_e", 0.0, units="Nm") # Material properties self.add_output("twist_r", 0.0, units="deg") self.add_output("twist_s", 0.0, units="deg") # Mass Outputs self.add_output("Structural_mass_rotor", 0.0, units="kg") self.add_output("Structural_mass_stator", 0.0, units="kg") self.add_output("Mass_tooth_stator", 0.0, units="kg") self.add_output("Mass_yoke_rotor", 0.0, units="kg") self.add_output("Mass_yoke_stator", 0.0, units="kg") self.add_output("rotor_mass", 0.0, units="kg") self.add_output("stator_mass", 0.0, units="kg") def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs rad_ag = float(inputs["rad_ag"]) len_s = float(inputs["len_s"]) p = float(inputs["p"]) b = float(inputs["b"]) c = float(inputs["c"]) h_m = float(inputs["h_m"]) h_ys = float(inputs["h_ys"]) h_yr = float(inputs["h_yr"]) h_s = float(inputs["h_s"]) h_ss = float(inputs["h_ss"]) h_0 = float(inputs["h_0"]) B_tmax = float(inputs["B_tmax"]) E_p = float(inputs["E_p"]) P_mech = float(inputs["P_mech"]) P_av_v = float(inputs["machine_rating"]) h_sr = float(inputs["h_sr"]) t_r = float(inputs["t_r"]) t_s = float(inputs["t_s"]) R_sh = 0.5 * float(inputs["D_shaft"]) R_no = 0.5 * float(inputs["D_nose"]) y_sh = float(inputs["y_sh"]) y_bd = float(inputs["y_bd"]) rho_Fes = float(inputs["rho_Fes"]) rho_Fe = float(inputs["rho_Fe"]) sigma = float(inputs["sigma"]) shaft_rpm = inputs["shaft_rpm"] # Grab constant values B_r = float(inputs["B_r"]) E = float(inputs["E"]) G = float(inputs["G"]) P_Fe0e = float(inputs["P_Fe0e"]) P_Fe0h = float(inputs["P_Fe0h"]) cofi = float(inputs["cofi"]) h_w = float(inputs["h_w"]) k_fes = float(inputs["k_fes"]) k_fills = float(inputs["k_fills"]) m = int(discrete_inputs["m"]) mu_0 = float(inputs["mu_0"]) mu_r = float(inputs["mu_r"]) p = float(inputs["p"]) phi = float(inputs["phi"]) ratio_mw2pp = float(inputs["ratio_mw2pp"]) resist_Cu = float(inputs["resist_Cu"]) v = float(inputs["v"]) """ #Assign values to universal constants B_r = 1.279 # Tesla remnant flux density E = 2e11 # N/m^2 young's modulus ratio = 0.8 # ratio of magnet width to pole pitch(bm/self.tau_p) mu_0 = np.pi4e-7 # permeability of free space mu_r = 1.06 # relative permeability cofi = 0.85 # power factor #Assign values to design constants h_0 = 0.005 # Slot opening height h_w = 0.004 # Slot wedge height m = 3 # no of phases #b_s_tau_s = 0.45 # slot width to slot pitch ratio k_fills = 0.65 # Slot fill factor P_Fe0h = 4 # specific hysteresis losses W/kg @ 1.5 T P_Fe0e = 1 # specific hysteresis losses W/kg @ 1.5 T k_fes = 0.8 # Iron fill factor #Assign values to universal constants phi = 902np.pi/360 # tilt angle (rotor tilt -90 degrees during transportation) v = 0.3 # Poisson's ratio G = 79.3e9 """ ######################## Electromagnetic design ################################### K_rad = len_s / (2 rad_ag) # Aspect ratio # Calculating air gap length dia = 2 * rad_ag # air gap diameter len_ag = 0.001 * dia # air gap length r_s = rad_ag - len_ag # Stator outer radius b_so = 2 * len_ag # Slot opening tau_p = np.pi * dia / (2 * p) # pole pitch # Calculating winding factor Slot_pole = b / c S = Slot_pole * 2 * p * m testval = S / (m * np.gcd(int(S), int(p))) if float(np.round(testval, 3)).is_integer(): k_w = winding_factor(int(S), b, c, int(p), m) b_m = ratio_mw2pp * tau_p # magnet width alpha_p = np.pi / 2 * ratio_mw2pp tau_s = np.pi * (dia - 2 * len_ag) / S # Calculating Carter factor for statorand effective air gap length gamma = ( 4 / np.pi * ( b_so / 2 / (len_ag + h_m / mu_r) * np.arctan(b_so / 2 / (len_ag + h_m / mu_r)) - np.log(np.sqrt(1 + (b_so / 2 / (len_ag + h_m / mu_r)) ** 2)) ) ) k_C = tau_s / (tau_s - gamma * (len_ag + h_m / mu_r)) # carter coefficient g_eff = k_C * (len_ag + h_m / mu_r) # angular frequency in radians om_m = 2 * np.pi * shaft_rpm / 60 om_e = p * om_m freq = om_e / 2 / np.pi # outout frequency # Calculating magnetic loading B_pm1 = B_r * h_m / mu_r / (g_eff) B_g = B_r * h_m / (mu_r * g_eff) * (4 / np.pi) * np.sin(alpha_p) B_symax = B_pm1 * b_m / (2 * h_ys) * k_fes B_rymax = B_pm1 * b_m * k_fes / (2 * h_yr) b_t = B_pm1 * tau_s / B_tmax N_c = 2 # Number of turns per coil q = (B_g) ** 2 / 2 / mu_0 # Stator winding length ,cross-section and resistance l_Cus = 2 * (len_s + np.pi / 4 * (tau_s + b_t)) # length of a turn # Calculating no-load voltage induced in the stator N_s = np.rint(E_p / (np.sqrt(2) * len_s * r_s * k_w * om_m * B_g)) # Z = P_av_v / (mE_p) # Calculating leakage inductance in stator V_1 = E_p / 1.1 I_n = P_av_v / 3 / cofi / V_1 J_s = 6.0 A_Cuscalc = I_n / J_s A_slot = 2 N_c * A_Cuscalc * (10 ** -6) / k_fills tau_s_new = np.pi * (dia - 2 * len_ag - 2 * h_w - 2 * h_0) / S b_s2 = tau_s_new - b_t # Slot top width b_s1 = np.sqrt(b_s2 ** 2 - 4 * np.pi * A_slot / S) b_s = (b_s1 + b_s2) * 0.5 N_coil = 2 * S P_s = mu_0 * (h_s / 3 / b_s + h_w * 2 / (b_s2 + b_so) + h_0 / b_so) # Slot permeance function L_ssigmas = S / 3 * 4 * N_c ** 2 * len_s * P_s # slot leakage inductance L_ssigmaew = ( N_coil * N_c ** 2 * mu_0 * tau_s * np.log((0.25 * np.pi * tau_s ** 2) / (0.5 * h_s * b_s)) ) # end winding leakage inductance L_aa = 2 * np.pi / 3 * (N_c ** 2 * mu_0 * len_s * r_s / g_eff) L_m = L_aa L_ssigma = L_ssigmas + L_ssigmaew L_s = L_m + L_ssigma G_leak = np.abs((1.1 * E_p) ** 4 - (1 / 9) * (P_av_v * om_e * L_s) ** 2) # Calculating stator current and electrical loading I_s = np.sqrt(2 * (np.abs((E_p * 1.1) 2 - G_leak 0.5)) / (om_e * L_s) ** 2) A_1 = 6 * I_s * N_s / np.pi / dia J_actual = I_s / (A_Cuscalc * 2 ** 0.5) L_Cus = N_s * l_Cus R_s = inputs["resist_Cu"] * (N_s) * l_Cus / (A_Cuscalc * (10 ** -6)) B_smax = np.sqrt(2) * I_s * mu_0 / g_eff # Calculating Electromagnetically active mass wedge_area = (b_s * 0.5 - b_so * 0.5) * (2 * h_0 + h_w) V_Cus = m * L_Cus * (A_Cuscalc * (10 ** -6)) # copper volume h_t = h_s + h_w + h_0 V_Fest = len_s * S * (b_t * (h_s + h_w + h_0) + wedge_area) # volume of iron in stator tooth V_Fesy = ( len_s * np.pi * ((rad_ag - len_ag - h_s - h_w - h_0) 2 - (rad_ag - len_ag - h_s - h_w - h_0 - h_ys) 2) ) # volume of iron in stator yoke V_Fery = len_s * np.pi * ((rad_ag + h_m + h_yr) 2 - (rad_ag + h_m) 2) Copper = V_Cus[-1] * inputs["rho_Copper"] M_Fest = V_Fest * rho_Fe # Mass of stator tooth M_Fesy = V_Fesy * rho_Fe # Mass of stator yoke M_Fery = V_Fery * rho_Fe # Mass of rotor yoke Iron = M_Fest + M_Fesy + M_Fery mass_PM = 2 * np.pi * (rad_ag + h_m) * len_s * h_m * ratio_mw2pp * inputs["rho_PM"] # Calculating Losses ##1. Copper Losses K_R = 1.0 # Skin effect correction co-efficient P_Cu = m * (I_s / 2 0.5) 2 * R_s * K_R # Iron Losses ( from Hysteresis and eddy currents) P_Hyys = ( M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in stator yoke P_Ftys = ( M_Fesy * ((B_symax / 1.5) ** 2) * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator yoke P_Fesynom = P_Hyys + P_Ftys P_Hyd = ( M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in stator teeth P_Ftd = ( M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator teeth P_Festnom = P_Hyd + P_Ftd # Iron Losses ( from Hysteresis and eddy currents) P_Hyyr = ( M_Fery * (B_rymax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in stator yoke P_Ftyr = ( M_Fery * ((B_rymax / 1.5) ** 2) * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator yoke P_Ferynom = P_Hyyr + P_Ftyr # additional stray losses due to leakage flux P_ad = 0.2 * (P_Hyys + P_Ftys + P_Hyd + P_Ftd + P_Hyyr + P_Ftyr) pFtm = 300 # specific magnet loss P_Ftm = pFtm * 2 * p * b_m * len_s Losses = P_Cu + P_Festnom + P_Fesynom + P_ad + P_Ftm + P_Ferynom gen_eff = (P_mech - Losses) / (P_mech) I_snom = gen_eff * (P_mech / m / E_p / cofi) # rated current I_qnom = gen_eff * P_mech / (m * E_p) X_snom = om_e * (L_m + L_ssigma) T_e = np.pi * rad_ag ** 2 * len_s * 2 * sigma Stator = M_Fesy + M_Fest + Copper # modified mass_stru_steel Rotor = M_Fery + mass_PM # modified (N_r(R_1-self.R_sh)a_rself.rho_Fes)) Mass_tooth_stator = M_Fest + Copper Mass_yoke_rotor = M_Fery Mass_yoke_stator = M_Fesy R_out = (dia + 2 h_m + 2 * h_yr + 2 * inputs["h_sr"]) * 0.5 Losses = Losses generator_efficiency = gen_eff else: # Bad design for k in outputs.keys(): outputs[k] = 1e30 return ######################## Rotor inactive (structural) design ################################### # Radial deformation of rotor R = rad_ag + h_m L_r = len_s + t_r + 0.125 constants_x_0 = shell_constant(R, t_r, L_r, 0, E, v) constants_x_L = shell_constant(R, t_r, L_r, L_r, E, v) f_d_denom1 = R / (E * ((R) 2 - (R_sh) 2)) * ((1 - v) * R ** 2 + (1 + v) * (R_sh) ** 2) f_d_denom2 = ( t_r / (2 * constants_x_0[0] * (constants_x_0[1]) ** 3) * ( constants_x_0[2] / (2 * constants_x_0[3]) * constants_x_0[4] - constants_x_0[5] / constants_x_0[3] * constants_x_0[6] - 0.5 * constants_x_0[7] ) ) f = q * (R) ** 2 * t_r / (E * (h_yr + h_sr) * (f_d_denom1 + f_d_denom2)) u_d = ( f / (constants_x_L[0] * (constants_x_L[1]) ** 3) * ( ( constants_x_L[2] / (2 * constants_x_L[3]) * constants_x_L[4] - constants_x_L[5] / constants_x_L[3] * constants_x_L[6] - 0.5 * constants_x_L[7] ) ) + y_sh ) u_ar = (q * (R) ** 2) / (E * (h_yr + h_sr)) - u_d u_ar = np.abs(u_ar + y_sh) u_allow_r = 2 * rad_ag / 1000 * inputs["u_allow_pcent"] / 100 # axial deformation of rotor W_back_iron = plate_constant(R + h_sr + h_yr, R_sh, E, v, 0.5 * h_yr + R, t_r) W_ssteel = plate_constant(R + h_sr + h_yr, R_sh, E, v, h_yr + R + h_sr * 0.5, t_r) W_mag = plate_constant(R + h_sr + h_yr, R_sh, E, v, h_yr + R - 0.5 * h_m, t_r) W_ir = rho_Fe * gravity * np.sin(phi) * (L_r - t_r) * h_yr y_ai1r = ( -W_ir * (0.5 * h_yr + R) ** 4 / (R_sh * W_back_iron[0]) * (W_back_iron[1] * W_back_iron[4] / W_back_iron[3] - W_back_iron[2]) ) W_sr = rho_Fes * gravity * np.sin(phi) * (L_r - t_r) * h_sr y_ai2r = ( -W_sr * (h_sr * 0.5 + h_yr + R) ** 4 / (R_sh * W_ssteel[0]) * (W_ssteel[1] * W_ssteel[4] / W_ssteel[3] - W_ssteel[2]) ) W_m = np.sin(phi) * mass_PM / (2 * np.pi * (R - h_m * 0.5)) y_ai3r = -W_m * (R - h_m) ** 4 / (R_sh * W_mag[0]) * (W_mag[1] * W_mag[4] / W_mag[3] - W_mag[2]) w_disc_r = rho_Fes * gravity * np.sin(phi) * t_r a_ii = R + h_sr + h_yr r_oii = R_sh M_rb = ( -w_disc_r * a_ii ** 2 / W_ssteel[5] * (W_ssteel[6] * 0.5 / (a_ii * R_sh) * (a_ii 2 - r_oii 2) - W_ssteel[8]) ) Q_b = w_disc_r * 0.5 / R_sh * (a_ii 2 - r_oii 2) y_aiir = ( M_rb * a_ii ** 2 / W_ssteel[0] * W_ssteel[1] + Q_b * a_ii ** 3 / W_ssteel[0] * W_ssteel[2] - w_disc_r * a_ii ** 4 / W_ssteel[0] * W_ssteel[7] ) I = np.pi * 0.25 * (R 4 - (R_sh) 4) F_ecc = q * 2 * np.pi * K_rad * rad_ag ** 3 M_ar = F_ecc * L_r * 0.5 y_ar = ( np.abs(y_ai1r + y_ai2r + y_ai3r) + y_aiir + (R + h_yr + h_sr) * inputs["theta_sh"] + M_ar * L_r ** 2 * 0 / (2 * E * I) ) y_allow_r = L_r / 100 * inputs["y_allow_pcent"] # Torsional deformation of rotor J_dr = 0.5 * np.pi * ((R + h_yr + h_sr) 4 - R_sh 4) J_cylr = 0.5 * np.pi * ((R + h_yr + h_sr) 4 - R 4) twist_r = 180 / np.pi * inputs["rated_torque"] / G * (t_r / J_dr + (L_r - t_r) / J_cylr) Structural_mass_rotor = ( rho_Fes * np.pi * (((R + h_yr + h_sr) 2 - (R_sh) 2) * t_r + ((R + h_yr + h_sr) 2 - (R + h_yr) 2) * len_s) ) TC1 = inputs["rated_torque"] / (2 * np.pi * sigma) TC2r = (R + (h_yr + h_sr)) ** 2 * L_r ######################## Stator inactive (structural) design ################################### # Radial deformation of Stator L_stator = len_s + t_s + 0.1 R_stator = rad_ag - len_ag - h_t - h_ys - h_ss constants_x_0 = shell_constant(R_stator, t_s, L_stator, 0, E, v) constants_x_L = shell_constant(R_stator, t_s, L_stator, L_stator, E, v) f_d_denom1 = ( R_stator / (E * ((R_stator) 2 - (R_no) 2)) * ((1 - v) * R_stator ** 2 + (1 + v) * (R_no) ** 2) ) f_d_denom2 = ( t_s / (2 * constants_x_0[0] * (constants_x_0[1]) ** 3) * ( constants_x_0[2] / (2 * constants_x_0[3]) * constants_x_0[4] - constants_x_0[5] / constants_x_0[3] * constants_x_0[6] - 0.5 * constants_x_0[7] ) ) f = q * (R_stator) ** 2 * t_s / (E * (h_ys + h_ss) * (f_d_denom1 + f_d_denom2)) # TODO: Adds y_bd twice? u_as = ( (q * (R_stator) ** 2) / (E * (h_ys + h_ss)) - f * 0 / (constants_x_L[0] * (constants_x_L[1]) ** 3) * ( ( constants_x_L[2] / (2 * constants_x_L[3]) * constants_x_L[4] - constants_x_L[5] / constants_x_L[3] * constants_x_L[6] - 1 / 2 * constants_x_L[7] ) ) + y_bd ) u_as = np.abs(u_as + y_bd) u_allow_s = 2 * rad_ag / 1000 * inputs["u_allow_pcent"] / 100 # axial deformation of stator W_back_iron = plate_constant(R_stator + h_ss + h_ys + h_t, R_no, E, v, 0.5 * h_ys + h_ss + R_stator, t_s) W_ssteel = plate_constant(R_stator + h_ss + h_ys + h_t, R_no, E, v, R_stator + h_ss * 0.5, t_s) W_active = plate_constant(R_stator + h_ss + h_ys + h_t, R_no, E, v, R_stator + h_ss + h_ys + h_t * 0.5, t_s) W_is = rho_Fe * gravity * np.sin(phi) * (L_stator - t_s) * h_ys y_ai1s = ( -W_is * (0.5 * h_ys + R_stator) ** 4 / (R_no * W_back_iron[0]) * (W_back_iron[1] * W_back_iron[4] / W_back_iron[3] - W_back_iron[2]) ) W_ss = rho_Fes * gravity * np.sin(phi) * (L_stator - t_s) * h_ss y_ai2s = ( -W_ss * (h_ss * 0.5 + h_ys + R_stator) ** 4 / (R_no * W_ssteel[0]) * (W_ssteel[1] * W_ssteel[4] / W_ssteel[3] - W_ssteel[2]) ) W_cu = np.sin(phi) * Mass_tooth_stator / (2 * np.pi * (R_stator + h_ss + h_ys + h_t * 0.5)) y_ai3s = ( -W_cu * (R_stator + h_ss + h_ys + h_t * 0.5) ** 4 / (R_no * W_active[0]) * (W_active[1] * W_active[4] / W_active[3] - W_active[2]) ) w_disc_s = rho_Fes * gravity * np.sin(phi) * t_s a_ii = R_stator + h_ss + h_ys + h_t r_oii = R_no M_rb = ( -w_disc_s * a_ii ** 2 / W_ssteel[5] * (W_ssteel[6] * 0.5 / (a_ii * R_no) * (a_ii 2 - r_oii 2) - W_ssteel[8]) ) Q_b = w_disc_s * 0.5 / R_no * (a_ii 2 - r_oii 2) y_aiis = ( M_rb * a_ii ** 2 / W_ssteel[0] * W_ssteel[1] + Q_b * a_ii ** 3 / W_ssteel[0] * W_ssteel[2] - w_disc_s * a_ii ** 4 / W_ssteel[0] * W_ssteel[7] ) I = np.pi * 0.25 * (R_stator 4 - (R_no) 4) F_ecc = q * 2 * np.pi * K_rad * rad_ag ** 2 M_as = F_ecc * L_stator * 0.5 y_as = np.abs( y_ai1s + y_ai2s + y_ai3s + y_aiis + (R_stator + h_ys + h_ss + h_t) * inputs["theta_bd"] ) + M_as * L_stator ** 2 * 0 / (2 * E * I) y_allow_s = L_stator * inputs["y_allow_pcent"] / 100 # Torsional deformation of stator J_ds = 0.5 * np.pi * ((R_stator + h_ys + h_ss + h_t) 4 - R_no 4) J_cyls = 0.5 * np.pi * ((R_stator + h_ys + h_ss + h_t) 4 - R_stator 4) twist_s = 180.0 / np.pi * inputs["rated_torque"] / G * (t_s / J_ds + (L_stator - t_s) / J_cyls) Structural_mass_stator = rho_Fes * ( np.pi * ((R_stator + h_ys + h_ss + h_t) 2 - (R_no) 2) * t_s + np.pi * ((R_stator + h_ss) 2 - R_stator 2) * len_s ) TC2s = (R_stator + h_ys + h_ss + h_t) ** 2 * L_stator ######################## Outputs ################################### outputs["K_rad"] = K_rad outputs["len_ag"] = len_ag outputs["tau_p"] = tau_p outputs["S"] = S outputs["tau_s"] = tau_s outputs["b_m"] = b_m outputs["f"] = freq outputs["B_pm1"] = B_pm1 outputs["B_g"] = B_g outputs["B_symax"] = B_symax outputs["B_rymax"] = B_rymax outputs["b_t"] = b_t outputs["q"] = q outputs["N_s"] = N_s[-1] outputs["A_Cuscalc"] = A_Cuscalc outputs["b_s"] = b_s outputs["L_s"] = L_s outputs["J_s"] = J_s outputs["Slot_aspect_ratio"] = h_s / b_s outputs["I_s"] = I_s outputs["A_1"] = A_1 outputs["J_actual"] = J_actual outputs["R_s"] = R_s outputs["B_smax"] = B_smax[-1] outputs["h_t"] = h_t outputs["Copper"] = Copper outputs["Iron"] = Iron outputs["mass_PM"] = mass_PM outputs["T_e"] = T_e outputs["Mass_tooth_stator"] = Mass_tooth_stator outputs["Mass_yoke_rotor"] = Mass_yoke_rotor outputs["Mass_yoke_stator"] = Mass_yoke_stator outputs["R_out"] = R_out outputs["Losses"] = Losses outputs["eandm_efficiency"] = np.maximum(eps, gen_eff) outputs["u_ar"] = u_ar outputs["u_allow_r"] = u_allow_r outputs["y_ar"] = y_ar outputs["y_allow_r"] = y_allow_r outputs["twist_r"] = twist_r outputs["Structural_mass_rotor"] = Structural_mass_rotor outputs["TC1"] = TC1 outputs["TC2r"] = TC2r outputs["u_as"] = u_as outputs["u_allow_s"] = u_allow_s outputs["y_as"] = y_as outputs["y_allow_s"] = y_allow_s outputs["twist_s"] = twist_s outputs["Structural_mass_stator"] = Structural_mass_stator outputs["TC2s"] = TC2s outputs["Structural_mass"] = outputs["Structural_mass_rotor"] + outputs["Structural_mass_stator"] outputs["stator_mass"] = Stator + outputs["Structural_mass_stator"] outputs["rotor_mass"] = Rotor + outputs["Structural_mass_rotor"] outputs["generator_mass"] = Stator + Rotor + outputs["Structural_mass"] # ---------------------------------------------------------------------------------------- class PMSG_Disc(GeneratorBase): """ Estimates overall mass dimensions and Efficiency of PMSG-disc rotor generator. Parameters ---------- tau_p : float, [m] Pole pitch self.tau_p t_d : float, [m] disc thickness h_yr : float, [m] rotor yoke height h_ys : float, [m] Yoke height Returns ------- B_tmax : float, [T] Peak Teeth flux density B_smax : float, [T] Peak Stator Yoke flux density B_ymax B_symax : float, [T] Peak Stator Yoke flux density B_ymax E_p : float Stator phase voltage """ def initialize(self): super(PMSG_Disc, self).initialize() def setup(self): super(PMSG_Disc, self).setup() self.add_input("tau_p", val=0.0, units="m") self.add_input("t_d", val=0.0, units="m") self.add_input("h_yr", val=0.0, units="m") self.add_input("h_ys", val=0.0, units="m") self.add_output("B_tmax", val=0.0, units="T") self.add_output("B_smax", val=0.0, units="T") self.add_output("B_symax", val=0.0, units="T") self.add_output("E_p", val=np.zeros(self.options["n_pc"])) def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs rad_ag = inputs["rad_ag"] len_s = inputs["len_s"] h_s = inputs["h_s"] tau_p = inputs["tau_p"] h_m = inputs["h_m"] h_ys = inputs["h_ys"] h_yr = inputs["h_yr"] machine_rating = inputs["machine_rating"] shaft_rpm = inputs["shaft_rpm"] Torque = inputs["rated_torque"] b_st = inputs["b_st"] d_s = inputs["d_s"] t_ws = inputs["t_ws"] n_s = inputs["n_s"] t_d = inputs["t_d"] R_sh = 0.5 * inputs["D_shaft"] rho_Fe = inputs["rho_Fe"] rho_Copper = inputs["rho_Copper"] rho_Fes = inputs["rho_Fes"] rho_PM = inputs["rho_PM"] # Grab constant values B_r = inputs["B_r"] E = inputs["E"] P_Fe0e = inputs["P_Fe0e"] P_Fe0h = inputs["P_Fe0h"] S_N = inputs["S_N"] alpha_p = inputs["alpha_p"] b_r_tau_r = inputs["b_r_tau_r"] b_ro = inputs["b_ro"] b_s_tau_s = inputs["b_s_tau_s"] b_so = inputs["b_so"] cofi = inputs["cofi"] freq = inputs["freq"] h_i = inputs["h_i"] h_sy0 = inputs["h_sy0"] h_w = inputs["h_w"] k_fes = inputs["k_fes"] k_fillr = inputs["k_fillr"] k_fills = inputs["k_fills"] k_s = inputs["k_s"] m = discrete_inputs["m"] mu_0 = inputs["mu_0"] mu_r = inputs["mu_r"] p = inputs["p"] phi = inputs["phi"] q1 = discrete_inputs["q1"] ratio_mw2pp = inputs["ratio_mw2pp"] resist_Cu = inputs["resist_Cu"] sigma = inputs["sigma"] v = inputs["v"] y_tau_p = inputs["y_tau_p"] y_tau_pr = inputs["y_tau_pr"] """ # Assign values to universal constants B_r = 1.2 # remnant flux density (Tesla = kg / (s^2 A)) E = 2e11 # N / m^2 young's modulus sigma = 40000.0 # shear stress assumed ratio_mw2pp = 0.7 # ratio of magnet width to pole pitch(bm / self.tau_p) mu_0 = np.pi * 4e-7 # permeability of free space in m * kg / (s*2 A*2) mu_r = 1.06 # relative permeability (probably for neodymium magnets, often given as 1.05 - GNS) phi = np.deg2rad(90) # tilt angle (rotor tilt -90 degrees during transportation) cofi = 0.85 # power factor # Assign values to design constants h_w = 0.005 # wedge height y_tau_p = 1.0 # coil span to pole pitch m = 3 # no of phases q1 = 1 # no of slots per pole per phase b_s_tau_s = 0.45 # slot width / slot pitch ratio k_fills = 0.65 # Slot fill factor P_Fe0h = 4.0 # specific hysteresis losses W / kg @ 1.5 T P_Fe0e = 1.0 # specific hysteresis losses W / kg @ 1.5 T resist_Cu = 1.8e-8 1.4 # resistivity of copper b_so = 0.004 # stator slot opening k_fes = 0.9 # useful iron stack length #T = Torque v = 0.3 # poisson's ratio """ # back iron thickness for rotor and stator t_s = h_ys t = h_yr # Aspect ratio K_rad = len_s / (2 * rad_ag) # aspect ratio ###################################################### Electromagnetic design############################################# dia_ag = 2 * rad_ag # air gap diameter len_ag = 0.001 * dia_ag # air gap length b_m = ratio_mw2pp * tau_p # magnet width l_u = k_fes * len_s # useful iron stack length l_e = len_s + 2 * 0.001 * rad_ag # equivalent core length r_r = rad_ag - len_ag # rotor radius p = np.round(np.pi * rad_ag / tau_p) # pole pairs Eq.(11) f = p * shaft_rpm / 60.0 # rpm to frequency (Hz) S = 2 * p * q1 * m # Stator slots Eq.(12) N_conductors = S * 2 N_s = N_conductors / 2 / m # Stator turns per phase tau_s = np.pi * dia_ag / S # slot pitch Eq.(13) b_s = b_s_tau_s * tau_s # slot width b_t = tau_s - b_s # tooth width Eq.(14) Slot_aspect_ratio = h_s / b_s alpha_p = np.pi / 2 * 0.7 # Calculating Carter factor for stator and effective air gap length gamma = ( 4 / np.pi * ( b_so / 2 / (len_ag + h_m / mu_r) * np.arctan(b_so / 2 / (len_ag + h_m / mu_r)) - np.log(np.sqrt(1 + (b_so / 2 / (len_ag + h_m / mu_r)) ** 2)) ) ) k_C = tau_s / (tau_s - gamma * (len_ag + h_m / mu_r)) # carter coefficient g_eff = k_C * (len_ag + h_m / mu_r) # angular frequency in radians / sec om_m = 2 * np.pi * (shaft_rpm / 60.0) # rpm to rad/s om_e = p * om_m / 2 # Calculating magnetic loading B_pm1 = B_r * h_m / mu_r / g_eff B_g = B_r * h_m / mu_r / g_eff * (4.0 / np.pi) * np.sin(alpha_p) B_symax = B_g * b_m * l_e / (2 * h_ys * l_u) B_rymax = B_g * b_m * l_e / (2 * h_yr * len_s) B_tmax = B_g * tau_s / b_t k_wd = np.sin(np.pi / 6) / q1 / np.sin(np.pi / 6 / q1) # winding factor L_t = len_s + 2 * tau_p # Stator winding length, cross-section and resistance l_Cus = 2 * N_s * (2 * tau_p + L_t) A_s = b_s * (h_s - h_w) * q1 * p # m^2 A_scalc = b_s * 1e3 * (h_s - h_w) * 1e3 * q1 * p # mm^2 A_Cus = A_s * k_fills / N_s A_Cuscalc = A_scalc * k_fills / N_s R_s = l_Cus * resist_Cu / A_Cus # Calculating leakage inductance in stator L_m = 2 * mu_0 * N_s ** 2 / p * m * k_wd ** 2 * tau_p * L_t / np.pi ** 2 / g_eff L_ssigmas = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * ((h_s - h_w) / (3 * b_s) + h_w / b_so) ) # slot leakage inductance L_ssigmaew = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * 0.34 * len_ag * (l_e - 0.64 * tau_p * y_tau_p) / len_s ) # end winding leakage inductance L_ssigmag = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * (5 * (len_ag * k_C / b_so) / (5 + 4 * (len_ag * k_C / b_so))) ) # tooth tip leakage inductance L_ssigma = L_ssigmas + L_ssigmaew + L_ssigmag L_s = L_m + L_ssigma # Calculating no-load voltage induced in the stator and stator current E_p = np.sqrt(2) * N_s * L_t * rad_ag * k_wd * om_m * B_g Z = machine_rating / (m * E_p) G = np.maximum(0.0, E_p ** 2 - (om_e * L_s * Z) 2) # Calculating stator current and electrical loading I_s = np.sqrt(Z 2 + (((E_p - G ** 0.5) / (om_e * L_s) 2) 2)) B_smax = np.sqrt(2) * I_s * mu_0 / g_eff J_s = I_s / A_Cuscalc A_1 = 6 * N_s * I_s / (np.pi * dia_ag) I_snom = machine_rating / (m * E_p * cofi) # rated current I_qnom = machine_rating / (m * E_p) X_snom = om_e * (L_m + L_ssigma) # Calculating electromagnetically active mass V_Cus = m * l_Cus * A_Cus # copper volume V_Fest = L_t * 2 * p * q1 * m * b_t * h_s # volume of iron in stator tooth V_Fesy = L_t * np.pi * ((rad_ag + h_s + h_ys) 2 - (rad_ag + h_s) 2) # volume of iron in stator yoke V_Fery = L_t * np.pi * ((r_r - h_m) 2 - (r_r - h_m - h_yr) 2) # volume of iron in rotor yoke Copper = V_Cus * rho_Copper M_Fest = V_Fest * rho_Fe # mass of stator tooth M_Fesy = V_Fesy * rho_Fe # mass of stator yoke M_Fery = V_Fery * rho_Fe # mass of rotor yoke Iron = M_Fest + M_Fesy + M_Fery # Calculating losses # 1.Copper losses K_R = 1.2 # Skin effect correction co - efficient P_Cu = m * I_snom ** 2 * R_s * K_R # Iron Losses ( from Hysteresis and eddy currents) P_Hyys = M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator yoke P_Ftys = ( M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator yoke P_Fesynom = P_Hyys + P_Ftys P_Hyd = M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator teeth P_Ftd = ( M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator teeth P_Festnom = P_Hyd + P_Ftd P_ad = 0.2 * (P_Hyys + P_Ftys + P_Hyd + P_Ftd) # additional stray losses due to leakage flux pFtm = 300 # specific magnet loss P_Ftm = pFtm * 2 * p * b_m * len_s # magnet losses Losses = P_Cu + P_Festnom + P_Fesynom + P_ad + P_Ftm gen_eff = machine_rating / (machine_rating + Losses) ################################################## Structural Design ############################################################ ## Structural deflection calculations # rotor structure R = rad_ag - len_ag - h_m - 0.5 * t # mean radius of the rotor rim # l = L_t using L_t everywhere now b = R_sh # Shaft radius (not used) R_b = R - 0.5 * t # Inner radius of the rotor R_a = R + 0.5 * h_yr # Outer radius of rotor yoke a = R - 0.5 * t # same as R_b a_1 = R_b # same as R_b, a c = R / 500 u_allow_r = c / 20 # allowable radial deflection y_allow = 2 * L_t / 100 # allowable axial deflection R_1 = R - 0.5 * t # inner radius of rotor cylinder # same as R_b, a, a_1 (not used) K = 4 * (np.sin(ratio_mw2pp * np.pi / 2)) / np.pi # (not used) q3 = B_g ** 2 / (2 * mu_0) # normal component of Maxwell's stress mass_PM = 2 * np.pi * (R + 0.5 * t) * L_t * h_m * ratio_mw2pp * rho_PM # magnet mass mass_st_lam = rho_Fe * 2 * np.pi * R * L_t * h_yr # mass of rotor yoke steel # Calculation of radial deflection of rotor # cylindrical shell function and circular plate parameters for disc rotor based on Table 11.2 Roark's formulas # lamb, C* and F* parameters are from Appendix A of McDonald lamb = (3 * (1 - v 2) / R_a 2 / h_yr 2) 0.25 # m^-1 x1 = lamb * L_t # no units # ---------------- C_2 = chsPshc(x1) C_4 = chsMshc(x1) C_13 = chsMshc(x1) # (not used) C_a2 = chsPshc(x1 * 0.5) F_2_x0 = chsPshc(lamb * 0) F_2_ls2 = chsPshc(x1 / 2) F_a4_x0 = chsMshc(lamb * (0)) Fa4arg = np.pi / 180 * lamb * (0.5 * len_s - a) F_a4_ls2 = chsMshc(Fa4arg) # print('pmsg_disc: F_a4_ls2, Fa4arg, lamb, len_s, a ', F_a4_ls2, Fa4arg, lamb, len_s, a) # if np.isnan(F_a4_ls2): # sys.stderr.write('*** pmsg_discSE error: F_a4_ls2 is nan\n') # C_2 = np.cosh(x1) * np.sin(x1) + np.sinh(x1) * np.cos(x1) C_3 = np.sinh(x1) * np.sin(x1) # C_4 = np.cosh(x1) * np.sin(x1) - np.sinh(x1) * np.cos(x1) C_11 = (np.sinh(x1)) 2 - (np.sin(x1)) 2 # C_13 = np.cosh(x1) * np.sinh(x1) - np.cos(x1) * np.sin(x1) # (not used) C_14 = np.sinh(x1) 2 + np.sin(x1) 2 # (not used) C_a1 = np.cosh(x1 * 0.5) * np.cos(x1 * 0.5) # C_a2 = np.cosh(x1 * 0.5) * np.sin(x1 * 0.5) + np.sinh(x1 * 0.5) * np.cos(x1 * 0.5) F_1_x0 = np.cosh(lamb * 0) * np.cos(lamb * 0) F_1_ls2 = np.cosh(lamb * 0.5 * len_s) * np.cos(lamb * 0.5 * len_s) # F_2_x0 = np.cosh(lamb * 0) * np.sin(lamb * 0) + np.sinh(lamb * 0) * np.cos(lamb * 0) # F_2_ls2 = np.cosh(x1 / 2) * np.sin(x1 / 2) + np.sinh(x1 / 2) * np.cos(x1 / 2) if len_s < 2 * a: a = len_s / 2 else: a = len_s * 0.5 - 1 # F_a4_x0 = np.cosh(lamb * (0)) * np.sin(lamb * (0)) \ # - np.sinh(lamb * (0)) * np.cos(lamb * (0)) # F_a4_ls2 = np.cosh(np.pi / 180 * lamb * (0.5 * len_s - a)) * np.sin(np.pi / 180 * lamb * (0.5 * len_s - a)) \ # - np.sinh(np.pi / 180 * lamb * (0.5 * len_s - a)) * np.cos(np.pi / 180 * lamb * (0.5 * len_s - a)) """ Where did the np.pi/180 factor (conversion to radians) come from? lamb is m^-1 0.5len_s - a is m """ # ---------------- D_r = E h_yr ** 3 / (12 * (1 - v ** 2)) D_ax = E * t_d ** 3 / (12 * (1 - v ** 2)) # Radial deflection analytical model from McDonald's thesis defined in parts Part_1 = R_b * ((1 - v) * R_b ** 2 + (1 + v) * R_sh 2) / (R_b 2 - R_sh ** 2) / E Part_2 = (C_2 * C_a2 - 2 * C_3 * C_a1) / 2 / C_11 Part_3 = (C_3 * C_a2 - C_4 * C_a1) / C_11 Part_4 = 0.25 / D_r / lamb ** 3 Part_5 = q3 * R_b ** 2 / (E * (R_a - R_b)) f_d = Part_5 / (Part_1 - t_d * (Part_4 * Part_2 * F_2_ls2 - Part_3 * 2 * Part_4 * F_1_ls2 - Part_4 * F_a4_ls2)) fr = f_d * t_d u_ar = abs( Part_5 + fr / (2 * D_r * lamb ** 3) * ( (-F_1_x0 / C_11) * (C_3 * C_a2 - C_4 * C_a1) + (F_2_x0 / 2 / C_11) * (C_2 * C_a2 - 2 * C_3 * C_a1) - F_a4_x0 / 2 ) ) # Calculation of Axial deflection of rotor W = ( 0.5 * gravity * np.sin(phi) * ((L_t - t_d) * h_yr * rho_Fes) ) # uniform annular line load acting on rotor cylinder assumed as an annular plate w = rho_Fes * gravity * np.sin(phi) * t_d # disc assumed as plate with a uniformly distributed pressure between a_i = R_sh # Flat circular plate constants according to Roark's table 11.2 C_2p = 0.25 * (1 - (((R_sh / R) ** 2) * (1 + (2 * np.log(R / R_sh))))) C_3p = (R_sh / 4 / R) * ((1 + (R_sh / R) ** 2) * np.log(R / R_sh) + (R_sh / R) ** 2 - 1) C_6 = (R_sh / 4 / R_a) * ((R_sh / R_a) ** 2 - 1 + 2 * np.log(R_a / R_sh)) C_5 = 0.5 * (1 - (R_sh / R) ** 2) C_8 = 0.5 * (1 + v + (1 - v) * ((R_sh / R) ** 2)) C_9 = (R_sh / R) * (0.5 * (1 + v) * np.log(R / R_sh) + (1 - v) / 4 * (1 - (R_sh / R) ** 2)) # Flat circular plate loading constants L_11 = ( 1 + 4 * (R_sh / a_1) ** 2 - 5 * (R_sh / a_1) ** 4 - 4 * ((R_sh / a_1) ** 2) * np.log(a_1 / R_sh) * (2 + (R_sh / a_1) 2) ) / 64 L_14 = (1 - (R_sh / R_b) 4 - 4 * (R_sh / R_b) ** 2 * np.log(R_b / R_sh)) / 16 y_ai = ( -W * (a_1 ** 3) * (C_2p * (C_6 * a_1 / R_sh - C_6) / C_5 - a_1 * C_3p / R_sh + C_3p) / D_ax ) # Axial deflection of plate due to deflection of an annular plate with a uniform annular line load # Axial Deflection due to uniformaly distributed pressure load M_rb = -w * R ** 2 * (C_6 * (R 2 - R_sh 2) * 0.5 / R / R_sh - L_14) / C_5 Q_b = w * 0.5 * (R 2 - R_sh 2) / R_sh y_aii = M_rb * R_a ** 2 * C_2p / D_ax + Q_b * R_a ** 3 * C_3p / D_ax - w * R_a ** 4 * L_11 / D_ax y_ar = abs(y_ai + y_aii) z_allow_r = np.deg2rad(0.05 * R) # allowable torsional deflection of rotor # stator structure deflection calculation R_out = R / 0.995 + h_s + h_ys a_s = (b_st * d_s) - ((b_st - 2 * t_ws) * (d_s - 2 * t_ws)) # cross-sectional area of stator armms A_st = L_t * t_s # cross-sectional area of rotor cylinder N_st = np.round(n_s) theta_s = np.pi * 1 / N_st # half angle between spokes I_st = L_t * t_s ** 3 / 12 # second moment of area of stator cylinder I_arm_axi_s = ( (b_st * d_s ** 3) - ((b_st - 2 * t_ws) * (d_s - 2 * t_ws) ** 3) ) / 12 # second moment of area of stator arm I_arm_tor_s = ( (d_s * b_st ** 3) - ((d_s - 2 * t_ws) * (b_st - 2 * t_ws) ** 3) ) / 12 # second moment of area of rotot arm w.r.t torsion R_st = rad_ag + h_s + h_ys * 0.5 k_2 = np.sqrt(I_st / A_st) # radius of gyration b_allow_s = 2 * np.pi * R_sh / N_st m2 = (k_2 / R_st) ** 2 c1 = R_st / 500 R_1s = R_st - t_s * 0.5 d_se = dia_ag + 2 * (h_ys + h_s + h_w) # stator outer diameter # Calculation of radial deflection of stator Numers = R_st ** 3 * ( (0.25 * (np.sin(theta_s) - (theta_s * np.cos(theta_s))) / (np.sin(theta_s)) 2) - (0.5 / np.sin(theta_s)) + (0.5 / theta_s) ) Povs = ((theta_s / (np.sin(theta_s)) 2) + 1 / np.tan(theta_s)) * ( (0.25 * R_st / A_st) + (0.25 * R_st 3 / I_st) ) Qovs = R_st 3 / (2 * I_st * theta_s * (m2 + 1)) Lovs = (R_1s - R_sh) * 0.5 / a_s Denoms = I_st * (Povs - Qovs + Lovs) u_as = (q3 * R_st ** 2 / E / t_s) * (1 + Numers / Denoms) # Calculation of axial deflection of stator mass_st_lam_s = M_Fest + np.pi * L_t * rho_Fe * ((R_st + 0.5 * h_ys) ** 2 - (R_st - 0.5 * h_ys) ** 2) W_is = ( 0.5 * gravity * np.sin(phi) * (rho_Fes * L_t * d_s ** 2) ) # length of stator arm beam at which self-weight acts W_iis = ( gravity * np.sin(phi) * (mass_st_lam_s + V_Cus * rho_Copper) / 2 / N_st ) # weight of stator cylinder and teeth w_s = rho_Fes * gravity * np.sin(phi) * a_s * N_st # uniformly distributed load of the arms l_is = R_st - R_sh # distance at which the weight of the stator cylinder acts l_iis = l_is # distance at which the weight of the stator cylinder acts l_iiis = l_is # distance at which the weight of the stator cylinder acts u_allow_s = c1 / 20 X_comp1 = ( W_is * l_is ** 3 / 12 / E / I_arm_axi_s ) # deflection component due to stator arm beam at which self-weight acts X_comp2 = W_iis * l_iis ** 4 / 24 / E / I_arm_axi_s # deflection component due to 1/nth of stator cylinder X_comp3 = w_s * l_iiis ** 4 / 24 / E / I_arm_axi_s # deflection component due to weight of arms y_as = X_comp1 + X_comp2 + X_comp3 # axial deflection # Stator circumferential deflection z_allow_s = np.deg2rad(0.05 * R_st) # allowable torsional deflection z_as = ( 2 * np.pi * (R_st + 0.5 * t_s) * L_t / (2 * N_st) * sigma * (l_is + 0.5 * t_s) ** 3 / (3 * E * I_arm_tor_s) ) mass_stru_steel = 2 * (N_st * (R_1s - R_sh) * a_s * rho_Fes) TC1 = Torque * 1.0 / (2 * np.pi * sigma) # Torque / shear stress TC2r = R ** 2 * L_t # Evaluating Torque constraint for rotor TC2s = R_st ** 2 * L_t # Evaluating Torque constraint for stator Structural_mass = mass_stru_steel + (np.pi * (R 2 - R_sh 2) * t_d * rho_Fes) Mass = Structural_mass + Iron + Copper + mass_PM outputs["B_tmax"] = B_tmax outputs["B_rymax"] = B_rymax outputs["B_symax"] = B_symax outputs["B_smax"] = B_smax[-1] outputs["B_pm1"] = B_pm1 outputs["B_g"] = B_g outputs["N_s"] = N_s outputs["b_s"] = b_s outputs["b_t"] = b_t outputs["A_Cuscalc"] = A_Cuscalc outputs["b_m"] = b_m outputs["E_p"] = E_p outputs["f"] = f outputs["I_s"] = I_s outputs["R_s"] = R_s outputs["L_s"] = L_s outputs["A_1"] = A_1 outputs["J_s"] = J_s outputs["Losses"] = Losses outputs["K_rad"] = K_rad outputs["eandm_efficiency"] = np.maximum(eps, gen_eff) outputs["S"] = S outputs["Slot_aspect_ratio"] = Slot_aspect_ratio outputs["Copper"] = Copper outputs["Iron"] = Iron outputs["u_ar"] = u_ar outputs["y_ar"] = y_ar outputs["u_as"] = u_as outputs["y_as"] = y_as outputs["z_as"] = z_as outputs["u_allow_r"] = u_allow_r outputs["u_allow_s"] = u_allow_s outputs["y_allow_r"] = outputs["y_allow_s"] = y_allow outputs["z_allow_s"] = z_allow_s outputs["z_allow_r"] = z_allow_r outputs["b_allow_s"] = b_allow_s outputs["TC1"] = TC1 outputs["TC2r"] = TC2r outputs["TC2s"] = TC2s outputs["R_out"] = R_out outputs["Structural_mass"] = Structural_mass outputs["generator_mass"] = Mass outputs["mass_PM"] = mass_PM # ---------------------------------------------------------------------------------------- class PMSG_Arms(GeneratorBase): """ Estimates overall mass dimensions and Efficiency of PMSG-disc rotor generator. Parameters ---------- b_arm : float, [m] arm width tau_p : float, [m] Pole pitch self.tau_p h_yr : float, [m] rotor yoke height h_ys : float, [m] Yoke height Returns ------- B_tmax : float, [T] Peak Teeth flux density B_smax : float, [T] Peak Stator Yoke flux density B_ymax B_symax : float, [T] Peak Stator Yoke flux density B_ymax E_p : float Stator phase voltage """ def initialize(self): super(PMSG_Arms, self).initialize() def setup(self): super(PMSG_Arms, self).setup() self.add_input("b_arm", val=0.0, units="m") self.add_input("tau_p", val=0.0, units="m") self.add_input("h_yr", val=0.0, units="m") self.add_input("h_ys", val=0.0, units="m") self.add_output("B_tmax", val=0.0, units="T") self.add_output("B_smax", val=0.0, units="T") self.add_output("B_symax", val=0.0, units="T") self.add_output("E_p", val=np.zeros(self.options["n_pc"])) def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs # r_s = inputs['r_s'] rad_ag = inputs["rad_ag"] len_s = inputs["len_s"] h_s = inputs["h_s"] tau_p = inputs["tau_p"] h_m = inputs["h_m"] h_ys = inputs["h_ys"] h_yr = inputs["h_yr"] machine_rating = inputs["machine_rating"] shaft_rpm = inputs["shaft_rpm"] Torque = inputs["rated_torque"] b_st = inputs["b_st"] d_s = inputs["d_s"] t_ws = inputs["t_ws"] n_r = inputs["n_r"] n_s = inputs["n_s"] b_r = inputs["b_arm"] d_r = inputs["d_r"] t_wr = inputs["t_wr"] R_sh = 0.5 * inputs["D_shaft"] rho_Fe = inputs["rho_Fe"] rho_Copper = inputs["rho_Copper"] rho_Fes = inputs["rho_Fes"] rho_PM = inputs["rho_PM"] # Grab constant values B_r = inputs["B_r"] E = inputs["E"] P_Fe0e = inputs["P_Fe0e"] P_Fe0h = inputs["P_Fe0h"] S_N = inputs["S_N"] alpha_p = inputs["alpha_p"] b_r_tau_r = inputs["b_r_tau_r"] b_ro = inputs["b_ro"] b_s_tau_s = inputs["b_s_tau_s"] b_so = inputs["b_so"] cofi = inputs["cofi"] freq = inputs["freq"] h_i = inputs["h_i"] h_sy0 = inputs["h_sy0"] h_w = inputs["h_w"] k_fes = inputs["k_fes"] k_fillr = inputs["k_fillr"] k_fills = inputs["k_fills"] k_s = inputs["k_s"] m = discrete_inputs["m"] mu_0 = inputs["mu_0"] mu_r = inputs["mu_r"] p = inputs["p"] phi = inputs["phi"] q1 = discrete_inputs["q1"] ratio_mw2pp = inputs["ratio_mw2pp"] resist_Cu = inputs["resist_Cu"] sigma = inputs["sigma"] v = inputs["v"] y_tau_p = inputs["y_tau_p"] y_tau_pr = inputs["y_tau_pr"] """ # Assign values to universal constants B_r = 1.2 # Tesla remnant flux density E = 2e11 # N / m^2 young's modulus sigma = 40e3 # shear stress assumed (yield strength of ?? steel, in psi - GNS) ratio_mw2pp = 0.7 # ratio of magnet width to pole pitch(bm / tau_p) mu_0 = np.pi * 4e-7 # permeability of free space in m * kg / (s*2 A*2) mu_r = 1.06 # relative permeability (probably for neodymium magnets, often given as 1.05 - GNS) phi = np.deg2rad(90) # tilt angle (rotor tilt -90 degrees during transportation) cofi = 0.85 # power factor # Assign values to design constants h_w = 0.005 # Slot wedge height h_i = 0.001 # coil insulation thickness y_tau_p = 1 # Coil span to pole pitch m = 3 # no of phases q1 = 1 # no of slots per pole per phase b_s_tau_s = 0.45 # slot width to slot pitch ratio k_fills = 0.65 # Slot fill factor P_Fe0h = 4 # specific hysteresis losses W / kg @ 1.5 T P_Fe0e = 1 # specific eddy losses W / kg @ 1.5 T resist_Cu = 1.8e-8 1.4 # Copper resisitivty k_fes = 0.9 # Stator iron fill factor per Grauers b_so = 0.004 # Slot opening alpha_p = np.pi / 2 * 0.7 """ # back iron thickness for rotor and stator t_s = h_ys t = h_yr ###################################################### Electromagnetic design############################################# K_rad = len_s / (2 * rad_ag) # Aspect ratio # T = Torque # rated torque l_u = k_fes * len_s # useful iron stack length We = tau_p l_b = 2 * tau_p # end winding length l_e = len_s + 2 * 0.001 * rad_ag # equivalent core length b_m = 0.7 * tau_p # magnet width # Calculating air gap length dia_ag = 2 * rad_ag # air gap diameter len_ag = 0.001 * dia_ag # air gap length r_m = rad_ag + h_ys + h_s # magnet radius r_r = rad_ag - len_ag # rotor radius p = np.round(np.pi * dia_ag / (2 * tau_p)) # pole pairs f = shaft_rpm * p / 60.0 # outout frequency rpm to Hz S = 2 * p * q1 * m # Stator slots N_conductors = S * 2 N_s = N_conductors / (2 * m) # Stator turns per phase tau_s = np.pi * dia_ag / S # Stator slot pitch b_s = b_s_tau_s * tau_s # slot width b_t = tau_s - b_s # tooth width Slot_aspect_ratio = h_s / b_s # Calculating Carter factor for stator and effective air gap length ahm = len_ag + h_m / mu_r ba = b_so / (2 * ahm) gamma = 4 / np.pi * (ba * np.arctan(ba) - np.log(np.sqrt(1 + ba ** 2))) k_C = tau_s / (tau_s - gamma * ahm) # carter coefficient g_eff = k_C * ahm # angular frequency in radians om_m = 2 * np.pi * shaft_rpm / 60.0 # rpm to radians per second om_e = p * om_m / 2 # electrical output frequency (Hz) # Calculating magnetic loading B_pm1 = B_r * h_m / mu_r / g_eff B_g = B_r * h_m / mu_r / g_eff * (4 / np.pi) * np.sin(alpha_p) B_symax = B_g * b_m * l_e / (2 * h_ys * l_u) B_rymax = B_g * b_m * l_e / (2 * h_yr * len_s) B_tmax = B_g * tau_s / b_t # Calculating winding factor k_wd = np.sin(np.pi / 6) / q1 / np.sin(np.pi / 6 / q1) L_t = len_s + 2 * tau_p # overall stator len w/end windings - should be tau_s??? # l = L_t # length - now using L_t everywhere # Stator winding length, cross-section and resistance l_Cus = 2 * N_s * (2 * tau_p + L_t) A_s = b_s * (h_s - h_w) * q1 * p A_scalc = b_s * 1000 * (h_s - h_w) * 1000 * q1 * p A_Cus = A_s * k_fills / N_s A_Cuscalc = A_scalc * k_fills / N_s R_s = l_Cus * resist_Cu / A_Cus # Calculating leakage inductance in stator L_m = 2 * mu_0 * N_s ** 2 / p * m * k_wd ** 2 * tau_p * L_t / np.pi ** 2 / g_eff L_ssigmas = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * ((h_s - h_w) / (3 * b_s) + h_w / b_so) ) # slot leakage inductance L_ssigmaew = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * 0.34 * len_ag * (l_e - 0.64 * tau_p * y_tau_p) / len_s ) # end winding leakage inductance L_ssigmag = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * (5 * (len_ag * k_C / b_so) / (5 + 4 * (len_ag * k_C / b_so))) ) # tooth tip leakage inductance L_ssigma = L_ssigmas + L_ssigmaew + L_ssigmag L_s = L_m + L_ssigma # Calculating no-load voltage induced in the stator E_p = 2 * N_s * L_t * rad_ag * k_wd * om_m * B_g / np.sqrt(2) Z = machine_rating / (m * E_p) G = np.maximum(0.0, E_p ** 2 - (om_e * L_s * Z) 2) # Calculating stator current and electrical loading is2 = Z 2 + (((E_p - G ** 0.5) / (om_e * L_s) 2) 2) I_s = np.sqrt(Z 2 + (((E_p - G 0.5) / (om_e * L_s) 2) 2)) J_s = I_s / A_Cuscalc A_1 = 6 * N_s * I_s / (np.pi * dia_ag) I_snom = machine_rating / (m * E_p * cofi) # rated current I_qnom = machine_rating / (m * E_p) X_snom = om_e * (L_m + L_ssigma) B_smax = np.sqrt(2) * I_s * mu_0 / g_eff # Calculating Electromagnetically active mass V_Cus = m * l_Cus * A_Cus # copper volume V_Fest = L_t * 2 * p * q1 * m * b_t * h_s # volume of iron in stator tooth V_Fesy = L_t * np.pi * ((rad_ag + h_s + h_ys) 2 - (rad_ag + h_s) 2) # volume of iron in stator yoke V_Fery = L_t * np.pi * ((r_r - h_m) 2 - (r_r - h_m - h_yr) 2) Copper = V_Cus * rho_Copper M_Fest = V_Fest * rho_Fe # Mass of stator tooth M_Fesy = V_Fesy * rho_Fe # Mass of stator yoke M_Fery = V_Fery * rho_Fe # Mass of rotor yoke Iron = M_Fest + M_Fesy + M_Fery # Calculating Losses ##1. Copper Losses K_R = 1.2 # Skin effect correction co-efficient P_Cu = m * I_snom ** 2 * R_s * K_R # Iron Losses ( from Hysteresis and eddy currents) P_Hyys = M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator yoke P_Ftys = ( M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator yoke P_Fesynom = P_Hyys + P_Ftys P_Hyd = M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator teeth P_Ftd = ( M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator teeth P_Festnom = P_Hyd + P_Ftd # additional stray losses due to leakage flux P_ad = 0.2 * (P_Hyys + P_Ftys + P_Hyd + P_Ftd) pFtm = 300 # specific magnet loss P_Ftm = pFtm * 2 * p * b_m * len_s Losses = P_Cu + P_Festnom + P_Fesynom + P_ad + P_Ftm gen_eff = machine_rating / (machine_rating + Losses) #################################################### Structural Design ############################################################ ## Deflection Calculations ## # rotor structure calculations a_r = (b_r * d_r) - ((b_r - 2 * t_wr) * (d_r - 2 * t_wr)) # cross-sectional area of rotor arms A_r = L_t * t # cross-sectional area of rotor cylinder N_r = np.round(n_r) # rotor arms theta_r = np.pi * 1 / N_r # half angle between spokes I_r = L_t * t ** 3 / 12 # second moment of area of rotor cylinder I_arm_axi_r = ( (b_r * d_r ** 3) - ((b_r - 2 * t_wr) * (d_r - 2 * t_wr) ** 3) ) / 12 # second moment of area of rotor arm I_arm_tor_r = ( (d_r * b_r ** 3) - ((d_r - 2 * t_wr) * (b_r - 2 * t_wr) ** 3) ) / 12 # second moment of area of rotot arm w.r.t torsion R = rad_ag - len_ag - h_m - 0.5 * t # Rotor mean radius c = R / 500 u_allow_r = c / 20 # allowable radial deflection R_1 = R - t * 0.5 # inner radius of rotor cylinder k_1 = np.sqrt(I_r / A_r) # radius of gyration m1 = (k_1 / R) ** 2 l_ir = R # length of rotor arm beam at which rotor cylinder acts l_iir = R_1 b_allow_r = 2 * np.pi * R_sh / N_r # allowable circumferential arm dimension for rotor q3 = B_g ** 2 / 2 / mu_0 # normal component of Maxwell stress mass_PM = 2 * np.pi * (R + 0.5 * t) * L_t * h_m * ratio_mw2pp * rho_PM # magnet mass # Calculating radial deflection of the rotor Numer = R ** 3 * ( (0.25 * (np.sin(theta_r) - (theta_r * np.cos(theta_r))) / (np.sin(theta_r)) 2) - (0.5 / np.sin(theta_r)) + (0.5 / theta_r) ) Pov = ((theta_r / (np.sin(theta_r)) 2) + 1 / np.tan(theta_r)) * ((0.25 * R / A_r) + (0.25 * R 3 / I_r)) Qov = R 3 / (2 * I_r * theta_r * (m1 + 1)) Lov = (R_1 - R_sh) / a_r Denom = I_r * (Pov - Qov + Lov) # radial deflection % rotor u_ar = (q3 * R ** 2 / E / t) * (1 + Numer / Denom) # Calculating axial deflection of the rotor under its own weight w_r = rho_Fes * gravity * np.sin(phi) * a_r * N_r # uniformly distributed load of the weight of the rotor arm mass_st_lam = rho_Fe * 2 * np.pi * R * L_t * h_yr # mass of rotor yoke steel W = gravity * np.sin(phi) * (mass_st_lam / N_r + mass_PM / N_r) # weight of 1/nth of rotor cylinder y_a1 = W * l_ir ** 3 / 12 / E / I_arm_axi_r # deflection from weight component of back iron y_a2 = w_r * l_iir ** 4 / 24 / E / I_arm_axi_r # deflection from weight component of the arms y_ar = y_a1 + y_a2 # axial deflection y_allow = 2 * L_t / 100 # allowable axial deflection # Calculating # circumferential deflection of the rotor z_allow_r = np.deg2rad(0.05 * R) # allowable torsional deflection z_ar = ( (2 * np.pi * (R - 0.5 * t) * L_t / N_r) * sigma * (l_ir - 0.5 * t) ** 3 / 3 / E / I_arm_tor_r ) # circumferential deflection val_str_rotor = mass_PM + (mass_st_lam + (N_r * (R_1 - R_sh) * a_r * rho_Fes)) # rotor mass # stator structure deflection calculation a_s = (b_st * d_s) - ((b_st - 2 * t_ws) * (d_s - 2 * t_ws)) # cross-sectional area of stator armms A_st = L_t * t_s # cross-sectional area of stator cylinder N_st = np.round(n_s) # stator arms theta_s = np.pi * 1 / N_st # half angle between spokes I_st = L_t * t_s ** 3 / 12 # second moment of area of stator cylinder k_2 = np.sqrt(I_st / A_st) # radius of gyration I_arm_axi_s = ( (b_st * d_s ** 3) - ((b_st - 2 * t_ws) * (d_s - 2 * t_ws) ** 3) ) / 12 # second moment of area of stator arm I_arm_tor_s = ( (d_s * b_st ** 3) - ((d_s - 2 * t_ws) * (b_st - 2 * t_ws) ** 3) ) / 12 # second moment of area of rotot arm w.r.t torsion R_st = rad_ag + h_s + h_ys * 0.5 # stator cylinder mean radius R_1s = R_st - t_s * 0.5 # inner radius of stator cylinder, m m2 = (k_2 / R_st) ** 2 d_se = dia_ag + 2 * (h_ys + h_s + h_w) # stator outer diameter # allowable radial deflection of stator c1 = R_st / 500 u_allow_s = c1 / 20 R_out = R / 0.995 + h_s + h_ys l_is = R_st - R_sh # distance at which the weight of the stator cylinder acts l_iis = l_is # distance at which the weight of the stator cylinder acts l_iiis = l_is # distance at which the weight of the stator cylinder acts mass_st_lam_s = M_Fest + np.pi * L_t * rho_Fe * ((R_st + 0.5 * h_ys) ** 2 - (R_st - 0.5 * h_ys) ** 2) W_is = ( 0.5 * gravity * np.sin(phi) * (rho_Fes * L_t * d_s ** 2) ) # length of stator arm beam at which self-weight acts W_iis = ( gravity * np.sin(phi) * (mass_st_lam_s + V_Cus * rho_Copper) / 2 / N_st ) # weight of stator cylinder and teeth w_s = rho_Fes * gravity * np.sin(phi) * a_s * N_st # uniformly distributed load of the arms mass_stru_steel = 2 * (N_st * (R_1s - R_sh) * a_s * rho_Fes) # Structural mass of stator arms # Calculating radial deflection of the stator Numers = R_st ** 3 * ( (0.25 * (np.sin(theta_s) - (theta_s * np.cos(theta_s))) / (np.sin(theta_s)) 2) - (0.5 / np.sin(theta_s)) + (0.5 / theta_s) ) Povs = ((theta_s / (np.sin(theta_s)) 2) + 1 / np.tan(theta_s)) * ( (0.25 * R_st / A_st) + (0.25 * R_st 3 / I_st) ) Qovs = R_st 3 / (2 * I_st * theta_s * (m2 + 1)) Lovs = (R_1s - R_sh) * 0.5 / a_s Denoms = I_st * (Povs - Qovs + Lovs) u_as = (q3 * R_st ** 2 / E / t_s) * (1 + Numers / Denoms) # Calculating axial deflection of the stator X_comp1 = ( W_is * l_is ** 3 / 12 / E / I_arm_axi_s ) # deflection component due to stator arm beam at which self-weight acts X_comp2 = W_iis * l_iis ** 4 / 24 / E / I_arm_axi_s # deflection component due to 1 / nth of stator cylinder X_comp3 = w_s * l_iiis ** 4 / 24 / E / I_arm_axi_s # deflection component due to weight of arms y_as = X_comp1 + X_comp2 + X_comp3 # axial deflection # Calculating circumferential deflection of the stator z_as = 2 * np.pi * (R_st + 0.5 * t_s) * L_t / (2 * N_st) * sigma * (l_is + 0.5 * t_s) ** 3 / 3 / E / I_arm_tor_s z_allow_s = np.deg2rad(0.05 * R_st) # allowable torsional deflection b_allow_s = 2 * np.pi * R_sh / N_st # allowable circumferential arm dimension val_str_stator = mass_stru_steel + mass_st_lam_s val_str_mass = val_str_rotor + val_str_stator TC1 = Torque / (2 * np.pi * sigma) # Desired shear stress TC2r = R ** 2 * L_t # Evaluating Torque constraint for rotor TC2s = R_st ** 2 * L_t # Evaluating Torque constraint for stator Structural_mass = mass_stru_steel + (N_r * (R_1 - R_sh) * a_r * rho_Fes) Stator = mass_st_lam_s + mass_stru_steel + Copper Rotor = ((2 * np.pi * t * L_t * R * rho_Fe) + (N_r * (R_1 - R_sh) * a_r * rho_Fes)) + mass_PM Mass = Stator + Rotor outputs["B_tmax"] = B_tmax outputs["B_rymax"] = B_rymax outputs["B_symax"] = B_symax outputs["B_smax"] = B_smax[-1] outputs["B_pm1"] = B_pm1 outputs["B_g"] = B_g outputs["N_s"] = N_s outputs["b_s"] = b_s outputs["b_t"] = b_t outputs["A_Cuscalc"] = A_Cuscalc outputs["b_m"] = b_m outputs["E_p"] = E_p outputs["f"] = f outputs["I_s"] = I_s outputs["R_s"] = R_s outputs["L_s"] = L_s outputs["A_1"] = A_1 outputs["J_s"] = J_s outputs["Losses"] = Losses outputs["K_rad"] = K_rad outputs["eandm_efficiency"] = np.maximum(eps, gen_eff) outputs["S"] = S outputs["Slot_aspect_ratio"] = Slot_aspect_ratio outputs["Copper"] = Copper outputs["Iron"] = Iron outputs["u_ar"] = u_ar outputs["y_ar"] = y_ar outputs["z_ar"] = z_ar outputs["u_as"] = u_as outputs["y_as"] = y_as outputs["z_as"] = z_as outputs["u_allow_r"] = u_allow_r outputs["u_allow_s"] = u_allow_s outputs["y_allow_r"] = outputs["y_allow_s"] = y_allow outputs["z_allow_s"] = z_allow_s outputs["z_allow_r"] = z_allow_r outputs["b_allow_s"] = b_allow_s outputs["b_allow_r"] = b_allow_r outputs["TC1"] = TC1 outputs["TC2r"] = TC2r outputs["TC2s"] = TC2s outputs["R_out"] = R_out outputs["Structural_mass"] = Structural_mass outputs["generator_mass"] = Mass outputs["mass_PM"] = mass_PM # ---------------------------------------------------------------------------------------- class DFIG(GeneratorBase): """ Estimates overall mass, dimensions and Efficiency of DFIG generator. Parameters ---------- S_Nmax : float Max rated Slip B_symax : float, [T] Peak Stator Yoke flux density B_ymax Returns ------- N_r : float Rotor turns L_r : float Rotor inductance h_yr : float rotor yoke height h_ys : float Stator Yoke height tau_p : float Pole pitch Current_ratio : float Rotor current ratio E_p : float Stator phase voltage """ def initialize(self): super(DFIG, self).initialize() def setup(self): super(DFIG, self).setup() n_pc = self.options["n_pc"] self.add_input("S_Nmax", val=0.0) self.add_input("B_symax", val=0.0, units="T") self.add_output("N_r", val=0.0) self.add_output("L_r", val=0.0) self.add_output("h_yr", val=0.0) self.add_output("h_ys", val=0.0) self.add_output("tau_p", val=0.0) self.add_output("Current_ratio", val=np.zeros(n_pc)) self.add_output("E_p", val=np.zeros(n_pc)) def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs rad_ag = inputs["rad_ag"] len_s = inputs["len_s"] h_s = inputs["h_s"] h_0 = inputs["h_0"] I_0 = inputs["I_0"] machine_rating = inputs["machine_rating"] shaft_rpm = inputs["shaft_rpm"] rho_Fe = inputs["rho_Fe"] rho_Copper = inputs["rho_Copper"] B_symax = inputs["B_symax"] S_Nmax = inputs["S_Nmax"] # Grab constant values B_r = inputs["B_r"] E = inputs["E"] P_Fe0e = inputs["P_Fe0e"] P_Fe0h = inputs["P_Fe0h"] S_N = inputs["S_N"] alpha_p = inputs["alpha_p"] b_r_tau_r = inputs["b_r_tau_r"] b_ro = inputs["b_ro"] b_s_tau_s = inputs["b_s_tau_s"] b_so = inputs["b_so"] cofi = inputs["cofi"] freq = inputs["freq"] h_i = inputs["h_i"] h_sy0 = inputs["h_sy0"] h_w = inputs["h_w"] k_fes = inputs["k_fes"] k_fillr = inputs["k_fillr"] k_s = inputs["k_s"] m = discrete_inputs["m"] mu_0 = inputs["mu_0"] mu_r = inputs["mu_r"] p = inputs["p"] phi = inputs["phi"] q1 = discrete_inputs["q1"] q2 = q1 - 1 # Rotor slots per pole per phase ratio_mw2pp = inputs["ratio_mw2pp"] resist_Cu = inputs["resist_Cu"] sigma = inputs["sigma"] v = inputs["v"] y_tau_p = inputs["y_tau_p"] y_tau_pr = inputs["y_tau_pr"] """ #Assign values to universal constants sigma = 21.5e3 # shear stress in psi (what material? Al, brass, Cu?) ~148e6 Pa mu_0 = np.pi * 4e-7 # permeability of free space in m * kg / (s*2 A*2) cofi = 0.9 # power factor h_w = 0.005 # wedge height m = 3 # Number of phases resist_Cu = 1.8e-8 1.4 # copper resisitivity h_sy0 = 0 #Assign values to design constants b_so = 0.004 # Stator slot opening width b_ro = 0.004 # Rotor slot opening width q1 = 5 # Stator slots per pole per phase b_s_tau_s = 0.45 # Stator slot-width / slot-pitch ratio b_r_tau_r = 0.45 # Rotor slot-width / slot-pitch ratio y_tau_p = 12. / 15 # Stator coil span to pole pitch y_tau_pr = 10. / 12 # Rotor coil span to pole pitch p = 3 # pole pairs freq = 60 # grid frequency in Hz k_fillr = 0.55 # Rotor Slot fill factor P_Fe0h = 4 # specific hysteresis losses W / kg @ 1.5 T P_Fe0e = 1 # specific eddy losses W / kg @ 1.5 T """ K_rs = 1 / (-1 * S_Nmax) # Winding turns ratio between rotor and Stator I_SN = machine_rating / (np.sqrt(3) * 3000) # Rated current I_SN_r = I_SN / K_rs # Stator rated current reduced to rotor # Calculating winding factor for stator and rotor k_y1 = np.sin(np.pi / 2 * y_tau_p) # winding chording factor k_q1 = np.sin(np.pi / 6) / (q1 * np.sin(np.pi / (6 * q1))) # winding zone factor k_y2 = np.sin(np.pi / 2 * y_tau_pr) # winding chording factor k_q2 = np.sin(np.pi / 6) / (q2 * np.sin(np.pi / (6 * q2))) # winding zone factor k_wd1 = k_y1 * k_q1 # Stator winding factor k_wd2 = k_q2 * k_y2 # Rotor winding factor ag_dia = 2 * rad_ag # air gap diameter ag_len = (0.1 + 0.012 * machine_rating ** (1.0 / 3)) * 0.001 # air gap length in m K_rad = len_s / ag_dia # Aspect ratio rad_r = rad_ag - ag_len # rotor radius (was r_r) tau_p = np.pi * ag_dia / (2 * p) # pole pitch S = 2 * p * q1 * m # Stator slots N_slots_pp = S / (m * p * 2) # Number of stator slots per pole per phase n = S / 2 * p / q1 # no of slots per pole per phase tau_s = tau_p / (m * q1) # Stator slot pitch b_s = b_s_tau_s * tau_s # Stator slot width b_t = tau_s - b_s # Stator tooth width Q_r = 2 * p * m * q2 # Rotor slots tau_r = np.pi * (ag_dia - 2 * ag_len) / Q_r # Rotor slot pitch b_r = b_r_tau_r * tau_r # Rotor slot width b_tr = tau_r - b_r # Rotor tooth width # Calculating equivalent slot openings mu_rs = 0.005 mu_rr = 0.005 W_s = (b_s / mu_rs) * 1e-3 # Stator, in m W_r = (b_r / mu_rr) * 1e-3 # Rotor, in m Slot_aspect_ratio1 = h_s / b_s Slot_aspect_ratio2 = h_0 / b_r # Calculating Carter factor for stator,rotor and effective air gap length gamma_s = (2 * W_s / ag_len) ** 2 / (5 + 2 * W_s / ag_len) K_Cs = tau_s / (tau_s - ag_len * gamma_s * 0.5) # page 3 - 13 gamma_r = (2 * W_r / ag_len) ** 2 / (5 + 2 * W_r / ag_len) K_Cr = tau_r / (tau_r - ag_len * gamma_r * 0.5) # page 3 - 13 K_C = K_Cs * K_Cr g_eff = K_C * ag_len om_m = 2 * np.pi * shaft_rpm / 60 # mechanical frequency om_e = p * om_m # electrical frequency f = shaft_rpm * p / 60 # generator output freq K_s = 0.3 # saturation factor for Iron n_c1 = 2 # number of conductors per coil a1 = 2 # number of parallel paths N_s = np.round(2 * p * N_slots_pp * n_c1 / a1) # Stator winding turns per phase N_r = np.round(N_s * k_wd1 * K_rs / k_wd2) # Rotor winding turns per phase n_c2 = N_r / (Q_r / m) # rotor turns per coil # Calculating peak flux densities and back iron thickness B_g1 = mu_0 * 3 * N_r * I_0 * np.sqrt(2) * k_y2 * k_q2 / (np.pi * p * g_eff * (1 + K_s)) B_g = B_g1 * K_C h_ys = B_g * tau_p / (B_symax * np.pi) B_rymax = B_symax h_yr = h_ys B_tsmax = B_g * tau_s / b_t d_se = ag_dia + 2 * (h_ys + h_s + h_w) # stator outer diameter D_ratio = d_se / ag_dia # Diameter ratio # Stator slot fill factor if ag_dia > 2: k_fills = 0.65 else: k_fills = 0.4 # Stator winding calculation # End connection length for stator winding coils l_fs = 2 * (0.015 + y_tau_p * tau_p / (2 * np.cos(np.deg2rad(40)))) + np.pi * h_s # added radians() 2019 09 11 l_Cus = 2 * N_s * (l_fs + len_s) / a1 # Length of Stator winding # Conductor cross-section A_s = b_s * (h_s - h_w) A_scalc = b_s * 1000 * (h_s - h_w) * 1000 A_Cus = A_s * q1 * p * k_fills / N_s A_Cuscalc = A_scalc * q1 * p * k_fills / N_s # Stator winding resistance R_s = l_Cus * resist_Cu / A_Cus tau_r_min = np.pi * (ag_dia - 2 * (ag_len + h_0)) / Q_r # Peak magnetic loading on the rotor tooth b_trmin = tau_r_min - b_r_tau_r * tau_r_min B_trmax = B_g * tau_r / b_trmin # Calculating leakage inductance in stator K_01 = 1 - 0.033 * (W_s ** 2 / ag_len / tau_s) sigma_ds = 0.0042 L_ssigmas = (2 * mu_0 * len_s * n_c1 ** 2 * S / m / a1 ** 2) * ( (h_s - h_w) / (3 * b_s) + h_w / b_so ) # slot leakage inductance L_ssigmaew = ( (2 * mu_0 * len_s * n_c1 ** 2 * S / m / a1 ** 2) * 0.34 * q1 * (l_fs - 0.64 * tau_p * y_tau_p) / len_s ) # end winding leakage inductance L_ssigmag = (2 * mu_0 * len_s * n_c1 ** 2 * S / m / a1 ** 2) * ( 0.9 * tau_s * q1 * k_wd1 * K_01 * sigma_ds / g_eff ) # tooth tip leakage inductance L_ssigma = L_ssigmas + L_ssigmaew + L_ssigmag # stator leakage inductance L_sm = 6 * mu_0 * len_s * tau_p * (k_wd1 * N_s) 2 / (np.pi 2 * (p) * g_eff * (1 + K_s)) L_s = L_ssigmas + L_ssigmaew + L_ssigmag # stator inductance # Calculating leakage inductance in rotor K_02 = 1 - 0.033 * (W_r ** 2 / ag_len / tau_r) sigma_dr = 0.0062 l_fr = (0.015 + y_tau_pr * tau_r / 2 / np.cos(np.deg2rad(40))) + np.pi * h_0 # Rotor end connection length L_rsl = (mu_0 * len_s * (2 * n_c2) ** 2 * Q_r / m) * ( (h_0 - h_w) / (3 * b_r) + h_w / b_ro ) # slot leakage inductance L_rel = ( (mu_0 * len_s * (2 * n_c2) ** 2 * Q_r / m) * 0.34 * q2 * (l_fr - 0.64 * tau_r * y_tau_pr) / len_s ) # end winding leakage inductance L_rtl = (mu_0 * len_s * (2 * n_c2) ** 2 * Q_r / m) * ( 0.9 * tau_s * q2 * k_wd2 * K_02 * sigma_dr / g_eff ) # tooth tip leakage inductance L_r = (L_rsl + L_rtl + L_rel) / K_rs 2 # rotor leakage inductance sigma1 = 1 - (L_sm 2 / L_s / L_r) # Rotor Field winding # conductor cross-section diff = h_0 - h_w A_Cur = k_fillr * p * q2 * b_r * diff / N_r A_Curcalc = A_Cur * 1e6 L_cur = 2 * N_r * (l_fr + len_s) # rotor winding length Resist_r = resist_Cu * L_cur / A_Cur # Rotor resistance R_R = Resist_r / K_rs ** 2 # Equivalent rotor resistance reduced to stator om_s = shaft_rpm * 2 * np.pi / 60 # synchronous speed in rad / s P_e = machine_rating / (1 - S_Nmax) # Air gap power # Calculating No-load voltage E_p = om_s * N_s * k_wd1 * rad_ag * len_s * B_g1 * np.sqrt(2) I_r = P_e / m / E_p # rotor active current I_sm = E_p / (2 * np.pi * freq * (L_s + L_sm)) # stator reactive current I_s = np.sqrt(I_r 2 + I_sm 2) # Stator current I_srated = machine_rating / 3 / K_rs / E_p # Rated current # Calculating winding current densities and specific current loading J_s = I_s / A_Cuscalc J_r = I_r / A_Curcalc A_1 = 2 * m * N_s * I_s / (np.pi * 2 * rad_ag) Current_ratio = I_0 / I_srated # Ratio of magnetization current to rated current # Calculating masses of the electromagnetically active materials V_Cuss = m * l_Cus * A_Cus V_Cusr = m * L_cur * A_Cur V_Fest = len_s * np.pi * ((rad_ag + h_s) 2 - rad_ag 2) - (2 * m * q1 * p * b_s * h_s * len_s) V_Fesy = len_s * np.pi * ((rad_ag + h_s + h_ys) 2 - (rad_ag + h_s) 2) V_Fert = len_s * np.pi * (rad_r 2 - (rad_r - h_0) 2) - 2 * m * q2 * p * b_r * h_0 * len_s V_Fery = len_s * np.pi * ((rad_r - h_0) 2 - (rad_r - h_0 - h_yr) 2) Copper = (V_Cuss + V_Cusr) * rho_Copper M_Fest = V_Fest * rho_Fe M_Fesy = V_Fesy * rho_Fe M_Fert = V_Fert * rho_Fe M_Fery = V_Fery * rho_Fe Iron = M_Fest + M_Fesy + M_Fert + M_Fery M_gen = (Copper) + (Iron) # K_gen = Cu * C_Cu + (Iron) * C_Fe #%M_pm * K_pm L_tot = len_s Structural_mass = 0.0002 * M_gen ** 2 + 0.6457 * M_gen + 645.24 Mass = M_gen + Structural_mass # Calculating Losses and efficiency # 1. Copper losses K_R = 1.2 # skin effect correction coefficient P_Cuss = m * I_s ** 2 * R_s * K_R # Copper loss - stator P_Cusr = m * I_r ** 2 * R_R # Copper loss - rotor P_Cusnom = P_Cuss + P_Cusr # Copper loss - total # Iron Losses ( from Hysteresis and eddy currents) P_Hyys = M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator yoke P_Ftys = M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) # Eddy losses in stator yoke P_Hyd = M_Fest * (B_tsmax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator teeth P_Ftd = M_Fest * (B_tsmax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) # Eddy losses in stator teeth P_Hyyr = ( M_Fery * (B_rymax / 1.5) ** 2 * (P_Fe0h * abs(S_Nmax) * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in rotor yoke P_Ftyr = ( M_Fery * (B_rymax / 1.5) ** 2 * (P_Fe0e * (abs(S_Nmax) * om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in rotor yoke P_Hydr = ( M_Fert * (B_trmax / 1.5) ** 2 * (P_Fe0h * abs(S_Nmax) * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in rotor teeth P_Ftdr = ( M_Fert * (B_trmax / 1.5) ** 2 * (P_Fe0e * (abs(S_Nmax) * om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in rotor teeth P_add = 0.5 * machine_rating / 100 # additional losses P_Fesnom = P_Hyys + P_Ftys + P_Hyd + P_Ftd + P_Hyyr + P_Ftyr + P_Hydr + P_Ftdr # Total iron loss delta_v = 1 # allowable brush voltage drop p_b = 3 * delta_v * I_r # Brush loss Losses = P_Cusnom + P_Fesnom + p_b + P_add gen_eff = (P_e - Losses) / P_e # Calculating stator winding current density J_s = I_s / A_Cuscalc # Calculating electromagnetic torque T_e = p * (machine_rating * 1.01) / (2 * np.pi * freq * (1 - S_Nmax)) # Calculating for tangential stress constraints TC1 = T_e / (2 * np.pi * sigma) TC2r = rad_ag ** 2 * len_s r_out = d_se * 0.5 outputs["R_out"] = r_out outputs["B_g"] = B_g outputs["B_g1"] = B_g1 outputs["B_rymax"] = B_rymax outputs["B_tsmax"] = B_tsmax outputs["B_trmax"] = B_trmax outputs["N_s"] = N_s outputs["S"] = S outputs["h_ys"] = h_ys outputs["b_s"] = b_s outputs["b_t"] = b_t outputs["D_ratio"] = D_ratio outputs["A_Cuscalc"] = A_Cuscalc outputs["Slot_aspect_ratio1"] = Slot_aspect_ratio1 outputs["h_yr"] = h_yr outputs["tau_p"] = tau_p outputs["Q_r"] = Q_r outputs["N_r"] = N_r outputs["b_r"] = b_r outputs["b_trmin"] = b_trmin outputs["b_tr"] = b_tr outputs["A_Curcalc"] = A_Curcalc outputs["Slot_aspect_ratio2"] = Slot_aspect_ratio2 outputs["E_p"] = E_p outputs["f"] = f outputs["I_s"] = I_s outputs["A_1"] = A_1 outputs["J_s"] = J_s outputs["J_r"] = J_r outputs["R_s"] = R_s outputs["R_R"] = R_R outputs["L_r"] = L_r outputs["L_s"] = L_s outputs["L_sm"] = L_sm outputs["generator_mass"] = Mass outputs["K_rad"] = K_rad outputs["Losses"] = Losses outputs["eandm_efficiency"] = np.maximum(eps, gen_eff) outputs["Copper"] = Copper outputs["Iron"] = Iron outputs["Structural_mass"] = Structural_mass outputs["TC1"] = TC1 outputs["TC2r"] = TC2r outputs["Current_ratio"] = Current_ratio # ---------------------------------------------------------------------------------------- class SCIG(GeneratorBase): """ Estimates overall mass dimensions and Efficiency of Squirrel cage Induction generator. Parameters ---------- B_symax : float, [T] Peak Stator Yoke flux density B_ymax Returns ------- h_yr : float rotor yoke height h_ys : float Stator Yoke height tau_p : float Pole pitch D_ratio_UL : float Dia ratio upper limit D_ratio_LL : float Dia ratio Lower limit K_rad_UL : float Aspect ratio upper limit K_rad_LL : float Aspect ratio Lower limit rad_r : float rotor radius A_bar : float Rotor Conductor cross-section mm^2 E_p : float Stator phase voltage """ def initialize(self): super(SCIG, self).initialize() def setup(self): super(SCIG, self).setup() self.add_input("B_symax", val=0.0, units="T") self.add_output("h_yr", val=0.0) self.add_output("h_ys", val=0.0) self.add_output("tau_p", val=0.0) self.add_output("D_ratio_UL", val=0.0) self.add_output("D_ratio_LL", val=0.0) self.add_output("K_rad_UL", val=0.0) self.add_output("K_rad_LL", val=0.0) self.add_output("rad_r", val=0.0) self.add_output("A_bar", val=0.0) self.add_output("E_p", val=np.zeros(self.options["n_pc"])) def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs rad_ag = inputs["rad_ag"] len_s = inputs["len_s"] h_s = inputs["h_s"] h_0 = inputs["h_0"] machine_rating = inputs["machine_rating"] shaft_rpm = inputs["shaft_rpm"] I_0 = inputs["I_0"] rho_Fe = inputs["rho_Fe"] rho_Copper = inputs["rho_Copper"] B_symax = inputs["B_symax"] # Grab constant values B_r = inputs["B_r"] E = inputs["E"] P_Fe0e = inputs["P_Fe0e"] P_Fe0h = inputs["P_Fe0h"] S_N = inputs["S_N"] alpha_p = inputs["alpha_p"] b_r_tau_r = inputs["b_r_tau_r"] b_ro = inputs["b_ro"] b_s_tau_s = inputs["b_s_tau_s"] b_so = inputs["b_so"] cofi = inputs["cofi"] freq = inputs["freq"] h_i = inputs["h_i"] h_sy0 = inputs["h_sy0"] h_w = inputs["h_w"] k_fes = inputs["k_fes"] k_fillr = inputs["k_fillr"] k_s = inputs["k_s"] m = discrete_inputs["m"] mu_0 = inputs["mu_0"] mu_r = inputs["mu_r"] p = inputs["p"] phi = inputs["phi"] q1 = discrete_inputs["q1"] q2 = discrete_inputs["q2"] ratio_mw2pp = inputs["ratio_mw2pp"] resist_Cu = inputs["resist_Cu"] sigma = inputs["sigma"] v = inputs["v"] y_tau_p = inputs["y_tau_p"] y_tau_pr = inputs["y_tau_pr"] """ # Assign values to universal constants sigma = 21.5e3 # shear stress (psi) what material? mu_0 = np.pi4e-7 # permeability of free space in m kg / (s*2 A*2) cofi = 0.9 # power factor h_w = 0.005 # wedge height m = 3 # Number of phases resist_Cu = 1.8e-8 1.4 # Copper resistivity #Assign values to design constants b_so = 0.004 # Stator slot opening width b_ro = 0.004 # Rotor slot opening width q1 = 6 # Stator slots per pole per phase q2 = 4 # Rotor slots per pole per phase b_s_tau_s = 0.45 # Stator Slot width/Slot pitch ratio b_r_tau_r = 0.45 # Rotor Slot width/Slot pitch ratio y_tau_p = 12./15 # Coil span/pole pitch p = 3 # number of pole pairs freq = 60 # frequency in Hz k_fillr = 0.7 # Rotor slot fill factor P_Fe0h = 4 # specific hysteresis losses W / kg @ 1.5 T @50 Hz P_Fe0e = 1 # specific eddy losses W / kg @ 1.5 T @50 Hz S_N = -0.002 # Slip """ n_1 = shaft_rpm / (1 - S_N) # actual rotor speed (rpm) # Calculating winding factor k_y1 = np.sin(np.pi / 2 * y_tau_p) # winding chording factor k_q1 = np.sin(np.pi / 6) / (q1 * np.sin(np.pi / (6 * q1))) # zone factor k_wd = k_y1 * k_q1 # winding factor # Calculating air gap length ag_dia = 2 * rad_ag # air gap diameter ag_len = (0.1 + 0.012 * machine_rating ** (1.0 / 3)) * 0.001 # air gap length in m K_rad = len_s / ag_dia # Aspect ratio K_rad_LL = 0.5 # lower limit on aspect ratio K_rad_UL = 1.5 # upper limit on aspect ratio rad_r = rad_ag - ag_len # rotor radius tau_p = np.pi * ag_dia / (2 * p) # pole pitch S = 2 * p * q1 * m # Stator slots N_slots_pp = S / (m * p * 2) # Number of stator slots per pole per phase tau_s = tau_p / (m * q1) # Stator slot pitch b_s = b_s_tau_s * tau_s # Stator slot width b_t = tau_s - b_s # Stator tooth width Q_r = 2 * p * m * q2 # Rotor slots tau_r = np.pi * (ag_dia - 2 * ag_len) / Q_r # Rotor slot pitch b_r = b_r_tau_r * tau_r # Rotor slot width b_tr = tau_r - b_r # Rotor tooth width tau_r_min = np.pi * (ag_dia - 2 * (ag_len + h_0)) / Q_r b_trmin = tau_r_min - b_r_tau_r * tau_r_min # minumum rotor tooth width # Calculating equivalent slot openings mu_rs = 0.005 mu_rr = 0.005 W_s = (b_s / mu_rs) * 1e-3 # Stator, in m W_r = (b_r / mu_rr) * 1e-3 # Rotor, in m Slot_aspect_ratio1 = h_s / b_s # Stator slot aspect ratio Slot_aspect_ratio2 = h_0 / b_r # Rotor slot aspect ratio # Calculating Carter factor for stator,rotor and effective air gap length """ gamma_s = (2 * W_s / ag_len)*2 / (5 + 2 W_s / ag_len) K_Cs = tau_s / (tau_s - ag_len * gamma_s * 0.5) # page 3-13 Boldea Induction machines Chapter 3 gamma_r = (2 * W_r / ag_len)*2 / (5 + 2 W_r / ag_len) K_Cr = tau_r / (tau_r - ag_len * gamma_r * 0.5) # page 3-13 Boldea Induction machines Chapter 3 """ K_Cs = carterFactor(ag_len, W_s, tau_s) K_Cr = carterFactor(ag_len, W_r, tau_r) K_C = K_Cs * K_Cr g_eff = K_C * ag_len om_m = 2 * np.pi * shaft_rpm / 60 # mechanical frequency om_e = p * om_m # electrical frequency f = shaft_rpm * p / 60 # generator output freq K_s = 0.3 # saturation factor for Iron n_c = 2 # number of conductors per coil a1 = 2 # number of parallel paths # Calculating stator winding turns N_s = np.round(2 * p * N_slots_pp * n_c / a1) # Calculating Peak flux densities B_g1 = mu_0 * 3 * N_s * I_0 * np.sqrt(2) * k_y1 * k_q1 / (np.pi * p * g_eff * (1 + K_s)) B_g = B_g1 * K_C B_rymax = B_symax # calculating back iron thickness h_ys = B_g * tau_p / (B_symax * np.pi) h_yr = h_ys d_se = ag_dia + 2 * (h_ys + h_s + h_w) # stator outer diameter D_ratio = d_se / ag_dia # Diameter ratio # limits for Diameter ratio depending on pole pair if 2 * p == 2: D_ratio_LL = 1.65 D_ratio_UL = 1.69 elif 2 * p == 4: D_ratio_LL = 1.46 D_ratio_UL = 1.49 elif 2 * p == 6: D_ratio_LL = 1.37 D_ratio_UL = 1.4 elif 2 * p == 8: D_ratio_LL = 1.27 D_ratio_UL = 1.3 else: D_ratio_LL = 1.2 D_ratio_UL = 1.24 # Stator slot fill factor if ag_dia > 2: k_fills = 0.65 else: k_fills = 0.4 # Stator winding length and cross-section l_fs = 2 * (0.015 + y_tau_p * tau_p / 2 / np.cos(np.deg2rad(40))) + np.pi * h_s # end connection l_Cus = 2 * N_s * (l_fs + len_s) / a1 # shortpitch A_s = b_s * (h_s - h_w) # Slot area A_scalc = b_s * 1000 * (h_s - h_w) * 1000 # Conductor cross-section (mm^2) A_Cus = A_s * q1 * p * k_fills / N_s # Conductor cross-section (m^2) A_Cuscalc = A_scalc * q1 * p * k_fills / N_s # Stator winding resistance R_s = l_Cus * resist_Cu / A_Cus # Calculating no-load voltage om_s = shaft_rpm * 2 * np.pi / 60 # rated angular frequency P_e = machine_rating / (1 - S_N) # Electrical power E_p = om_s * N_s * k_wd * rad_ag * len_s * B_g1 * np.sqrt(2) S_GN = (1.0 - S_N) * machine_rating # same as P_e? T_e = p * S_GN / (2 * np.pi * freq * (1 - S_N)) I_srated = machine_rating / (3 * E_p * cofi) # Rotor design diff = h_0 - h_w A_bar = b_r * diff # bar cross section Beta_skin = np.sqrt(np.pi * mu_0 * freq / 2 / resist_Cu) # coefficient for skin effect correction k_rm = Beta_skin * h_0 # coefficient for skin effect correction J_b = 6e06 # Bar current density K_i = 0.864 I_b = 2 * m * N_s * k_wd * I_srated / Q_r # bar current # Calculating bar resistance R_rb = resist_Cu * k_rm * len_s / A_bar I_er = I_b / (2 * np.sin(np.pi * p / Q_r)) # End ring current J_er = 0.8 * J_b # End ring current density A_er = I_er / J_er # End ring cross-section b = h_0 # End ring dimension a = A_er / b # End ring dimension D_er = (rad_ag * 2 - 2 * ag_len) - 0.003 # End ring diameter l_er = np.pi * (D_er - b) / Q_r # End ring segment length if debug: sys.stderr.write("l_er {:.4f} A_er {:.4f} D_er {:.4f}\n".format(l_er[0], A_er[0], D_er[0])) # Calculating end ring resistance R_re = resist_Cu * l_er / (2 * A_er * (np.sin(np.pi * p / Q_r)) ** 2) # Calculating equivalent rotor resistance if debug: sys.stderr.write("R_rb {:.3e} R_re {:.3e} k_wd {:.4f} N_s {} Q_r {}\n".format(R_rb, R_re, k_wd, N_s, Q_r)) R_R = (R_rb + R_re) * 4 * m * (k_wd * N_s) ** 2 / Q_r # Calculating Rotor and Stator teeth flux density B_trmax = B_g * tau_r / b_trmin B_tsmax = B_g * tau_s / b_t # Calculating Equivalent core lengths l_r = len_s + 4 * ag_len # for axial cooling l_se = len_s + (2 / 3) * ag_len K_fe = 0.95 # Iron factor L_e = l_se * K_fe # radial cooling # Calculating leakage inductance in stator if debug: sys.stderr.write("b_s {:.3e} b_so {:.3e}\n".format(b_s[0], b_so[0])) L_ssigmas = ( 2 * mu_0 * len_s * N_s ** 2 / p / q1 * ((h_s - h_w) / (3 * b_s) + h_w / b_so) ) # slot leakage inductance L_ssigmaew = ( 2 * mu_0 * len_s * N_s ** 2 / p / q1 * 0.34 * q1 * (l_fs - 0.64 * tau_p * y_tau_p) / len_s ) # end winding leakage inductance L_ssigmag = ( 2 * mu_0 * len_s * N_s ** 2 / p / q1 * (5 * (ag_len * K_C / b_so) / (5 + 4 * (ag_len * K_C / b_so))) ) # tooth tip leakage inductance L_s = L_ssigmas + L_ssigmaew + L_ssigmag # stator leakage inductance L_sm = 6 * mu_0 * len_s * tau_p * (k_wd * N_s) 2 / (np.pi 2 * p * g_eff * (1 + K_s)) # Calculating leakage inductance in rotor lambda_ei = 2.3 * D_er / (4 * Q_r * len_s * (np.sin(np.pi * p / Q_r) ** 2)) * np.log(4.7 * ag_dia / (a + 2 * b)) lambda_b = h_0 / (3 * b_r) + h_w / b_ro L_i = np.pi * ag_dia / Q_r L_rsl = mu_0 * len_s * ((h_0 - h_w) / (3 * b_r) + h_w / b_ro) # slot leakage inductance L_rel = mu_0 * (len_s * lambda_b + 2 * lambda_ei * L_i) # end winding leakage inductance L_rtl = mu_0 * len_s * (0.9 * tau_r * 0.09 / g_eff) # tooth tip leakage inductance L_rsigma = (L_rsl + L_rtl + L_rel) * 4 * m * (k_wd * N_s) ** 2 / Q_r # rotor leakage inductance # Calculating rotor current if debug: sys.stderr.write( "S_N {} P_e {:.1f} m {} R_R {:.4f} = {:.1f}\n".format(S_N, P_e, m, R_R, -S_N * P_e / m / R_R) ) I_r = np.sqrt(-S_N * P_e / m / R_R) I_sm = E_p / (2 * np.pi * freq * L_sm) # Calculating stator currents and specific current loading I_s = np.sqrt((I_r 2 + I_sm 2)) A_1 = 2 * m * N_s * I_s / (np.pi * 2 * rad_ag) # Calculating masses of the electromagnetically active materials V_Cuss = m * l_Cus * A_Cus # Volume of copper in stator V_Cusr = Q_r * len_s * A_bar + np.pi * (D_er * A_er - A_er * b) # Volume of copper in rotor V_Fest = ( len_s * np.pi * ((rad_ag + h_s) 2 - rad_ag 2) - 2 * m * q1 * p * b_s * h_s * len_s ) # Volume of iron in stator teeth V_Fesy = len_s * np.pi * ((rad_ag + h_s + h_ys) 2 - (rad_ag + h_s) 2) # Volume of iron in stator yoke rad_r = rad_ag - ag_len # rotor radius V_Fert = ( np.pi * len_s * (rad_r 2 - (rad_r - h_0) 2) - 2 * m * q2 * p * b_r * h_0 * len_s ) # Volume of iron in rotor teeth V_Fery = np.pi * len_s * ((rad_r - h_0) 2 - (rad_r - h_0 - h_yr) 2) # Volume of iron in rotor yoke Copper = (V_Cuss + V_Cusr)[-1] * rho_Copper # Mass of Copper M_Fest = V_Fest * rho_Fe # Mass of stator teeth M_Fesy = V_Fesy * rho_Fe # Mass of stator yoke M_Fert = V_Fert * rho_Fe # Mass of rotor tooth M_Fery = V_Fery * rho_Fe # Mass of rotor yoke Iron = M_Fest + M_Fesy + M_Fert + M_Fery Active_mass = Copper + Iron L_tot = len_s Structural_mass = 0.0001 * Active_mass ** 2 + 0.8841 * Active_mass - 132.5 Mass = Active_mass + Structural_mass # Calculating Losses and efficiency # 1. Copper losses K_R = 1.2 # skin effect correction coefficient P_Cuss = m * I_s ** 2 * R_s * K_R # Copper loss - stator P_Cusr = m * I_r ** 2 * R_R # Copper loss - rotor P_Cusnom = P_Cuss + P_Cusr # Copper loss - total # Iron Losses ( from Hysteresis and eddy currents) P_Hyys = M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator yoke P_Ftys = ( M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator yoke P_Hyd = M_Fest * (B_tsmax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator tooth P_Ftd = ( M_Fest * (B_tsmax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator tooth P_Hyyr = ( M_Fery * (B_rymax / 1.5) ** 2 * (P_Fe0h * abs(S_N) * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in rotor yoke P_Ftyr = ( M_Fery * (B_rymax / 1.5) ** 2 * (P_Fe0e * (abs(S_N) * om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in rotor yoke P_Hydr = ( M_Fert * (B_trmax / 1.5) ** 2 * (P_Fe0h * abs(S_N) * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in rotor tooth P_Ftdr = ( M_Fert * (B_trmax / 1.5) ** 2 * (P_Fe0e * (abs(S_N) * om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in rotor tooth # Calculating Additional losses P_add = 0.5 * machine_rating / 100 P_Fesnom = P_Hyys + P_Ftys + P_Hyd + P_Ftd + P_Hyyr + P_Ftyr + P_Hydr + P_Ftdr Losses = P_Cusnom + P_Fesnom + P_add gen_eff = (P_e - Losses) / P_e # Calculating current densities in the stator and rotor J_s = I_s / A_Cuscalc J_r = I_r / A_bar / 1e6 # Calculating Tangential stress constraints TC1 = T_e / (2 * np.pi * sigma) TC2r = rad_ag ** 2 * len_s # Calculating mass moments of inertia and center of mass r_out = d_se * 0.5 outputs["R_out"] = r_out outputs["B_tsmax"] = B_tsmax outputs["B_trmax"] = B_trmax outputs["B_rymax"] = B_rymax outputs["B_g"] = B_g outputs["B_g1"] = B_g1 outputs["N_s"] = N_s outputs["S"] = S outputs["h_ys"] = h_ys outputs["b_s"] = b_s outputs["b_t"] = b_t outputs["D_ratio"] = D_ratio outputs["D_ratio_UL"] = D_ratio_UL outputs["D_ratio_LL"] = D_ratio_LL outputs["A_Cuscalc"] = A_Cuscalc outputs["Slot_aspect_ratio1"] = Slot_aspect_ratio1 outputs["h_yr"] = h_yr outputs["tau_p"] = tau_p outputs["Q_r"] = Q_r outputs["b_r"] = b_r outputs["b_trmin"] = b_trmin outputs["b_tr"] = b_tr outputs["rad_r"] = rad_r outputs["A_bar"] = A_bar outputs["Slot_aspect_ratio2"] = Slot_aspect_ratio2 outputs["E_p"] = E_p outputs["f"] = f outputs["I_s"] = I_s outputs["A_1"] = A_1 outputs["J_s"] = J_s outputs["J_r"] = J_r outputs["R_s"] = R_s outputs["R_R"] = R_R[-1] outputs["L_s"] = L_s outputs["L_sm"] = L_sm outputs["generator_mass"] = Mass outputs["K_rad"] = K_rad outputs["K_rad_UL"] = K_rad_UL outputs["K_rad_LL"] = K_rad_LL outputs["Losses"] = Losses outputs["eandm_efficiency"] = np.maximum(eps, gen_eff) outputs["Copper"] = Copper outputs["Iron"] = Iron outputs["Structural_mass"] = Structural_mass outputs["TC1"] = TC1 outputs["TC2r"] = TC2r # ---------------------------------------------------------------------------------------- class EESG(GeneratorBase): """ Estimates overall mass dimensions and Efficiency of Electrically Excited Synchronous generator. Parameters ---------- I_f : float, [A] Excitation current N_f : float field turns b_arm : float, [m] arm width h_yr : float, [m] rotor yoke height h_ys : float, [m] Yoke height tau_p : float, [m] Pole pitch self.tau_p Returns ------- n_brushes : float number of brushes h_p : float, [m] Pole height b_p : float, [m] Pole width L_m : float, [H] Stator synchronising inductance R_r : float, [ohm] Rotor resistance B_tmax : float, [T] Peak Teeth flux density B_gfm : float, [T] Average air gap flux density B_g B_pc : float, [T] Pole core flux density B_symax : float, [T] Peak Stator Yoke flux density B_ymax E_s : float, [V] Stator phase voltage J_f : float, [Am-2] rotor Current density Power_ratio : float Power_ratio Load_mmf_ratio : float mmf_ratio """ def initialize(self): super(EESG, self).initialize() def setup(self): super(EESG, self).setup() self.add_input("I_f", val=0.0, units="A") self.add_input("N_f", val=0.0) self.add_input("b_arm", val=0.0, units="m") self.add_input("h_yr", val=0.0, units="m") self.add_input("h_ys", val=0.0, units="m") self.add_input("tau_p", val=0.0, units="m") self.add_output("n_brushes", val=0.0) self.add_output("h_p", val=0.0, units="m") self.add_output("b_p", val=0.0, units="m") self.add_output("L_m", val=0.0, units="H") self.add_output("R_r", val=0.0, units="ohm") self.add_output("B_tmax", val=0.0, units="T") self.add_output("B_gfm", val=0.0, units="T") self.add_output("B_pc", val=0.0, units="T") self.add_output("B_symax", val=0.0, units="T") self.add_output("E_s", val=np.zeros(self.options["n_pc"]), units="V") self.add_output("J_f", val=0.0, units="Am*-2") self.add_output("Power_ratio", val=0.0) self.add_output("Load_mmf_ratio", val=0.0) def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs rad_ag = inputs["rad_ag"] len_s = inputs["len_s"] h_s = inputs["h_s"] tau_p = inputs["tau_p"] N_f = inputs["N_f"] I_f = inputs["I_f"] h_ys = inputs["h_ys"] h_yr = inputs["h_yr"] machine_rating = inputs["machine_rating"] shaft_rpm = inputs["shaft_rpm"] Torque = inputs["rated_torque"] b_st = inputs["b_st"] d_s = inputs["d_s"] t_ws = inputs["t_ws"] n_r = inputs["n_r"] n_s = inputs["n_s"] b_r = inputs["b_arm"] d_r = inputs["d_r"] t_wr = inputs["t_wr"] R_sh = 0.5 inputs["D_shaft"] rho_Fe = inputs["rho_Fe"] rho_Copper = inputs["rho_Copper"] rho_Fes = inputs["rho_Fes"] # Grab constant values B_r = inputs["B_r"] E = inputs["E"] P_Fe0e = inputs["P_Fe0e"] P_Fe0h = inputs["P_Fe0h"] S_N = inputs["S_N"] alpha_p = inputs["alpha_p"] b_r_tau_r = inputs["b_r_tau_r"] b_ro = inputs["b_ro"] b_s_tau_s = inputs["b_s_tau_s"] b_so = inputs["b_so"] cofi = inputs["cofi"] freq = inputs["freq"] h_i = inputs["h_i"] h_sy0 = inputs["h_sy0"] h_w = inputs["h_w"] k_fes = inputs["k_fes"] k_fillr = inputs["k_fillr"] k_fills = inputs["k_fills"] k_s = inputs["k_s"] m = discrete_inputs["m"] mu_0 = inputs["mu_0"] mu_r = inputs["mu_r"] p = inputs["p"] phi = inputs["phi"] q1 = discrete_inputs["q1"] q2 = discrete_inputs["q2"] ratio_mw2pp = inputs["ratio_mw2pp"] resist_Cu = inputs["resist_Cu"] sigma = inputs["sigma"] v = inputs["v"] y_tau_p = inputs["y_tau_p"] y_tau_pr = inputs["y_tau_pr"] """ # Assign values to universal constants E = 2e11 # N / m^2 young's modulus sigma = 48.373e3 # shear stress of steel in psi (~333 MPa) mu_0 = np.pi * 4e-7 # permeability of free space in m * kg / (s*2 A*2) phi = np.deg2rad(90) # Assign values to design constants h_w = 0.005 b_so = 0.004 # Stator slot opening m = 3 # number of phases q1 = 2 # no of stator slots per pole per phase b_s_tau_s = 0.45 # ratio of slot width to slot pitch P_Fe0h = 4 # specific hysteresis losses W / kg @ 1.5 T @50 Hz P_Fe0e = 1 # specific eddy losses W / kg @ 1.5 T @50 Hz resist_Cu = 1.8e-8 1.4 # resisitivity of copper # ohm-meter (Why the 1.4 factor?) k_fes = 0.9 # iron fill factor (not used) y_tau_p = 1 # coil span / pole pitch fullpitch k_fillr = 0.7 # rotor slot fill factor k_s = 0.2 # magnetic saturation factor for iron cofi = 0.85 # power factor """ T = Torque # back iron thickness for rotor and stator t_s = h_ys t = h_yr # Aspect ratio K_rad = len_s / (2 * rad_ag) ###################################################### Electromagnetic design############################################# alpha_p = np.pi / 2 * 0.7 # (not used) dia = 2 * rad_ag # air gap diameter # air gap length and minimum values g = 0.001 * dia if g < 0.005: g = 0.005 r_r = rad_ag - g # rotor radius d_se = dia + 2 * h_s + 2 * h_ys # stator outer diameter (not used) p = np.round(np.pi * dia / (2 * tau_p)) # number of pole pairs S = 2 * p * q1 * m # number of slots of stator phase winding N_conductors = S * 2 N_s = N_conductors / 2 / m # Stator turns per phase alpha = 180 / S / p # electrical angle (not used) tau_s = np.pi * dia / S # slot pitch h_ps = 0.1 * tau_p # height of pole shoe b_pc = 0.4 * tau_p # width of pole core h_pc = 0.6 * tau_p # height of pole core h_p = 0.7 * tau_p # pole height b_p = h_p b_s = tau_s * b_s_tau_s # slot width Slot_aspect_ratio = h_s / b_s b_t = tau_s - b_s # tooth width # Calculating Carter factor and effective air gap g_a = g K_C1 = (tau_s + 10 * g_a) / (tau_s - b_s + 10 * g_a) # salient pole rotor g_1 = K_C1 * g # calculating angular frequency om_m = 2 * np.pi * shaft_rpm / 60 om_e = 60 f = shaft_rpm * p / 60 # Slot fill factor according to air gap radius if 2 * rad_ag > 2: K_fills = 0.65 else: K_fills = 0.4 # Calculating Stator winding factor k_y1 =	np.sin(y_tau_p * np.pi / 2)	numpy.sin
# -------------------------------------------------------- # Licensed under The MIT License [see LICENSE for details] # -------------------------------------------------------- import random import os import time import sys import pybullet as p import numpy as np import IPython from env.tm5_gripper_hand_camera import Panda from transforms3d.quaternions import * import scipy.io as sio from core.utils import * import json from itertools import product import OMG.ycb_render.robotPose.robot_pykdl as robot_pykdl from OMG.omg.config import cfg as planner_cfg from OMG.omg.core import PlanningScene BASE_LINK = -1 MAX_DISTANCE = 0.000 def get_num_joints(body, CLIENT=None): return p.getNumJoints(body, physicsClientId=CLIENT) def get_links(body, CLIENT=None): return list(range(get_num_joints(body, CLIENT))) def get_all_links(body, CLIENT=None): return [BASE_LINK] + list(get_links(body, CLIENT)) def pairwise_link_collision(body1, link1, body2, link2=BASE_LINK, max_distance=MAX_DISTANCE, CLIENT=None): # 10000 return len(p.getClosestPoints(bodyA=body1, bodyB=body2, distance=max_distance, linkIndexA=link1, linkIndexB=link2, physicsClientId=CLIENT)) != 0 def any_link_pair_collision(body1, body2, links1=None, links2=None, CLIENT=None, kwargs): if links1 is None: links1 = get_all_links(body1, CLIENT) if links2 is None: links2 = get_all_links(body2, CLIENT) for link1, link2 in product(links1, links2): if (body1 == body2) and (link1 == link2): continue if pairwise_link_collision(body1, link1, body2, link2, CLIENT=CLIENT, kwargs): return True return False def body_collision(body1, body2, max_distance=MAX_DISTANCE, CLIENT=None): # 10000 return len(p.getClosestPoints(bodyA=body1, bodyB=body2, distance=max_distance, physicsClientId=CLIENT)) != 0 def pairwise_collision(body1, body2, kwargs): if isinstance(body1, tuple) or isinstance(body2, tuple): body1, links1 = expand_links(body1) body2, links2 = expand_links(body2) return any_link_pair_collision(body1, body2, links1, links2, kwargs) return body_collision(body1, body2, *kwargs) class PandaJointSpace(): def __init__(self): self.high = np.ones(7) 0.25 self.low = np.ones(7) * -0.25 self.shape = [7] self.bounds = np.vstack([self.low, self.high]) class PandaTaskSpace6D(): def __init__(self): self.high = np.array([0.06, 0.06, 0.06, np.pi/6, np.pi/6, np.pi/6]) # , np.pi/10 self.low = np.array([-0.06, -0.06, -0.06, -np.pi/6, -np.pi/6, -np.pi/6]) # , -np.pi/3 self.shape = [6] self.bounds = np.vstack([self.low, self.high]) class PandaYCBEnv(): """ Class for franka panda environment with YCB objects. """ def __init__(self, renders=False, maxSteps=100, random_target=False, blockRandom=0.5, cameraRandom=0, action_space='configuration', use_expert_plan=False, accumulate_points=False, use_hand_finger_point=False, expert_step=20, expert_dynamic_timestep=False, data_type='RGB', filter_objects=[], img_resize=(224, 224), regularize_pc_point_count=False, egl_render=False, width=224, height=224, uniform_num_pts=1024, numObjects=7, termination_heuristics=True, domain_randomization=False, change_dynamics=False, pt_accumulate_ratio=0.95, initial_near=0.2, initial_far=0.5, disable_unnece_collision=True, omg_config=None): self._timeStep = 1. / 1000. self._observation = [] self._renders = renders self._maxSteps = maxSteps self._env_step = 0 self._resize_img_size = img_resize self._p = p self._window_width = width self._window_height = height self._blockRandom = blockRandom self._cameraRandom = cameraRandom self._numObjects = numObjects self._random_target = random_target self._accumulate_points = accumulate_points self._use_expert_plan = use_expert_plan self._expert_step = expert_step self._use_hand_finger_point = use_hand_finger_point self._data_type = data_type self._egl_render = egl_render self._action_space = action_space self._disable_unnece_collision = disable_unnece_collision self._pt_accumulate_ratio = pt_accumulate_ratio self._change_dynamics = change_dynamics self._domain_randomization = domain_randomization self._initial_near = initial_near self._initial_far = initial_far self._expert_dynamic_timestep = expert_dynamic_timestep self._termination_heuristics = termination_heuristics self._filter_objects = filter_objects self._omg_config = omg_config self._regularize_pc_point_count = regularize_pc_point_count self._uniform_num_pts = uniform_num_pts self.observation_dim = (self._window_width, self._window_height, 3) self.init_constant() self.connect() def init_constant(self): self._shift = [0.8, 0.8, 0.8] # to work without axis in DIRECT mode self._max_episode_steps = 50 self.root_dir = os.path.join(os.path.dirname(os.path.abspath(__file__)), '..') self.data_root_dir = os.path.join(self.root_dir, 'data/scenes') self._planner_setup = False self.retracted = False self._standoff_dist = 0.08 self.cam_offset = np.eye(4) self.cam_offset[:3, 3] = (np.array([0.1186, 0., 0.0191344123493])) # camera offset self.cam_offset[:3, :3] = euler2mat(0, 0, -np.pi/2) self.cur_goal = np.eye(4) self.target_idx = 0 self.objects_loaded = False self.parallel = False self.curr_acc_points = np.zeros([3, 0]) self.connected = False self.action_dim = 6 self.hand_finger_points = hand_finger_point self.action_space = PandaTaskSpace6D() def connect(self): """ Connect pybullet. """ if self._renders: self.cid = p.connect(p.SHARED_MEMORY) if (self.cid < 0): self.cid = p.connect(p.GUI) p.resetDebugVisualizerCamera(1.3, 180.0, -41.0, [-0.35, -0.58, -0.88]) else: self.cid = p.connect(p.DIRECT) if self._egl_render: import pkgutil egl = pkgutil.get_loader("eglRenderer") if egl: p.loadPlugin(egl.get_filename(), "_eglRendererPlugin") self.connected = True def disconnect(self): """ Disconnect pybullet. """ p.disconnect() self.connected = False def reset(self, save=False, init_joints=None, scene_file=None, data_root_dir=None, cam_random=0, reset_free=False, enforce_face_target=False): """ Environment reset called at the beginning of an episode. """ self.retracted = False if data_root_dir is not None: self.data_root_dir = data_root_dir self._cur_scene_file = scene_file if reset_free: return self.cache_reset(scene_file, init_joints, enforce_face_target) self.disconnect() self.connect() # Set the camera . look = [0.1 - self._shift[0], 0.2 - self._shift[1], 0 - self._shift[2]] distance = 2.5 pitch = -56 yaw = 245 roll = 0. fov = 20. aspect = float(self._window_width) / self._window_height self.near = 0.1 self.far = 10 self._view_matrix = p.computeViewMatrixFromYawPitchRoll(look, distance, yaw, pitch, roll, 2) self._proj_matrix = p.computeProjectionMatrixFOV(fov, aspect, self.near, self.far) self._light_position = np.array([-1.0, 0, 2.5]) p.resetSimulation() p.setTimeStep(self._timeStep) p.setPhysicsEngineParameter(enableConeFriction=0) p.setGravity(0, 0, -9.81) p.stepSimulation() # Set table and plane plane_file = os.path.join(self.root_dir, 'data/objects/floor/model_normalized.urdf') # _white table_file = os.path.join(self.root_dir, 'data/objects/table/models/model_normalized.urdf') self.obj_path = [plane_file, table_file] self.plane_id = p.loadURDF(plane_file, [0 - self._shift[0], 0 - self._shift[1], -.82 - self._shift[2]]) self.table_pos = np.array([0.5 - self._shift[0], 0.0 - self._shift[1], -.82 - self._shift[2]]) self.table_id = p.loadURDF(table_file, self.table_pos[0], self.table_pos[1], self.table_pos[2], 0.707, 0., 0., 0.707) # Intialize robot and objects if init_joints is None: self._panda = Panda(stepsize=self._timeStep, base_shift=self._shift) else: self._panda = Panda(stepsize=self._timeStep, init_joints=init_joints, base_shift=self._shift) for _ in range(1000): p.stepSimulation() if not self.objects_loaded: self._objectUids = self.cache_objects() if self._use_expert_plan: self.setup_expert_scene() if scene_file is None or not os.path.exists(os.path.join(self.data_root_dir, scene_file + '.mat')): self._randomly_place_objects(self._get_random_object(self._numObjects), scale=1) else: self.place_objects_from_scene(scene_file) self._objectUids += [self.plane_id, self.table_id] self._env_step = 0 self.collided = False self.collided_before = False self.obj_names, self.obj_poses = self.get_env_info() self.init_target_height = self._get_target_relative_pose()[2, 3] self.curr_acc_points = np.zeros([3, 0]) return None # observation def step(self, action, delta=False, obs=True, repeat=150, config=False, vis=False): """ Environment step. """ action = self.process_action(action, delta, config) self._panda.setTargetPositions(action) for _ in range(int(repeat)): p.stepSimulation() if self._renders: time.sleep(self._timeStep) observation = self._get_observation(vis=vis) test_termination_obs = observation[0][1] depth = test_termination_obs[[3]].T mask = test_termination_obs[[4]].T observation = self.input_selection(observation) done = self._termination(depth.copy(), mask, use_depth_heuristics=self._termination_heuristics) self.collision_check() reward = self._reward() info = {'grasp_success': reward, 'goal_dist': self._get_goal_dist(), 'point_num': self.curr_acc_points.shape[1], 'collided': self.collided, 'cur_ef_pose': self._get_ef_pose(mat=True)} self._env_step += 1 return observation, reward, done, info def _get_observation(self, pose=None, vis=False, acc=True): """ Get observation """ object_pose = self._get_target_relative_pose('ef') # self._get_relative_ef_pose() ef_pose = self._get_ef_pose('mat') joint_pos, joint_vel = self._panda.getJointStates() near, far = self.near, self.far view_matrix, proj_matrix = self._view_matrix, self._proj_matrix extra_overhead_camera = False camera_info = tuple(view_matrix) + tuple(proj_matrix) hand_cam_view_matrix, hand_proj_matrix, lightDistance, lightColor, lightDirection, near, far = self._get_hand_camera_view(pose) camera_info += tuple(hand_cam_view_matrix.flatten()) + tuple(hand_proj_matrix) _, _, rgba, depth, mask = p.getCameraImage(width=self._window_width, height=self._window_height, viewMatrix=tuple(hand_cam_view_matrix.flatten()), projectionMatrix=hand_proj_matrix, physicsClientId=self.cid, renderer=p.ER_BULLET_HARDWARE_OPENGL) depth = (far * near / (far - (far - near) * depth) * 5000).astype(np.uint16) # transform depth from NDC to actual depth mask[mask >= 0] += 1 # transform mask to have target id 0 target_idx = self.target_idx + 4 mask[mask == target_idx] = 0 mask[mask == -1] = 50 mask[mask != 0] = 1 obs = np.concatenate([rgba[..., :3], depth[..., None], mask[..., None]], axis=-1) obs = self.process_image(obs[..., :3], obs[..., [3]], obs[..., [4]], tuple(self._resize_img_size)) intrinsic_matrix = projection_to_intrinsics(hand_proj_matrix, self._window_width, self._window_height) point_state = backproject_camera_target(obs[3].T, intrinsic_matrix, obs[4].T) # obs[4].T point_state = self.cam_offset[:3, :3].dot(point_state) + self.cam_offset[:3, [3]] point_state[1] = -1 point_state = self.process_pointcloud(point_state, vis, acc) obs = (point_state, obs) pose_info = (object_pose, ef_pose) return [obs, joint_pos, camera_info, pose_info] def retract(self, record=False): """ Move the arm to lift the object. """ cur_joint = np.array(self._panda.getJointStates()[0]) cur_joint[-1] = 0.8 # close finger observations = [self.step(cur_joint, repeat=300, config=True, vis=False)[0]] pos, orn = p.getLinkState(self._panda.pandaUid, self._panda.pandaEndEffectorIndex)[4:6] for i in range(10): pos = (pos[0], pos[1], pos[2] + 0.03) jointPoses = np.array(p.calculateInverseKinematics(self._panda.pandaUid, self._panda.pandaEndEffectorIndex, pos, maxNumIterations=500, residualThreshold=1e-8)) jointPoses[6] = 0.8 jointPoses = jointPoses[:7].copy() obs = self.step(jointPoses, config=True)[0] if record: observations.append(obs) self.retracted = True rew = self._reward() if record: return (rew, observations) return rew def _reward(self): """ Calculates the reward for the episode. """ reward = 0 if self.retracted and self.target_lifted(): print('target {} lifted !'.format(self.target_name)) reward = 1 return reward def _termination(self, depth_img, mask_img, use_depth_heuristics=False): """ Target depth heuristics for determining if grasp can be executed. The threshold is based on depth in the middle of the camera and the finger is near the bottom two sides """ depth_heuristics = False nontarget_mask = mask_img[..., 0] != 0 if use_depth_heuristics: depth_img = depth_img[..., 0] depth_img[nontarget_mask] = 10 # hard coded region depth_img_roi = depth_img[int(58. self._window_height / 64):, int(21. * self._window_width / 64):int(42 * self._window_width / 64)] depth_img_roi_ = depth_img_roi[depth_img_roi < 0.21] if depth_img_roi_.shape[0] > 1: depth_heuristics = (depth_img_roi_ < 0.115).sum() > 10 return self._env_step >= self._maxSteps or depth_heuristics or self.target_fall_down() def cache_objects(self): """ Load all YCB objects and set up """ obj_path = os.path.join(self.root_dir, 'data/objects/') objects = self.obj_indexes obj_path = [obj_path + objects[i] for i in self._all_obj] self.target_obj_indexes = [self._all_obj.index(idx) for idx in self._target_objs] pose = np.zeros([len(obj_path), 3]) pose[:, 0] = -0.5 - np.linspace(0, 4, len(obj_path)) pos, orn = p.getBasePositionAndOrientation(self._panda.pandaUid) objects_paths = [p_.strip() + '/' for p_ in obj_path] objectUids = [] self.object_heights = [] self.obj_path = objects_paths + self.obj_path self.placed_object_poses = [] for i, name in enumerate(objects_paths): trans = pose[i] + np.array(pos) # fixed position self.placed_object_poses.append((trans.copy(), np.array(orn).copy())) uid = self._add_mesh(os.path.join(self.root_dir, name, 'model_normalized.urdf'), trans, orn) # xyzw if self._change_dynamics: p.changeDynamics(uid, -1, lateralFriction=0.15, spinningFriction=0.1, rollingFriction=0.1) point_z = np.loadtxt(os.path.join(self.root_dir, name, 'model_normalized.extent.txt')) half_height = float(point_z.max()) / 2 if len(point_z) > 0 else 0.01 self.object_heights.append(half_height) objectUids.append(uid) p.setCollisionFilterPair(uid, self.plane_id, -1, -1, 0) if self._disable_unnece_collision: for other_uid in objectUids: p.setCollisionFilterPair(uid, other_uid, -1, -1, 0) self.objects_loaded = True self.placed_objects = [False] * len(self.obj_path) return objectUids def cache_reset(self, scene_file, init_joints, enforce_face_target): """ Hack to move the loaded objects around to avoid loading multiple times """ self._panda.reset(init_joints) self.place_back_objects() if scene_file is None or not os.path.exists(os.path.join(self.data_root_dir, scene_file + '.mat')): self._randomly_place_objects(self._get_random_object(self._numObjects), scale=1) else: self.place_objects_from_scene(scene_file, self._objectUids) self._env_step = 0 self.retracted = False self.collided = False self.collided_before = False self.obj_names, self.obj_poses = self.get_env_info() self.init_target_height = self._get_target_relative_pose()[2, 3] self.curr_acc_points = np.zeros([3, 0]) if self._domain_randomization: self.load_textures() rand_tex_id = np.random.choice(len(self.table_textures)) p.changeVisualShape(self._objectUids[self.target_idx], -1, textureUniqueId=self.table_textures[rand_tex_id]) rand_tex_id = np.random.choice(len(self.table_textures)) p.changeVisualShape(self._objectUids[-2], -1, textureUniqueId=self.table_textures[rand_tex_id]) rand_tex_id = np.random.choice(len(self.table_textures)) p.changeVisualShape(self._objectUids[-1], -1, textureUniqueId=self.table_textures[rand_tex_id]) observation = self.enforce_face_target() if enforce_face_target else self._get_observation() observation = self.input_selection(observation) return observation def place_objects_from_scene(self, scene_file, objectUids=None): """ Place objects with poses based on the scene file """ if self.objects_loaded: objectUids = self._objectUids scene = sio.loadmat(os.path.join(self.data_root_dir, scene_file + '.mat')) poses = scene['pose'] path = scene['path'] pos, orn = p.getBasePositionAndOrientation(self._panda.pandaUid) new_objs = objectUids is None objects_paths = [p_.strip() + '/' for p_ in path] for i, name in enumerate(objects_paths[:-2]): pose = poses[i] trans = pose[:3, 3] + np.array(pos) # fixed position orn = ros_quat(mat2quat(pose[:3, :3])) full_name = os.path.join(self.root_dir, name) if full_name not in self.obj_path: continue k = self.obj_path.index(full_name) if self.objects_loaded else i self.placed_objects[k] = True p.resetBasePositionAndOrientation(objectUids[k], trans, orn) p.resetBaseVelocity( objectUids[k], (0.0, 0.0, 0.0), (0.0, 0.0, 0.0) ) rand_name = objects_paths[0] self.target_idx = self.obj_path.index(os.path.join(self.root_dir, rand_name)) self.target_name = rand_name.split('/')[-2] print('==== loaded scene: {} target: {} idx: {} init joint'.format(scene_file.split('/')[-1], self.target_name, self.target_idx)) if 'init_joints' in scene: self.reset_joint(scene['init_joints']) return objectUids def place_back_objects(self): for idx, obj in enumerate(self._objectUids): if self.placed_objects[idx]: p.resetBasePositionAndOrientation(obj, self.placed_object_poses[idx][0], self.placed_object_poses[idx][1]) self.placed_objects[idx] = False def load_textures(self): if hasattr(self, 'table_textures'): return texture_dir = os.path.join(self.root_dir, 'data/random_textures/textures') files = os.listdir(texture_dir) random_files = random.sample(files, 200) table_textures = [p.loadTexture(os.path.join(texture_dir, f)) for f in random_files] print('number of textures:', len(table_textures)) self.table_textures = table_textures def input_selection(self, observation): """ Select input channels based on data type """ return observation def update_curr_acc_points(self, new_points): """ Update accumulated points in world coordinate """ pos, rot = self._get_ef_pose() ef_pose = unpack_pose(np.hstack((pos, tf_quat(rot)))) new_points = ef_pose[:3, :3].dot(new_points) + ef_pose[:3, [3]] # accumulate points index = np.random.choice(range(new_points.shape[1]), size=int(self._pt_accumulate_ratio*self._env_step new_points.shape[1]), replace=False).astype(np.int) self.curr_acc_points = np.concatenate((new_points[:, index], self.curr_acc_points), axis=1) def _get_init_info(self): return [self.obj_names, self.obj_poses, np.array(self._panda.getJointStates()[0])] def _add_mesh(self, obj_file, trans, quat, scale=1): """ Add a mesh with URDF file. """ bid = p.loadURDF(obj_file, trans, quat, globalScaling=scale, flags=p.URDF_ENABLE_CACHED_GRAPHICS_SHAPES) return bid def reset_joint(self, init_joints): if init_joints is not None: self._panda.reset(np.array(init_joints).flatten()) def process_action(self, action, delta=False, config=False): """ Process different action types """ if config: if delta: cur_joint = np.array(self._panda.getJointStates()[0]) action = cur_joint + action elif self._action_space == 'task6d': # transform to local coordinate cur_ef = np.array(self._panda.getJointStates()[0])[-3] pos, orn = p.getLinkState(self._panda.pandaUid, self._panda.pandaEndEffectorIndex)[4:6] pose = np.eye(4) pose[:3, :3] = quat2mat(tf_quat(orn)) pose[:3, 3] = pos pose_delta = np.eye(4) pose_delta[:3, :3] = euler2mat(action[3], action[4], action[5]) pose_delta[:3, 3] = action[:3] new_pose = pose.dot(pose_delta) orn = ros_quat(mat2quat(new_pose[:3, :3])) pos = new_pose[:3, 3] jointPoses = np.array(p.calculateInverseKinematics(self._panda.pandaUid, self._panda.pandaEndEffectorIndex, pos, orn, maxNumIterations=500, residualThreshold=1e-8)) jointPoses[6] = 0.0 action = jointPoses[:7] return action def _sample_ef(self, target, near=0.35, far=0.50): # sample a camera extrinsics count = 0 ik = None outer_loop_num = 20 inner_loop_num = 5 if not self._planner_setup: try: self.setup_expert_scene() except: print(f"{bcolors.FAIL}Expert Scene Setup Error.{bcolors.RESET}") pass for _ in range(outer_loop_num): theta = np.random.uniform(low=0, high=2np.pi/3) phi = np.random.uniform(low=np.pi/2, high=3np.pi/2) # top sphere r = np.random.uniform(low=self._initial_near, high=self._initial_far) # sphere radius pos = np.array([rnp.sin(theta)np.cos(phi), rnp.sin(theta)np.sin(phi), r*np.cos(theta)]) trans = pos + target + np.random.uniform(-0.03, 0.03, 3) trans[2] = np.clip(trans[2], 0.2, 0.6) trans[1] = np.clip(trans[1], -0.3, 0.3) trans[0] =	np.clip(trans[0], 0.0, 0.5)	numpy.clip
import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D # noqa: F401 from .. import style def make_axes(fig_width, wpad_edge=0, wpad_mid=0.05, hpad_top=0.05, hpad_bottom=0.05, small_sq_width=0.07): sq_width = (1. - 2 * wpad_edge - small_sq_width - 4 * wpad_mid) / 4. sq_height = 1. - hpad_top - hpad_bottom fig_height = sq_width * fig_width / sq_height small_sq_height = small_sq_width * fig_width / fig_height fig = plt.figure(figsize=(fig_width, fig_height)) # 2 small squares ax2 = fig.add_axes((wpad_edge, hpad_bottom, small_sq_width, small_sq_height)) ax1 = fig.add_axes((wpad_edge, 1. - hpad_top - small_sq_height, small_sq_width, small_sq_height)) # 3 big squares ax3 = fig.add_axes((wpad_edge + small_sq_width + wpad_mid, hpad_bottom, sq_width, sq_height)) ax4 = fig.add_axes((wpad_edge + small_sq_width + 2 * wpad_mid + sq_width, hpad_bottom, sq_width, sq_height)) ax5 = fig.add_axes((wpad_edge + small_sq_width + 3 * wpad_mid + 2 * sq_width, hpad_bottom, sq_width, sq_height)) ax6 = fig.add_axes((wpad_edge + small_sq_width + 4 * wpad_mid + 3 * sq_width, hpad_bottom, sq_width, sq_height)) axes = [ax1, ax2, ax3, ax4, ax5, ax6] for ax in axes: ax.set_xticks([]) ax.set_yticks([]) label_dx = -0.02 label_dy = 0.05 label_y = hpad_bottom + sq_height + label_dy fig.text(wpad_edge + label_dx, label_y, "A", va="bottom", ha="right", color="black", style.panel_letter_fontstyle) fig.text(wpad_edge + small_sq_width + wpad_mid, label_y, "B", va="bottom", ha="center", color="black", style.panel_letter_fontstyle) fig.text(wpad_edge + small_sq_width + 2 * wpad_mid + sq_width, label_y, "C", va="bottom", ha="center", color="black", *style.panel_letter_fontstyle) fig.text(wpad_edge + small_sq_width + 3 wpad_mid + 2 * sq_width, label_y, "D", va="bottom", ha="center", color="black", *style.panel_letter_fontstyle) fig.text(wpad_edge + small_sq_width + 4 wpad_mid + 3 * sq_width, label_y, "E", va="bottom", ha="center", color="black", *style.panel_letter_fontstyle) return axes def disp_heatmap(ax, heatmap, show_xlabels=True, show_ylabels=True, title=None): N_theta, N_phi = heatmap.shape ax.imshow(heatmap, origin="lower left", cmap="gray", aspect="equal") if show_xlabels: ax.set_xlabel("$\phi$", fontsize=style.axis_label_fontsize, labelpad=-8.5) ax.set_xticks([0, N_phi - 1]) ax.set_xticklabels(["0", "$\pi$"], fontsize=style.ticklabel_fontsize) else: ax.set_xticks([]) if show_ylabels: ax.set_ylabel("$\\theta$", fontsize=style.axis_label_fontsize, labelpad=-8.5) ax.set_yticks([0, N_theta - 1]) ax.set_yticklabels(["0", "$\pi$"], fontsize=style.ticklabel_fontsize) else: ax.set_yticks([]) ax.set_xlim([0, heatmap.shape[1] - 1]) ax.set_ylim([0, heatmap.shape[0] - 1]) if title is not None: ax.set_title(title, fontsize=style.axis_label_fontsize 0.8, pad=1) def disp_scatter(ax, pi_gp, pi_knn, trajectories=None, diag_text=False, arrow=True, xlabel="full PI", ylabel="Gaussian PI"): # Note that gp=y and knn=x, but 0 index is gp and 1 is knn in data arrays! traj_color = "#C63F3A" all_gp_vals = [pi_gp] all_knn_vals = [pi_knn] if trajectories is not None: all_gp_vals += [traj[:, 0] for traj in trajectories] all_knn_vals += [traj[:, 1] for traj in trajectories] all_gp_vals =	np.concatenate(all_gp_vals)	numpy.concatenate
# this tells python to act as if though We are one folder up import sys sys.path.insert(0,'..') import pandas as pd import FixedEffectModelPyHDFE.api as FEM from FixedEffectModelPyHDFE.DemeanDataframe import get_np_columns #import FixedEffectModel.api as FEM import numpy as np from patsy import dmatrices import statsmodels.formula.api as smf import statsmodels.api as sm from fastreg import linear from datetime import datetime import unittest from math import isclose NLS_WORK = "./../data/test_dropped_na.dta" CEREAL = "./../data/cereal.dta" AUTO = "./../data/auto_drop_na.dta" TOLERANCE = 0.01 class FixedEffectsModelTestsVSfastreg(unittest.TestCase): def setup(self, data_directory, target, regressors, absorb, cluster): print(self._testMethodName) print("target: ", target) print("regressors: ", regressors) print("absorb: ", absorb) print("cluster: ", cluster) df = pd.read_stata(data_directory) df.reset_index(drop=True, inplace=True) fem_start = datetime.now() self.result = FEM.ols_high_d_category(df, regressors, target, absorb, cluster, formula=None, robust=False, epsilon = 1e-8, max_iter = 1e6) fem_end = datetime.now() print("FEM time taken: " + str(fem_end-fem_start)) self.result.summary() print() if absorb[0] == '0': absorb=None fastreg_start = datetime.now() fastreg = linear.ols(y=target[0], x=regressors, absorb=absorb, cluster=cluster, data=df) fastreg_end = datetime.now() print(fastreg) print("fastreg time taken: " + str(fastreg_end - fastreg_start)) print("\n\n\n\n\n") ######################################################################### ######################################################################### def test_just_absorb_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['idcode', 'birth_yr', 'fifty_clusts', 'sixty_clusts'], cluster=[]) def test_no_absorb_cluster_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['0'], cluster=['idcode', 'birth_yr', 'fifty_clusts', 'sixty_clusts']) # comparing fvalue def test_clustering_single_variable_no_absorb2_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['0'], cluster=['race']) # comparing fvalue assert(np.isclose(self.result.fvalue, 127593.72, atol=TOLERANCE)) # comparing standard errors assert(np.all(np.isclose(self.result.bse, np.asarray([.148934, .0065111, .0113615]), atol=TOLERANCE))) # comparing tvalues assert(np.all(np.isclose(self.result.tvalues, np.asarray([27.75, 2.32, 66.61]), atol=TOLERANCE))) def test_clustering_single_variable_no_absorb_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['0'], cluster=['fifty_clusts']) assert(np.isclose(self.result.fvalue, 10230.63, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.048274, .0044294, .0052923]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([85.60, 3.42, 143.00]), atol=TOLERANCE))) def test_clustering_two_variables_no_absorb_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['0'], cluster=['fifty_clusts', 'sixty_clusts']) assert(np.isclose(self.result.fvalue, 12347.24, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0518019, .0048228, .00492]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([79.77, 3.14, 153.82]), atol=TOLERANCE))) def test_clustering_many_variables_no_absorb_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['0'], cluster=['fifty_clusts', 'sixty_clusts', 'birth_yr', 'idcode']) assert(np.isclose(self.result.fvalue, 4664.62, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0551555, .0080815, .007881]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([74.92, 1.87, 96.03]), atol=TOLERANCE))) def test_just_absorb_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts', 'sixty_clusts', 'birth_yr', 'idcode'], cluster=[]) assert(np.isclose(self.result.fvalue, 3891.51, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0047052, .0096448]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([6.48, 88.22]), atol=TOLERANCE))) def test_cluster_1_absorb_1_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts'], cluster=['sixty_clusts']) assert(np.isclose(self.result.fvalue, 9884.24, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.004654, .0055812]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([3.18, 135.54]), atol=TOLERANCE))) def test_cluster_1_absorb_1_2_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts'], cluster=['fifty_clusts']) assert(np.isclose(self.result.fvalue, 10100.50, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0044538, .005324]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([3.33, 142.09]), atol=TOLERANCE))) def test_cluster_many_absorb_1_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts'], cluster=['fifty_clusts', 'sixty_clusts', 'idcode', 'year']) assert(np.isclose(self.result.fvalue, 86.89, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0189465, .0574001]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([0.78, 13.18]), atol=TOLERANCE))) def test_cluster_3_absorb_3_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts', 'sixty_clusts', 'ind_code'], cluster=['idcode', 'year', 'grade']) assert(np.isclose(self.result.fvalue, 113.61, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0168144, .0501467]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([0.93, 15.03]), atol=TOLERANCE))) def test_cluster_3_absorb_3_2_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts', 'sixty_clusts', 'ind_code'], cluster=['fifty_clusts', 'sixty_clusts', 'ind_code']) assert(np.isclose(self.result.fvalue, 2525.34, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.004604, .0106474]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([3.41, 70.78]), atol=TOLERANCE))) def test_cluster_4_absorb_4_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts', 'sixty_clusts', 'ind_code', 'idcode'], cluster=['fifty_clusts', 'sixty_clusts', 'ind_code', 'idcode']) assert(np.isclose(self.result.fvalue, 3191.76, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.00498, .010914]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([6.17, 77.85]), atol=TOLERANCE))) ######################################################################### ######################################################################### # Boston auto dataset def test_pure_regression_boston_auto_dataset(self): self.setup(AUTO, target=['price'], regressors=['weight', 'length', 'turn'], absorb=['0'], cluster=[]) # comparing fvalue assert(np.isclose(self.result.fvalue, 14.78, atol=TOLERANCE)) # comparing standard errors assert(np.all(np.isclose(self.result.bse, np.asarray([4667.441, 1.143408, 40.13139, 128.8455]), atol=TOLERANCE))) # comparing tvalues assert(np.all(np.isclose(self.result.tvalues, np.asarray([3.19, 4.67, -1.75, -2.28]), atol=TOLERANCE))) def test_clustering_one_variable_no_absorb_auto_dataset(self): self.setup(AUTO, target=['price'], regressors=['weight', 'length', 'turn'], absorb=['0'], cluster=['rep78']) # comparing fvalue assert(np.isclose(self.result.fvalue, 17.17, atol=TOLERANCE)) # comparing standard errors assert(np.all(np.isclose(self.result.bse, np.asarray([6132.17, .8258151, 24.15393, 191.4521]), atol=TOLERANCE))) # comparing tvalues assert(np.all(np.isclose(self.result.tvalues, np.asarray([2.42, 6.46, -2.91, -1.53]), atol=TOLERANCE))) def test_clustering_two_variables_no_absorb_auto_dataset(self): self.setup(AUTO, target=['price'], regressors=['weight', 'length', 'turn'], absorb=['0'], cluster=['rep78', 'headroom']) # comparing fvalue assert(np.isclose(self.result.fvalue, 27.03, atol=TOLERANCE)) # comparing standard errors assert(np.all(np.isclose(self.result.bse,	np.asarray([6037.897, 1.210828, 44.88812, 183.8683])	numpy.asarray
#!/bin/python import re import os import logging import yaml import pandas as pd import numpy as np import soundfile as sf from math import floor, ceil from pathlib import Path from dotenv import find_dotenv, load_dotenv def lengthAdjust(): logger = logging.getLogger(__name__) logger.info('adjusting length for label congruity') data_dir = 'data/raw/nips4b/wav/train/' out_dir = 'data/interim/nips4b/wav/train/' for filename in os.listdir(data_dir): [data, samplerate] = sf.read(data_dir + filename) desired_length = int(samplerate * N) logger.info('Processing ' + filename) logger.info("Number of Samples: " + str(desired_length)) logger.info("File length: " + str(desired_length/samplerate) + "s") data = np.asarray(data) zero_pad_length = desired_length - data.size zero_pad = np.zeros(zero_pad_length) data =	np.append(data, zero_pad)	numpy.append
"""test_rules - test the CPA rules parser """ import unittest from io import StringIO import numpy as np import cellprofiler_core.measurement import cellprofiler.utilities.rules as R OBJECT_NAME = "MyObject" M_FEATURES = ["Measurement%d" % i for i in range(1, 11)] class TestRules(unittest.TestCase): def test_01_01_load_rules(self): data = """IF (Nuclei_Intensity_UpperQuartileIntensity_CorrDend > 0.12762499999999999, [0.79607587785712131, -0.79607587785712131], [-0.94024303819690347, 0.94024303819690347]) IF (Nuclei_Intensity_MinIntensity_CorrAxon > 0.026831299999999999, [0.68998040630066426, -0.68998040630066426], [-0.80302016375137986, 0.80302016375137986]) IF (Nuclei_Intensity_UpperQuartileIntensity_CorrDend > 0.19306000000000001, [0.71934712791500899, -0.71934712791500899], [-0.47379648809429048, 0.47379648809429048]) IF (Nuclei_Intensity_UpperQuartileIntensity_CorrDend > 0.100841, [0.24553066971563919, -0.24553066971563919], [-1.0, 1.0]) IF (Nuclei_Location_Center_Y > 299.32499999999999, [-0.61833689824912363, 0.61833689824912363], [0.33384091087462237, -0.33384091087462237]) IF (Nuclei_Intensity_MaxIntensity_CorrNuclei > 0.76509499999999997, [-0.95683305069726121, 0.95683305069726121], [0.22816438860290775, -0.22816438860290775]) IF (Nuclei_Neighbors_NumberOfNeighbors_5 > 2.0, [-0.92848043428127192, 0.92848043428127192], [0.20751332434602923, -0.20751332434602923]) IF (Nuclei_Intensity_MedianIntensity_CorrDend > 0.15327499999999999, [0.79784566567342285, -0.79784566567342285], [-0.35665314560825129, 0.35665314560825129]) IF (Nuclei_Neighbors_SecondClosestXVector_5 > -11.5113, [-0.21859862538067179, 0.21859862538067179], [0.71270785008847592, -0.71270785008847592]) IF (Nuclei_Intensity_StdIntensity_CorrDend > 0.035382299999999998, [0.28838229530755011, -0.28838229530755011], [-0.75312050069265968, 0.75312050069265968]) IF (Nuclei_Intensity_MaxIntensityEdge_CorrNuclei > 0.63182899999999997, [-0.93629855522957672, 0.93629855522957672], [0.1710257492070047, -0.1710257492070047]) IF (Nuclei_Intensity_StdIntensityEdge_CorrNuclei > 0.037909400000000003, [0.28514731668218346, -0.28514731668218346], [-0.60783543053602795, 0.60783543053602795]) IF (Nuclei_Intensity_MedianIntensity_CorrAxon > 0.042631500000000003, [0.20227787378316109, -0.20227787378316109], [-0.78282539096589077, 0.78282539096589077]) IF (Nuclei_Intensity_MinIntensity_CorrDend > 0.042065400000000003, [0.52616744135942872, -0.52616744135942872], [-0.32613209033812068, 0.32613209033812068]) IF (Nuclei_Neighbors_FirstClosestYVector_5 > 3.8226100000000001, [0.69128399165300047, -0.69128399165300047], [-0.34874605597401531, 0.34874605597401531]) IF (Nuclei_Intensity_MeanIntensity_CorrNuclei > 0.283188, [-0.79881507037552979, 0.79881507037552979], [0.24825909570051025, -0.24825909570051025]) IF (Nuclei_Location_Center_Y > 280.154, [-0.50545174099468504, 0.50545174099468504], [0.3297202808867149, -0.3297202808867149]) IF (Nuclei_Intensity_UpperQuartileIntensity_CorrDend > 0.132241, [0.35771841831789791, -0.35771841831789791], [-0.63545019489162846, 0.63545019489162846]) IF (Nuclei_AreaShape_MinorAxisLength > 6.4944899999999999, [0.5755128363506562, -0.5755128363506562], [-0.41737581982462335, 0.41737581982462335]) IF (Nuclei_Intensity_LowerQuartileIntensity_CorrDend > 0.075424000000000005, [0.50557978238660795, -0.50557978238660795], [-0.35606081901385256, 0.35606081901385256]) """ fd = StringIO(data) rules = R.Rules() rules.parse(fd) self.assertEqual(len(rules.rules), 20) for rule in rules.rules: self.assertEqual(rule.object_name, "Nuclei") self.assertEqual(rule.comparitor, ">") rule = rules.rules[0] self.assertEqual(rule.feature, "Intensity_UpperQuartileIntensity_CorrDend") self.assertAlmostEqual(rule.threshold, 0.127625) self.assertAlmostEqual(rule.weights[0, 0], 0.79607587785712131) self.assertAlmostEqual(rule.weights[0, 1], -0.79607587785712131) self.assertAlmostEqual(rule.weights[1, 0], -0.94024303819690347) self.assertAlmostEqual(rule.weights[1, 1], 0.94024303819690347) def test_02_00_no_measurements(self): m = cellprofiler_core.measurement.Measurements() m.add_measurement(OBJECT_NAME, M_FEATURES[0], np.array([], float)) rules = R.Rules() rules.rules += [ R.Rules.Rule( OBJECT_NAME, M_FEATURES[0], ">", 0, np.array([[1.0, -1.0], [-1.0, 1.0]]) ) ] score = rules.score(m) self.assertEqual(score.shape[0], 0) self.assertEqual(score.shape[1], 2) def test_02_01_score_one_positive(self): m = cellprofiler_core.measurement.Measurements() m.add_measurement(OBJECT_NAME, M_FEATURES[0], np.array([1.5], float)) rules = R.Rules() rules.rules += [ R.Rules.Rule( OBJECT_NAME, M_FEATURES[0], ">", 0, np.array([[1.0, -0.5], [-2.0, 0.6]]) ) ] score = rules.score(m) self.assertEqual(score.shape[0], 1) self.assertEqual(score.shape[1], 2) self.assertAlmostEqual(score[0, 0], 1.0) self.assertAlmostEqual(score[0, 1], -0.5) def test_02_02_score_one_negative(self): m = cellprofiler_core.measurement.Measurements() m.add_measurement(OBJECT_NAME, M_FEATURES[0], np.array([1.5], float)) rules = R.Rules() rules.rules += [ R.Rules.Rule( OBJECT_NAME, M_FEATURES[0], ">", 2.0, np.array([[1.0, -0.5], [-2.0, 0.6]]), ) ] score = rules.score(m) self.assertEqual(score.shape[0], 1) self.assertEqual(score.shape[1], 2) self.assertAlmostEqual(score[0, 0], -2.0) self.assertAlmostEqual(score[0, 1], 0.6) def test_02_03_score_one_nan(self): m = cellprofiler_core.measurement.Measurements() m.add_measurement(OBJECT_NAME, M_FEATURES[0], np.array([np.NaN], float)) rules = R.Rules() rules.rules += [ R.Rules.Rule( OBJECT_NAME, M_FEATURES[0], ">", 2.0,	np.array([[1.0, -0.5], [-2.0, 0.6]])	numpy.array
from autoarray import exc from autoarray import util import numpy as np import pytest class TestMask1D: def test__total_image_pixels_1d_from(self): mask_1d = np.array([False, True, False, False, False, True]) assert util.mask_1d.total_pixels_1d_from(mask_1d=mask_1d) == 4 def test__total_sub_pixels_1d_from(self): mask_1d = np.array([False, True, False, False, False, True]) assert util.mask_1d.total_sub_pixels_1d_from(mask_1d=mask_1d, sub_size=2) == 8 def test__sub_native_index_for_sub_slim_index_1d_from(self): mask_1d = np.array([False, False, False, False]) sub_native_index_for_sub_slim_index_1d = util.mask_1d.native_index_for_slim_index_1d_from( mask_1d=mask_1d, sub_size=1 ) assert (sub_native_index_for_sub_slim_index_1d ==	np.array([0, 1, 2, 3])	numpy.array
""" Crystal class Class to store definition of a crystal, along with some analysis 1. geometric analysis (nearest neighbor displacements) 2. space group operations 3. point group operations for each basis position 4. Wyckoff position generation (for interstitials) """ __author__ = '<NAME>' import numpy as np import collections, copy, itertools from numbers import Number from math import gcd import yaml # use crystal.yaml to call--may need to change in the future from functools import reduce # YAML tags: # interfaces are either at the bottom, or staticmethods in the corresponding object NDARRAY_YAMLTAG = '!numpy.ndarray' GROUPOP_YAMLTAG = '!GroupOp' def gcdlist(lis): """Returns the GCD of a list of integers""" return reduce(gcd, lis) def incell(vec): """ Returns the vector inside the unit cell (in [0,1)3) :param vec: 3-vector (unit coord) :return: 3-vector """ return vec - np.floor(vec + 1.0e-8) def inhalf(vec): """ Returns the vector inside the centered cell (in [-0.5,0.5)3) :param vec: 3-vector (unit coord) :return: 3-vector """ return vec - np.floor(vec + 0.5) def maptranslation(oldpos, newpos, oldspins=None, newspins=None, threshold=1e-8): """ Given a list of transformed positions, identify if there's a translation vector that maps from the current positions to the new position. The mapping specifies the index that the translated atom corresponds to in the original position set. If unable to construct a mapping, the mapping return is None; the translation vector will be meaningless. If old/newspins are given then ONLY mappings that maintain spin are considered. This means that a loop is needed to consider possible spin phase factors. :param oldpos: list of list of array[3] :param newpos: list of list of array[3], same layout as oldpos :param oldspins: (optional) list of list of numbers/arrays :param newspins: (optional) list of list of numbers/arrays :return translation: array[3] :return mapping: list of list of indices """ # type-checking: if __debug__: if type(oldpos) is not list: raise TypeError('oldpos is not a list') if type(newpos) is not list: raise TypeError('newpos is not a list') if len(oldpos) != len(newpos): raise IndexError("{} and {} do not have the same length".format(oldpos, newpos)) for a, b in zip(oldpos, newpos): if type(a) is not list: raise TypeError("element of oldpos {} is not a list".format(a)) if type(b) is not list: raise TypeError("element of newpos {} is not a list".format(b)) if len(a) != len(b): raise IndexError("{} and {} do not have the same length".format(a, b)) if (oldspins is None) != (newspins is None): raise TypeError('give both or neither spin arguments') if oldspins is not None: if type(oldspins) is not list: raise TypeError('oldspins is not a list') if type(newspins) is not list: raise TypeError('newspins is not a list') if len(oldspins) != len(newspins): raise IndexError( "{} and {} do not have the same length".format(oldspins, newspins)) for a, b in zip(oldspins, newspins): if type(a) is not list: raise TypeError("element of oldspins {} is not a list".format(a)) if type(b) is not list: raise TypeError("element of newspins {} is not a list".format(b)) if len(a) != len(b): raise IndexError("{} and {} do not have the same length".format(a, b)) if oldspins is None: oldspins = [[0 for u in atomlist] for atomlist in oldpos] if newspins is None: newspins = oldspins # Work with the shortest possible list for identifying translations atomindex = 0 maxlen = len(oldpos[atomindex]) for i, ulist in enumerate(oldpos): if len(ulist) < maxlen: maxlen = len(ulist) atomindex = i ru0 = newpos[atomindex][0] for ub in oldpos[atomindex]: trans = inhalf(ub - ru0) foundmap = True # now check against all the others, and construct the mapping indexmap = [] for atomlist0, spinlist0, atomlist1, spinlist1 in zip(oldpos, oldspins, newpos, newspins): # work through the "new" positions if not foundmap: break maplist = [] for rua, sp1 in zip(atomlist1, spinlist1): for j, uj, sp0 in zip(itertools.count(), atomlist0, spinlist0): if not np.allclose(sp0, sp1, atol=threshold): continue # only allow maps that have same spin if np.allclose(inhalf(uj - rua - trans), 0, atol=threshold): maplist.append(j) break if len(maplist) != len(atomlist0): foundmap = False else: indexmap.append(tuple(maplist)) if foundmap: break if foundmap: return trans, tuple(indexmap) else: return None, None class GroupOp(collections.namedtuple('GroupOp', 'rot trans cartrot indexmap')): """ A class corresponding to a group operation. Based on namedtuple, so it is immutable. Intended to be used in combination with Crystal, we have a few operations that can be defined out-of-the-box. :param rot: np.array(3,3) integer idempotent matrix :param trans: np.array(3) real vector :param cartrot: np.array(3,3) real unitary matrix :param indexmap: tuples of tuples, containing the atom mapping """ def incell(self): """Return a version of groupop where the translation is in the unit cell""" return GroupOp(self.rot, incell(self.trans), self.cartrot, self.indexmap) def inhalf(self): """Return a version of groupop where the translation is in the centered unit cell""" return GroupOp(self.rot, inhalf(self.trans), self.cartrot, self.indexmap) @classmethod def ident(cls, basis): """Return a group operation corresponding to identity for a given basis""" return cls(rot=np.eye(3, dtype=int), trans=np.zeros(3), cartrot=np.eye(3), indexmap=tuple(tuple(i for i in range(len(atomlist))) for atomlist in basis)) def __str__(self): """Human-readable version of groupop""" str_rep = "#Rotation (lattice, cartesian):\n {}\t{}\n {}\t{}\n".format( self.rot[0], self.cartrot[0], self.rot[1], self.cartrot[1]) if self.rot.shape == (3,3): str_rep += " {}\t{}\n".format(self.rot[2], self.cartrot[2]) str_rep += "#Translation: {}\n#Indexmap:".format(self.trans) for chemind, atoms in enumerate(self.indexmap): for origind, finalind in enumerate(atoms): str_rep = str_rep + "\n {chem}.{o} -> {chem}.{f}".format(chem=chemind, o=origind, f=finalind) return str_rep def _asdict(self): """Return a proper dict""" return {'rot': self.rot, 'trans': self.trans, 'cartrot': self.cartrot, 'indexmap': self.indexmap} def __eq__(self, other): """Test for equality--we use numpy.isclose for comparison, since that's what we usually care about""" return isinstance(other, self.__class__) and \ np.all(self.rot == other.rot) and \ np.allclose(self.trans, other.trans) and \ np.allclose(self.cartrot, other.cartrot) and \ self.indexmap == other.indexmap def __ne__(self, other): """Inequality == not __eq__""" return not self.__eq__(other) def __hash__(self): """Hash, so that we can make sets of group operations""" ### we are a little conservative, and only use the rotation and indexmap to define the hash. This means ### we will get collisions for the same rotation but different unit cell translations. The reason is ### that __eq__ uses "isclose" on our translations, and we don't have a good way to handle ### that in a hash function. We lose a little bit on efficiency if we construct a set that ### has a whole lot of translation operations, but that's not usually what we will do. # return hash(self.rot.data.tobytes()) return hash(self.rot.data.tobytes()) ^ hash(self.indexmap) def __add__(self, other): """Add a translation to our group operation""" if __debug__: if type(other) is not np.ndarray: raise TypeError('Can only add a translation to a group operation') if other.shape != (self.rot.shape[0],): raise IndexError('Can only add a {} dimensional vector'.format(self.rot.shape[0])) if not np.issubdtype(other.dtype, np.integer): raise TypeError('Can only add a lattice vector translation') return GroupOp(self.rot, self.trans + other, self.cartrot, self.indexmap) def __sub__(self, other): """Add a (negative) translation to our group operation""" return self.__add__(-other) def __mul__(self, other): """Multiply two group operations to produce a new group operation""" if __debug__: if type(other) is not GroupOp: return NotImplemented return GroupOp(np.dot(self.rot, other.rot), np.dot(self.rot, other.trans) + self.trans, np.dot(self.cartrot, other.cartrot), tuple(tuple(atomlist0[i] for i in atomlist1) for atomlist0, atomlist1 in zip(self.indexmap, other.indexmap))) def __sane__(self): """Return true if the cartrot and rot are consistent and 'sane'""" tr = self.rot.trace() det = np.int(np.round(np.linalg.det(self.rot))) # consistency: if np.int(np.round(self.cartrot.trace())) != tr: return False if np.int(np.round(np.linalg.det(self.cartrot))) != det: return False # sanity: if abs(det) != 1: return False dimshift = 0 if self.rot.shape[0] == 3 else -1 if det * tr < (-1+dimshift) or det * tr > (3+dimshift): return False return True def inv(self): """Construct and return the inverse of the group operation""" inverse = (np.round(np.linalg.inv(self.rot))).astype(int) return GroupOp(inverse, -np.dot(inverse, self.trans), self.cartrot.T, tuple(tuple(x for i, x in sorted([(y, j) for j, y in enumerate(atomlist)])) for atomlist in self.indexmap)) @staticmethod def optype(rot): """Returns the type of group operation (single integer): 1 = identity 2, 3, 4, 6 = n- fold rotation around an axis negative = rotation + mirror operation, perpendicular to axis "special cases": -1 = mirror, -2 = inversion :param rot: rotation matrix (can be the integer rot) :return type: integer """ # dim = rot.shape[0] dimindexpos, dimindexneg = (1, 3) if rot.shape[0] == 3 else (2, 4) tr = np.int(rot.trace()) if np.linalg.det(rot) > 0: return (2, 3, 4, 6, 1)[tr + dimindexpos] # trace determines the rotation type [tr + 1] for 3d else: return (-2, -3, -4, -6, -1)[tr + dimindexneg] # trace determines the rotation type [tr + 3] fpr 3d def eigen(self): """Returns the type of group operation (single integer) and eigenvectors. 1 = identity 2, 3, 4, 6 = n- fold rotation around an axis negative = rotation + mirror operation, perpendicular to axis "special cases": -1 = mirror, -2 = inversion eigenvect[0] = axis of rotation / mirror eigenvect[1], eigenvect[2] = orthonormal vectors to define the plane giving a right-handed coordinate system and where rotation around [0] is positive, and the positive imaginary eigenvector for the complex eigenvalue is [1] + i [2]. :return type: integer :return eigenvectors: list of [ev0, ev1, ev2] """ if __debug__: if not self.__sane__(): raise ValueError('Bad GroupOp:\n{}'.format(self)) optype = self.optype(self.rot) det = 1 if optype > 0 else -1 tr = np.int(self.rot.trace()) # two trivial cases: identity, inversion: if optype == 1 or optype == -2: return optype, np.eye(self.rot.shape[0]) if self.rot.shape[0] == 2: if optype != -1: return optype, np.eye(self.rot.shape[0]) # only interesting case is how to deal with is the mirror plane; find the angle of the mirror phi = 0.5np.arctan2(self.cartrot[0,1]+self.cartrot[1,0], self.cartrot[0,0]-self.cartrot[1,1]) return optype, np.array([[np.cos(phi), -np.sin(phi)], [np.sin(phi), np.cos(phi)]]) # otherwise, there's an axis to find: vmat = np.eye(3) vsum = np.zeros((3, 3)) if det > 0: for n in range(optype): vsum += vmat vmat = np.dot(self.cartrot, vmat) else: for n in range((0, 6, 4, 3, 2)[tr + 3]): # vsum += vmat vmat = -np.dot(self.cartrot, vmat) # vmat should* equal identity if we didn't fail... if __debug__: if not np.allclose(vmat, np.eye(3)): raise ArithmeticError('eigenvalue analysis fail') vsum = 1. / n # now the columns of vsum should either be (a) our rotation / mirror axis, or (b) zero eig0 = vsum[:, 0] magn0 = np.dot(eig0, eig0) if magn0 < 1e-2: eig0 = vsum[:, 1] magn0 = np.dot(eig0, eig0) if magn0 < 1e-2: eig0 = vsum[:, 2] magn0 = np.dot(eig0, eig0) eig0 /= np.sqrt(magn0) # now, construct the other two directions: if abs(eig0[2]) < 0.75: eig1 = np.array([eig0[1], -eig0[0], 0]) else: eig1 = np.array([-eig0[2], 0, eig0[0]]) eig1 /= np.sqrt(np.dot(eig1, eig1)) eig2 = np.cross(eig0, eig1) # we have a right-handed coordinate system; test that we have a positive rotation around the axis if abs(optype) > 2: if np.dot(eig2, np.dot(self.cartrot, eig1)) > 0: eig0 = -eig0 eig2 = -eig2 return optype, [eig0, eig1, eig2] @staticmethod def GroupOp_representer(dumper, data): """Output a GroupOp""" # asdict() returns an OrderedDictionary, so pass through dict() # had to rewrite _asdict() for some reason...? return dumper.represent_mapping(GROUPOP_YAMLTAG, data._asdict()) @staticmethod def GroupOp_constructor(loader, node): """Construct a GroupOp from YAML""" # * turns the dictionary into parameters for GroupOp constructor return GroupOp(**loader.construct_mapping(node, deep=True)) def VectorBasis(rottype, eigenvect): """ Returns a vector basis corresponding to the optype and eigenvectors for a GroupOp :param rottype: output from eigen() :param eigenvect: eigenvectors :return dim: dimensionality, 0..3 :return vect: vector defining line direction (1) or plane normal (2) """ # 2d first if len(eigenvect) == 2: if rottype == 1: return (2, np.zeros(2)) # sphere (identity) if rottype == -1: return (1, eigenvect[0]) # plane (pure mirror) return (0, np.zeros(2)) # all others are rotation, which leaves nothing unchanged in 2d # edge cases first: if rottype == 1: return (3,	np.zeros(3)	numpy.zeros
""" rnn_lstm_cell_test_cy.py Test the correctness of the LSTM-cell implementation. """ import os import unittest from random import random from numpy import asarray, ones, zeros from torch import float64, FloatTensor, tensor from torch.nn import LSTMCell as PytorchLSTM from population.utils.rnn_cell_util.cy.lstm_cy import LSTMCellCy as LSTMCell EPSILON = 1e-5 def get_lstm(input_size): """Get a LSTM-cell of the requested input-size, completely initialized with zeros.""" bias_h = zeros((4,)) weight_hh = zeros((4, 1)) weight_xh = zeros((4, input_size)) return LSTMCell( input_size=input_size, bias=bias_h, weight_hh=weight_hh, weight_xh=weight_xh, ) def get_pytorch_lstm(input_size, used_lstm): """Load in a PyTorch LSTM that is a copy of the currently used LSTM.""" lstm = PytorchLSTM(input_size, 1) lstm.bias_hh[:] = tensor(zeros((4,)), dtype=float64)[:] lstm.bias_ih[:] = tensor(used_lstm.bias, dtype=float64)[:] lstm.weight_hh[:] = tensor(used_lstm.weight_hh, dtype=float64)[:] lstm.weight_ih[:] = tensor(used_lstm.weight_xh, dtype=float64)[:] return lstm # noinspection PyArgumentList class LSTM(unittest.TestCase): """Test the custom numpy implementation of the LSTM-cell.""" def test_single_input_single_batch(self): """> Test when only one input given and batch-size is only one.""" # Folder must be root to load in make_net properly if os.getcwd().split('\\')[-1] == 'tests': os.chdir('..') # Get 'empty' LSTM lstm = get_lstm(1) # Completely zero LSTM, all inputs get ignored self.assertEqual(lstm(asarray([[0]])), 0) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it self.assertEqual(lstm(asarray([[1]])), 0) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it # Modify the LSTM to have weight-arrays of one lstm.weight_hh = asarray(ones((4, 1))) lstm.weight_xh = asarray(ones((4, 1))) # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(1, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i]])) self.assertEqual(a.shape, b.shape) self.assertTrue(float(a) - EPSILON <= float(b) <= float(a) + EPSILON) # Set bias to minus ones lstm.bias = ones((4,)) * -1 # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(1, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i]])) self.assertEqual(a.shape, b.shape) self.assertTrue(float(a) - EPSILON <= float(b) <= float(a) + EPSILON) def test_single_input_multi_batch(self): """> Test when only one input given and batch-size is more than one.""" # Folder must be root to load in make_net properly if os.getcwd().split('\\')[-1] == 'tests': os.chdir('..') # Get 'empty' LSTM lstm = get_lstm(1) # Completely zero LSTM, all inputs get ignored result = lstm(asarray([[0], [0]])) for aa, bb in zip(result, asarray([[0], [0]])): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it result = lstm(asarray([[1], [1]])) for aa, bb in zip(result, asarray([[0], [0]])): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it # Modify the LSTM to have weight-arrays of one lstm.weight_hh = ones((4, 1)) lstm.weight_xh = ones((4, 1)) # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(1, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i], [i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i], [i]])) self.assertEqual(a.shape, b.shape) for aa, bb in zip(a, b): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) # Set bias to minus ones lstm.bias = ones((4,)) * -1 # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(1, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i], [i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i], [i]])) self.assertEqual(a.shape, b.shape) for aa, bb in zip(a, b): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) def test_multi_input_single_batch(self): """> Test when only one input given and batch-size is more than one.""" # Folder must be root to load in make_net properly if os.getcwd().split('\\')[-1] == 'tests': os.chdir('..') # Get 'empty' LSTM lstm = get_lstm(2) # Completely zero LSTM, all inputs get ignored self.assertEqual(lstm(asarray([[0, 0]])), 0) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it self.assertEqual(lstm(asarray([[1, 1]])), 0) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it # Modify the LSTM to have weight-arrays of one lstm.weight_hh = ones((4, 1)) lstm.weight_xh = ones((4, 2)) # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(2, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i, i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i, i]])) self.assertEqual(a.shape, b.shape) for aa, bb in zip(a, b): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) # Set bias to minus ones lstm.bias = ones((4,)) * -1 # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(2, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i, i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i, i]])) self.assertEqual(a.shape, b.shape) for aa, bb in zip(a, b): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) def test_multi_input_multi_batch(self): """> Test when only one input given and batch-size is more than one.""" # Folder must be root to load in make_net properly if os.getcwd().split('\\')[-1] == 'tests': os.chdir('..') # Get 'empty' LSTM lstm = get_lstm(2) # Completely zero LSTM, all inputs get ignored result = lstm(asarray([[0, 0], [0, 0]])) for aa, bb in zip(result,	asarray([[0], [0]])	numpy.asarray
# -- coding: utf-8 -- # pylint: disable=invalid-name, too-many-arguments, too-many-instance-attributes """Copyright 2015 <NAME>. FilterPy library. http://github.com/rlabbe/filterpy Documentation at: https://filterpy.readthedocs.org Supporting book at: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python This is licensed under an MIT license. See the readme.MD file for more information. """ from __future__ import (absolute_import, division, unicode_literals) from copy import deepcopy from math import log, exp, sqrt import sys import warnings import numpy as np from numpy import dot, zeros, eye import scipy.linalg as linalg from filterpy.stats import logpdf from filterpy.common import pretty_str class FadingKalmanFilter(object): """ Fading memory Kalman filter. This implements a linear Kalman filter with a fading memory effect controlled by `alpha`. This is obsolete. The class KalmanFilter now incorporates the `alpha` attribute, and should be used instead. You are responsible for setting the various state variables to reasonable values; the defaults below will not give you a functional filter. Parameters ---------- alpha : float, >= 1 alpha controls how much you want the filter to forget past measurements. alpha==1 yields identical performance to the Kalman filter. A typical application might use 1.01 dim_x : int Number of state variables for the Kalman filter. For example, if you are tracking the position and velocity of an object in two dimensions, dim_x would be 4. This is used to set the default size of P, Q, and u dim_z : int Number of of measurement inputs. For example, if the sensor provides you with position in (x,y), dim_z would be 2. dim_u : int (optional) size of the control input, if it is being used. Default value of 0 indicates it is not used. Attributes ---------- You will have to assign reasonable values to all of these before running the filter. All must have dtype of float x : ndarray (dim_x, 1), default = [0,0,0...0] state of the filter P : ndarray (dim_x, dim_x), default identity matrix covariance matrix x_prior : numpy.array(dim_x, 1) Prior (predicted) state estimate. The _prior and _post attributes are for convienence; they store the prior and posterior of the current epoch. Read Only. P_prior : numpy.array(dim_x, dim_x) Prior (predicted) state covariance matrix. Read Only. x_post : numpy.array(dim_x, 1) Posterior (updated) state estimate. Read Only. P_post : numpy.array(dim_x, dim_x) Posterior (updated) state covariance matrix. Read Only. z : ndarray Last measurement used in update(). Read only. Q : ndarray (dim_x, dim_x), default identity matrix Process uncertainty matrix R : ndarray (dim_z, dim_z), default identity matrix measurement uncertainty H : ndarray (dim_z, dim_x) measurement function F : ndarray (dim_x, dim_x) state transition matrix B : ndarray (dim_x, dim_u), default 0 control transition matrix y : numpy.array Residual of the update step. Read only. K : numpy.array(dim_x, dim_z) Kalman gain of the update step. Read only. S : numpy.array System uncertainty (P projected to measurement space). Read only. S : numpy.array Inverse system uncertainty. Read only. log_likelihood : float log-likelihood of the last measurement. Read only. likelihood : float likelihood of last measurement. Read only. Computed from the log-likelihood. The log-likelihood can be very small, meaning a large negative value such as -28000. Taking the exp() of that results in 0.0, which can break typical algorithms which multiply by this value, so by default we always return a number >= sys.float_info.min. mahalanobis : float mahalanobis distance of the innovation. Read only. Examples -------- See my book Kalman and Bayesian Filters in Python https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python """ def __init__(self, alpha, dim_x, dim_z, dim_u=0): warnings.warn( "Use KalmanFilter class instead; it also provides the alpha attribute", DeprecationWarning) assert alpha >= 1 assert dim_x > 0 assert dim_z > 0 assert dim_u >= 0 self.alpha_sq = alpha*2 self.dim_x = dim_x self.dim_z = dim_z self.dim_u = dim_u self.x = zeros((dim_x, 1)) # state self.P = eye(dim_x) # uncertainty covariance self.Q = eye(dim_x) # process uncertainty self.B = 0. # control transition matrix self.F = np.eye(dim_x) # state transition matrix self.H = zeros((dim_z, dim_x)) # Measurement function self.R = eye(dim_z) # state uncertainty self.z = np.array([[None]dim_z]).T # gain and residual are computed during the innovation step. We # save them so that in case you want to inspect them for various # purposes self.K = 0 # kalman gain self.y = zeros((dim_z, 1)) self.S = np.zeros((dim_z, dim_z)) # system uncertainty (measurement space) self.SI = np.zeros((dim_z, dim_z)) # inverse system uncertainty # identity matrix. Do not alter this. self.I = np.eye(dim_x) # Only computed only if requested via property self._log_likelihood = log(sys.float_info.min) self._likelihood = sys.float_info.min self._mahalanobis = None # these will always be a copy of x,P after predict() is called self.x_prior = self.x.copy() self.P_prior = self.P.copy() # these will always be a copy of x,P after update() is called self.x_post = self.x.copy() self.P_post = self.P.copy() def update(self, z, R=None): """ Add a new measurement (z) to the kalman filter. If z is None, nothing is changed. Parameters ---------- z : np.array measurement for this update. R : np.array, scalar, or None Optionally provide R to override the measurement noise for this one call, otherwise self.R will be used. """ if z is None: self.z = np.array([[None]*self.dim_z]).T self.x_post = self.x.copy() self.P_post = self.P.copy() return if R is None: R = self.R elif	np.isscalar(R)	numpy.isscalar
"""Define the DefaultAllocator class.""" from __future__ import division import warnings import numpy as np from six.moves import range from openmdao.proc_allocators.proc_allocator import ProcAllocator, ProcAllocationError from openmdao.utils.mpi import MPI class DefaultAllocator(ProcAllocator): """ Default processor allocator. """ def _divide_procs(self, req_procs, comm): """ Perform the parallel processor allocation. Parameters ---------- req_procs : list of (int, int) List of min/max usable procs for each subsystem. comm : MPI.Comm or <FakeComm> communicator of the owning system. Returns ------- isubs : [int, ...] indices of the owned local subsystems. sub_comm : MPI.Comm or <FakeComm> communicator to pass to the subsystems. sub_proc_range : (int, int) The range of processors that the subcomm owns, among those of comm. """ iproc = comm.rank nproc = comm.size nsub = len(req_procs) min_req_procs = [minproc for minproc, _ in req_procs] max_req_procs = [maxproc for _, maxproc in req_procs] assigned_procs = np.zeros(nsub, dtype=int) assigned = 0 total_req = np.sum(min_req_procs) if None in max_req_procs: limit = nproc max_requested = nproc else: max_requested = np.sum(max_req_procs) limit = min(nproc, max_requested) # first, just use simple round robin assignment of requested procs # until everybody has what they asked for or we run out if total_req: if nproc >= total_req: # we have enough for all subsystems while assigned < limit: for i, max_req in enumerate(max_req_procs): if max_req is None or assigned_procs[i] < max_req: assigned_procs[i] += 1 assigned += 1 if assigned == limit: break # create buckets (one sub per bucket) to be consistent in how # we split procs below buckets = [(n, [i]) for i, n in enumerate(assigned_procs)] else: # we don't have enough, so have to group subsystems remaining = nproc # sort req procs in descending order tups = sorted([(req[0], i) for i, req in enumerate(req_procs)], reverse=True) buckets = [] for i, (req, sub_idx) in enumerate(tups): if remaining >= req: buckets.append([req, [sub_idx]]) remaining -= req elif i == 0: # since we sorted in descending order by number of # requested procs, only in the first iteration is there # a chance that we've requested more procs than we have raise ProcAllocationError(sub_idx, req, remaining) else: # we already have at least one in the bucket list that's # big enough, so go through buckets, find all that are # big enough, and add the current sub to the one with # the fewest number of subs already in it. In the event # of a tie, take the bucket with the lowest number of # requested procs. lenlist = sorted([b for b in buckets if b[0] >= req], key=lambda t: len(t[1])) shortest = len(lenlist[0][1]) final = sorted(b for b in lenlist if len(b[1]) == shortest) final[0][1].append(sub_idx) warnings.warn("System requested %d processes to run fully " "in parallel, but it only got %d" % (total_req, nproc)) # if we have any procs left over, apply them to any sub that # can use them while remaining > 0: for i, max_req in enumerate(max_req_procs): procs, subs = buckets[i] for sub_idx in subs: if (max_req is None or max_req > procs): # add 1 to procs for this bucket buckets[i][0] += 1 remaining -= 1 break if remaining == 0: break assigned = nproc - remaining # a 'color' is assigned to each bucket, with # an entry for each processor it will be given # e.g. [0, 1, 1, 1, 1, 2, 2, 3, 3, 3, UND, UND] color = np.full(nproc, MPI.UNDEFINED, dtype=int) comm_sizes = np.empty(nproc, int) start, end = 0, 0 for i, b in enumerate(buckets): num_procs = b[0] end += num_procs color[start:end] = i comm_sizes[start:end] = num_procs start += num_procs # create a sub-communicator for each color and # get the one assigned to our color/process rank_color = color[iproc] sub_comm = comm.Split(rank_color) sub_proc_range = (np.sum(comm_sizes[:iproc]),	np.sum(comm_sizes[:iproc + 1])	numpy.sum
# -- coding: utf-8 -- """ Created on Tue Dec 18 20:56:46 2018 @author: nooteboom """ import numpy as np import matplotlib.pylab as plt import matplotlib from matplotlib.font_manager import FontProperties import seaborn as sns sns.set(style="darkgrid") font = {'family' : 'Helvetica', # 'weight' : 'bold', 'size' : 22} matplotlib.rc('font', **font) res = 10000 z = np.linspace(10,6000,res) c3 = np.full(res, 3) c6 = np.full(res, 6) c11 = np.full(res, 11) c25 = np.full(res, 25) c50 = np.full(res, 50) c100 = np.full(res, 100) c200 =	np.full(res, 200)	numpy.full
# Copyright (c) Facebook, Inc. and its affiliates # Copyright (c) MTRF authors import collections import numpy as np from typing import Any, Dict, Optional, NewType, Sequence, Union, Tuple from r3l.r3l_envs.inhand_env.base import ObjectType from r3l.r3l_envs.inhand_env.reposition import SawyerDhandInHandObjectRepositionFixed from r3l.robot.object import ObjectState from r3l.utils.quatmath import quat2euler, euler2quat from r3l.utils.range import get_range_from_params from r3l.utils.circle_math import circle_distance, circle_distance_mod from r3l.robot.default_configs import REORIENT_SAWYER_ROBOT_CONFIG class SawyerDhandInHandObjectReorientFixed(SawyerDhandInHandObjectRepositionFixed): DEFAULT_REWARD_KEYS_AND_WEIGHTS = { "object_to_target_circle_distance_reward": 1.0, "object_to_target_xy_distance_reward": 1.0, "object_to_hand_xyz_distance_reward": 1.0, # "span_dist": 1.0, "small_bonus": 1.0, "big_bonus": 1.0, } def __init__( self, object_type: ObjectType = ObjectType.Rod, random_init_angle: bool = False, random_target_angle: bool = False, symmetric_task: bool = True, reorient_only: bool = False, **kwargs ): if random_init_angle: init_euler_params = { "type": "UniformRange", "values": [np.array([0, 0, -np.pi]), np.array([0, 0, np.pi])], } else: init_euler_params = { "type": "DiscreteRange", "values": [np.array([0, 0, 0])], } target_xyz_params = { "type": "DiscreteRange", "values": [	np.array([0.72, 0.15, 0.76])	numpy.array
# *** BEGIN GPL LICENSE BLOCK * # # # This program is free software; you can redistribute it and/or # modify it under the terms of the GNU General Public License # as published by the Free Software Foundation; either version 2 # of the License, or (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; if not, write to the Free Software Foundation, # Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. # # * END GPL LICENCE BLOCK *** # # ----------------------------------------------------------------------- # Author: <NAME> (Clockmender), <NAME> (ermo) Copyright (c) 2019 # ----------------------------------------------------------------------- # import bmesh import numpy as np from math import sqrt, tan, pi from mathutils import Vector from mathutils.geometry import intersect_point_line from .pdt_functions import ( set_mode, oops, get_percent, dis_ang, check_selection, arc_centre, intersection, view_coords_i, view_coords, view_dir, set_axis, ) from . import pdt_exception PDT_SelectionError = pdt_exception.SelectionError PDT_InvalidVector = pdt_exception.InvalidVector PDT_ObjectModeError = pdt_exception.ObjectModeError PDT_InfRadius = pdt_exception.InfRadius PDT_NoObjectError = pdt_exception.NoObjectError PDT_IntersectionError = pdt_exception.IntersectionError PDT_InvalidOperation = pdt_exception.InvalidOperation PDT_VerticesConnected = pdt_exception.VerticesConnected PDT_InvalidAngle = pdt_exception.InvalidAngle from .pdt_msg_strings import ( PDT_ERR_BAD3VALS, PDT_ERR_BAD2VALS, PDT_ERR_BAD1VALS, PDT_ERR_CONNECTED, PDT_ERR_SEL_2_VERTS, PDT_ERR_EDOB_MODE, PDT_ERR_NO_ACT_OBJ, PDT_ERR_VERT_MODE, PDT_ERR_SEL_3_VERTS, PDT_ERR_SEL_3_OBJS, PDT_ERR_EDIT_MODE, PDT_ERR_NON_VALID, PDT_LAB_NOR, PDT_ERR_STRIGHT_LINE, PDT_LAB_ARCCENTRE, PDT_ERR_SEL_4_VERTS, PDT_ERR_INT_NO_ALL, PDT_LAB_INTERSECT, PDT_ERR_SEL_4_OBJS, PDT_INF_OBJ_MOVED, PDT_ERR_SEL_2_VERTIO, PDT_ERR_SEL_2_OBJS, PDT_ERR_SEL_3_VERTIO, PDT_ERR_TAPER_ANG, PDT_ERR_TAPER_SEL, PDT_ERR_INT_LINES, PDT_LAB_PLANE, ) def vector_build(context, pg, obj, operation, values, num_values): """Build Movement Vector from Input Fields. Args: context: Blender bpy.context instance. pg: PDT Parameters Group - our variables obj: The Active Object operation: The Operation e.g. Create New Vertex values: The paramters passed e.g. 1,4,3 for Cartesian Coordinates num_values: The number of values passed - determines the function Returns: Vector to position, or offset, items. """ scene = context.scene plane = pg.plane flip_angle = pg.flip_angle flip_percent= pg.flip_percent # Cartesian 3D coordinates if num_values == 3 and len(values) == 3: output_vector = Vector((float(values[0]), float(values[1]), float(values[2]))) # Polar 2D coordinates elif num_values == 2 and len(values) == 2: output_vector = dis_ang(values, flip_angle, plane, scene) # Percentage of imaginary line between two 3D coordinates elif num_values == 1 and len(values) == 1: output_vector = get_percent(obj, flip_percent, float(values[0]), operation, scene) else: if num_values == 3: pg.error = PDT_ERR_BAD3VALS elif num_values == 2: pg.error = PDT_ERR_BAD2VALS else: pg.error = PDT_ERR_BAD1VALS context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_InvalidVector return output_vector def placement_normal(context, operation): """Manipulates Geometry, or Objects by Normal Intersection between 3 points. Args: context: Blender bpy.context instance. operation: The Operation e.g. Create New Vertex Returns: Status Set. """ scene = context.scene pg = scene.pdt_pg extend_all = pg.extend obj = context.view_layer.objects.active if obj.mode == "EDIT": if obj is None: pg.error = PDT_ERR_NO_ACT_OBJ context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_ObjectModeError obj_loc = obj.matrix_world.decompose()[0] bm = bmesh.from_edit_mesh(obj.data) if len(bm.select_history) == 3: vector_a, vector_b, vector_c = check_selection(3, bm, obj) if vector_a is None: pg.error = PDT_ERR_VERT_MODE context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_FeatureError else: pg.error = f"{PDT_ERR_SEL_3_VERTIO} {len(bm.select_history)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError elif obj.mode == "OBJECT": objs = context.view_layer.objects.selected if len(objs) != 3: pg.error = f"{PDT_ERR_SEL_3_OBJS} {len(objs)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError objs_s = [ob for ob in objs if ob.name != obj.name] vector_a = obj.matrix_world.decompose()[0] vector_b = objs_s[-1].matrix_world.decompose()[0] vector_c = objs_s[-2].matrix_world.decompose()[0] vector_delta = intersect_point_line(vector_a, vector_b, vector_c)[0] if operation == "C": if obj.mode == "EDIT": scene.cursor.location = obj_loc + vector_delta elif obj.mode == "OBJECT": scene.cursor.location = vector_delta elif operation == "P": if obj.mode == "EDIT": pg.pivot_loc = obj_loc + vector_delta elif obj.mode == "OBJECT": pg.pivot_loc = vector_delta elif operation == "G": if obj.mode == "EDIT": if extend_all: for v in [v for v in bm.verts if v.select]: v.co = vector_delta bm.select_history.clear() bmesh.ops.remove_doubles(bm, verts=[v for v in bm.verts if v.select], dist=0.0001) else: bm.select_history[-1].co = vector_delta bm.select_history.clear() bmesh.update_edit_mesh(obj.data) elif obj.mode == "OBJECT": context.view_layer.objects.active.location = vector_delta elif operation == "N": if obj.mode == "EDIT": vertex_new = bm.verts.new(vector_delta) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() for v in [v for v in bm.verts if v.select]: v.select_set(False) vertex_new.select_set(True) else: pg.error = f"{PDT_ERR_EDIT_MODE} {obj.mode})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") return elif operation == "V" and obj.mode == "EDIT": vector_new = vector_delta vertex_new = bm.verts.new(vector_new) if extend_all: for v in [v for v in bm.verts if v.select]: bm.edges.new([v, vertex_new]) else: bm.edges.new([bm.select_history[-1], vertex_new]) for v in [v for v in bm.verts if v.select]: v.select_set(False) vertex_new.select_set(True) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() else: pg.error = f"{operation} {PDT_ERR_NON_VALID} {PDT_LAB_NOR}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") def placement_arc_centre(context, operation): """Manipulates Geometry, or Objects to an Arc Centre defined by 3 points on an Imaginary Arc. Args: context: Blender bpy.context instance. operation: The Operation e.g. Create New Vertex Returns: Status Set. """ scene = context.scene pg = scene.pdt_pg extend_all = pg.extend obj = context.view_layer.objects.active if obj.mode == "EDIT": if obj is None: pg.error = PDT_ERR_NO_ACT_OBJ context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_ObjectModeError obj = context.view_layer.objects.active obj_loc = obj.matrix_world.decompose()[0] bm = bmesh.from_edit_mesh(obj.data) verts = [v for v in bm.verts if v.select] if len(verts) != 3: pg.error = f"{PDT_ERR_SEL_3_VERTS} {len(verts)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError vector_a = verts[0].co vector_b = verts[1].co vector_c = verts[2].co vector_delta, radius = arc_centre(vector_a, vector_b, vector_c) if str(radius) == "inf": pg.error = PDT_ERR_STRIGHT_LINE context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_InfRadius pg.distance = radius if operation == "C": scene.cursor.location = obj_loc + vector_delta elif operation == "P": pg.pivot_loc = obj_loc + vector_delta elif operation == "N": vector_new = vector_delta vertex_new = bm.verts.new(vector_new) for v in [v for v in bm.verts if v.select]: v.select_set(False) vertex_new.select_set(True) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() vertex_new.select_set(True) elif operation == "G": if extend_all: for v in [v for v in bm.verts if v.select]: v.co = vector_delta bm.select_history.clear() bmesh.ops.remove_doubles(bm, verts=[v for v in bm.verts if v.select], dist=0.0001) else: bm.select_history[-1].co = vector_delta bm.select_history.clear() bmesh.update_edit_mesh(obj.data) elif operation == "V": vertex_new = bm.verts.new(vector_delta) if extend_all: for v in [v for v in bm.verts if v.select]: bm.edges.new([v, vertex_new]) v.select_set(False) vertex_new.select_set(True) bm.select_history.clear() bmesh.ops.remove_doubles(bm, verts=[v for v in bm.verts if v.select], dist=0.0001) bmesh.update_edit_mesh(obj.data) else: bm.edges.new([bm.select_history[-1], vertex_new]) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() else: pg.error = f"{operation} {PDT_ERR_NON_VALID} {PDT_LAB_ARCCENTRE}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") elif obj.mode == "OBJECT": if len(context.view_layer.objects.selected) != 3: pg.error = f"{PDT_ERR_SEL_3_OBJS} {len(context.view_layer.objects.selected)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError vector_a = context.view_layer.objects.selected[0].matrix_world.decompose()[0] vector_b = context.view_layer.objects.selected[1].matrix_world.decompose()[0] vector_c = context.view_layer.objects.selected[2].matrix_world.decompose()[0] vector_delta, radius = arc_centre(vector_a, vector_b, vector_c) pg.distance = radius if operation == "C": scene.cursor.location = vector_delta elif operation == "P": pg.pivot_loc = vector_delta elif operation == "G": context.view_layer.objects.active.location = vector_delta else: pg.error = f"{operation} {PDT_ERR_NON_VALID} {PDT_LAB_ARCCENTRE}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") def placement_intersect(context, operation): """Manipulates Geometry, or Objects by Convergance Intersection between 4 points, or 2 Edges. Args: context: Blender bpy.context instance. operation: The Operation e.g. Create New Vertex Returns: Status Set. """ scene = context.scene pg = scene.pdt_pg plane = pg.plane obj = context.view_layer.objects.active if obj.mode == "EDIT": if obj is None: pg.error = PDT_ERR_NO_ACT_OBJ context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_NoObjectError obj_loc = obj.matrix_world.decompose()[0] bm = bmesh.from_edit_mesh(obj.data) edges = [e for e in bm.edges if e.select] extend_all = pg.extend if len(edges) == 2: vertex_a = edges[0].verts[0] vertex_b = edges[0].verts[1] vertex_c = edges[1].verts[0] vertex_d = edges[1].verts[1] else: if len(bm.select_history) != 4: pg.error = ( PDT_ERR_SEL_4_VERTS + str(len(bm.select_history)) + " Vertices/" + str(len(edges)) + " Edges)" ) context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError vertex_a = bm.select_history[-1] vertex_b = bm.select_history[-2] vertex_c = bm.select_history[-3] vertex_d = bm.select_history[-4] vector_delta, done = intersection(vertex_a.co, vertex_b.co, vertex_c.co, vertex_d.co, plane) if not done: pg.error = f"{PDT_ERR_INT_LINES} {plane} {PDT_LAB_PLANE}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_IntersectionError if operation == "C": scene.cursor.location = obj_loc + vector_delta elif operation == "P": pg.pivot_loc = obj_loc + vector_delta elif operation == "N": vector_new = vector_delta vertex_new = bm.verts.new(vector_new) for v in [v for v in bm.verts if v.select]: v.select_set(False) for f in bm.faces: f.select_set(False) for e in bm.edges: e.select_set(False) vertex_new.select_set(True) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() elif operation in {"G", "V"}: vertex_new = None process = False if (vertex_a.co - vector_delta).length < (vertex_b.co - vector_delta).length: if operation == "G": vertex_a.co = vector_delta process = True else: vertex_new = bm.verts.new(vector_delta) bm.edges.new([vertex_a, vertex_new]) process = True else: if operation == "G" and extend_all: vertex_b.co = vector_delta elif operation == "V" and extend_all: vertex_new = bm.verts.new(vector_delta) bm.edges.new([vertex_b, vertex_new]) else: return if (vertex_c.co - vector_delta).length < (vertex_d.co - vector_delta).length: if operation == "G" and extend_all: vertex_c.co = vector_delta elif operation == "V" and extend_all: bm.edges.new([vertex_c, vertex_new]) else: return else: if operation == "G" and extend_all: vertex_d.co = vector_delta elif operation == "V" and extend_all: bm.edges.new([vertex_d, vertex_new]) else: return bm.select_history.clear() bmesh.ops.remove_doubles(bm, verts=bm.verts, dist=0.0001) if not process and not extend_all: pg.error = PDT_ERR_INT_NO_ALL context.window_manager.popup_menu(oops, title="Error", icon="ERROR") bmesh.update_edit_mesh(obj.data) return for v in bm.verts: v.select_set(False) for f in bm.faces: f.select_set(False) for e in bm.edges: e.select_set(False) if vertex_new is not None: vertex_new.select_set(True) for v in bm.select_history: if v is not None: v.select_set(True) bmesh.update_edit_mesh(obj.data) else: pg.error = f"{operation} {PDT_ERR_NON_VALID} {PDT_LAB_INTERSECT}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_InvalidOperation elif obj.mode == "OBJECT": if len(context.view_layer.objects.selected) != 4: pg.error = f"{PDT_ERR_SEL_4_OBJS} {len(context.view_layer.objects.selected)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError order = pg.object_order.split(",") objs = sorted(context.view_layer.objects.selected, key=lambda x: x.name) pg.error = ( "Original Object Order (1,2,3,4) was: " + objs[0].name + ", " + objs[1].name + ", " + objs[2].name + ", " + objs[3].name ) context.window_manager.popup_menu(oops, title="Info", icon="INFO") vector_a = objs[int(order[0]) - 1].matrix_world.decompose()[0] vector_b = objs[int(order[1]) - 1].matrix_world.decompose()[0] vector_c = objs[int(order[2]) - 1].matrix_world.decompose()[0] vector_d = objs[int(order[3]) - 1].matrix_world.decompose()[0] vector_delta, done = intersection(vector_a, vector_b, vector_c, vector_d, plane) if not done: pg.error = f"{PDT_ERR_INT_LINES} {plane} {PDT_LAB_PLANE}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_IntersectionError if operation == "C": scene.cursor.location = vector_delta elif operation == "P": pg.pivot_loc = vector_delta elif operation == "G": context.view_layer.objects.active.location = vector_delta pg.error = f"{PDT_INF_OBJ_MOVED} {context.view_layer.objects.active.name}" context.window_manager.popup_menu(oops, title="Info", icon="INFO") else: pg.error = f"{operation} {PDT_ERR_NON_VALID} {PDT_LAB_INTERSECT}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") return else: return def join_two_vertices(context): """Joins 2 Free Vertices that do not form part of a Face. Note: Joins two vertices that do not form part of a single face It is designed to close open Edge Loops, where a face is not required or to join two disconnected Edges. Args: context: Blender bpy.context instance. Returns: Status Set. """ scene = context.scene pg = scene.pdt_pg obj = context.view_layer.objects.active if all([bool(obj), obj.type == "MESH", obj.mode == "EDIT"]): bm = bmesh.from_edit_mesh(obj.data) verts = [v for v in bm.verts if v.select] if len(verts) == 2: try: bm.edges.new([verts[-1], verts[-2]]) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() return except ValueError: pg.error = PDT_ERR_CONNECTED context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_VerticesConnected else: pg.error = f"{PDT_ERR_SEL_2_VERTS} {len(verts)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError else: pg.error = f"{PDT_ERR_EDOB_MODE},{obj.mode})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_ObjectModeError def set_angle_distance_two(context): """Measures Angle and Offsets between 2 Points in View Plane. Note: Uses 2 Selected Vertices to set pg.angle and pg.distance scene variables also sets delta offset from these 2 points using standard Numpy Routines Works in Edit and Oject Modes. Args: context: Blender bpy.context instance. Returns: Status Set. """ scene = context.scene pg = scene.pdt_pg plane = pg.plane flip_angle = pg.flip_angle obj = context.view_layer.objects.active if obj is None: pg.error = PDT_ERR_NO_ACT_OBJ context.window_manager.popup_menu(oops, title="Error", icon="ERROR") return if obj.mode == "EDIT": bm = bmesh.from_edit_mesh(obj.data) verts = [v for v in bm.verts if v.select] if len(verts) == 2: if len(bm.select_history) == 2: vector_a, vector_b = check_selection(2, bm, obj) if vector_a is None: pg.error = PDT_ERR_VERT_MODE context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_FeatureError else: pg.error = f"{PDT_ERR_SEL_2_VERTIO} {len(bm.select_history)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError else: pg.error = f"{PDT_ERR_SEL_2_VERTIO} {len(verts)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError elif obj.mode == "OBJECT": objs = context.view_layer.objects.selected if len(objs) < 2: pg.error = f"{PDT_ERR_SEL_2_OBJS} {len(objs)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError objs_s = [ob for ob in objs if ob.name != obj.name] vector_a = obj.matrix_world.decompose()[0] vector_b = objs_s[-1].matrix_world.decompose()[0] if plane == "LO": vector_difference = vector_b - vector_a vector_b = view_coords_i(vector_difference.x, vector_difference.y, vector_difference.z) vector_a = Vector((0, 0, 0)) v0 = np.array([vector_a.x + 1, vector_a.y]) - np.array([vector_a.x, vector_a.y]) v1 = np.array([vector_b.x, vector_b.y]) - np.array([vector_a.x, vector_a.y]) else: a1, a2, _ = set_mode(plane) v0 = np.array([vector_a[a1] + 1, vector_a[a2]]) - np.array([vector_a[a1], vector_a[a2]]) v1 = np.array([vector_b[a1], vector_b[a2]]) - np.array([vector_a[a1], vector_a[a2]]) ang = np.rad2deg(np.arctan2(np.linalg.det([v0, v1]),	np.dot(v0, v1)	numpy.dot
import numpy as np import cv2 import matplotlib.pyplot as plt import matplotlib.image as mpimg ############################################################################################## #---------------------------CALIBRATION CAMERA + DISTORSION CORRECTION------------------------ def calculation_undistort(image, objpoints, imgpoints): # get image size img_size = (image.shape[1], image.shape[0]) # Camera Calibration ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, img_size, None, None) # Distorsion Correction undist = cv2.undistort(image,mtx,dist,None,mtx) return undist ################################################################################################ #--------------------------------------GRADIENT------------------------------------------------ def image_computing(image_undistorted): # Grayscale image to compute the gradient gray = cv2.cvtColor(image_undistorted, cv2.COLOR_RGB2GRAY) # HLS color space and separate the S channel for the color hls = cv2.cvtColor(image_undistorted, cv2.COLOR_RGB2HLS) l_channel = hls[:,:,1] s_channel = hls[:,:,2] #------------------------------------------------------------------------------------------- # Sobel x sobelx = cv2.Sobel(gray, cv2.CV_64F, 1, 0) abs_sobelx = np.absolute(sobelx) # x derivative accentuates lines away from horizontal scaled_sobelx = np.uint8(255abs_sobelx/np.max(abs_sobelx)) # Sobel y sobely = cv2.Sobel(gray, cv2.CV_64F, 0, 1) abs_sobely = np.absolute(sobely) # y derivative accentuates lines away from horizontal scaled_sobely = np.uint8(255abs_sobely/np.max(abs_sobely)) #--------------------------------------------------------------------------------------------- # x-gradient Thresholding thresh_min = 40 thresh_max = 100 sxbinary = np.zeros_like(scaled_sobelx) sxbinary[(scaled_sobelx >= thresh_min) & (scaled_sobelx <= thresh_max)] = 1 # y-gradient Thresholding thresh_min = 40 thresh_max = 100 sybinary = np.zeros_like(scaled_sobely) sybinary[(scaled_sobely >= thresh_min) & (scaled_sobely <= thresh_max)] = 1 #---------------------------------------------------------------------------------------------- # color channel Thresholding s_thresh_min = 150 s_thresh_max = 255 s_binary = np.zeros_like(s_channel) s_binary[(s_channel >= s_thresh_min) & (s_channel <= s_thresh_max)] = 1 l_thresh_min = 150 l_thresh_max = 255 l_binary = np.zeros_like(l_channel) l_binary[(l_channel >= l_thresh_min) & (l_channel <= l_thresh_max)] = 1 # Gradient direction thresholding thresh=(0.7, 1.3) direction = np.arctan2 (abs_sobely, abs_sobelx) # Calculate the direction dir_binary = np.zeros_like (direction) dir_binary[(direction >= thresh[0]) & (direction<=thresh[1])] =1 # Gradient magnitude thresholding mag_thresh=(30, 100) magnitude = np.sqrt((sobelx)2 + (sobely)2) # Calculate the magnitude scaled_magnitude = np.uint8 (255* magnitude/np.max(magnitude)) # Scale to 8-bit (0 - 255) and convert to type = np.uint8 mag_binary = np.zeros_like (scaled_magnitude) # Create a binary mask where mag thresholds are met mag_binary[(scaled_magnitude >= mag_thresh[0]) & (scaled_magnitude<=mag_thresh[1])] =1 #----------------------------------------------------------------------------------------------- #----------------------------------------------------------------------------------------------- # Combine the two binary thresholds : Only color and sobel x combined_binary = np.zeros_like(sxbinary) combined_binary[((s_binary == 1) & (l_binary == 1)) \|(sxbinary == 1)] = 1 #----------------------------------------------------------------------------------------------- # Combine the two binary thresholds : color and sobel x + magnitude/direction gradient combined_binary_b = np.zeros_like(dir_binary) combined_binary_b[(sxbinary == 1 \| ((mag_binary == 1) & (dir_binary == 1))) \| s_binary == 1] = 1 #----------------------------------------------------------------------------------------------- # return the combinaison color and sobelx return sxbinary, sybinary, mag_binary, dir_binary, s_binary, l_binary, combined_binary, combined_binary_b ######################################################################################################### # ----------------------------PERPECTIVE TRANSFORM------------------------------------------------------- def warper(img, src, dst): img_size = (img.shape[1], img.shape[0]) M = cv2.getPerspectiveTransform(src, dst) Minv = cv2.getPerspectiveTransform(dst, src) warped = cv2.warpPerspective(img, M, img_size, flags=cv2.INTER_NEAREST) # keep same size as input image return warped,Minv ################################################################################################## #---------------------------------FIND LANE PIXEL - Methodic : Histrogramm and Window ------------ def find_lanes_pixels(binary_warped): # Take a histogram of the bottom half of the image # creation de l'histogramme avec les 2 pics, image coupé en 2 # et prendre en consideration que la demie-partie d'en bas --> shape[0] = axe y histogram = np.sum(binary_warped[binary_warped.shape[0]//2:,:], axis=0) #plt.plot(histogram) # Create an output image to draw on and visualize the result # creation d'une image resultat nommé out_img out_img = np.dstack((binary_warped, binary_warped, binary_warped)) # Find the peak of the left and right halves of the histogram # These will be the starting point for the left and right lines # analyse de d'histogramme : # 1) graphe histogramme coupe en 2 en x (partie droite et partie gauche) # 2) prise de la partie gauche en x et prendre le point le plus haut # 3) prise de la partie droite en x et prendre le point le plus haut midpoint = np.int(histogram.shape[0]//2) leftx_base = np.argmax(histogram[:midpoint]) rightx_base = np.argmax(histogram[midpoint:]) + midpoint #-------------------------------------------------------- # HYPERPARAMETERS # Choose the number of sliding windows # nombre de fenetres qui vont se succeder nwindows = 9 # Set the width of the windows +/- margin # tolerance en x margin = 50 # Set minimum number of pixels found to recenter window # nombre minimum de pixel trouve pour recentrer la fenetre minpix = 100 #------------------------------------------------------------ # DERNIERES PARAMETRAGES # definition de la hauteur des 9 fenetre : taille de la fenetre total / 9 # Set height of windows - based on nwindows above and image shape window_height = np.int(binary_warped.shape[0]//nwindows) # position x et y de tous les pixels actives dans l'image # Identify the x and y positions of all nonzero pixels in the image nonzero = binary_warped.nonzero() nonzeroy = np.array(nonzero[0]) # axe y nonzerox = np.array(nonzero[1]) # axe x # Current positions to be updated later for each window in nwindows #position courante des deux fenetres (gauche et droite), ici initalisation # donc fenetre (ligne) de base = fenetre (ligne) courante, qui va evoluer leftx_current = leftx_base rightx_current = rightx_base # Create empty lists to receive left and right lane pixel indices # creation de liste vide pour recevoir les indices des pixels des lignes (droite et gauche) left_lane_inds = [] right_lane_inds = [] #--------------------------------------------------------------- # Step through the windows one by one for window in range(nwindows): # iterer de 1 a 9 : # limites en y pour les fenetres : #hauteur de l'image/ ((hauteur_fenetre)fenetre (0->9)), # Identify window boundaries in x and y (and right and left) win_y_low = binary_warped.shape[0] - (window+1)window_height win_y_high = binary_warped.shape[0] - window*window_height # limite en x des fenetres : avec les tolerances margin en x a partir # du positionnement de la courbe ### TO-DO: Find the four below boundaries of the window ### win_xleft_low = leftx_current - margin win_xleft_high = leftx_current + margin win_xright_low = rightx_current - margin win_xright_high = rightx_current + margin # --------------------- # Draw the windows on the visualization image # tracage de la fenetre dans l'image de sortie avec les coodonnées donnés ci-dessus cv2.rectangle(out_img,(win_xleft_low,win_y_low), (win_xleft_high,win_y_high),(0,255,0), 2) cv2.rectangle(out_img,(win_xright_low,win_y_low), (win_xright_high,win_y_high),(0,255,0), 2) #------------------------ # identification des pixels activés en x et y dans la fenetre good_left_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xleft_low) & (nonzerox < win_xleft_high)).nonzero()[0] good_right_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xright_low) & (nonzerox < win_xright_high)).nonzero()[0] # Append these indices to the lists # ajout des indices des pixels activés left_lane_inds.append(good_left_inds) right_lane_inds.append(good_right_inds) # si le nombre de pixel dans la fentre est >50 # on calcule la moyenne des indices pour donner leftx_current # et recentrer la fenetre if len(good_left_inds) > minpix: leftx_current = np.int(	np.mean(nonzerox[good_left_inds])	numpy.mean
from __future__ import print_function import threading import multiprocessing from collections import namedtuple import os try: from queue import Queue, Full, Empty except ImportError: from Queue import Queue, Full, Empty try: import cPickle as pickle except ImportError: import pickle import numpy as np import h5py import tensorflow as tf from pybh import math_utils, hdf5_utils def write_samples_to_hdf5_file(filename, samples, attr_dict=None, dataset_kwargs): stacked_samples = {} for key in samples[0]: stacked_samples[key] = np.empty((len(samples),) + samples[0][key].shape, dtype=samples[0][key].dtype) for key in samples[0]: for i, sample in enumerate(samples): stacked_samples[key][i, ...] = sample[key] hdf5_utils.write_numpy_dict_to_hdf5_file(filename, stacked_samples, attr_dict=attr_dict, dataset_kwargs) def read_samples_from_hdf5_file(filename, field_dict=None, read_attributes=True): result = hdf5_utils.read_hdf5_file_to_numpy_dict(filename, field_dict, read_attributes) if read_attributes: data, attr_dict = result else: data = result key_list = list(data.keys()) sample_dict = {} for key in key_list: assert(data[key].shape[0] == data[key_list[0]].shape[0]) sample_dict[key] = [] for i in range(data[key].shape[0]): sample_dict[key].append(data[key][i, ...]) samples = [] for i in range(data[key_list[0]].shape[0]): samples.append({key: sample_dict[key][i] for key in sample_dict}) if read_attributes: return samples, attr_dict else: return samples Record = namedtuple("Record", ["obs_levels", "grid_3d", "rewards", "prob_rewards", "scores"]) RecordBatch = namedtuple("RecordBatch", ["obs_levels", "grid_3ds", "rewards", "prob_rewards", "scores"]) RecordV2 = namedtuple("RecordV2", ["obs_levels", "grid_3d", "rewards", "norm_rewards", "prob_rewards", "norm_prob_rewards", "scores"]) RecordV2Batch = namedtuple("RecordV2Batch", ["obs_levels", "grid_3ds", "rewards", "norm_rewards", "prob_rewards", "norm_prob_rewards", "scores"]) RecordV3 = namedtuple("RecordV3", ["obs_levels", "in_grid_3d", "out_grid_3d", "rewards", "scores"]) RecordV3Batch = namedtuple("RecordV3Batch", ["obs_levels", "in_grid_3ds", "out_grid_3ds", "rewards", "scores"]) RecordV4 = namedtuple("RecordV4", ["intrinsics", "map_resolution", "axis_mode", "forward_factor", "obs_levels", "in_grid_3d", "out_grid_3d", "rewards", "scores", "rgb_image", "depth_image", "normal_image"]) RecordV4Batch = namedtuple("RecordV4Batch", ["intrinsics", "map_resolution", "axis_mode", "forward_factor", "obs_levels", "in_grid_3ds", "out_grid_3ds", "rewards", "scores", "rgb_images", "depth_images", "normal_images"]) def write_hdf5_records(filename, records): f = h5py.File(filename, "w") (obs_levels, grid_3d, rewards, prob_rewards, scores) = records[0] assert(grid_3d.shape[-1] == 2 * len(obs_levels)) rewards_shape = (len(records),) + rewards.shape rewards_dset = f.create_dataset("rewards", rewards_shape, dtype='f') prob_rewards_shape = (len(records),) + prob_rewards.shape prob_rewards_dset = f.create_dataset("prob_rewards", prob_rewards_shape, dtype='f') scores_shape = (len(records),) + scores.shape scores_dset = f.create_dataset("scores", scores_shape, dtype='f') grid_3ds_shape = (len(records),) + grid_3d.shape grid_3ds_dset = f.create_dataset("grid_3ds", grid_3ds_shape, dtype='f') grid_3ds_dset.attrs["obs_levels"] = obs_levels grid_3ds_dset.attrs["obs_channels"] = grid_3ds_shape[-1] / len(obs_levels) for i, record in enumerate(records): (obs_levels, grid_3d, rewards, prob_rewards, scores) = record rewards_dset[i, ...] = rewards prob_rewards_dset[i, ...] = prob_rewards scores_dset[i, ...] = scores grid_3ds_dset[i, ...] = grid_3d f.close() def read_hdf5_records(filename): try: f = h5py.File(filename, "r") obs_levels = f["grid_3ds"].attrs["obs_levels"] obs_channels = f["grid_3ds"].attrs["obs_channels"] rewards = np.array(f["rewards"]) prob_rewards = np.array(f["prob_rewards"]) scores = np.array(f["scores"]) grid_3ds = np.array(f["grid_3ds"]) assert(rewards.shape[0] == grid_3ds.shape[0]) assert(prob_rewards.shape[0] == grid_3ds.shape[0]) assert(scores.shape[0] == grid_3ds.shape[0]) assert(grid_3ds.shape[-1] == len(obs_levels) * obs_channels) return RecordBatch(obs_levels, grid_3ds, rewards, prob_rewards, scores) except Exception as err: print("ERROR: Exception raised when reading as HDF5 v1 file \"{}\": {}".format(filename, err)) def write_hdf5_records_v2(filename, records): f = h5py.File(filename, "w") (obs_levels, grid_3d, rewards, norm_rewards, prob_rewards, norm_prob_rewards, scores) = records[0] assert(grid_3d.shape[-1] == 2 * len(obs_levels)) rewards_shape = (len(records),) + rewards.shape rewards_dset = f.create_dataset("rewards", rewards_shape, dtype='f') norm_rewards_shape = (len(records),) + norm_rewards.shape norm_rewards_dset = f.create_dataset("norm_rewards", norm_rewards_shape, dtype='f') prob_rewards_shape = (len(records),) + prob_rewards.shape prob_rewards_dset = f.create_dataset("prob_rewards", prob_rewards_shape, dtype='f') norm_prob_rewards_shape = (len(records),) + norm_prob_rewards.shape norm_prob_rewards_dset = f.create_dataset("norm_prob_rewards", norm_prob_rewards_shape, dtype='f') scores_shape = (len(records),) + scores.shape scores_dset = f.create_dataset("scores", scores_shape, dtype='f') grid_3ds_shape = (len(records),) + grid_3d.shape grid_3ds_dset = f.create_dataset("grid_3ds", grid_3ds_shape, dtype='f') grid_3ds_dset.attrs["obs_levels"] = obs_levels grid_3ds_dset.attrs["obs_channels"] = grid_3ds_shape[-1] / len(obs_levels) for i, record in enumerate(records): (obs_levels, grid_3d, rewards, norm_rewards, prob_rewards, norm_prob_rewards, scores) = record rewards_dset[i, ...] = rewards norm_rewards_dset[i, ...] = norm_rewards prob_rewards_dset[i, ...] = prob_rewards norm_prob_rewards_dset[i, ...] = norm_prob_rewards scores_dset[i, ...] = scores grid_3ds_dset[i, ...] = grid_3d f.close() def write_hdf5_records_v3(filename, records): f = h5py.File(filename, "w") (obs_levels, in_grid_3d, out_grid_3d, rewards, scores) = records[0] assert(in_grid_3d.shape[-1] == 2 * len(obs_levels)) assert(	np.all(in_grid_3d.shape == out_grid_3d.shape)	numpy.all
#!/usr/bin/env python # -- coding: UTF-8 -- """ Class of pytorch data loader --- <NAME> <EMAIL> Nanjing University of Science and Technology Aug 10, 2019 """ import glob import imageio import numpy as np import numpy.matlib import torch.utils.data from torchvision import transforms #from config import colorMap # C_NUM = 12 # number of classes # 'empty','ceiling','floor','wall','window','chair','bed','sofa','table','tvs','furn','objs' # 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 seg_class_map = [0, 1, 2, 3, 4, 11, 5, 6, 7, 8, 8, 10, 10, 10, 11, 11, 9, 8, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 10, 11, 8, 10, 11, 9, 11, 11, 11] # 0 - 11 # 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 class NYUDataset(torch.utils.data.Dataset): def __init__(self, root, istest=False): self.param = {'voxel_size': (240, 144, 240), 'voxel_unit': 0.02, # 0.02m, length of each grid == 20mm 'cam_k': [[518.8579, 0, 320], # K is [fx 0 cx; 0 fy cy; 0 0 1]; [0, 518.8579, 240], # cx = K(1,3); cy = K(2,3); [0, 0, 1]], # fx = K(1,1); fy = K(2,2); } # self.subfix = 'npz' self.istest = istest self.downsample = 4 # int, downsample = 4, in labeled data, get 1 voxel from each 4 self.filepaths = self.get_filelist(root, self.subfix) # Converts a PIL Image or numpy.ndarray (H x W x C) in the range [0, 255] \ # to a torch.FloatTensor of shape (C x H x W) in the range [0.0, 1.0]. self.transforms_rgb = transforms.Compose([ transforms.ToTensor(), transforms.Normalize(mean=[0.485, 0.456, 0.406], std=[0.229, 0.224, 0.225]), ]) print('Dataset:{} files'.format(len(self.filepaths))) def __getitem__(self, index): _name = self.filepaths[index][:-4] # print(_name) # --------------------------------------------------------------------------- # Processing repackaged data provided by DDRNet # --------------------------------------------------------------------------- if self.subfix == 'npz': with np.load(self.filepaths[index]) as npz_file: # print(npz_file.files) rgb_tensor = npz_file['rgb'] depth_tensor = npz_file['depth'] tsdf_hr = npz_file['tsdf_hr'] # flipped TSDF, (240, 144, 240, 1) # target_hr = npz_file['target_hr'] target_lr = npz_file['target_lr'] position = npz_file['position'] if self.istest: tsdf_lr = npz_file['tsdf_lr'] # ( 60, 36, 60) # nonempty = self.get_nonempty(tsdf, 'TSDF') nonempty = self.get_nonempty2(tsdf_lr, target_lr, 'TSDF') # 这个更符合SUNCG的做法 return rgb_tensor, depth_tensor, tsdf_hr, target_lr.T, nonempty.T, position, _name + '.png' return rgb_tensor, depth_tensor, tsdf_hr, target_lr.T, position, _name + '.png' # else: # # --------------------------------------------------------------------------- # Processing data provided by SSCNet # --------------------------------------------------------------------------- # --- read depth, shape: (h, w) depth = self._read_depth(_name + '.png') # depth_tensor = depth.reshape((1,) + depth.shape) # --- read rgb image, shape: (h, w, 3) # rgb = self._read_rgb(_name + '.jpg') # rgb = self._read_rgb(_name[:-4] + 'rgb.png') rgb_tensor = self.transforms_rgb(rgb) # channel first, shape: (3, h, w) # --- read ground truth vox_origin, cam_pose, rle = self._read_rle(_name + '.bin') target_hr = self._rle2voxel(rle, self.param['voxel_size'], _name + '.bin') target_lr = self._downsample_label(target_hr, self.param['voxel_size'], self.downsample) binary_vox, _, position, position4 = self._depth2voxel(depth, cam_pose, vox_origin, self.param) npz_file = np.load(_name + '.npz') tsdf_hr = npz_file['tsdf'] # SUNCG (W, H, D) if self.istest: tsdf_lr = self._downsample_tsdf(tsdf_hr, self.downsample) # nonempty = self.get_nonempty(tsdf, 'TSDF') nonempty = self.get_nonempty2(tsdf_lr, target_lr, 'TSDF') # 这个更符合SUNCG的做法 return rgb_tensor, depth_tensor, tsdf_hr, target_lr.T, nonempty.T, position, _name + '.png' return rgb_tensor, depth_tensor, tsdf_hr, target_lr.T, position, _name + '.png' def __len__(self): return len(self.filepaths) def get_filelist(self, root, subfix): if root is None: raise Exception("Oops! 'root' is None, please set the right file path.") _filepaths = list() if isinstance(root, list): # 将多个root for root_i in root: fp = glob.glob(root_i + '/.' + subfix) fp.sort() _filepaths.extend(fp) elif isinstance(root, str): _filepaths = glob.glob(root + '/.' + subfix) # List all files in data folder _filepaths.sort() if len(_filepaths) == 0: raise Exception("Oops! That was no valid data in '{}'.".format(root)) return _filepaths @staticmethod def _read_depth(depth_filename): r"""Read a depth image with size H x W and save the depth values (in millimeters) into a 2d numpy array. The depth image file is assumed to be in 16-bit PNG format, depth in millimeters. """ # depth = misc.imread(depth_filename) / 8000.0 # numpy.float64 depth = imageio.imread(depth_filename) / 8000.0 # numpy.float64 # assert depth.shape == (img_h, img_w), 'incorrect default size' depth = np.asarray(depth) return depth @staticmethod def _read_rgb(rgb_filename): # 0.01s r"""Read a RGB image with size H x W """ # rgb = misc.imread(rgb_filename) # <type 'numpy.ndarray'>, numpy.uint8, (480, 640, 3) rgb = imageio.imread(rgb_filename) # <type 'numpy.ndarray'>, numpy.uint8, (480, 640, 3) # rgb = np.rollaxis(rgb, 2, 0) # (H, W, 3)-->(3, H, W) return rgb @staticmethod def _read_rle(rle_filename): # 0.0005s r"""Read RLE compression data Return: vox_origin, cam_pose, vox_rle, voxel label data from file Shape: vox_rle, (240, 144, 240) """ fid = open(rle_filename, 'rb') vox_origin = np.fromfile(fid, np.float32, 3).T # Read voxel origin in world coordinates cam_pose = np.fromfile(fid, np.float32, 16).reshape((4, 4)) # Read camera pose vox_rle = np.fromfile(fid, np.uint32).reshape((-1, 1)).T # Read voxel label data from file vox_rle = np.squeeze(vox_rle) # 2d array: (1 x N), to 1d array: (N , ) fid.close() return vox_origin, cam_pose, vox_rle # this version takes 0.9s @classmethod def _rle2voxel(cls, rle, voxel_size=(240, 144, 240), rle_filename=''): r"""Read voxel label data from file (RLE compression), and convert it to fully occupancy labeled voxels. In the data loader of pytorch, only single thread is allowed. For multi-threads version and more details, see 'readRLE.py'. output: seg_label: 3D numpy array, size 240 x 144 x 240 """ # ---- Read RLE # vox_origin, cam_pose, rle = cls._read_rle(rle_filename) # ---- Uncompress RLE, 0.9s seg_label = np.zeros(voxel_size[0] * voxel_size[1] * voxel_size[2], dtype=np.uint8) # segmentation label vox_idx = 0 for idx in range(int(rle.shape[0] / 2)): check_val = rle[idx * 2] check_iter = rle[idx * 2 + 1] if check_val >= 37 and check_val != 255: # 37 classes to 12 classes print('RLE {} check_val: {}'.format(rle_filename, check_val)) # seg_label_val = 1 if check_val < 37 else 0 # 37 classes to 2 classes: empty or occupancy # seg_label_val = 255 if check_val == 255 else seg_class_map[check_val] seg_label_val = seg_class_map[check_val] if check_val != 255 else 255 # 37 classes to 12 classes seg_label[vox_idx: vox_idx + check_iter] = np.matlib.repmat(seg_label_val, 1, check_iter) vox_idx = vox_idx + check_iter seg_label = seg_label.reshape(voxel_size) # 3D array, size 240 x 144 x 240 return seg_label # this version takes 3s @classmethod # method 2, new def _depth2voxel(cls, depth, cam_pose, vox_origin, param): cam_k = param['cam_k'] voxel_size = param['voxel_size'] # (240, 144, 240) unit = param['voxel_unit'] # 0.02 # ---- Get point in camera coordinate H, W = depth.shape gx, gy = np.meshgrid(range(W), range(H)) pt_cam = np.zeros((H, W, 3), dtype=np.float32) pt_cam[:, :, 0] = (gx - cam_k[0][2]) * depth / cam_k[0][0] # x pt_cam[:, :, 1] = (gy - cam_k[1][2]) * depth / cam_k[1][1] # y pt_cam[:, :, 2] = depth # z, in meter # ---- Get point in world coordinate p = cam_pose pt_world = np.zeros((H, W, 3), dtype=np.float32) pt_world[:, :, 0] = p[0][0] * pt_cam[:, :, 0] + p[0][1] * pt_cam[:, :, 1] + p[0][2] * pt_cam[:, :, 2] + p[0][3] pt_world[:, :, 1] = p[1][0] * pt_cam[:, :, 0] + p[1][1] * pt_cam[:, :, 1] + p[1][2] * pt_cam[:, :, 2] + p[1][3] pt_world[:, :, 2] = p[2][0] * pt_cam[:, :, 0] + p[2][1] * pt_cam[:, :, 1] + p[2][2] * pt_cam[:, :, 2] + p[2][3] pt_world[:, :, 0] = pt_world[:, :, 0] - vox_origin[0] pt_world[:, :, 1] = pt_world[:, :, 1] - vox_origin[1] pt_world[:, :, 2] = pt_world[:, :, 2] - vox_origin[2] # ---- Aline the coordinates with labeled data (RLE .bin file) pt_world2 = np.zeros(pt_world.shape, dtype=np.float32) # (h, w, 3) # pt_world2 = pt_world pt_world2[:, :, 0] = pt_world[:, :, 0] # x 水平 pt_world2[:, :, 1] = pt_world[:, :, 2] # y 高低 pt_world2[:, :, 2] = pt_world[:, :, 1] # z 深度 # pt_world2[:, :, 0] = pt_world[:, :, 1] # x 原始paper方法 # pt_world2[:, :, 1] = pt_world[:, :, 2] # y # pt_world2[:, :, 2] = pt_world[:, :, 0] # z # ---- World coordinate to grid/voxel coordinate point_grid = pt_world2 / unit # Get point in grid coordinate, each grid is a voxel point_grid = np.rint(point_grid).astype(np.int32) # .reshape((-1, 3)) # (HW, 3) (H, W, 3) # ---- crop depth to grid/voxel # binary encoding '01': 0 for empty, 1 for occupancy # voxel_binary = np.zeros(voxel_size, dtype=np.uint8) # (W, H, D) voxel_binary = np.zeros([_ + 1 for _ in voxel_size], dtype=np.float32) # (W, H, D) voxel_xyz = np.zeros(voxel_size + (3,), dtype=np.float32) # (W, H, D, 3) position = np.zeros((H, W), dtype=np.int32) position4 = np.zeros((H, W), dtype=np.int32) # position44 = np.zeros((H/4, W/4), dtype=np.int32) voxel_size_lr = (voxel_size[0] // 4, voxel_size[1] // 4, voxel_size[2] // 4) for h in range(H): for w in range(W): i_x, i_y, i_z = point_grid[h, w, :] if 0 <= i_x < voxel_size[0] and 0 <= i_y < voxel_size[1] and 0 <= i_z < voxel_size[2]: voxel_binary[i_x, i_y, i_z] = 1 # the bin has at least one point (bin is not empty) voxel_xyz[i_x, i_y, i_z, :] = point_grid[h, w, :] # position[h, w, :] = point_grid[h, w, :] # 记录图片上的每个像素对应的voxel位置 # 记录图片上的每个像素对应的voxel位置 position[h, w] = np.ravel_multi_index(point_grid[h, w, :], voxel_size) # TODO 这个project的方式可以改进 position4[h, ] = np.ravel_multi_index((point_grid[h, w, :] / 4).astype(np.int32), voxel_size_lr) # position44[h / 4, w / 4] = np.ravel_multi_index(point_grid[h, w, :] / 4, voxel_size_lr) # output --- 3D Tensor, 240 x 144 x 240 del depth, gx, gy, pt_cam, pt_world, pt_world2, point_grid # Release Memory return voxel_binary, voxel_xyz, position, position4 # (W, H, D), (W, H, D, 3) # this version takes about 0.6s on CPU @staticmethod def _downsample_label(label, voxel_size=(240, 144, 240), downscale=4): r"""downsample the labeled data, Shape: label, (240, 144, 240) label_downscale, if downsample==4, then (60, 36, 60) """ if downscale == 1: return label ds = downscale small_size = (voxel_size[0] // ds, voxel_size[1] // ds, voxel_size[2] // ds) # small size label_downscale = np.zeros(small_size, dtype=np.uint8) empty_t = 0.95 ds * ds * ds # threshold s01 = small_size[0] * small_size[1] label_i = np.zeros((ds, ds, ds), dtype=np.int32) for i in range(small_size[0]small_size[1]small_size[2]): z = int(i / s01) y = int((i - z * s01) / small_size[0]) x = int(i - z * s01 - y * small_size[0]) # z, y, x = np.unravel_index(i, small_size) # 速度更慢了 # print(x, y, z) label_i[:, :, :] = label[x * ds:(x + 1) * ds, y * ds:(y + 1) * ds, z * ds:(z + 1) * ds] label_bin = label_i.flatten() # faltten 返回的是真实的数组，需要分配新的内存空间 # label_bin = label_i.ravel() # 将多维数组变成 1维数组，而ravel 返回的是数组的视图 # zero_count_0 = np.sum(label_bin == 0) # zero_count_255 = np.sum(label_bin == 255) zero_count_0 = np.array(np.where(label_bin == 0)).size # 要比sum更快 zero_count_255 = np.array(np.where(label_bin == 255)).size zero_count = zero_count_0 + zero_count_255 if zero_count > empty_t: label_downscale[x, y, z] = 0 if zero_count_0 > zero_count_255 else 255 else: # label_i_s = label_bin[np.nonzero(label_bin)] # get the none empty class labels label_i_s = label_bin[np.where(np.logical_and(label_bin > 0, label_bin < 255))] label_downscale[x, y, z] = np.argmax(np.bincount(label_i_s)) return label_downscale @staticmethod def _downsample_tsdf(tsdf, downscale=4): # 仅在Get None empty　时会用到 r""" Shape: tsdf, (240, 144, 240) tsdf_downscale, (60, 36, 60), (stsdf.shape[0]/4, stsdf.shape[1]/4, stsdf.shape[2]/4) """ if downscale == 1: return tsdf # TSDF_EMPTY = np.float32(0.001) # TSDF_SURFACE: 1, sign >= 0 # TSDF_OCCLUD: sign < 0 np.float32(-0.001) ds = downscale small_size = (int(tsdf.shape[0] / ds), int(tsdf.shape[1] / ds), int(tsdf.shape[2] / ds)) tsdf_downscale = np.ones(small_size, dtype=np.float32) * np.float32(0.001) # init 0.001 for empty s01 = small_size[0] * small_size[1] tsdf_sr = np.ones((ds, ds, ds), dtype=np.float32) # search region for i in range(small_size[0] * small_size[1] * small_size[2]): z = int(i / s01) y = int((i - z * s01) / small_size[0]) x = int(i - z * s01 - y * small_size[0]) tsdf_sr[:, :, :] = tsdf[x * ds:(x + 1) * ds, y * ds:(y + 1) * ds, z * ds:(z + 1) * ds] tsdf_bin = tsdf_sr.flatten() # none_empty_count = np.array(np.where(tsdf_bin != TSDF_EMPTY)).size none_empty_count = np.array(np.where(np.logical_or(tsdf_bin <= 0, tsdf_bin == 1))).size if none_empty_count > 0: # surface_count = np.array(np.where(stsdf_bin == 1)).size # occluded_count = np.array(np.where(stsdf_bin == -2)).size # surface_count = np.array(np.where(tsdf_bin > 0)).size # 这个存在问题 surface_count = np.array(np.where(tsdf_bin == 1)).size # occluded_count = np.array(np.where(tsdf_bin < 0)).size # tsdf_downscale[x, y, z] = 0 if surface_count > occluded_count else np.float32(-0.001) tsdf_downscale[x, y, z] = 1 if surface_count > 2 else np.float32(-0.001) # 1 or 0 ? # else: # tsdf_downscale[x, y, z] = empty # TODO 不应该将所有值均设为0.001 return tsdf_downscale @staticmethod def get_nonempty(voxels, encoding): # Get none empty from depth voxels data =	np.zeros(voxels.shape, dtype=np.float32)	numpy.zeros
""" Scaling of in and output """ import json import numpy as np class EnergyStandardScaler: def __init__(self): self.x_mean = np.zeros((1, 1, 1)) self.x_std = np.ones((1, 1, 1)) self.energy_mean = np.zeros((1, 1)) self.energy_std = np.ones((1, 1)) self._encountered_y_shape = None self._encountered_y_std = None def transform(self, x=None, y=None): x_res = x y_res = y if x is not None: x_res = (x - self.x_mean) / self.x_std if y is not None: y_res = (y - self.energy_mean) / self.energy_std return x_res, y_res def inverse_transform(self, x=None, y=None): energy = y x_res = x if y is not None: energy = y * self.energy_std + self.energy_mean if x is not None: x_res = x * self.x_std + self.x_mean return x_res, energy def fit(self, x=None, y=None, auto_scale=None): if auto_scale is None: auto_scale = {'x_mean': True, 'x_std': True, 'energy_std': True, 'energy_mean': True} npeps = np.finfo(float).eps if auto_scale['x_mean']: self.x_mean = np.mean(x) if auto_scale['x_std']: self.x_std = np.std(x) + npeps if auto_scale['energy_mean']: self.energy_mean = np.mean(y, axis=0, keepdims=True) if auto_scale['energy_std']: self.energy_std = np.std(y, axis=0, keepdims=True) + npeps self._encountered_y_shape = np.array(y.shape) self._encountered_y_std = np.std(y, axis=0) def fit_transform(self, x=None, y=None, auto_scale=None): self.fit(x=x,y=y,auto_scale=auto_scale) return self.transform(x=x,y=y) def save(self, filepath): outdict = {'x_mean': self.x_mean.tolist(), 'x_std': self.x_std.tolist(), 'energy_mean': self.energy_mean.tolist(), 'energy_std': self.energy_std.tolist() } with open(filepath, 'w') as f: json.dump(outdict, f) def load(self, filepath): with open(filepath, 'r') as f: indict = json.load(f) self.x_mean = np.array(indict['x_mean']) self.x_std = np.array(indict['x_std']) self.energy_mean = np.array(indict['energy_mean']) self.energy_std = np.array(indict['energy_std']) def get_params(self): outdict = {'x_mean': self.x_mean.tolist(), 'x_std': self.x_std.tolist(), 'energy_mean': self.energy_mean.tolist(), 'energy_std': self.energy_std.tolist(), } return outdict def set_params(self, indict): self.x_mean = np.array(indict['x_mean']) self.x_std = np.array(indict['x_std']) self.energy_mean = np.array(indict['energy_mean']) self.energy_std = np.array(indict['energy_std']) def print_params_info(self): print("Info: Total-Data energy std", self._encountered_y_shape, ":", self._encountered_y_std) print("Info: Using energy-std", self.energy_std.shape, ":", self.energy_std) print("Info: Using energy-mean", self.energy_mean.shape, ":", self.energy_mean) print("Info: Using x-scale", self.x_std.shape, ":", self.x_std) print("Info: Using x-offset", self.x_mean.shape, ":", self.x_mean) class EnergyGradientStandardScaler: def __init__(self): self.x_mean = np.zeros((1, 1, 1)) self.x_std = np.ones((1, 1, 1)) self.energy_mean = np.zeros((1, 1)) self.energy_std = np.ones((1, 1)) self.gradient_mean = np.zeros((1, 1, 1, 1)) self.gradient_std = np.ones((1, 1, 1, 1)) self._encountered_y_shape = [None, None] self._encountered_y_std = [None, None] def transform(self, x=None, y=None): x_res = x y_res = y if x is not None: x_res = (x - self.x_mean) / self.x_std if y is not None: energy = y[0] gradient = y[1] out_e = (energy - self.energy_mean) / self.energy_std out_g = gradient / self.gradient_std y_res = [out_e, out_g] return x_res, y_res def inverse_transform(self, x=None, y=None): x_res = x y_res = y if x is not None: x_res = x * self.x_std + self.x_mean if y is not None: energy = y[0] gradient = y[1] out_e = energy * self.energy_std + self.energy_mean out_g = gradient * self.gradient_std y_res = [out_e, out_g] return x_res, y_res def fit(self, x=None, y=None, auto_scale=None): if auto_scale is None: auto_scale = {'x_mean': True, 'x_std': True, 'energy_std': True, 'energy_mean': True} npeps = np.finfo(float).eps if auto_scale['x_mean']: self.x_mean = np.mean(x) if auto_scale['x_std']: self.x_std = np.std(x) + npeps if auto_scale['energy_mean']: y1 = y[0] self.energy_mean =	np.mean(y1, axis=0, keepdims=True)	numpy.mean
#!/usr/bin/env python3 # -- coding: utf-8 -- """ Created on Mon Jun 15 22:04:25 2020 @author: lukepinkel """ import numpy as np import pandas as pd from ..utilities.linalg_operations import vec, invec, vecl, vdg from ..utilities.special_mats import kmat, nmat, lmat class RotationMethod(object): def __init__(self, A, rotation_type="ortho"): self.p, self.m = A.shape self.A = A self.rotation_type = rotation_type self.Kmp = kmat(self.m, self.p) def rotate(self, T): if self.rotation_type == "ortho": L = np.dot(self.A, T) else: L = np.dot(self.A, np.linalg.inv(T.T)) return L def _d_rotate_oblique(self, T): A = self.A B = np.linalg.inv(T.T) L =	np.dot(A, B)	numpy.dot
import threading, queue, time, os, pickle # from queue import Queue import numpy as np import tensorflow as tf import sarnet_td3.common.tf_util as U from tensorflow.python.keras.backend import set_session lock = threading.Lock() class MultiTrainTD3(threading.Thread): def __init__(self, input_queue, output_queue, args=(), kwargs=None): threading.Thread.__init__(self, args=(), kwargs=None) self.input_queue = input_queue self.output_queue = output_queue self.daemon = True self.trainers = args[0] self.args = args[1] self.buffer_op = args[2] self.num_env = args[3] self.sess = args[4] self.num_agents = args[5] self.num_adversaries = args[6] self.ep_rewards = [[0.0] for _ in range(self.num_env)] self.ep_end_rewards = [[0.0] for _ in range(self.num_env)] self.ep_success = [[0.0] for _ in range(self.num_env)] self.agent_rewards = [[[0.0] for _ in range(self.num_agents)] for _ in range(self.num_env)] self.agent_info = [[[[]] for i in range(self.num_agents)] for _ in range(self.num_env)] # self.agent_info = [[[[]]] for _ in range(self.num_env)] self.final_ep_rewards = [] # Shape: (batch, #) sum of rewards for training curve self.final_ep_end_rewards = [] self.final_ep_ag_rewards = [] # agent rewards for training curve self.save_rate = self.args.max_episode_len * 100 self.save_n_ep = self.num_env * 10 self.print_step = -int(self.save_n_ep / self.num_env) self.q_h_init = np.zeros(shape=(self.num_env, self.args.critic_units)) self.mem_init = np.zeros(shape=(self.num_env, self.args.value_units)) self.time_prev = time.time() def run(self): # print(threading.currentThread().getName(), self.receive_messages) with self.sess.as_default(): # Freeze graph to avoid memory leaks # self.sess.graph.finalize() while True: try: action, p_index, data = self.input_queue.get() if action is "None": # If you send `None`, the thread will exit. return elif action is "get_action": out = self.get_action(data, p_index) self.output_queue.put(out) elif action is "get_qdebug": out = self.get_qdebug(data, p_index) self.output_queue.put(out) elif action is "get_loss": out = self.get_loss(data, p_index) self.output_queue.put(out) elif action is "write_tboard": self.write_tboard(data) elif action is "add_to_buffer": self.buffer_op.collect_exp(data) elif action is "save_rew_info": self.save_rew_info(data) elif action is "save_benchmark": out = self.save_benchmark(data) self.output_queue.put(out) elif action is "reset_rew_info": self.reset_rew_info() elif action is "save_model_rew": if not (self.args.benchmark or self.args.display): self.save_model(data) self.plot_rewards(data) except queue.Empty: continue def get_action(self, data, p_index): with lock: agent = self.trainers[p_index] obs_n_t, h_n_t, c_n_t, mem_n_t, q1_h_t, is_train = data obs_n_t = np.stack(obs_n_t, axis=-2) # This returns [agent, batch, dim] obs_n_t = np.expand_dims(obs_n_t, axis=1) # This adds [agent, time, batch, dim] p_input_j = agent.prep_input(obs_n_t, h_n_t, c_n_t, mem_n_t, q1_h_t[p_index], is_train) # print(np.shape(obs_n_t)) act_j_t, state_j_t1, mem_j_t1, attn_j_t = agent.action(p_input_j, is_train) if self.args.encoder_model == "LSTM" or self.args.encoder_model != "DDPG": c_j_t1, h_j_t1 = state_j_t1 else: h_j_t1 = state_j_t1 c_j_t1 = state_j_t1 if agent.comm_type in {"DDPG", "COMMNET", "IC3NET"}: mem_j_t1 = np.zeros(shape=(self.num_env, self.args.value_units)) return act_j_t, h_j_t1, c_j_t1, mem_j_t1, attn_j_t def get_qdebug(self, data, p_index): with lock: # with sess.as_default(): agent = self.trainers[p_index] obs_n_t, action_n_t, q1_h_n_t, q2_h_n_t = data obs_n_t = np.stack(obs_n_t, axis=-2) # This returns [agent, batch, dim] obs_n_t = np.expand_dims(obs_n_t, axis=1) # This adds [agent, time, batch, dim] q1_j_input = agent.prep_q_input(obs_n_t, action_n_t, q1_h_n_t[p_index]) _, q1_h_j_t1 = agent.q1_debug['q_values']((q1_j_input)) if self.args.td3: q2_input = agent.prep_q_input(obs_n_t, action_n_t, q2_h_n_t[p_index]) _, q2_h_j_t1 = agent.q2_debug['q_values']((q2_input)) else: q2_h_j_t1 = [] return q1_h_j_t1, q2_h_j_t1 def get_loss(self, data, p_index): with lock: # with sess.as_default(): agent = self.trainers[p_index] train_step = data loss = agent.update(self.trainers, self.buffer_op, train_step) return loss def write_tboard(self, data): with lock: loss, train_step, writer, summary_ops, summary_vars, num_agents = data # Tensorboard episode_b_rewards = [] for j in range(self.num_env): if self.args.env_type == "mpe": episode_b_rewards.append(np.mean(self.ep_rewards[j][self.print_step:])) else: episode_b_rewards.append(np.mean(self.ep_success[j][self.print_step:])) episode_b_rewards = np.mean(np.array(episode_b_rewards)) num_steps = train_step * self.num_env # Add to tensorboard only when actor agent is updated if loss[0][1] is not None: fd = {} for i, key in enumerate(summary_vars): if i == 0: fd[key] = episode_b_rewards else: agnt_idx = int((i - 1) / 5) if agnt_idx == num_agents: agnt_idx -= 1 if loss[agnt_idx] is not None: fd[key] = loss[agnt_idx][int((i - 1) % 5)] summary_str = U.get_session().run(summary_ops, feed_dict=fd) writer.add_summary(summary_str, num_steps) writer.flush() def save_rew_info(self, data): with lock: rew_n, info_n, ep_step = data # rew_n (num_env, num_agents) if self.args.env_type == "mpe": for j in range(self.num_env): for i, rew in enumerate(rew_n[j]): if ep_step >= self.args.max_episode_len - 10: # Compute only last 10 episode step rewards self.ep_end_rewards[j][-1] += rew self.ep_rewards[j][-1] += rew self.agent_rewards[j][i][-1] += rew elif self.args.env_type == "ic3net": for j in range(self.num_env): self.ep_success[j][-1] += info_n[j] if self.args.benchmark and self.args.env_type == "mpe": for j in range(self.num_env): for i, info in enumerate(info_n[j]): self.agent_info[j][i][-1].append(info) def reset_rew_info(self): with lock: for j in range(self.num_env): self.ep_rewards[j].append(0) self.ep_success[j].append(0) self.ep_end_rewards[j].append(0) for i in range(self.num_agents): self.agent_rewards[j][i].append(0) if self.args.benchmark: for j in range(self.num_env): for i in range(self.num_agents): self.agent_info[j][i].append([[]]) def save_benchmark(self, data): with lock: exp_name, exp_itr = data benchmark_dir = os.path.join('./exp_data', exp_name, exp_itr, self.args.benchmark_dir) if not os.path.exists(benchmark_dir): os.mkdir(benchmark_dir) file_name = './exp_data/' + exp_name + '/' + exp_itr + '/' + self.args.benchmark_dir + '/' + exp_name + '.pkl' print('Finished benchmarking, now saving...') # pickle_info = [self.agent_info[j] for j in range(self.num_env)] with open(file_name, 'wb') as fp: # Dump files as [num_env, [# agents, [#ep, [#stps, [dim]]]] pickle.dump(self.agent_info, fp) return "bench_saved" def save_model(self, data): with lock: # train_step = t_step * num_env train_step, num_episodes, time_taken, exp_name, exp_itr, data_file, saver = data # Policy File if num_episodes % (self.save_n_ep) == 0: save_dir = './exp_data/' + exp_name + '/' + exp_itr + '/' + self.args.save_dir + str(train_step) U.save_state(save_dir, self.sess, saver=saver) # episode_rewards, agent_rewards, final_ep_rewards, final_ep_ag_rewards = rewards if self.args.env_type == "mpe": # print statement depends on whether or not there are adversaries if self.num_adversaries == 0: episode_b_rewards = [] ep_end_b_rewards = [] ep_ag_b_rewards = [] for j in range(self.num_env): episode_b_rewards.append(np.mean(self.ep_rewards[j][self.print_step:])) ep_end_b_rewards.append(np.mean(self.ep_end_rewards[j][self.print_step:])) episode_b_rewards = np.mean(	np.array(episode_b_rewards)	numpy.array
#!/usr/bin/env python3 # -- coding: utf-8 -- import os import json import math import numpy class Wavefront(): def __init__(self, path, triangulateQuads = True): # These are the arrays we're going to produce, and which might # make sense to manipulate from the outside: self.vertexCoords = None # XYZ coordinated for each vertex self.vertexNormals = None # Normal (in XYZ form) for each vertex self.faces = None # Faces, specified by listing indexes for participating vertices # These are internal work arrays self._rawVertices = [] self._rawTexCo = [] self._rawVertexTexCo = []; self._rawFaces = [] self._vertexBelongsToFaces = None self._faceVertCache = None self.triangulateQuads = triangulateQuads if not os.path.exists(path): raise IOError(path + " does not exist") self.content = [] with open(path,'r') as file: self.content = file.readlines() # self._mode can be: # ONLYTRIS: The incoming mesh only contains tris (so no need to do anything) # TRIANGULATE: The incoming mesh contains quads (and may contain tris). Triangulate to get only tris. # ONLYQUADS: The incoming mesh contains only quads. Keep these rather than triangulating self._mode = None # Check if mesh contains quads and/or tris self._scanForMode() # Make a sweep for vertices as faces need that information self._extractVertices() # Make a sweep for texture coordinates, as faces need that too self._extractTextureCoordinates() # Make a sweep for faces self._extractFaces() # TODO: Find texture coordinates for vertices # create numpy arrays to contain vertices, faces and normals self._createVerticesNumpyArray() self._createFacesNumpyArray() # These two operations need to be redone if vertex coordinates # are changed self.recalculateFaceNormals() self.recalculateVertexNormals() def _scanForMode(self): containsTris = False containsQuads = False for line in self.content: strippedLine = line.strip() if not strippedLine is None and not strippedLine == "" and not strippedLine[0] == "#": parts = strippedLine.split(' ') if len(parts) > 4: containsQuads = True if len(parts) == 4: containsTris = True if len(parts) > 5: raise ValueError("Found a face with more than four vertices. N-gons are not supported.") # TODO: Check for n-gons? if containsQuads: if self.triangulateQuads: self._mode = "TRIANGULATE" else: if containsTris: raise ValueError("Since the mesh contains both tris and quads, requesting the mesh to not be triangulated is illegal") else: self._mode = "ONLYQUADS" else: if containsTris: self._mode = "ONLYTRIS" else: raise ValueError("The mesh didn't contain tris nor quads!?") if self._mode == "ONLYQUADS": raise ValueError("The ONLYQUADS mode is not implemented yet") print("Tris " + str(containsTris)) print("Quads " + str(containsQuads)) print(self._mode) def _extractVertices(self): for line in self.content: strippedLine = line.strip() if not strippedLine is None and not strippedLine == "" and not strippedLine[0] == "#": parts = strippedLine.split(' ') if len(parts) > 1: command = parts[0] if command == "v": x = float(parts[1]) y = float(parts[2]) z = float(parts[3]) vertex = [x, y, z] self._rawVertices.append(vertex) self._rawVertexTexCo.append([0,0]) def _extractTextureCoordinates(self): self.hasTexCo = False for line in self.content: strippedLine = line.strip() if not strippedLine is None and not strippedLine == "" and not strippedLine[0] == "#": parts = strippedLine.split(' ') if len(parts) > 1: command = parts[0] if command == "vt": x = float(parts[1]) y = float(parts[2]) texco = [x, y] self._rawTexCo.append(texco) def _distanceBetweenVerticesByIdx(self, idx1, idx2): vert1 = numpy.array(self._rawVertices[idx1]) vert2 = numpy.array(self._rawVertices[idx2]) difference = vert2 - vert1 x = difference[0] y = difference[1] z = difference[2] distance = math.sqrt( xx + yy + z*z ) return distance def _extractFaces(self): # Note that wavefront lists starts at 1, not 0 for line in self.content: strippedLine = line.strip() if not strippedLine is None and not strippedLine == "" and not strippedLine[0] == "#": parts = strippedLine.split(' ') if len(parts) > 1: command = parts[0] if command == "f": # Face info is vertIdx / texCoIdx / faceNormalIdx OR vertIdx / texCoIdx OR vertIdx vInfo1 = parts[1].split('/') vInfo2 = parts[2].split('/') vInfo3 = parts[3].split('/') # Find indexes of vertices making up the face. Note "-1" since wavefront indexes start # at 1 rather than 0 vidx1 = int(vInfo1[0]) - 1 vidx2 = int(vInfo2[0]) - 1 vidx3 = int(vInfo3[0]) - 1 if len(parts) == 4: if self._mode == "ONLYQUADS": raise ValueError("Found tri although mode was ONLYQUADS") face = [vidx1, vidx2, vidx3] self._rawFaces.append(face) else: vInfo4 = parts[4].split('/') vidx4 = int(vInfo4[0]) - 1 if self._mode == "ONLYTRIS": raise ValueError("Found quad although mode was ONLYTRIS") if self._mode == "ONLYQUADS": raise ValueError("ONLYQUADS mode not implemented yet") # Perform triangulation by splitting quad into two tris, using the shortest diagonal distance13 = self._distanceBetweenVerticesByIdx(vidx1, vidx3) distance24 = self._distanceBetweenVerticesByIdx(vidx2, vidx4) if distance13 > distance24: face = [vidx1, vidx2, vidx4] self._rawFaces.append(face) face = [vidx3, vidx4, vidx2] self._rawFaces.append(face) else: face = [vidx1, vidx3, vidx4] self._rawFaces.append(face) face = [vidx2, vidx3, vidx1] self._rawFaces.append(face) i = 1 while i < len(parts): f = parts[i].split('/') if len(f) > 1: vidx = int(f[0]) - 1 # Vertex index ti = f[1] # May be empty if no UV unwrap if ti != "": tidx = int(ti) - 1 # Texture coordinate index texco = self._rawTexCo[tidx] # Actual texture coordinats, x/y self._rawVertexTexCo[vidx] = texco self.hasTexCo = True i = i + 1 def _createFacesNumpyArray(self, assumeQuads = False): numberOfFaces = len(self._rawFaces) vertsPerFace = 3 if assumeQuads: vertsPerFace = 4 # Create a two-dimensional int array with shape (numFace/vertsPerFace) and # fill it values from the wavefront obj. This will contain vert indices. self.faces = numpy.array( self._rawFaces, dtype=int ) # Values will be copied from self._rawFaces # Create a two-dimensional float array with shape (numFace/ 3 ) and # fill it with zeros. This will contain faces normals, but needs to # be recalculated. self.faceNormals = numpy.zeros( (numberOfFaces, 3), dtype=float ) def _createVerticesNumpyArray(self): numberOfVertices = len(self._rawVertices) if numberOfVertices != len(self._rawVertexTexCo): raise ValueError("Not same number of elements in texco array") # Convert raw coords from wavefront into a 2d numpy array self.vertexCoords = numpy.array( self._rawVertices, dtype=float ) # Create a two-dimensional float array with shape (numVerts/3) and # fill it with zeros. This will contain vertex normals. self.vertexNormals = numpy.zeros( (numberOfVertices, 3), dtype=float ) # Create a two-dimensional float array with shape (numVerts/2) and # fill it with texture coordinates. self.vertexTexCo = numpy.array( self._rawVertexTexCo, dtype=float ) def recalculateVertexNormals(self, assumeQuads = False): # Build a cache where we, per vertex, list which faces are relevant # for it. We need this in order to calculate the vertex normal later, # as an average of the face normals surrounding it if self._vertexBelongsToFaces is None: self._vertexBelongsToFaces = [] numberOfFaces = len(self.faces) numberOfVertices = len(self.vertexCoords) vertsPerFace = 3 if assumeQuads: vertsPerFace = 4 currentVert = 0 while currentVert < numberOfVertices: self._vertexBelongsToFaces.append([]) currentVert = currentVert + 1 currentFace = 0 while currentFace < numberOfFaces: fv = self.faces[currentFace] currentVert = 0 while currentVert < vertsPerFace: vertexIndex = fv[currentVert] self._vertexBelongsToFaces[vertexIndex].append(currentFace) currentVert = currentVert + 1 currentFace = currentFace + 1 # Calculate vertex normals as an average of the surrounding face # normals. currentVert = 0 zeroNormal = numpy.array([0.0, 0.0, 0.0], dtype=float) while currentVert < numberOfVertices: faces = self._vertexBelongsToFaces[currentVert] numberOfFaces = len(faces) currentNormal = numpy.array([0,0,0], dtype=float) currentFace = 0 firstNormal = None while currentFace < numberOfFaces: fidx = faces[currentFace] fnormal = self.faceNormals[fidx] if firstNormal is None: firstNormal = fnormal currentNormal = currentNormal + fnormal currentFace = currentFace + 1 if numberOfFaces < 1: raise ValueError("Found a vertex (" + str(currentVert) + ") which did not belong to any face") averageNormal = currentNormal / numberOfFaces if numpy.array_equal(averageNormal, zeroNormal): print("WARNING: found zero vertex normal for vertex " + str(currentVert)) averageNormal = firstNormal self.vertexNormals[currentVert] = self._unitVector(averageNormal) currentVert = currentVert + 1 def recalculateFaceNormals(self): self._copyVertCoordsToCache() # Calculate the face normal from the first three vertices. This might produce # strange results if using quads. In that case we should probably triangulate and # and weight together the face normals of the resulting two tris. numberOfFaces = len(self.faces) currentFace = 0 while currentFace < numberOfFaces: U = self._faceVertCache[currentFace][1] - self._faceVertCache[currentFace][0] V = self._faceVertCache[currentFace][2] - self._faceVertCache[currentFace][0] cross =	numpy.cross(U,V)	numpy.cross
''' 本模块用于数据预处理 This module is used for data preproccessing ''' import numpy as np from maysics.utils import e_distances from matplotlib import pyplot as plt plt.rcParams['font.sans-serif'] = ['FangSong'] plt.rcParams['axes.unicode_minus'] = False from io import BytesIO from lxml import etree import base64 import math def _rc(arg): cov_mat = np.cov(arg) var_mat = np.diagonal(cov_mat)0.5 var_mat[var_mat == 0] = 1 for i in range(cov_mat.shape[0]): cov_mat[i] /= var_mat[i] cov_mat[:, i] /= var_mat[i] return cov_mat def _preview_process(data, value_round): ''' 预览处理 ''' data = np.array(data, dtype=float) name_list = ['平均值', '中位数', '方差', '标准差', '最大值', '最小值', '偏度', '峰度'] value_list = [] mean_ = data.mean(axis=0) value_list.append(np.round(mean_, value_round)) value_list.append(np.round(np.median(data, axis=0), value_round)) value_list.append(np.round(data.var(axis=0), value_round)) value_list.append(np.round(data.std(axis=0), value_round)) value_list.append(np.round(data.max(axis=0), value_round)) value_list.append(np.round(data.min(axis=0), value_round)) value_list.append(np.round(((data - mean_)3).mean(axis=0), value_round)) value_list.append(np.round(((data - mean_)*4).mean(axis=0), value_round)) value_list = np.array(value_list).flatten() style = ''' <style> table{ border-collapse: collapse; } table, table tr td { border:1px solid #ccc; } table tr td{ padding: 5px 10px; } </style> ''' table = '<h2 style="padding-left:50px; border-top:1px solid #ccc">数值特征</h2>' + style + '<table align="center"><caption></caption>' for i in range(8): table += '<tr><td>' + name_list[i] + '</td>' + '<td>%s</td>' data.shape[1] + '</tr>' table = '<h1 style="padding-left:50px;">数据信息</h1>' + table % tuple(value_list) + '</table>' data = np.ascontiguousarray(data.T) num = data.shape[0] plt.figure(figsize=(9, 3 * num)) for i in range(num): q1, q2, q3 = np.percentile(data[i], [25, 50, 75]) plt.scatter(mean_[i], i+1, marker='o', color='white', s=30, zorder=3) plt.hlines(i+1, q1, q3, color='k', linestyle='-', lw=1) bx = plt.violinplot(data.tolist(), showextrema=False, vert=False) plt.title('分布图') buffer = BytesIO() plt.savefig(buffer) plt.close() plot_data = buffer.getvalue() imb = base64.b64encode(plot_data) ims = imb.decode() imd = 'data:image/png;base64,' + ims im1 = '<div align="center"><img src="%s"></div>' % imd im1 = '<br></br><h2 style="padding-left:50px; border-top:1px solid #ccc">密度分布</h2>' + im1 cov_mat = _rc(data) matrix = '<table border="0"><caption></caption>' for i in range(num): matrix += '<tr>' + '<td>%s</td>' * num + '</tr>' matrix = matrix % tuple(np.round(cov_mat.flatten(), value_round)) + '</table>' plt.figure(figsize=(8, 8)) plt.matshow(cov_mat, fignum=0, cmap='Blues') plt.colorbar() plt.title('相关系数图') buffer = BytesIO() plt.savefig(buffer) plt.close() plot_data = buffer.getvalue() imb = base64.b64encode(plot_data) ims = imb.decode() imd = 'data:image/png;base64,' + ims im2 = '<div style="display:flex;flex-direction:row;vertical-align:middle;justify-content:center;width:100%;height:80vh"><div style="margin:auto 0;white-space:pre-wrap;max-width:50%">' im2 = im2 +'相关矩阵：'+ matrix + '</div><img style="object-fit:contain;max-width:45%;max-height:80vh" src="{}"/></div>'.format(imd) im2 = '<br></br><h2 style="padding-left:50px; border-top:1px solid #ccc">相关性</h2>' + im2 plt.figure(figsize=(2.5 * num, 2.5 * num)) for i in range(num * num): ax = plt.subplot(num, num, i+1) ax.plot(data[i//num], data[i%num], 'o') buffer = BytesIO() plt.savefig(buffer) plt.close() plot_data = buffer.getvalue() imb = base64.b64encode(plot_data) ims = imb.decode() imd = "data:image/png;base64," + ims im3 = '<div align="center"><img src="%s"></div>' % imd im3 = '<br></br><h2 style="padding-left:50px; border-top:1px solid #ccc">散点关系</h2>' + im3 return '<title>数据信息预览</title>' + table + im1 + im2 + im3 def preview_file(filename, data, value_round=3): ''' 生成数据预览报告的html文件参数 ---- filename：字符串类型，文件名 data：二维数组，数据 value_round：整型，数字特征保留的小数点后的位数 Generate preview report with html file Parameters ---------- filename: str, file name data: 2-D array, data value_round: int, the number of digits after the decimal point retained by numeric features ''' root = _preview_process(data=data, value_round=value_round) html = etree.HTML(root) tree = etree.ElementTree(html) tree.write(filename) def preview(data, value_round=3): ''' 在jupyter中显示数据预览报告参数 ---- data：二维数组，数据 value_round：整型，数字特征保留的小数点后的位数 Display preview report in jupyter Parameters ---------- data: 2-D array, data value_round: int, the number of digits after the decimal point retained by numeric features ''' root = _preview_process(data=data, value_round=value_round) from IPython.core.display import display, HTML display(HTML(root)) def length_pad(seq, maxlen=None, value=0, padding='pre', dtype=float): ''' 填充二维列表，使得每行长度都为maxlen 参数 ---- seq：二维列表，需要填充的对象 maxlen：整型，可选，每行的最大长度，默认为原二维列表最大的长度 value：数类型，可选，填充值，默认为0 padding：字符串类型，可选，填充位置，'pre'代表从前面填充，'post'代表从后面填充，默认为'pre' dtype：可选，输出的元素类型，默认为float 返回 ---- 二维ndarray Pad the 2-D list so that every row is 'maxlen' in length Parameters ---------- seq: 2-D list, objects that need to be padded maxlen: int, callable, the maximum length of each row, default = the maximum length of the original 2-D list value: num, callable, padding value, default=0 padding: str, callable, padding location, 'pre' means padding from the front and 'post' from the back, default='pre' dtype: callable, the element type of the output, default=float Return ------ 2-D ndarray ''' seq = list(seq) if not maxlen: maxlen = 0 for i in seq: if len(i) > maxlen: maxlen = len(i) if padding == 'pre': for i in range(len(seq)): if maxlen > len(seq[i]): seq[i] = [value] * (maxlen - len(seq[i])) + seq[i] elif maxlen < len(seq[i]): seq[i] = seq[i][-1 * maxlen:] elif padding == 'post': for i in range(len(seq)): if maxlen > len(seq[i]): seq[i] += [value] * (maxlen - len(seq[i])) elif maxlen < len(seq[i]): seq[i] = seq[i][:maxlen] return np.array(seq, dtype=dtype) def sample_pad(data, index=0, padding=None): ''' 对二维数据进行样本填充先对data中的每个二维数据进行遍历，以各个index列的值作为全集，再对data的每个二维数据进行填充如：data1 = [[0, 1], [1, 2], [2, 3]] data2 = [[2, 3], [3, 4], [4, 5]] data = (data1, data2) 则得到输出： output = [array([[0, 1], [1, 2], [2, 3], [3, nan], [4, nan]]), array([[0, nan], [1,nan], [2, 3], [3, 4], [4, 5]])] data：元组或列表类型，数据 index：整型，作为扩充全集的标准列的索引 padding：填充值，可选，默认为None Sample filling for 2D data Values of each index column will be taken as the complete set, then each two-dimensional data of data is padded e.g. data1 = [[0, 1], [1, 2], [2, 3]] data2 = [[2, 3], [3, 4], [4, 5]] data = (data1, data2) output = [array([[0, 1], [1, 2], [2, 3], [3, nan], [4, nan]]), array([[0, nan], [1,nan], [2, 3], [3, 4], [4, 5]])] data: tuple or list, data index: int, the index of a standard column as an extended complete set padding: padding value, optional, default=None ''' time_set = set() result = [] if not padding: padding = [np.nan] * (len(data[0][0]) - 1) else: padding = list([padding]) for i in range(len(data)): data_part = np.array(data[i], dtype=np.object) result.append(data_part) time_set = time_set \| set(data_part[:, index]) for i in range(len(result)): different_set_list = np.array([list(time_set - set(result[i][:, index]))], dtype=np.object).T num = len(different_set_list) padding_new = np.array(padding * num, dtype=np.object).reshape(num, -1) different_set_list = np.hstack((padding_new[:, :index], different_set_list, padding_new[:, index:])) result[i] = np.vstack((result[i], different_set_list)) return result def shuffle(arg): ''' 打乱一个序列或以相同方法打乱多个序列返回 ---- 一个ndarray Shuffle a sequence or shuffle multiple sequences in the same way Return ------ a ndarray ''' state = np.random.get_state() a_new_list = [] for li in arg: np.random.set_state(state) np.random.shuffle(li) a_new_list.append(li) return np.array(a_new_list) def data_split(data, targets, train_size=None, test_size=None, shuffle=True, random_state=None): ''' 分离数据参数 ---- data：数据 targets：指标 train_size：浮点数类型，可选，训练集占总数据量的比，取值范围为(0, 1]，默认为0.75 test_size：浮点数类型，可选，测试集占总数据量的比，取值范围为[0, 1)，当train_size被定义时，该参数无效 shuffle：布尔类型，可选，True表示打乱数据，False表示不打乱数据，默认为True random_state：整型，可选，随机种子返回 ---- 元组，(数据测试集, 指标测试集, 数据验证集, 指标验证集) split the data Parameters ---------- data: data targets: targets train_size: float, callable, ratio of training set to total data, value range is (0, 1], default=0.75 test_size: float, callable, ratio of test set to total data, value range is [0, 1) shuffle: bool, callable, 'True' will shuffle the data, 'False' will not, default = True random_state: int, callable, random seed Return ------ tuple, (train_data, train_target, validation_data, validation_target) ''' data = np.array(data) targets = np.array(targets) if not (train_size or test_size): train_size = 0.75 elif test_size: train_size = 1 - test_size if train_size <= 0 or train_size > 1: raise Exception("'train_size' should be in (0, 1], 'test_size' should be in [0, 1)") if shuffle: np.random.seed(random_state) state = np.random.get_state() np.random.shuffle(data) np.random.set_state(state) np.random.shuffle(targets) num_of_data = len(data) train_data = data[:int(num_of_data train_size)] train_target = targets[:int(num_of_data * train_size)] validation_data = data[int(num_of_data * train_size):] validation_target = targets[int(num_of_data * train_size):] return train_data, train_target, validation_data, validation_target def kfold(data, targets, n, k=5): ''' 参数 ---- data：数据 targets：指标 n：整型，表示将第n折作为验证集，从0开始 k：整型，可选，k折验证的折叠数，默认k=5 返回 ---- 元组，(数据测试集, 指标测试集, 数据验证集, 指标验证集) Parameters ---------- data: data targets: targets n: int, take the nth part as validation set, starting from 0 k: int, callable, the number of k-fold, default = 5 Return ------ tuple, (train_data, train_target, validation_data, validation_target) ''' data = np.array(data) targets = np.array(targets) num_validation_samples = len(data) // k validation_data = data[num_validation_samples * n: num_validation_samples * (n + 1)] validation_targets = targets[num_validation_samples * n: num_validation_samples * (n + 1)] train_data = np.concatenate([data[: num_validation_samples * n], data[num_validation_samples * (n + 1):]]) train_targets = np.concatenate([targets[: num_validation_samples * n], targets[num_validation_samples * (n + 1):]]) return train_data, train_targets, validation_data, validation_targets def dataloader(data, targets, choose_rate=0.3, shuffle=True, random_state=None): ''' 数据随机生成器参数 ---- data：数据 targets：指标 choose_rate：浮点数类型，可选，生成率，即一次生成数据量在原数据量的占比，范围为[0, 1]，默认为0.3 shuffle：布尔类型，可选，True表示打乱数据，False表示不打乱数据，默认为True random_state：整型，可选，随机种子返回 ---- 生成器 Data Random Generator Parameters ---------- data: data targets: targets choose_rate: float, callable, generation rate (the proportion of data generated at one time in the original data) whose range is [0, 1], default=0.3 shuffle: bool, callable, 'True' will shuffle the data, 'False' will not, default = True random_state: int, callable, random seed Return ------ generator ''' data = np.array(data) targets = np.array(targets) if shuffle: np.random.seed(random_state) state = np.random.get_state() np.random.shuffle(data) np.random.set_state(state)	np.random.shuffle(targets)	numpy.random.shuffle
import tensorflow as tf import numpy as np import sys tf.logging.set_verbosity(tf.logging.ERROR) class Judge: def __init__(self, N_to_mask, model_dir, binary_rewards=True): self.N_to_mask = N_to_mask self.binary_rewards = binary_rewards # Create the Estimator try: self.estimator = tf.estimator.Estimator( model_fn=self.model_fn, model_dir=model_dir, # directory to restore model from and save model to ) except AttributeError: raise Exception("Subclass needs to define a model_fn") # Create the predictor from the present model. Important when restoring a model. self.update_predictor() def update_predictor(self): # Predictors are used to get predictions fast once the model has been trained. # We create it from an estimator. self.predictor = tf.contrib.predictor.from_estimator( self.estimator, # The serving input receiver fn is witchcraft, which I don't quite understand. # It's supposed to set up the data in a way that tensorflow can handle. tf.estimator.export.build_raw_serving_input_receiver_fn( # The input is a dictionary that corresponds to the data we feed the predictor. # Each key stores a tensor that is replaced by data when the predictor is used. {"masked_x": tf.placeholder(shape=[None, 28, 28, 2], dtype=tf.float32)} ), ) def mask_image_batch(self, image_batch): """ Takes a batch of two-dimensional images, reshapes them, runs them through mask_batch, reshapes them back to images, and returns them. """ shape = tf.shape(image_batch) batch_flat = tf.reshape(image_batch, (shape[0], shape[1] * shape[2])) mask_flat = self.mask_batch(batch_flat) return tf.reshape(mask_flat, (shape[0], shape[1], shape[2], 2)) def mask_batch(self, batch): """ Create mask for each feature-vector in a batch, that contains N_to_mask nonzero features of the input vector. Combine this with the vector to create the input for the DNN. """ shape = tf.shape(batch) n_zero = tf.random.categorical(logits=self.zero_logits,num_samples=1,dtype=tf.int32) p = tf.random_uniform(shape, 0, 1) p = tf.where(batch > 0, p, -p) # each number is positive if > 0, else negative _, nonzero_indices = tf.nn.top_k(p, self.N_to_mask - n_zero[0][0]) # sample positive _, zero_indices = tf.nn.top_k(-p, n_zero[0][0]) # sample negative indices = tf.concat([nonzero_indices,zero_indices],1) mask = tf.one_hot(indices, shape[1], axis=1) mask = tf.reduce_sum(mask, axis=2) return tf.stack((mask, mask * batch), 2) def train(self, n_steps, n_zero=0): # Train the model train_input_fn = tf.estimator.inputs.numpy_input_fn( x={"x": self.train_data}, y=self.train_labels, batch_size=self.batch_size, num_epochs=None, shuffle=True, ) if type(n_zero) != list: self.zero_logits = [[0 if i == n_zero else -np.inf for i in range(self.N_to_mask + 1)]] else: assert len(n_zero) == self.N_to_mask + 1 self.zero_logits = np.log(n_zero).reshape((1,-1)) self.estimator.train(input_fn=train_input_fn, steps=n_steps) # Replace the old predictor with one created from the new estimator self.update_predictor() def evaluate_accuracy(self, n_zero=0): # Evaluate the accuracy on all the eval_data eval_input_fn = tf.estimator.inputs.numpy_input_fn( x={"x": self.eval_data}, y=self.eval_labels, num_epochs=1, shuffle=False ) if type(n_zero) != list: self.zero_logits = [[0 if i == n_zero else -np.inf for i in range(self.N_to_mask + 1)]] else: assert len(n_zero) == self.N_to_mask + 1 self.zero_logits = np.log(n_zero).reshape((1,-1)) return self.estimator.evaluate(input_fn=eval_input_fn) def evaluate_accuracy_using_predictor(self): """ Evaluates the test set accuracy using the tensorflow predictor instead of the estimator. Can be useful for debugging. """ correct = 0 count = 0 for i in range(len(self.eval_labels)): # print(i) image = self.eval_data[i].flat mask = np.zeros_like(image) while mask.sum() < self.N_to_mask: a = np.random.randint(mask.shape[0]) if image[a] > 0: mask[a] = 1 input = np.stack((mask, image * mask), axis=1) input =	np.reshape(input, self.shape)	numpy.reshape
#!/usr/bin/env python """ Perform the population demonstration test in Section IIIB. This will generate Figures 8 and 9. For more details on the method see https://arxiv.org/abs/2106.13785. For more details on the analysis see https://arxiv.org/abs/1712.00688. """ import os import dill import matplotlib.pyplot as plt import numpy as np import pandas as pd from bilby.core.utils import create_frequency_series from bilby.gw.conversion import convert_to_lal_binary_black_hole_parameters from bilby.gw.detector import PowerSpectralDensity from bilby.gw.source import lal_binary_black_hole from bilby.gw.waveform_generator import WaveformGenerator from scipy.signal.windows import tukey from scipy.special import logsumexp from tqdm.auto import trange from coarse_psd_matrix.utils import ( compute_psd_matrix, fetch_psd_data, regularized_inversion, ) from matplotlib import rcParams rcParams["font.family"] = "serif" rcParams["font.serif"] = "Computer Modern Roman" rcParams["font.size"] = 20 rcParams["text.usetex"] = True rcParams["grid.alpha"] = 0 def run_tbs(signal_model, signal_parameter, outdir): sampling_frequency = 2048 duration = 128 data_duration = 32 short_duration = 4 low_frequency = 16 minimum_frequency = 20 maximum_frequency = 800 tukey_alpha = 0.1 label = f"{signal_model}_{signal_parameter}" data = fetch_psd_data( interferometer_name="L1", event="GW170814", outdir="GW170814", medium_duration=duration, sampling_frequency=sampling_frequency, tukey_alpha=tukey_alpha, duration=short_duration, low_frequency=low_frequency, ) psd = data["psd"] freqs_ = data["frequencies"] del data psd_ = PowerSpectralDensity.from_power_spectral_density_array( frequency_array=freqs_, psd_array=psd ) short_window = tukey(sampling_frequency * short_duration, tukey_alpha) long_frequencies = np.fft.fftfreq( sampling_frequency * data_duration, 1 / sampling_frequency ) long_psd = psd_.power_spectral_density_interpolated(abs(long_frequencies)) print("PSD matrix") data = dict(frequencies=freqs_, medium_psd=long_psd) data_file = f"{outdir}/GW170814_data_coarse_{data_duration}_{sampling_frequency}_{tukey_alpha}_L1.pkl" with open(data_file, "wb") as ff: dill.dump(data, ff) _svd = compute_psd_matrix( interferometer_name="L1", event="GW170814", duration=short_duration, sampling_frequency=sampling_frequency, low_frequency=low_frequency, tukey_alpha=tukey_alpha, minimum_frequency=minimum_frequency, maximum_frequency=maximum_frequency, medium_duration=data_duration, outdir=outdir, ) finite_psd = abs((_svd[0] * _svd[1]) @ _svd[2]).diagonal() regularization_method = "window" cutoff = 0.1 regularized_inverse = regularized_inversion(_svd, (regularization_method, cutoff)) SIGNAL_MODELS = dict(cbc=generate_cbc_signal, gaussian=generate_gaussian_signal) short_frequencies = np.fft.rfftfreq( short_duration * sampling_frequency, 1 / sampling_frequency ) mask = (short_frequencies >= minimum_frequency) & ( short_frequencies <= maximum_frequency ) np.save(f"{outdir}/frequencies.npy", short_frequencies[mask]) np.save(f"{outdir}/finite_psd.npy", finite_psd) signal = SIGNAL_MODELS[signal_model]( signal_parameter, sampling_frequency=sampling_frequency, duration=short_duration, ) np.save(f"{outdir}/signal_{label}", normalize_signal(signal=signal[mask], psd=finite_psd)) signal = np.fft.rfft(np.fft.irfft(signal) * short_window)[mask] signal = normalize_signal(signal=signal, psd=finite_psd) data_file = f"{outdir}/ln_bfs_{label}.hdf5" if os.path.isfile(data_file): data = pd.read_hdf(data_file) else: data = run_tbs_test( signal=signal, psd=psd_, sampling_frequency=sampling_frequency, duration=duration, short_duration=short_duration, short_psd=finite_psd, mask=mask, inverse=regularized_inverse, tukey_alpha=tukey_alpha, n_average=5000, ) data.to_hdf(f"{outdir}/ln_bfs_{label}.hdf5", key="bayes_factors") data.to_hdf(f"{outdir}/ln_bfs_{label}.hdf5", key="bayes_factors") fig = plot_tbs_bayes_factors(data) fig.savefig(f"{outdir}/ln_bfs_{label}.png") plt.close(fig) fig = plot_tbs_posterior(data) fig.savefig(f"{outdir}/xi_post_{label}.png", transparent=True) plt.close(fig) def generate_cbc_signal(mass, sampling_frequency, duration): waveform_arguments = dict( waveform_approximant="IMRPhenomXPHM", minimum_frequency=10.0, reference_frequency=20.0, maximum_frequency=1024.0, ) waveform_generator = WaveformGenerator( duration=duration, sampling_frequency=sampling_frequency, frequency_domain_source_model=lal_binary_black_hole, parameter_conversion=convert_to_lal_binary_black_hole_parameters, waveform_arguments=waveform_arguments, ) injection_parameters = dict( mass_1=mass, mass_2=mass, a_1=0.0, a_2=0.0, tilt_1=0.0, tilt_2=0.0, phi_12=0.0, phi_jl=0.0, luminosity_distance=2000.0, theta_jn=0.4, phase=0, ) signal = waveform_generator.frequency_domain_strain(injection_parameters)["plus"] signal = np.exp(1j 2 * np.pi * waveform_generator.frequency_array * 2) return signal def generate_gaussian_signal(peak_frequency, sampling_frequency, duration): frequencies = create_frequency_series( sampling_frequency=sampling_frequency, duration=duration ) signal = np.exp(-((frequencies - peak_frequency) 2) / 2 / 10 2) * np.exp( 1j * np.random.uniform(0, 2 * np.pi, len(frequencies)) ) return signal def normalize_signal(signal, psd, snr=4): signal /= np.sum(abs(signal) 2 / psd) 0.5 signal = snr * 0.5 return signal def run_tbs_test( signal, psd, sampling_frequency, duration, short_duration, mask, short_psd, inverse, tukey_alpha=0.1, n_average=50, ): short_window = tukey(sampling_frequency * short_duration, tukey_alpha) normalization = 2 / short_duration ln_bfs_1 = np.array([]) ln_bfs_2 = np.array([]) for _ in trange(n_average): noise, _ = psd.get_noise_realisation( sampling_frequency=sampling_frequency, duration=duration ) fd_noise = np.fft.rfft(	np.fft.irfft(noise)	numpy.fft.irfft
import numpy as np from typing import Tuple, Union, List import matplotlib.pyplot as plt class PPOReplayBuffer: def __init__(self, state_size, action_size, capacity, batch_size=64): self.state_size = state_size self.action_size = action_size self.capacity = capacity self.batch_size = batch_size self.size = 0 self.idx = 0 self._initialize_empty_buffers() def _initialize_empty_buffers(self) -> None: self.buffer_state = np.zeros(shape=(self.capacity, self.state_size)) self.buffer_action = np.zeros(shape=(self.capacity, self.action_size)) self.buffer_reward = np.zeros(shape=(self.capacity, 1)) self.buffer_mask = np.zeros(shape=(self.capacity, 1)) self.buffer_value = np.zeros(shape=(self.capacity, 1)) self.buffer_logp = np.zeros(shape=(self.capacity, 1)) self.buffer_adv = np.zeros(shape=(self.capacity, 1)) self.buffer_return = np.zeros(shape=(self.capacity, 1)) def store_transition(self, transition: Tuple) -> None: state, action, reward, mask, value, logp, adv, ret = transition # This will make sure to overwrite the oldest transition if full current_index = self.idx % self.capacity self.buffer_state[current_index] = state self.buffer_action[current_index] = action self.buffer_reward[current_index] = reward self.buffer_mask[current_index] = mask self.buffer_value[current_index] = value self.buffer_logp[current_index] = logp self.buffer_adv[current_index] = adv self.buffer_return[current_index] = ret # Increment counters if self.size < self.capacity: self.size += 1 self.idx += 1 def all(self) -> Union[None, Tuple]: # We can't sample if we don't have enough transitions if self.size < self.capacity: return return ( self.buffer_state, self.buffer_action, self.buffer_reward, self.buffer_mask, self.buffer_value, self.buffer_logp, self.buffer_adv, self.buffer_return ) def sample(self) -> Union[None, Tuple]: """ Returns a batch_size of random transitions from the buffer. If there are less than batch_size transitions in the buffer, this returns None. Note that sampling does not remove the transitions from the buffer so they could be sampled again. """ # We can't sample if we don't have enough transitions if self.size < self.capacity: return idxs = np.random.choice(self.size, self.batch_size) batch_state = self.buffer_state[idxs] batch_action = self.buffer_action[idxs] batch_reward = self.buffer_reward[idxs] batch_mask = self.buffer_mask[idxs] batch_value = self.buffer_value[idxs] batch_logp = self.buffer_logp[idxs] batch_adv = self.buffer_adv[idxs] batch_return = self.buffer_return[idxs] return (batch_state, batch_action, batch_reward, batch_mask, batch_value, batch_logp, batch_adv, batch_return) def flush(self) -> None: self.size = 0 self.idx = 0 self._initialize_empty_buffers() def __len__(self) -> int: return self.size def plot_training_results(rewards_history: List, running_rewards_history: List, steps_history: List, wallclock_history: List, test_freq: int = 1, save_dir: str = None): fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2, figsize=(12, 8)) fig.suptitle("Results", fontsize=16) # Epochs vs rewards num_epochs = len(rewards_history) ax1.plot(	np.arange(num_epochs)	numpy.arange
import pymbar from fe import endpoint_correction from collections import namedtuple import pickle import dataclasses import time import functools import copy import jax import numpy as np from md import minimizer from typing import Tuple, List, Any import os from fe import standard_state from fe.utils import sanitize_energies, extract_delta_Us_from_U_knk from timemachine.lib import potentials, custom_ops @dataclasses.dataclass class SimulationResult: xs: np.array boxes: np.array du_dps: np.array lambda_us: np.array def flatten(v): return tuple(), (v.xs, v.boxes, v.du_dps, v.lambda_us) def unflatten(aux_data, children): xs, boxes, du_dps, lambda_us = aux_data return SimulationResult(xs, boxes, du_dps, lambda_us) jax.tree_util.register_pytree_node(SimulationResult, flatten, unflatten) def run_model_simulations(model, sys_params): assert len(sys_params) == len(model.unbound_potentials) bound_potentials = [] for params, unbound_pot in zip(sys_params, model.unbound_potentials): bp = unbound_pot.bind(np.asarray(params)) bound_potentials.append(bp) all_args = [] for lamb_idx, lamb in enumerate(model.lambda_schedule): subsample_interval = 1000 all_args.append( ( lamb, model.box, model.x0, model.v0, bound_potentials, model.integrator, model.barostat, model.equil_steps, model.prod_steps, subsample_interval, subsample_interval, model.lambda_schedule, ) ) if model.endpoint_correct: assert isinstance(bound_potentials[-1], potentials.HarmonicBond) all_args.append( ( 1.0, model.box, model.x0, model.v0, bound_potentials[:-1], # strip out the restraints model.integrator, model.barostat, model.equil_steps, model.prod_steps, subsample_interval, subsample_interval, [], # no need to evaluate Us for the endpoint correction ) ) results = [] if model.client is None: for args in all_args: results.append(simulate(args)) else: futures = [] for args in all_args: futures.append(model.client.submit(simulate, args)) for future in futures: results.append(future.result()) return results def simulate( lamb, box, x0, v0, final_potentials, integrator, barostat, equil_steps, prod_steps, x_interval, u_interval, lambda_windows, ): """ Run a simulation and collect relevant statistics for this simulation. Parameters ---------- lamb: float lambda value used for the equilibrium simulation box: np.array 3x3 numpy array of the box, dtype should be np.float64 x0: np.array Nx3 numpy array of the coordinates v0: np.array Nx3 numpy array of the velocities final_potentials: list list of unbound potentials integrator: timemachine.Integrator integrator to be used for dynamics barostat: timemachine.Barostat barostat to be used for equilibration equil_steps: int number of equilibration steps prod_steps: int number of production steps x_interval: int how often we store coordinates. If x_interval == 0 then no frames are returned. u_interval: int how often we store energies. If u_interval == 0 then no energies are returned lambda_windows: list of float lambda windows we evaluate energies at. Returns ------- SimulationResult Results of the simulation. """ all_impls = [] # set up observables for du_dps here as well. du_dp_obs = [] for bp in final_potentials: impl = bp.bound_impl(np.float32) all_impls.append(impl) du_dp_obs.append(custom_ops.AvgPartialUPartialParam(impl, 25)) # fire minimize once again, needed for parameter interpolation x0 = minimizer.fire_minimize(x0, all_impls, box, np.ones(100, dtype=np.float64) * lamb) # sanity check that forces are well behaved for bp in all_impls: du_dx, du_dl, u = bp.execute(x0, box, lamb) norm_forces = np.linalg.norm(du_dx, axis=1) assert np.all(norm_forces < 25000), "Forces much greater than expected after minimization" if integrator.seed == 0: # this deepcopy is needed if we're running if client == None integrator = copy.deepcopy(integrator) integrator.seed = np.random.randint(np.iinfo(np.int32).max) if barostat.seed == 0: barostat = copy.deepcopy(barostat) barostat.seed = np.random.randint(np.iinfo(np.int32).max) intg_impl = integrator.impl() # technically we need to only pass in the nonbonded impl barostat_impl = barostat.impl(all_impls) # context components: positions, velocities, box, integrator, energy fxns ctxt = custom_ops.Context(x0, v0, box, intg_impl, all_impls, barostat_impl) # equilibration equil_schedule = np.ones(equil_steps) * lamb ctxt.multiple_steps(equil_schedule) # (ytz): intentionally hard-coded, I'd rather the end-user not # muck with this unless they have a good reason to. barostat_impl.set_interval(25) for obs in du_dp_obs: ctxt.add_observable(obs) full_us, xs, boxes = ctxt.multiple_steps_U(lamb, prod_steps, np.array(lambda_windows), u_interval, x_interval) # keep the structure of grads the same as that of final_potentials so we can properly # form their vjps. grads = [] for obs in du_dp_obs: grads.append(obs.avg_du_dp()) result = SimulationResult( xs=xs.astype("float32"), boxes=boxes.astype("float32"), du_dps=grads, lambda_us=full_us, ) return result FreeEnergyModel = namedtuple( "FreeEnergyModel", [ "unbound_potentials", "endpoint_correct", "client", "box", "x0", "v0", "integrator", "barostat", "lambda_schedule", "equil_steps", "prod_steps", "beta", "prefix", ], ) gradient = List[Any] # TODO: make this more descriptive of dG_grad structure def _deltaG_from_results(model, results, sys_params) -> Tuple[Tuple[float, List], np.array]: assert len(sys_params) == len(model.unbound_potentials) bound_potentials = [] for params, unbound_pot in zip(sys_params, model.unbound_potentials): bp = unbound_pot.bind(	np.asarray(params)	numpy.asarray
''' @file end_eff_lqr_gain_computation.py @package momentumopt @author <NAME> (<EMAIL>) @license License BSD-3-Clause @copyright Copyright (c) 2019, New York University and Max Planck Gesellschaft. @date 2019-06-05 Computes gains using lqr in the end_effector space for solo (assumes legs are weightless) and performs a backward pass to compute gains using a trajectory ''' ### ### ### Author: <NAME> ### Date:6/5/2019 import numpy as np from numpy.linalg import inv from matplotlib import pyplot as plt from scipy.spatial.transform import Rotation as Rot import scipy np.set_printoptions(linewidth=13000) class end_effector_lqr: def __init__(self, dir): self.dir = dir self.com_pos = np.loadtxt(dir + "/quadruped_com.dat", dtype=float)[:, [1,2,3]] self.com_vel = np.loadtxt(dir + "/quadruped_com_vel.dat", dtype=float)[:, [1,2,3]] self.com_ori = np.loadtxt(dir + "/quadruped_quaternion.dat", dtype=float)[:, [1,2,3,4]] self.com_ang_vel = np.loadtxt(dir + "/quadruped_base_ang_velocities.dat", dtype=float)[:, [1,2,3]] self.end_eff_forces = np.loadtxt(dir + "/quadruped_forces.dat", dtype=float)[:, 1:] self.end_eff_abs_pos = np.loadtxt(dir + "/quadruped_positions_abs_with_horizon_part.dat", dtype=float)[:, 1:] self.delta = 0.000001 self.dt = 0.001 self.mass = 2.17 self.inertia_com_frame = [[0.00578574, 0.0, 0.0], [0.0, 0.01938108, 0.0], [0.0, 0.0, 0.02476124]] def compute_r_cross(self, end_eff_abs_pos, com_pos): r_cross_mat = [[0, -(end_eff_abs_pos[2] - com_pos[2]), (end_eff_abs_pos[1] - com_pos[1])], [(end_eff_abs_pos[2] - com_pos[2]), 0, -(end_eff_abs_pos[0] - com_pos[0])], [-(end_eff_abs_pos[1] - com_pos[1]), -(end_eff_abs_pos[0] - com_pos[0]), 0]] return r_cross_mat def compute_dyn(self,t , x_t, u_t): ### quat_d = omega * quat omega = np.array([[0, x_t[: , 12], -1x_t[:, 11], x_t[:, 10]], [-1x_t[:,12], 0, x_t[:,10], x_t[:, 11]], [x_t[:,11], -1x_t[:,10], 0, x_t[:,12]], [-1x_t[:, 10], -1x_t[:, 11], -1x_t[:,12], 0]]) self.A_t = np.block([[np.zeros((3,3)), np.identity(3), np.zeros((3,4)), np.zeros((3,3))], [np.zeros((3,3)), np.zeros((3,3)), np.zeros((3,4)), np.zeros((3,3))], [np.zeros((4,3)),np.zeros((4,3)), 0.5omega, np.zeros((4,3))], [np.zeros((3,3)), np.zeros((3,3)), np.zeros((3,4)), np.zeros((3,3))]]) rot_t = np.reshape(Rot.from_quat(x_t[:, [6,7,8,9]]).as_dcm(), (3,3)) inertia = np.matmul(np.matmul(np.transpose(rot_t),self.inertia_com_frame), rot_t) inv_inertia = inv(np.matrix(inertia)) r_cross_inv_inertia_fl = np.matmul(inv_inertia, self.compute_r_cross(self.end_eff_abs_pos[t][0:3], self.com_pos[t])) r_cross_inv_inertia_fr = np.matmul(inv_inertia, self.compute_r_cross(self.end_eff_abs_pos[t][3:6], self.com_pos[t])) r_cross_inv_inertia_hl = np.matmul(inv_inertia, self.compute_r_cross(self.end_eff_abs_pos[t][6:9], self.com_pos[t])) r_cross_inv_inertia_hr = np.matmul(inv_inertia, self.compute_r_cross(self.end_eff_abs_pos[t][9:12], self.com_pos[t])) self.B_t = np.block([[np.zeros((3,3)), np.zeros((3,3)),np.zeros((3,3)), np.zeros((3,3))], [(1/self.mass)np.identity(3), (1/self.mass)np.identity(3), (1/self.mass)np.identity(3), (1/self.mass)np.identity(3)], [np.zeros((4,3)), np.zeros((4,3)), np.zeros((4,3)), np.zeros((4,3))], [r_cross_inv_inertia_fl, r_cross_inv_inertia_fr, r_cross_inv_inertia_hl, r_cross_inv_inertia_hr]]) self.A_t = np.matrix(self.A_t) self.B_t = np.matrix(self.B_t) return np.matmul(self.A_t, np.transpose(x_t)) + np.matmul(self.B_t, np.transpose(u_t)) def compute_lin_dyn(self,t): ### computes linearized dymamics x_t = np.matrix(np.hstack((self.com_pos[t], self.com_vel[t], self.com_ori[t], self.com_ang_vel[t]))) u_t = np.matrix(self.end_eff_forces[t]) dyn_t = self.compute_dyn(t, x_t, u_t) # print(dyn_t) # partial derivative of a w.r.t x x_t1 = np.matrix(np.hstack((self.com_pos[t+1], self.com_vel[t+1], self.com_ori[t+1], self.com_ang_vel[t+1]))) u_t1 = np.matrix(self.end_eff_forces[t+1]) lin_A_t = np.zeros((13,13)) for i in range(13): pd_x_t = x_t.copy() delta_x = x_t1[: ,i].copy() - x_t[: ,i].copy() pd_x_t[: ,i] = x_t1[: ,i].copy() if delta_x == 0.0: delta_x = self.delta pd_x_t[:, i] += self.delta lin_A_t[:, i] = np.reshape(((self.compute_dyn(t, pd_x_t, u_t) - dyn_t.copy())/(delta_x)), (13,)) lin_B_t = np.zeros((13,12)) if np.linalg.norm(sum(u_t1)) < 0.001: lin_B_t = np.zeros((13,12)) else: for i in range(12): pd_u_t = u_t.copy() delta_u = u_t1[: ,i].copy() - u_t[:, i].copy() pd_u_t[: ,i] = u_t1[:, i].copy() if delta_u == 0: delta_u = self.delta pd_u_t[:, i] += self.delta lin_B_t[:, i] = np.reshape(((self.compute_dyn(t, x_t, pd_u_t) - dyn_t.copy())/(delta_u)), (13,)) return lin_A_t, lin_B_t def descretise_dynamics(self, lin_A_t, lin_B_t): ## descritizes the dynamics adn returns descritized lin_A, lin_B_t des_lin_A_t = lin_A_tself.dt + np.identity(13) des_lin_B_t = lin_B_t*self.dt # print(des_lin_A_t) return des_lin_A_t, des_lin_B_t def compute_lqr_gains(self, Q, R, lin_A_t, lin_B_t, P_prev): ## input descritzed lin_A and lin_B ## solves ricati equation # print(lin_B_t) K = inv(R + np.matmul(np.matmul(	np.transpose(lin_B_t)	numpy.transpose
import argparse import pandas as pd import os import sys import numpy as np import torch from utils import computeMetricsAlt, evalThresholdAlt from ModelShokri import DataHandler, TrainWBAttacker from torch.utils.data import DataLoader parser = argparse.ArgumentParser(description='Analyse criteria obtained from different MIAs.') parser.add_argument('--model_type', type=str, help='Model Architecture to attack.') parser.add_argument('--num_iters', type=int, default=20, help='Number of iterations for empirical estimation.') parser.add_argument('--working_dir', type=str, default='./', help='Where to collect and store data.') exp_parameters = parser.parse_args() currdir = exp_parameters.working_dir num_runs_for_random = exp_parameters.num_iters model_type = exp_parameters.model_type # Extracting intermediate outputs and gradients of the model InterOuts_Grads0 = np.load(currdir + '/RawResults/NasrTrain0_' + model_type + '.npz') InterOuts_Grads1 = np.load(currdir + '/RawResults/NasrTrain1_' + model_type + '.npz') AdditionalInfo = np.load(currdir + '/RawResults/NasrAddInfo_' + model_type + '.npz') inter_outs0 = [] inter_outs1 = [] out_size_list = AdditionalInfo['arr_0'] layer_size_list = AdditionalInfo['arr_1'] kernel_size_list = AdditionalInfo['arr_2'] n_inter_outputs = len(out_size_list) n_layer_grads = len(kernel_size_list) for i in range(n_inter_outputs): inter_outs0.append(InterOuts_Grads0['arr_' + str(i)]) inter_outs1.append(InterOuts_Grads1['arr_' + str(i)]) lossval0 = InterOuts_Grads0['arr_' + str(n_inter_outputs)] lossval1 = InterOuts_Grads1['arr_' + str(n_inter_outputs)] labels1hot0 = InterOuts_Grads0['arr_' + str(n_inter_outputs + 1)] labels1hot1 = InterOuts_Grads1['arr_' + str(n_inter_outputs + 1)] grad_vals0 = [] grad_vals1 = [] for i in range(n_inter_outputs + 2, n_inter_outputs + 2 + n_layer_grads, 1): grad_vals0.append(InterOuts_Grads0['arr_' + str(i)]) grad_vals1.append(InterOuts_Grads1['arr_' + str(i)]) # Our Analysis FPR = np.linspace(0, 1, num=1001) try: dfMetricsBalanced = pd.read_csv(currdir + '/CompleteResults/BalancedMetrics_' + model_type + '.csv') dfTPRBalanced = pd.read_csv(currdir + '/CompleteResults/BalancedROC_' + model_type + '.csv') except FileNotFoundError: dfMetricsBalanced = pd.DataFrame(columns=['Attack Strategy', 'AUROC', 'AUROC STD', 'Best Accuracy', 'Best Accuracy STD', 'FPR at TPR80', 'FPR at TPR80 STD', 'FPR at TPR85', 'FPR at TPR85 STD', 'FPR at TPR90', 'FPR at TPR90 STD', 'FPR at TPR95', 'FPR at TPR95 STD']) dfTPRBalanced = pd.DataFrame(FPR, columns=['FPR']) aux_list_metrics = [] aux_list_TPR = [] for k in range(num_runs_for_random): np.random.seed(k) indx_train0 = np.random.choice(lossval0.shape[0], size=4000, replace=False) indx_train1 = np.random.choice(lossval1.shape[0], size=4000, replace=False) indx_test0 = np.setdiff1d(np.arange(lossval0.shape[0]), indx_train0) indx_test0 = np.random.choice(indx_test0, size=6000, replace=False) indx_test1 = np.setdiff1d(np.arange(lossval1.shape[0]), indx_train1) indx_test1 = np.random.choice(indx_test1, size=6000, replace=False) trainingData = DataHandler(inter_outs0, inter_outs1, lossval0, lossval1, labels1hot0, labels1hot1, grad_vals0, grad_vals1, indx_train0, indx_train1) Max = trainingData.Max Min = trainingData.Min testingData = DataHandler(inter_outs0, inter_outs1, lossval0, lossval1, labels1hot0, labels1hot1, grad_vals0, grad_vals1, indx_test0, indx_test1, Max=Max, Min=Min) AttackerShokri = TrainWBAttacker(trainingData, testingData, out_size_list, layer_size_list, kernel_size_list) dataloaderEval = DataLoader(testingData, batch_size=100, shuffle=False) scoresEval = [] EvalY = [] with torch.no_grad(): for i, batch in enumerate(dataloaderEval): example = batch[0] target = batch[1] scoresEval.append(AttackerShokri(*example).detach()) EvalY.append(target.cpu().data.numpy()) scoresEval = torch.cat(scoresEval, axis=0) scoresEval = torch.squeeze(scoresEval) scoresEval = scoresEval.cpu().data.numpy() EvalY = np.squeeze(np.concatenate(EvalY, axis=0)) TPR_, metrics_ = computeMetricsAlt(scoresEval, EvalY, FPR) aux_list_metrics.append(metrics_) aux_list_TPR.append(TPR_) metrics = np.stack(aux_list_metrics, 1) mean_metrics = np.mean(metrics, 1) std_metrics = np.std(metrics, 1) new_row = {"Attack Strategy": 'Nasr White-Box', 'AUROC': mean_metrics[0], 'AUROC STD': std_metrics[0], 'Best Accuracy': mean_metrics[1], 'Best Accuracy STD': std_metrics[1], 'FPR at TPR80': mean_metrics[2], 'FPR at TPR80 STD': std_metrics[2], 'FPR at TPR85': mean_metrics[3], 'FPR at TPR85 STD': std_metrics[3], 'FPR at TPR90': mean_metrics[4], 'FPR at TPR90 STD': std_metrics[4], 'FPR at TPR95': mean_metrics[5], 'FPR at TPR95 STD': std_metrics[5]} dfMetricsBalanced = dfMetricsBalanced.append(new_row, ignore_index=True) TPR = np.stack(aux_list_TPR, 1) mean_TPR = np.mean(TPR, 1) std_TPR = np.std(TPR, 1) dfTPRaux = pd.DataFrame(np.stack((mean_TPR, std_TPR), axis=1), columns=['Nasr White-Box TPR', 'Nasr White-Box TPR STD']) dfTPRBalanced = dfTPRBalanced.join(dfTPRaux) # Rezaei Analysis try: dfMetricsRezaei = pd.read_csv(currdir + '/CompleteResults/RezaeiMetrics_' + model_type + '.csv') except FileNotFoundError: dfMetricsRezaei = pd.DataFrame(columns=['Attack Strategy', 'Best Accuracy', 'Best Accuracy STD', 'FPR', 'FPR STD']) aux_list_metrics = [] for k in range(num_runs_for_random): np.random.seed(k) indx_train0 =	np.random.choice(lossval0.shape[0], size=8000, replace=False)	numpy.random.choice
""" Numpy是python很多科学计算与工程库的基础库，在量化数据分析中最常使用的Pandas 也是基于Numpy的封装。可以说Numpy就是量化数据分析领域中的基础数组，学会使用Numpy 是量化分析中关键的一步 Numpy底层实现中使用了C语言和Fortran语言的机制分配内存。可以理解为它的输出是一个非常大且联系的并且由同类型数据组成的内存区域，所以可以通过Numpy来构造一个比普通列表大的多的数组，并且灵活高效地对数组中所有的元素进行并行化操作 """ import timeit import time import numpy as np import matplotlib.pyplot as plt """ 使用timeit模块来计算构建10000个元素的列表循环求每个元素的平方所用的时间 timeit模块使用方法 timeit(stmt,number) stmt可以直接传简单的字符串表达式，也可以传变量，也可以传函数，接受匿名函数输入 """ '#######################################################################################################################' #1、使用普通方法构造列表 func1 = """ for i in range(10000): i2 """ print(timeit.timeit(stmt=func1,number=1)) #结果：0.003410174186735481 """ 或者在jupyternotebook中执行 normal_list = range(10000) %timeit [i2 for i in normal_list] 得到的时间为： 3.67 ms ± 67.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each) """ #2、使用numpy的arange模块来构造列表 """ 在jupyternotebook中执行下面代码， np_list = np.arange(10000) %timeit (np_list*2) 得到的时间为： 9.22 µs ± 24 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each) 可以看到使用numpy数组的速度远快于使用普通列表的速度 Numpy数组和普通列表的操作方式也是不同的，Numpy通过广播机制作用于每一个内部元素，是一种并行化执行的思想，普通list则作用于整体，示例如下： """ #注意：在numpy中3的操作被作用于数组的每一个元素中 np_list = np.ones(5) * 3 print(np_list) # [3. 3. 3. 3. 3.] #普通列表则把3操作认为是整体性操作 normal_list = [1,1,1,1,1] 3 print(normal_list) # <class 'list'>: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] print(len(normal_list)) # 15 '#######################################################################################################################' #numpy的初始化操作 """ 一些numpy常用的初始化方式 """ #1、100个0 np.zeros(100) # array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., # 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., # 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., # 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., # 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., # 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]) #2、shape: 3行2列全是0	np.zeros((3,2))	numpy.zeros
#!/usr/bin/env python # vim: tabstop=2 shiftwidth=2 expandtab # Copyright 2020 Maintainers of PSegs-ROS-Ext # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. import collections import os import random import subprocess import sys import numpy as np ############################################################################### ### Utils def nanostamp_to_rostime(nanostamp): import rospy # For a good time see: # https://github.com/pgao/roscpp_core/commit/dffa31afe8d7f1268a3fa227408aeb6e04a28b87#diff-65b9485bd6b5d3fb4b7a84cd975c3967L157 return rospy.Time( secs=int(nanostamp / 1000000000), nsecs=int(nanostamp % 1000000000)) def to_ros_arr(arr): return arr.flatten(order='C').tolist() ############################################################################### ### ROS Message Generators def gen_transform(nanostamp): import tf from tf2_msgs.msg import TFMessage from geometry_msgs.msg import Transform from geometry_msgs.msg import TransformStamped tf_msg = TFMessage() tf_transform = TransformStamped() tf_transform.header.stamp = nanostamp_to_rostime(nanostamp) tf_transform.header.frame_id = 'src_frame' tf_transform.child_frame_id = 'child_frame' transform = Transform() r_4x4 = np.ones((4, 4)) q = tf.transformations.quaternion_from_matrix(r_4x4) transform.rotation.x = q[0] transform.rotation.y = q[1] transform.rotation.z = q[2] transform.rotation.w = q[3] transform.translation.x = 1 transform.translation.y = 2 transform.translation.z = 3 tf_transform.transform = transform tf_msg.transforms.append(tf_transform) return tf_msg def gen_camera_info(nanostamp): from sensor_msgs.msg import CameraInfo info = CameraInfo() info.header.frame_id = 'camera_frame' info.header.stamp = nanostamp_to_rostime(nanostamp) info.width = 100 info.height = 200 info.distortion_model = 'plumb_bob' K = np.ones((3, 3)) info.K = to_ros_arr(K) P = np.zeros((3, 4)) info.P = to_ros_arr(P) return info def gen_camera_image(nanostamp): import cv2 from cv_bridge import CvBridge bridge = CvBridge() # Create a fake image img = np.zeros((200, 100, 3), dtype=np.uint8) from PIL import Image p_img = Image.fromarray(img) from io import BytesIO with BytesIO() as output: p_img.save(output, 'PNG') img_bytes = bytearray(output.getvalue()) # Do a dance to get a CV Img, which has good interop with ROS img_arr = np.asarray(img_bytes, dtype=np.uint8) cv_img = cv2.imdecode(img_arr, cv2.IMREAD_UNCHANGED) ros_img_msg = bridge.cv2_to_imgmsg(cv_img, encoding='bgr8') ros_img_msg.header.frame_id = 'camera_frame' ros_img_msg.header.stamp = nanostamp_to_rostime(nanostamp) return ros_img_msg def gen_pcl_cloud(nanostamp): from sensor_msgs.msg import PointField from std_msgs.msg import Header import sensor_msgs.point_cloud2 as pcl2 header = Header() header.frame_id = 'pointsensor' header.stamp = nanostamp_to_rostime(nanostamp) points = np.zeros((10, 3), dtype=np.float32) fields = [PointField('x', 0, PointField.FLOAT32, 1), PointField('y', 4, PointField.FLOAT32, 1), PointField('z', 8, PointField.FLOAT32, 1)] pcl_msg = pcl2.create_cloud(header, fields, points) return pcl_msg def gen_ros_color(): """color in [0, 1] -> ROS color""" from std_msgs.msg import ColorRGBA r, g, b = (.5, .5, .5) ros_color = ColorRGBA() ros_color.r = r ros_color.g = g ros_color.b = b ros_color.a = 1. return ros_color def gen_marker(): from geometry_msgs.msg import Point from visualization_msgs.msg import Marker m = Marker() m.type = Marker.LINE_LIST # pairs of points create a line m.action = Marker.MODIFY # or add m.color = gen_ros_color() m.scale.x = 0.1 startp = Point() startp.x, startp.y, startp.z = (1, 2, 3) endp = Point() endp.x, endp.y, endp.z = (3, 4, 5) m.points += [startp, endp] return m def gen_marker_array(nanostamp): from visualization_msgs.msg import MarkerArray marray = MarkerArray() for obj_id in range(10): from std_msgs.msg import Header header = Header() header.frame_id = 'marker' header.stamp = nanostamp_to_rostime(nanostamp) markers = [gen_marker() for _ in range(10)] for mid, m in enumerate(markers): m.id = obj_id * 10 + mid m.ns = str(obj_id) m.header = header marray.markers += markers return marray # A container compatible with both ROSBag as well as ROS Publishers ROSMsgEntry = collections.namedtuple( 'ROSMsgEntry', ('topic', 'timestamp', 'msg')) def gen_msg_fixture(start_time_sec=1, end_time_sec=10): for t in	np.arange(start_time_sec, end_time_sec + 1, 0.5)	numpy.arange
import os import numpy import pytest from chainer import serializers, Variable, cuda from chainer_chemistry.links.scaler.standard_scaler import StandardScaler @pytest.fixture def data(): x = numpy.array( [[0.1, 10., 0.3], [0.2, 20., 0.1], [0.3, 30., 0.], [0.4, 40., 0.]], dtype=numpy.float32) expect_x_scaled = numpy.array( [[-1.3416407, -1.3416408, 1.6329931], [-0.44721353, -0.4472136, 0.], [0.44721368, 0.4472136, -0.8164965], [1.3416407, 1.3416408, -0.8164965]], dtype=numpy.float32) return x, expect_x_scaled @pytest.mark.parametrize('indices', [None, [0], [1, 2]]) def test_standard_scaler_transform(data, indices): x, expect_x_scaled = data scaler = StandardScaler() scaler.fit(x, indices=indices) x_scaled = scaler.transform(x) if indices is None: indices = numpy.arange(x.shape[1]) for index in range(x.shape[1]): if index in indices: assert numpy.allclose(x_scaled[:, index], expect_x_scaled[:, index]) else: assert numpy.allclose(x_scaled[:, index], x[:, index]) def test_standard_scaler_transform_variable(data): x, expect_x_scaled = data xvar = Variable(x) scaler = StandardScaler() scaler.fit(xvar) x_scaled = scaler.transform(xvar) assert isinstance(x_scaled, Variable) assert numpy.allclose(x_scaled.array, expect_x_scaled) @pytest.mark.gpu def test_standard_scaler_transform_gpu(data): x, expect_x_scaled = data scaler = StandardScaler() scaler.to_gpu() x = cuda.to_gpu(x) scaler.fit(x) x_scaled = scaler.transform(x) assert isinstance(x_scaled, cuda.cupy.ndarray) assert numpy.allclose(cuda.to_cpu(x_scaled), expect_x_scaled) @pytest.mark.parametrize('indices', [None, [0], [1, 2]]) def test_standard_scaler_inverse_transform(data, indices): x, expect_x_scaled = data scaler = StandardScaler() scaler.fit(x, indices=indices) x_inverse = scaler.inverse_transform(expect_x_scaled) if indices is None: indices = numpy.arange(x.shape[1]) for index in range(x.shape[1]): if index in indices: assert numpy.allclose(x_inverse[:, index], x[:, index]) else: assert numpy.allclose(x_inverse[:, index], expect_x_scaled[:, index]) def test_standard_scaler_fit_transform(data): x, expect_x_scaled = data scaler = StandardScaler() x_scaled = scaler.fit_transform(x) assert numpy.allclose(x_scaled, expect_x_scaled) @pytest.mark.parametrize('indices', [None, [0]]) def test_standard_scaler_serialize(tmpdir, data, indices): x, expect_x_scaled = data scaler = StandardScaler() scaler.fit(x, indices=indices) scaler_filepath = os.path.join(str(tmpdir), 'scaler.npz') serializers.save_npz(scaler_filepath, scaler) scaler2 = StandardScaler() serializers.load_npz(scaler_filepath, scaler2) # print('scaler2 attribs:', scaler2.mean, scaler2.std, scaler2.indices) assert numpy.allclose(scaler.mean, scaler2.mean) assert	numpy.allclose(scaler.std, scaler2.std)	numpy.allclose
import argparse import os import multiprocessing from multiprocessing import Process, Queue, Array import pickle import gym from gym.spaces import Box, Discrete from keras.models import Model from keras.layers import Input, TimeDistributed, Convolution2D, Flatten, LSTM, Dense from keras.objectives import categorical_crossentropy from keras.optimizers import Adam from keras.utils import np_utils import keras.backend as K import numpy as np from atari_utils import RandomizedResetEnv, AtariRescale42x42Env def create_env(env_id): env = gym.make(env_id) env = RandomizedResetEnv(env) env = AtariRescale42x42Env(env) return env def create_model(env, batch_size, num_steps): # network inputs are observations and advantages h = x = Input(batch_shape=(batch_size, num_steps) + env.observation_space.shape, name="x") A = Input(batch_shape=(batch_size, num_steps), name="A") # convolutional layers h = TimeDistributed(Convolution2D(32, 3, 3, subsample=(2, 2), border_mode="same", activation='elu', dim_ordering='tf'), name='c1')(h) h = TimeDistributed(Convolution2D(32, 3, 3, subsample=(2, 2), border_mode="same", activation='elu', dim_ordering='tf'), name='c2')(h) h = TimeDistributed(Convolution2D(32, 3, 3, subsample=(2, 2), border_mode="same", activation='elu', dim_ordering='tf'), name='c3')(h) h = TimeDistributed(Convolution2D(64, 3, 3, subsample=(2, 2), border_mode="same", activation='elu', dim_ordering='tf'), name='c4')(h) h = TimeDistributed(Flatten(), name="fl")(h) # recurrent layer h = LSTM(32, return_sequences=True, stateful=True, name="r1")(h) # policy network p = TimeDistributed(Dense(env.action_space.n, activation='softmax'), name="p")(h) # baseline network b = TimeDistributed(Dense(1), name="b")(h) # inputs to the model are observation and advantages, # outputs are action probabilities and baseline model = Model(input=[x, A], output=[p, b]) # policy gradient loss and entropy bonus def policy_gradient_loss(l_sampled, l_predicted): return K.mean(A * categorical_crossentropy(l_sampled, l_predicted), axis=1) \ - 0.01 * K.mean(categorical_crossentropy(l_predicted, l_predicted), axis=1) # baseline is optimized with MSE model.compile(optimizer='adam', loss=[policy_gradient_loss, 'mse']) return model def predict(model, observation): # create inputs for batch (and timestep) of size 1 x = np.array([[observation]]) A = np.zeros((1, 1)) # dummy advantage # predict action probabilities (and baseline state value) p, b = model.predict_on_batch([x, A]) # return action probabilities and baseline return p[0, 0], b[0, 0, 0] def discount(rewards, terminals, v, gamma): # calculate discounted future rewards for this trajectory returns = [] # start with the predicted value of the last state R = v for r, t in zip(reversed(rewards), reversed(terminals)): # if it was terminal state then restart from 0 if t: R = 0 R = r + R * gamma returns.insert(0, R) return returns def runner(shared_buffer, fifo, num_timesteps, monitor, args): proc_name = multiprocessing.current_process().name print("Runner %s started" % proc_name) # local environment for runner env = create_env(args.env_id) # start monitor to record statistics and videos if monitor: env.monitor.start(args.env_id) # copy of model model = create_model(env, batch_size=1, num_steps=1) # record episode lengths and rewards for statistics episode_rewards = [] episode_lengths = [] episode_reward = 0 episode_length = 0 observation = env.reset() for i in range(num_timesteps // args.num_local_steps): # copy weights from main network at the beginning of iteration # the main network's weights are only read, never modified # but we create our own model instance, because Keras is not thread-safe model.set_weights(pickle.loads(shared_buffer.raw)) observations = [] actions = [] rewards = [] terminals = [] baselines = [] for t in range(args.num_local_steps): if args.display: env.render() # predict action probabilities (and baseline state value) p, b = predict(model, observation) # sample action using those probabilities p /= np.sum(p) # ensure p-s sum up to 1 action =	np.random.choice(env.action_space.n, p=p)	numpy.random.choice
# This module has been generated automatically from space group information # obtained from the Computational Crystallography Toolbox # """ Space groups This module contains a list of all the 230 space groups that can occur in a crystal. The variable space_groups contains a dictionary that maps space group numbers and space group names to the corresponding space group objects. .. moduleauthor:: <NAME> <<EMAIL>> """ #----------------------------------------------------------------------------- # Copyright (C) 2013 The Mosaic Development Team # # Distributed under the terms of the BSD License. The full license is in # the file LICENSE.txt, distributed as part of this software. #----------------------------------------------------------------------------- import numpy as N class SpaceGroup(object): """ Space group All possible space group objects are created in this module. Other modules should access these objects through the dictionary space_groups rather than create their own space group objects. """ def __init__(self, number, symbol, transformations): """ :param number: the number assigned to the space group by international convention :type number: int :param symbol: the Hermann-Mauguin space-group symbol as used in PDB and mmCIF files :type symbol: str :param transformations: a list of space group transformations, each consisting of a tuple of three integer arrays (rot, tn, td), where rot is the rotation matrix and tn/td are the numerator and denominator of the translation vector. The transformations are defined in fractional coordinates. :type transformations: list """ self.number = number self.symbol = symbol self.transformations = transformations self.transposed_rotations = N.array([N.transpose(t[0]) for t in transformations]) self.phase_factors = N.exp(N.array([(-2jN.pit[1])/t[2] for t in transformations])) def __repr__(self): return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol)) def __len__(self): """ :return: the number of space group transformations :rtype: int """ return len(self.transformations) def symmetryEquivalentMillerIndices(self, hkl): """ :param hkl: a set of Miller indices :type hkl: Scientific.N.array_type :return: a tuple (miller_indices, phase_factor) of two arrays of length equal to the number of space group transformations. miller_indices contains the Miller indices of each reflection equivalent by symmetry to the reflection hkl (including hkl itself as the first element). phase_factor contains the phase factors that must be applied to the structure factor of reflection hkl to obtain the structure factor of the symmetry equivalent reflection. :rtype: tuple """ hkls = N.dot(self.transposed_rotations, hkl) p = N.multiply.reduce(self.phase_factors**hkl, -1) return hkls, p space_groups = {} transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(1, 'P 1', transformations) space_groups[1] = sg space_groups['P 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(2, 'P -1', transformations) space_groups[2] = sg space_groups['P -1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(3, 'P 1 2 1', transformations) space_groups[3] = sg space_groups['P 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(4, 'P 1 21 1', transformations) space_groups[4] = sg space_groups['P 1 21 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(5, 'C 1 2 1', transformations) space_groups[5] = sg space_groups['C 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(6, 'P 1 m 1', transformations) space_groups[6] = sg space_groups['P 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(7, 'P 1 c 1', transformations) space_groups[7] = sg space_groups['P 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(8, 'C 1 m 1', transformations) space_groups[8] = sg space_groups['C 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(9, 'C 1 c 1', transformations) space_groups[9] = sg space_groups['C 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(10, 'P 1 2/m 1', transformations) space_groups[10] = sg space_groups['P 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(11, 'P 1 21/m 1', transformations) space_groups[11] = sg space_groups['P 1 21/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(12, 'C 1 2/m 1', transformations) space_groups[12] = sg space_groups['C 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(13, 'P 1 2/c 1', transformations) space_groups[13] = sg space_groups['P 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(14, 'P 1 21/c 1', transformations) space_groups[14] = sg space_groups['P 1 21/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(15, 'C 1 2/c 1', transformations) space_groups[15] = sg space_groups['C 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(16, 'P 2 2 2', transformations) space_groups[16] = sg space_groups['P 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(17, 'P 2 2 21', transformations) space_groups[17] = sg space_groups['P 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(18, 'P 21 21 2', transformations) space_groups[18] = sg space_groups['P 21 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(19, 'P 21 21 21', transformations) space_groups[19] = sg space_groups['P 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(20, 'C 2 2 21', transformations) space_groups[20] = sg space_groups['C 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(21, 'C 2 2 2', transformations) space_groups[21] = sg space_groups['C 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(22, 'F 2 2 2', transformations) space_groups[22] = sg space_groups['F 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(23, 'I 2 2 2', transformations) space_groups[23] = sg space_groups['I 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(24, 'I 21 21 21', transformations) space_groups[24] = sg space_groups['I 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(25, 'P m m 2', transformations) space_groups[25] = sg space_groups['P m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(26, 'P m c 21', transformations) space_groups[26] = sg space_groups['P m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(27, 'P c c 2', transformations) space_groups[27] = sg space_groups['P c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(28, 'P m a 2', transformations) space_groups[28] = sg space_groups['P m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(29, 'P c a 21', transformations) space_groups[29] = sg space_groups['P c a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(30, 'P n c 2', transformations) space_groups[30] = sg space_groups['P n c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(31, 'P m n 21', transformations) space_groups[31] = sg space_groups['P m n 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(32, 'P b a 2', transformations) space_groups[32] = sg space_groups['P b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(33, 'P n a 21', transformations) space_groups[33] = sg space_groups['P n a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(34, 'P n n 2', transformations) space_groups[34] = sg space_groups['P n n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(35, 'C m m 2', transformations) space_groups[35] = sg space_groups['C m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(36, 'C m c 21', transformations) space_groups[36] = sg space_groups['C m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(37, 'C c c 2', transformations) space_groups[37] = sg space_groups['C c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(38, 'A m m 2', transformations) space_groups[38] = sg space_groups['A m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(39, 'A b m 2', transformations) space_groups[39] = sg space_groups['A b m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(40, 'A m a 2', transformations) space_groups[40] = sg space_groups['A m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(41, 'A b a 2', transformations) space_groups[41] = sg space_groups['A b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(42, 'F m m 2', transformations) space_groups[42] = sg space_groups['F m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(43, 'F d d 2', transformations) space_groups[43] = sg space_groups['F d d 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(44, 'I m m 2', transformations) space_groups[44] = sg space_groups['I m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(45, 'I b a 2', transformations) space_groups[45] = sg space_groups['I b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(46, 'I m a 2', transformations) space_groups[46] = sg space_groups['I m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(47, 'P m m m', transformations) space_groups[47] = sg space_groups['P m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(48, 'P n n n :2', transformations) space_groups[48] = sg space_groups['P n n n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(49, 'P c c m', transformations) space_groups[49] = sg space_groups['P c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(50, 'P b a n :2', transformations) space_groups[50] = sg space_groups['P b a n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(51, 'P m m a', transformations) space_groups[51] = sg space_groups['P m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(52, 'P n n a', transformations) space_groups[52] = sg space_groups['P n n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(53, 'P m n a', transformations) space_groups[53] = sg space_groups['P m n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(54, 'P c c a', transformations) space_groups[54] = sg space_groups['P c c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(55, 'P b a m', transformations) space_groups[55] = sg space_groups['P b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(56, 'P c c n', transformations) space_groups[56] = sg space_groups['P c c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(57, 'P b c m', transformations) space_groups[57] = sg space_groups['P b c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(58, 'P n n m', transformations) space_groups[58] = sg space_groups['P n n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(59, 'P m m n :2', transformations) space_groups[59] = sg space_groups['P m m n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(60, 'P b c n', transformations) space_groups[60] = sg space_groups['P b c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(61, 'P b c a', transformations) space_groups[61] = sg space_groups['P b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(62, 'P n m a', transformations) space_groups[62] = sg space_groups['P n m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(63, 'C m c m', transformations) space_groups[63] = sg space_groups['C m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(64, 'C m c a', transformations) space_groups[64] = sg space_groups['C m c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(65, 'C m m m', transformations) space_groups[65] = sg space_groups['C m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(66, 'C c c m', transformations) space_groups[66] = sg space_groups['C c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(67, 'C m m a', transformations) space_groups[67] = sg space_groups['C m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(68, 'C c c a :2', transformations) space_groups[68] = sg space_groups['C c c a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(69, 'F m m m', transformations) space_groups[69] = sg space_groups['F m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(70, 'F d d d :2', transformations) space_groups[70] = sg space_groups['F d d d :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(71, 'I m m m', transformations) space_groups[71] = sg space_groups['I m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(72, 'I b a m', transformations) space_groups[72] = sg space_groups['I b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(73, 'I b c a', transformations) space_groups[73] = sg space_groups['I b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(74, 'I m m a', transformations) space_groups[74] = sg space_groups['I m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(75, 'P 4', transformations) space_groups[75] = sg space_groups['P 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(76, 'P 41', transformations) space_groups[76] = sg space_groups['P 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(77, 'P 42', transformations) space_groups[77] = sg space_groups['P 42'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(78, 'P 43', transformations) space_groups[78] = sg space_groups['P 43'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(79, 'I 4', transformations) space_groups[79] = sg space_groups['I 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(80, 'I 41', transformations) space_groups[80] = sg space_groups['I 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(81, 'P -4', transformations) space_groups[81] = sg space_groups['P -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(82, 'I -4', transformations) space_groups[82] = sg space_groups['I -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(83, 'P 4/m', transformations) space_groups[83] = sg space_groups['P 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(84, 'P 42/m', transformations) space_groups[84] = sg space_groups['P 42/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(85, 'P 4/n :2', transformations) space_groups[85] = sg space_groups['P 4/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(86, 'P 42/n :2', transformations) space_groups[86] = sg space_groups['P 42/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(87, 'I 4/m', transformations) space_groups[87] = sg space_groups['I 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(88, 'I 41/a :2', transformations) space_groups[88] = sg space_groups['I 41/a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(89, 'P 4 2 2', transformations) space_groups[89] = sg space_groups['P 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(90, 'P 4 21 2', transformations) space_groups[90] = sg space_groups['P 4 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(91, 'P 41 2 2', transformations) space_groups[91] = sg space_groups['P 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(92, 'P 41 21 2', transformations) space_groups[92] = sg space_groups['P 41 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(93, 'P 42 2 2', transformations) space_groups[93] = sg space_groups['P 42 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(94, 'P 42 21 2', transformations) space_groups[94] = sg space_groups['P 42 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(95, 'P 43 2 2', transformations) space_groups[95] = sg space_groups['P 43 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(96, 'P 43 21 2', transformations) space_groups[96] = sg space_groups['P 43 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(97, 'I 4 2 2', transformations) space_groups[97] = sg space_groups['I 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(98, 'I 41 2 2', transformations) space_groups[98] = sg space_groups['I 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(99, 'P 4 m m', transformations) space_groups[99] = sg space_groups['P 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(100, 'P 4 b m', transformations) space_groups[100] = sg space_groups['P 4 b m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(101, 'P 42 c m', transformations) space_groups[101] = sg space_groups['P 42 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(102, 'P 42 n m', transformations) space_groups[102] = sg space_groups['P 42 n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(103, 'P 4 c c', transformations) space_groups[103] = sg space_groups['P 4 c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(104, 'P 4 n c', transformations) space_groups[104] = sg space_groups['P 4 n c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(105, 'P 42 m c', transformations) space_groups[105] = sg space_groups['P 42 m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(106, 'P 42 b c', transformations) space_groups[106] = sg space_groups['P 42 b c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(107, 'I 4 m m', transformations) space_groups[107] = sg space_groups['I 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(108, 'I 4 c m', transformations) space_groups[108] = sg space_groups['I 4 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(109, 'I 41 m d', transformations) space_groups[109] = sg space_groups['I 41 m d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(110, 'I 41 c d', transformations) space_groups[110] = sg space_groups['I 41 c d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(111, 'P -4 2 m', transformations) space_groups[111] = sg space_groups['P -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(112, 'P -4 2 c', transformations) space_groups[112] = sg space_groups['P -4 2 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(113, 'P -4 21 m', transformations) space_groups[113] = sg space_groups['P -4 21 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(114, 'P -4 21 c', transformations) space_groups[114] = sg space_groups['P -4 21 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(115, 'P -4 m 2', transformations) space_groups[115] = sg space_groups['P -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(116, 'P -4 c 2', transformations) space_groups[116] = sg space_groups['P -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(117, 'P -4 b 2', transformations) space_groups[117] = sg space_groups['P -4 b 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(118, 'P -4 n 2', transformations) space_groups[118] = sg space_groups['P -4 n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(119, 'I -4 m 2', transformations) space_groups[119] = sg space_groups['I -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(120, 'I -4 c 2', transformations) space_groups[120] = sg space_groups['I -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(121, 'I -4 2 m', transformations) space_groups[121] = sg space_groups['I -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(122, 'I -4 2 d', transformations) space_groups[122] = sg space_groups['I -4 2 d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(123, 'P 4/m m m', transformations) space_groups[123] = sg space_groups['P 4/m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(124, 'P 4/m c c', transformations) space_groups[124] = sg space_groups['P 4/m c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(125, 'P 4/n b m :2', transformations) space_groups[125] = sg space_groups['P 4/n b m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot =	N.array([0,-1,0,-1,0,0,0,0,1])	numpy.array
from __future__ import division, print_function from typing import List import numpy import scipy class LinearRegression: def __init__(self, nb_features: int): self.nb_features = nb_features def train(self, features: List[List[float]], values: List[float]): # creating f(x) = W0 + sum((Wd)(Xd)) # finding W's # use LMS(least mean squared(minimizing residuals sum(mean squared error))) # LMS = ((X^tX)^-1) (X^tY) # make sure N > D+1 # features = X values = y y = numpy.array([values]).transpose() x = numpy.array(features) # add w0 x = numpy.append([[1]]len(features),x, axis=1) xtx = x.transpose().dot(x) xty = x.transpose().dot(y) xtxInv = numpy.linalg.inv(xtx) self.weights = xtxInv.dot(xty) def phi(self, x: List[float]) -> List[float]: aug = [] for i in range(1,len(x)): for k in range(2,self.nb_features+1): aug.append(numpy.power(x[i],k)) return aug def predict(self, features: List[List[float]]) -> List[float]: # f(x) = wtx # x -> p(x) [1,x,x^2...x^d] x = numpy.array(features) x = numpy.append([[1]]len(features),x, axis=1) return numpy.inner(self.weights.transpose(),x)[0] def get_weights(self) -> List[float]: """ for a model y = 1 + 3 * x_0 - 2 * x_1, the return value should be [1, 3, -2]. """ return self.weights class LinearRegressionWithL2Loss: '''Use L2 loss for weight regularization''' def __init__(self, nb_features: int, alpha: float): self.alpha = alpha self.nb_features = nb_features def train(self, features: List[List[float]], values: List[float]): # creating f(x) = W0 + sum((Wd)(Xd)) # finding W's # use LMS(least mean squared(minimizing residuals sum(mean squared error))) # LMS = ((X^tX)^-1) (X^tY) Now (X^tX -> X^tX + lI) # make sure N > D+1 # features = X values = y y = numpy.array([values]).transpose() x = numpy.array(features) # add w0 x = numpy.append([[1]]len(features),x, axis=1) # xtx -> xtx + lI xtx = numpy.add(x.transpose().dot(x), self.alpha numpy.identity(x.shape[1])) xty = x.transpose().dot(y) xtxInv = numpy.linalg.inv(xtx) self.weights = xtxInv.dot(xty) def phi(self, x: List[float]) -> List[float]: aug = [] for i in range(1,len(x)): for k in range(2,self.nb_features+1): aug.append(numpy.power(x[i],k)) return aug def predict(self, features: List[List[float]]) -> List[float]: # f(x) = wtx + l\|w\|^2 # x -> p(x) [1,x,x^2...x^d] x =	numpy.array(features)	numpy.array
""" Input/output utilities, adapted from https://github.com/vanderschaarlab/SyncTwin-NeurIPS-2021 """ # Author: <NAME> (<EMAIL>) # License: BSD 3 clause import os import pickle import numpy as np import torch def create_paths(args): for base_path in args: if not os.path.exists(base_path): os.makedirs(base_path) def load_config(data_path, fold="train"): with open(data_path.format(fold, "config", "pkl"), "rb") as f: config = pickle.load(file=f) n_units = config["n_units"] n_treated = config["n_treated"] n_units_total = config["n_units_total"] step = config["step"] train_step = config["train_step"] control_sample = config["control_sample"] noise = config["noise"] n_basis = config["n_basis"] n_cluster = config["n_cluster"] return ( n_units, n_treated, n_units_total, step, train_step, control_sample, noise, n_basis, n_cluster, ) def load_tensor(data_path, fold="train", device="cpu"): x_full = torch.load( data_path.format(fold, "x_full", "pth"), map_location=torch.device(device) ) t_full = torch.load( data_path.format(fold, "t_full", "pth"), map_location=torch.device(device) ) mask_full = torch.load( data_path.format(fold, "mask_full", "pth"), map_location=torch.device(device) ) batch_ind_full = torch.load( data_path.format(fold, "batch_ind_full", "pth"), map_location=torch.device(device), ) y_full = torch.load( data_path.format(fold, "y_full", "pth"), map_location=torch.device(device) ) y_control = torch.load( data_path.format(fold, "y_control", "pth"), map_location=torch.device(device) ) y_mask_full = torch.load( data_path.format(fold, "y_mask_full", "pth"), map_location=torch.device(device) ) m = torch.load( data_path.format(fold, "m", "pth"), map_location=torch.device(device) ) sd = torch.load( data_path.format(fold, "sd", "pth"), map_location=torch.device(device) ) treatment_effect = torch.load( data_path.format(fold, "treatment_effect", "pth"), map_location=torch.device(device), ) return ( x_full, t_full, mask_full, batch_ind_full, y_full, y_control, y_mask_full, m, sd, treatment_effect, ) def load_data_dict(version=1): if version == 1: version = "" else: version = str(version) val_arr1 = np.load(f"real_data{version}/val_arr1.npy") val_mask_arr1 = np.load(f"real_data{version}/val_mask_arr1.npy") ts_arr1 = np.load(f"real_data{version}/ts_arr1.npy") ts_mask_arr1 = np.load(f"real_data{version}/ts_mask_arr1.npy") patid1 = np.load(f"real_data{version}/patid1.npy") val_arr0 = np.load(f"real_data{version}/val_arr0.npy") val_mask_arr0 = np.load(f"real_data{version}/val_mask_arr0.npy") ts_arr0 = np.load(f"real_data{version}/ts_arr0.npy") ts_mask_arr0 = np.load(f"real_data{version}/ts_mask_arr0.npy") patid0 = np.load(f"real_data{version}/patid0.npy") Y0 = np.load(f"real_data{version}/Y0.npy") Y1 = np.load(f"real_data{version}/Y1.npy") data1 = { "val_arr": val_arr1, "val_mask_arr": val_mask_arr1, "ts_arr": ts_arr1, "ts_mask_arr": ts_mask_arr1, "patid": patid1, "Y": Y1, } data0 = { "val_arr": val_arr0, "val_mask_arr": val_mask_arr0, "ts_arr": ts_arr0, "ts_mask_arr": ts_mask_arr0, "patid": patid0, "Y": Y0, } return data1, data0 def get_units(d1, d0): n_units = d0[0].shape[0] n_treated = d1[0].shape[0] return n_units, n_treated, n_units + n_treated def to_tensor(device, dtype, args): return [torch.tensor(x, device=device, dtype=dtype) for x in args] def get_tensors(d1_train, d0_train, device): x_full =	np.concatenate([d0_train[0], d1_train[0]], axis=0)	numpy.concatenate
import numpy as np import numpy.random as npr import scipy as sc from operator import add from functools import reduce from sds.utils.general import Statistics as Stats from sds.utils.linalg import symmetrize class LinearGaussianWithPrecision: def __init__(self, column_dim, row_dim, A=None, lmbda=None, affine=True): self.column_dim = column_dim self.row_dim = row_dim self.A = A self.affine = affine self._lmbda = lmbda self._lmbda_chol = None self._lmbda_chol_inv = None @property def params(self): return self.A, self.lmbda @params.setter def params(self, values): self.A, self.lmbda = values @property def nb_params(self): return self.column_dim * self.row_dim \ + self.row_dim * (self.row_dim + 1) / 2 @property def input_dim(self): return self.column_dim - 1 if self.affine\ else self.column_dim @property def output_dim(self): return self.row_dim @property def lmbda(self): return self._lmbda @lmbda.setter def lmbda(self, value): self._lmbda = value self._lmbda_chol = None self._lmbda_chol_inv = None @property def lmbda_chol(self): if self._lmbda_chol is None: self._lmbda_chol = sc.linalg.cholesky(self.lmbda, lower=False) return self._lmbda_chol @property def lmbda_chol_inv(self): if self._lmbda_chol_inv is None: self._lmbda_chol_inv = sc.linalg.inv(self.lmbda_chol) return self._lmbda_chol_inv @property def sigma(self): return self.lmbda_chol_inv @ self.lmbda_chol_inv.T def predict(self, x): if self.affine: A, b = self.A[:, :-1], self.A[:, -1] y = np.einsum('dl,...l->...d', A, x, optimize=True) + b.T else: y = np.einsum('dl,...l->...d', self.A, x, optimize=True) return y def mean(self, x): return self.predict(x) def mode(self, x): return self.predict(x) def rvs(self, x): return self.mean(x) + npr.normal(size=self.output_dim).dot(self.lmbda_chol_inv.T) @property def base(self): return np.power(2. * np.pi, - self.output_dim / 2.) def log_base(self): return np.log(self.base) def statistics(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y = x[idx], y[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) contract = 'nd,nl->dl' yxT = np.einsum(contract, y, x, optimize=True) xxT = np.einsum(contract, x, x, optimize=True) yyT = np.einsum(contract, y, y, optimize=True) n = y.shape[0] return Stats([yxT, xxT, yyT, n]) else: stats = list(map(self.statistics, x, y)) return reduce(add, stats) def weighted_statistics(self, x, y, weights): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y, weights = x[idx], y[idx], weights[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) contract = 'nd,n,nl->dl' yxT = np.einsum(contract, y, weights, x, optimize=True) xxT = np.einsum(contract, x, weights, x, optimize=True) yyT = np.einsum(contract, y, weights, y, optimize=True) n = np.sum(weights) return Stats([yxT, xxT, yyT, n]) else: stats = list(map(self.weighted_statistics, x, y, weights)) return reduce(add, stats) def log_partition(self, x): mu = self.predict(x) return 0.5 * np.einsum('nd,dl,nl->n', mu, self.lmbda, mu)\ - np.sum(np.log(np.diag(self.lmbda_chol))) def log_likelihood(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): bads = np.logical_and(np.isnan(np.atleast_2d(x)).any(axis=1), np.isnan(np.atleast_2d(y)).any(axis=1)) x = np.nan_to_num(x, copy=False).reshape((-1, self.input_dim)) y = np.nan_to_num(y, copy=False).reshape((-1, self.output_dim)) mu = self.mean(x) log_lik = np.einsum('nd,dl,nl->n', mu, self.lmbda, y, optimize=True)\ - 0.5 * np.einsum('nd,dl,nl->n', y, self.lmbda, y, optimize=True) log_lik[bads] = 0. log_lik += - self.log_partition(x) + self.log_base() return log_lik else: return list(map(self.log_likelihood, x, y)) # Max likelihood def max_likelihood(self, x, y, weights=None): yxT, xxT, yyT, n = self.statistics(x, y) if weights is None\ else self.weighted_statistics(x, y, weights) self.A = np.linalg.solve(xxT, yxT.T).T sigma = (yyT - self.A.dot(yxT.T)) / n # numerical stabilization sigma = symmetrize(sigma) + 1e-16 * np.eye(self.output_dim) assert np.allclose(sigma, sigma.T) assert np.all(np.linalg.eigvalsh(sigma) > 0.) self.lmbda = np.linalg.inv(sigma) class StackedLinearGaussiansWithPrecision: def __init__(self, size, column_dim, row_dim, As=None, lmbdas=None, affine=True): self.size = size self.column_dim = column_dim self.row_dim = row_dim self.affine = affine As = [None] * self.size if As is None else As lmbdas = [None] * self.size if lmbdas is None else lmbdas self.dists = [LinearGaussianWithPrecision(column_dim, row_dim, As[k], lmbdas[k], affine=affine) for k in range(self.size)] @property def params(self): return self.As, self.lmbdas @params.setter def params(self, values): self.As, self.lmbdas = values @property def input_dim(self): return self.column_dim - 1 if self.affine\ else self.column_dim @property def output_dim(self): return self.row_dim @property def As(self): return np.array([dist.A for dist in self.dists]) @As.setter def As(self, value): for k, dist in enumerate(self.dists): dist.A = value[k] @property def lmbdas(self): return np.array([dist.lmbda for dist in self.dists]) @lmbdas.setter def lmbdas(self, value): for k, dist in enumerate(self.dists): dist.lmbda = value[k] @property def lmbdas_chol(self): return np.array([dist.lmbda_chol for dist in self.dists]) @property def lmbdas_chol_inv(self): return np.array([dist.lmbda_chol_inv for dist in self.dists]) @property def sigmas(self): return np.array([dist.sigma for dist in self.dists]) def predict(self, x): if self.affine: As, bs = self.As[:, :, :-1], self.As[:, :, -1] y = np.einsum('kdl,...l->...kd', As, x, optimize=True) + bs[None, ...] else: y = np.einsum('kdl,...l->...kd', self.As, x, optimize=True) return y def mean(self, x): return self.predict(x) def mode(self, x): return self.predict(x) def rvs(self, x): return np.array([dist.rvs(x) for dist in self.dists]) @property def base(self): return np.array([dist.base for dist in self.dists]) def log_base(self): return np.log(self.base) def statistics(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y = x[idx], y[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) contract = 'nd,nl->dl' yxT = np.einsum(contract, y, x, optimize=True) xxT = np.einsum(contract, x, x, optimize=True) yyT = np.einsum(contract, y, y, optimize=True) n = y.shape[0] yxTk = np.array([yxT for _ in range(self.size)]) xxTk = np.array([xxT for _ in range(self.size)]) yyTk = np.array([yyT for _ in range(self.size)]) nk = np.array([n for _ in range(self.size)]) return Stats([yxTk, xxTk, yyTk, nk]) else: stats = list(map(self.statistics, x, y)) return reduce(add, stats) def weighted_statistics(self, x, y, weights): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y, weights = x[idx], y[idx], weights[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) contract = 'nd,nk,nl->kdl' yxTk = np.einsum(contract, y, weights, x, optimize=True) xxTk = np.einsum(contract, x, weights, x, optimize=True) yyTk = np.einsum(contract, y, weights, y, optimize=True) nk = np.sum(weights, axis=0) return Stats([yxTk, xxTk, yyTk, nk]) else: stats = list(map(self.weighted_statistics, x, y, weights)) return reduce(add, stats) def log_partition(self, x): return np.array([dist.log_partition(x) for dist in self.dists]).T def log_likelihood(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): bads = np.logical_and(np.isnan(np.atleast_2d(x)).any(axis=1), np.isnan(np.atleast_2d(y)).any(axis=1)) x = np.nan_to_num(x, copy=False).reshape((-1, self.input_dim)) y = np.nan_to_num(y, copy=False).reshape((-1, self.output_dim)) mu = self.mean(x) log_lik = np.einsum('nkd,kdl,nl->nk', mu, self.lmbdas, y, optimize=True)\ - 0.5 * np.einsum('nd,kdl,nl->nk', y, self.lmbdas, y, optimize=True) log_lik[bads] = 0. log_lik += - self.log_partition(x) + self.log_base() return log_lik else: return list(map(self.log_likelihood, x, y)) # Max likelihood def max_likelihood(self, x, y, weights): yxTk, xxTk, yyTk, nk = self.weighted_statistics(x, y, weights) As = np.zeros((self.size, self.column_dim, self.row_dim)) lmbdas = np.zeros((self.size, self.output_dim, self.output_dim)) for k in range(self.size): As[k] = np.linalg.solve(xxTk[k], yxTk[k].T).T sigma = (yyTk[k] - As[k].dot(yxTk[k].T)) / nk[k] # numerical stabilization sigma = symmetrize(sigma) + 1e-16 * np.eye(self.output_dim) assert np.allclose(sigma, sigma.T) assert np.all(np.linalg.eigvalsh(sigma) > 0.) lmbdas[k] = np.linalg.inv(sigma) self.As = As self.lmbdas = lmbdas class TiedLinearGaussiansWithPrecision(StackedLinearGaussiansWithPrecision): def __init__(self, size, column_dim, row_dim, As=None, lmbdas=None, affine=True): super(TiedLinearGaussiansWithPrecision, self).__init__(size, column_dim, row_dim, As, lmbdas, affine) # Max likelihood def max_likelihood(self, x, y, weights): yxTk, xxTk, yyT, n = self.weighted_statistics(x, y, weights) As = np.zeros((self.size, self.column_dim, self.row_dim)) sigma = np.zeros((self.output_dim, self.output_dim)) sigma = yyT for k in range(self.size): As[k] = np.linalg.solve(xxTk[k], yxTk[k].T).T sigma -= As[k].dot(yxTk[k].T) sigma /= n # numerical stabilization sigma = symmetrize(sigma) + 1e-16 * np.eye(self.output_dim) assert np.allclose(sigma, sigma.T) assert np.all(np.linalg.eigvalsh(sigma) > 0.) self.As = As lmbda = np.linalg.inv(sigma) self.lmbdas = np.array(self.size * [lmbda]) class LinearGaussianWithDiagonalPrecision: def __init__(self, column_dim, row_dim, A=None, lmbda_diag=None, affine=True): self.column_dim = column_dim self.row_dim = row_dim self.A = A self.affine = affine self._lmbda_diag = lmbda_diag self._lmbda_chol = None self._lmbda_chol_inv = None @property def params(self): return self.A, self.lmbda_diag @params.setter def params(self, values): self.A, self.lmbda_diag = values @property def nb_params(self): return self.column_dim * self.row_dim + self.row_dim @property def input_dim(self): return self.column_dim - 1 if self.affine\ else self.column_dim @property def output_dim(self): return self.row_dim @property def lmbda_diag(self): return self._lmbda_diag @lmbda_diag.setter def lmbda_diag(self, value): self._lmbda_diag = value self._lmbda_chol = None self._lmbda_chol_inv = None @property def lmbda(self): assert self._lmbda_diag is not None return np.diag(self._lmbda_diag) @property def lmbda_chol(self): if self._lmbda_chol is None: self._lmbda_chol = np.diag(np.sqrt(self.lmbda_diag)) return self._lmbda_chol @property def lmbda_chol_inv(self): if self._lmbda_chol_inv is None: self._lmbda_chol_inv = np.diag(1. / np.sqrt(self.lmbda_diag)) return self._lmbda_chol_inv @property def sigma_diag(self): return 1. / self.lmbda_diag @property def sigma(self): return np.diag(self.sigma_diag) def predict(self, x): if self.affine: A, b = self.A[:, :-1], self.A[:, -1] y = np.einsum('dl,...l->...d', A, x, optimize=True) + b.T else: y = np.einsum('dl,...l->...d', self.A, x, optimize=True) return y def mean(self, x): return self.predict(x) def mode(self, x): return self.predict(x) def rvs(self, x): return self.mean(x) + npr.normal(size=self.output_dim).dot(self.lmbda_chol_inv.T) @property def base(self): return np.power(2. * np.pi, - self.output_dim / 2.) def log_base(self): return np.log(self.base) def statistics(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y = x[idx], y[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) xxT = np.einsum('nd,nl->dl', x, x, optimize=True) yxT = np.einsum('nd,nl->dl', y, x, optimize=True) yy = np.einsum('nd,nd->d', y, y, optimize=True) nd = np.broadcast_to(y.shape[0], (self.output_dim, )) return Stats([yxT, xxT, nd, yy]) else: stats = list(map(self.statistics, x, y)) return reduce(add, stats) def weighted_statistics(self, x, y, weights): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y, weights = x[idx], y[idx], weights[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) xxT = np.einsum('nd,n,nl->dl', x, weights, x, optimize=True) yxT = np.einsum('nd,n,nl->dl', y, weights, x, optimize=True) yy = np.einsum('nd,n,nd->d', y, weights, y, optimize=True) nd = np.broadcast_to(np.sum(weights), (self.output_dim, )) return Stats([yxT, xxT, nd, yy]) else: stats = list(map(self.weighted_statistics, x, y, weights)) return reduce(add, stats) def log_partition(self, x): mu = self.predict(x) return 0.5 * np.einsum('nd,dl,nl->n', mu, self.lmbda, mu)\ - np.sum(np.log(np.diag(self.lmbda_chol))) def log_likelihood(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): bads = np.logical_and(np.isnan(np.atleast_2d(x)).any(axis=1), np.isnan(np.atleast_2d(y)).any(axis=1)) x = np.nan_to_num(x, copy=False).reshape((-1, self.input_dim)) y = np.nan_to_num(y, copy=False).reshape((-1, self.output_dim)) mu = self.mean(x) log_lik = np.einsum('nd,dl,nl->n', mu, self.lmbda, y, optimize=True) \ - 0.5 * np.einsum('nd,dl,nl->n', y, self.lmbda, y, optimize=True) log_lik[bads] = 0. log_lik += - self.log_partition(x) + self.log_base() return log_lik else: return list(map(self.log_likelihood, x, y)) # Max likelihood def max_likelihood(self, x, y, weights=None): yxT, xxT, nd, yy = self.statistics(x, y) if weights is None\ else self.weighted_statistics(x, y, weights) self.A = np.linalg.solve(xxT, yxT.T).T sigmas = (yy - np.einsum('dl,dl->d', self.A, yxT)) / nd self.lmbda_diag = 1. / sigmas class StackedLinearGaussiansWithDiagonalPrecision: def __init__(self, size, column_dim, row_dim, As=None, lmbdas_diags=None, affine=True): self.size = size self.column_dim = column_dim self.row_dim = row_dim self.affine = affine As = [None] * self.size if As is None else As lmbdas_diags = [None] * self.size if lmbdas_diags is None else lmbdas_diags self.dists = [LinearGaussianWithDiagonalPrecision(column_dim, row_dim, As[k], lmbdas_diags[k], affine=affine) for k in range(self.size)] @property def params(self): return self.As, self.lmbdas_diags @params.setter def params(self, values): self.As, self.lmbdas_diags = values @property def input_dim(self): return self.column_dim - 1 if self.affine\ else self.column_dim @property def output_dim(self): return self.row_dim @property def As(self): return np.array([dist.A for dist in self.dists]) @As.setter def As(self, value): for k, dist in enumerate(self.dists): dist.A = value[k] @property def lmbdas_diags(self): return np.array([dist.lmbda_diag for dist in self.dists]) @lmbdas_diags.setter def lmbdas_diags(self, value): for k, dist in enumerate(self.dists): dist.lmbda_diag = value[k] @property def lmbdas(self): return np.array([dist.lmbda for dist in self.dists]) @property def lmbdas_chol(self): return np.array([dist.lmbda_chol for dist in self.dists]) @property def lmbdas_chol_inv(self): return np.array([dist.lmbda_chol_inv for dist in self.dists]) @property def sigmas_diag(self): return np.array([dist.sigma_diag for dist in self.dists]) @property def sigmas(self): return np.array([dist.sigma for dist in self.dists]) def predict(self, x): if self.affine: As, bs = self.As[:, :, :-1], self.As[:, :, -1] y = np.einsum('kdl,...l->...kd', As, x, optimize=True) + bs[None, ...] else: y = np.einsum('kdl,...l->...kd', self.As, x, optimize=True) return y def mean(self, x): return self.predict(x) def mode(self, x): return self.predict(x) def rvs(self, x): return np.array([dist.rvs(x) for dist in self.dists]) @property def base(self): return np.array([dist.base for dist in self.dists]) def log_base(self): return np.log(self.base) def statistics(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y = x[idx], y[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) xxT = np.einsum('nd,nl->dl', x, x, optimize=True) yxT = np.einsum('nd,nl->dl', y, x, optimize=True) yy = np.einsum('nd,nd->d', y, y, optimize=True) nd = np.broadcast_to(y.shape[0], (self.output_dim, )) xxTk = np.array([xxT for _ in range(self.size)]) yxTk = np.array([yxT for _ in range(self.size)]) yyk = np.array([yy for _ in range(self.size)]) ndk = np.array([nd for _ in range(self.size)]) return Stats([yxTk, xxTk, ndk, yyk]) else: stats = list(map(self.statistics, x, y)) return reduce(add, stats) def weighted_statistics(self, x, y, weights): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y, weights = x[idx], y[idx], weights[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) xxTk = np.einsum('nd,nk,nl->kdl', x, weights, x, optimize=True) yxTk = np.einsum('nd,nk,nl->kdl', y, weights, x, optimize=True) yyk = np.einsum('nd,nk,nd->kd', y, weights, y, optimize=True) ndk = np.broadcast_to(np.sum(weights, axis=0, keepdims=True), (self.size, self.output_dim)) return Stats([yxTk, xxTk, ndk, yyk]) else: stats = list(map(self.weighted_statistics, x, y, weights)) return reduce(add, stats) def log_partition(self, x): return np.array([dist.log_partition(x) for dist in self.dists]).T def log_likelihood(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): bads = np.logical_and(np.isnan(np.atleast_2d(x)).any(axis=1), np.isnan(np.atleast_2d(y)).any(axis=1)) x = np.nan_to_num(x, copy=False).reshape((-1, self.input_dim)) y = np.nan_to_num(y, copy=False).reshape((-1, self.output_dim)) mu = self.mean(x) log_lik =	np.einsum('nkd,kdl,nl->nk', mu, self.lmbdas, y, optimize=True)	numpy.einsum
from sys import getsizeof from typing import ( TYPE_CHECKING, Any, Callable, Hashable, Iterable, List, Optional, Sequence, Tuple, Union, ) import warnings import numpy as np from my_happy_pandas._config import get_option from my_happy_pandas._libs import algos as libalgos, index as libindex, lib from my_happy_pandas._libs.hashtable import duplicated_int64 from my_happy_pandas._typing import AnyArrayLike, Scalar from my_happy_pandas.compat.numpy import function as nv from my_happy_pandas.errors import InvalidIndexError, PerformanceWarning, UnsortedIndexError from my_happy_pandas.util._decorators import Appender, cache_readonly, doc from my_happy_pandas.core.dtypes.cast import coerce_indexer_dtype from my_happy_pandas.core.dtypes.common import ( ensure_int64, ensure_platform_int, is_categorical_dtype, is_hashable, is_integer, is_iterator, is_list_like, is_object_dtype, is_scalar, pandas_dtype, ) from my_happy_pandas.core.dtypes.dtypes import ExtensionDtype from my_happy_pandas.core.dtypes.generic import ABCDataFrame, ABCDatetimeIndex, ABCTimedeltaIndex from my_happy_pandas.core.dtypes.missing import array_equivalent, isna import my_happy_pandas.core.algorithms as algos from my_happy_pandas.core.arrays import Categorical from my_happy_pandas.core.arrays.categorical import factorize_from_iterables import my_happy_pandas.core.common as com import my_happy_pandas.core.indexes.base as ibase from my_happy_pandas.core.indexes.base import Index, _index_shared_docs, ensure_index from my_happy_pandas.core.indexes.frozen import FrozenList from my_happy_pandas.core.indexes.numeric import Int64Index import my_happy_pandas.core.missing as missing from my_happy_pandas.core.sorting import ( get_group_index, indexer_from_factorized, lexsort_indexer, ) from my_happy_pandas.io.formats.printing import ( format_object_attrs, format_object_summary, pprint_thing, ) if TYPE_CHECKING: from my_happy_pandas import Series # noqa:F401 _index_doc_kwargs = dict(ibase._index_doc_kwargs) _index_doc_kwargs.update( dict(klass="MultiIndex", target_klass="MultiIndex or list of tuples") ) class MultiIndexUIntEngine(libindex.BaseMultiIndexCodesEngine, libindex.UInt64Engine): """ This class manages a MultiIndex by mapping label combinations to positive integers. """ _base = libindex.UInt64Engine def _codes_to_ints(self, codes): """ Transform combination(s) of uint64 in one uint64 (each), in a strictly monotonic way (i.e. respecting the lexicographic order of integer combinations): see BaseMultiIndexCodesEngine documentation. Parameters ---------- codes : 1- or 2-dimensional array of dtype uint64 Combinations of integers (one per row) Returns ------- scalar or 1-dimensional array, of dtype uint64 Integer(s) representing one combination (each). """ # Shift the representation of each level by the pre-calculated number # of bits: codes <<= self.offsets # Now sum and OR are in fact interchangeable. This is a simple # composition of the (disjunct) significant bits of each level (i.e. # each column in "codes") in a single positive integer: if codes.ndim == 1: # Single key return np.bitwise_or.reduce(codes) # Multiple keys return np.bitwise_or.reduce(codes, axis=1) class MultiIndexPyIntEngine(libindex.BaseMultiIndexCodesEngine, libindex.ObjectEngine): """ This class manages those (extreme) cases in which the number of possible label combinations overflows the 64 bits integers, and uses an ObjectEngine containing Python integers. """ _base = libindex.ObjectEngine def _codes_to_ints(self, codes): """ Transform combination(s) of uint64 in one Python integer (each), in a strictly monotonic way (i.e. respecting the lexicographic order of integer combinations): see BaseMultiIndexCodesEngine documentation. Parameters ---------- codes : 1- or 2-dimensional array of dtype uint64 Combinations of integers (one per row) Returns ------- int, or 1-dimensional array of dtype object Integer(s) representing one combination (each). """ # Shift the representation of each level by the pre-calculated number # of bits. Since this can overflow uint64, first make sure we are # working with Python integers: codes = codes.astype("object") << self.offsets # Now sum and OR are in fact interchangeable. This is a simple # composition of the (disjunct) significant bits of each level (i.e. # each column in "codes") in a single positive integer (per row): if codes.ndim == 1: # Single key return np.bitwise_or.reduce(codes) # Multiple keys return np.bitwise_or.reduce(codes, axis=1) class MultiIndex(Index): """ A multi-level, or hierarchical, index object for pandas objects. Parameters ---------- levels : sequence of arrays The unique labels for each level. codes : sequence of arrays Integers for each level designating which label at each location. .. versionadded:: 0.24.0 sortorder : optional int Level of sortedness (must be lexicographically sorted by that level). names : optional sequence of objects Names for each of the index levels. (name is accepted for compat). copy : bool, default False Copy the meta-data. verify_integrity : bool, default True Check that the levels/codes are consistent and valid. Attributes ---------- names levels codes nlevels levshape Methods ------- from_arrays from_tuples from_product from_frame set_levels set_codes to_frame to_flat_index is_lexsorted sortlevel droplevel swaplevel reorder_levels remove_unused_levels get_locs See Also -------- MultiIndex.from_arrays : Convert list of arrays to MultiIndex. MultiIndex.from_product : Create a MultiIndex from the cartesian product of iterables. MultiIndex.from_tuples : Convert list of tuples to a MultiIndex. MultiIndex.from_frame : Make a MultiIndex from a DataFrame. Index : The base pandas Index type. Notes ----- See the `user guide <https://pandas.pydata.org/pandas-docs/stable/user_guide/advanced.html>`_ for more. Examples -------- A new ``MultiIndex`` is typically constructed using one of the helper methods :meth:`MultiIndex.from_arrays`, :meth:`MultiIndex.from_product` and :meth:`MultiIndex.from_tuples`. For example (using ``.from_arrays``): >>> arrays = [[1, 1, 2, 2], ['red', 'blue', 'red', 'blue']] >>> pd.MultiIndex.from_arrays(arrays, names=('number', 'color')) MultiIndex([(1, 'red'), (1, 'blue'), (2, 'red'), (2, 'blue')], names=['number', 'color']) See further examples for how to construct a MultiIndex in the doc strings of the mentioned helper methods. """ _deprecations = Index._deprecations \| frozenset() # initialize to zero-length tuples to make everything work _typ = "multiindex" _names = FrozenList() _levels = FrozenList() _codes = FrozenList() _comparables = ["names"] rename = Index.set_names _tuples = None sortorder: Optional[int] # -------------------------------------------------------------------- # Constructors def __new__( cls, levels=None, codes=None, sortorder=None, names=None, dtype=None, copy=False, name=None, verify_integrity: bool = True, _set_identity: bool = True, ): # compat with Index if name is not None: names = name if levels is None or codes is None: raise TypeError("Must pass both levels and codes") if len(levels) != len(codes): raise ValueError("Length of levels and codes must be the same.") if len(levels) == 0: raise ValueError("Must pass non-zero number of levels/codes") result = object.__new__(MultiIndex) result._cache = {} # we've already validated levels and codes, so shortcut here result._set_levels(levels, copy=copy, validate=False) result._set_codes(codes, copy=copy, validate=False) result._names = [None] * len(levels) if names is not None: # handles name validation result._set_names(names) if sortorder is not None: result.sortorder = int(sortorder) else: result.sortorder = sortorder if verify_integrity: new_codes = result._verify_integrity() result._codes = new_codes if _set_identity: result._reset_identity() return result def _validate_codes(self, level: List, code: List): """ Reassign code values as -1 if their corresponding levels are NaN. Parameters ---------- code : list Code to reassign. level : list Level to check for missing values (NaN, NaT, None). Returns ------- new code where code value = -1 if it corresponds to a level with missing values (NaN, NaT, None). """ null_mask = isna(level) if np.any(null_mask): code = np.where(null_mask[code], -1, code) return code def _verify_integrity( self, codes: Optional[List] = None, levels: Optional[List] = None ): """ Parameters ---------- codes : optional list Codes to check for validity. Defaults to current codes. levels : optional list Levels to check for validity. Defaults to current levels. Raises ------ ValueError If length of levels and codes don't match, if the codes for any level would exceed level bounds, or there are any duplicate levels. Returns ------- new codes where code value = -1 if it corresponds to a NaN level. """ # NOTE: Currently does not check, among other things, that cached # nlevels matches nor that sortorder matches actually sortorder. codes = codes or self.codes levels = levels or self.levels if len(levels) != len(codes): raise ValueError( "Length of levels and codes must match. NOTE: " "this index is in an inconsistent state." ) codes_length = len(codes[0]) for i, (level, level_codes) in enumerate(zip(levels, codes)): if len(level_codes) != codes_length: raise ValueError( f"Unequal code lengths: {[len(code_) for code_ in codes]}" ) if len(level_codes) and level_codes.max() >= len(level): raise ValueError( f"On level {i}, code max ({level_codes.max()}) >= length of " f"level ({len(level)}). NOTE: this index is in an " "inconsistent state" ) if len(level_codes) and level_codes.min() < -1: raise ValueError(f"On level {i}, code value ({level_codes.min()}) < -1") if not level.is_unique: raise ValueError( f"Level values must be unique: {list(level)} on level {i}" ) if self.sortorder is not None: if self.sortorder > self._lexsort_depth(): raise ValueError( "Value for sortorder must be inferior or equal to actual " f"lexsort_depth: sortorder {self.sortorder} " f"with lexsort_depth {self._lexsort_depth()}" ) codes = [ self._validate_codes(level, code) for level, code in zip(levels, codes) ] new_codes = FrozenList(codes) return new_codes @classmethod def from_arrays(cls, arrays, sortorder=None, names=lib.no_default) -> "MultiIndex": """ Convert arrays to MultiIndex. Parameters ---------- arrays : list / sequence of array-likes Each array-like gives one level's value for each data point. len(arrays) is the number of levels. sortorder : int or None Level of sortedness (must be lexicographically sorted by that level). names : list / sequence of str, optional Names for the levels in the index. Returns ------- MultiIndex See Also -------- MultiIndex.from_tuples : Convert list of tuples to MultiIndex. MultiIndex.from_product : Make a MultiIndex from cartesian product of iterables. MultiIndex.from_frame : Make a MultiIndex from a DataFrame. Examples -------- >>> arrays = [[1, 1, 2, 2], ['red', 'blue', 'red', 'blue']] >>> pd.MultiIndex.from_arrays(arrays, names=('number', 'color')) MultiIndex([(1, 'red'), (1, 'blue'), (2, 'red'), (2, 'blue')], names=['number', 'color']) """ error_msg = "Input must be a list / sequence of array-likes." if not is_list_like(arrays): raise TypeError(error_msg) elif is_iterator(arrays): arrays = list(arrays) # Check if elements of array are list-like for array in arrays: if not is_list_like(array): raise TypeError(error_msg) # Check if lengths of all arrays are equal or not, # raise ValueError, if not for i in range(1, len(arrays)): if len(arrays[i]) != len(arrays[i - 1]): raise ValueError("all arrays must be same length") codes, levels = factorize_from_iterables(arrays) if names is lib.no_default: names = [getattr(arr, "name", None) for arr in arrays] return MultiIndex( levels=levels, codes=codes, sortorder=sortorder, names=names, verify_integrity=False, ) @classmethod def from_tuples(cls, tuples, sortorder=None, names=None): """ Convert list of tuples to MultiIndex. Parameters ---------- tuples : list / sequence of tuple-likes Each tuple is the index of one row/column. sortorder : int or None Level of sortedness (must be lexicographically sorted by that level). names : list / sequence of str, optional Names for the levels in the index. Returns ------- MultiIndex See Also -------- MultiIndex.from_arrays : Convert list of arrays to MultiIndex. MultiIndex.from_product : Make a MultiIndex from cartesian product of iterables. MultiIndex.from_frame : Make a MultiIndex from a DataFrame. Examples -------- >>> tuples = [(1, 'red'), (1, 'blue'), ... (2, 'red'), (2, 'blue')] >>> pd.MultiIndex.from_tuples(tuples, names=('number', 'color')) MultiIndex([(1, 'red'), (1, 'blue'), (2, 'red'), (2, 'blue')], names=['number', 'color']) """ if not is_list_like(tuples): raise TypeError("Input must be a list / sequence of tuple-likes.") elif is_iterator(tuples): tuples = list(tuples) if len(tuples) == 0: if names is None: raise TypeError("Cannot infer number of levels from empty list") arrays = [[]] * len(names) elif isinstance(tuples, (np.ndarray, Index)): if isinstance(tuples, Index): tuples = tuples._values arrays = list(lib.tuples_to_object_array(tuples).T) elif isinstance(tuples, list): arrays = list(lib.to_object_array_tuples(tuples).T) else: arrays = zip(tuples) return MultiIndex.from_arrays(arrays, sortorder=sortorder, names=names) @classmethod def from_product(cls, iterables, sortorder=None, names=lib.no_default): """ Make a MultiIndex from the cartesian product of multiple iterables. Parameters ---------- iterables : list / sequence of iterables Each iterable has unique labels for each level of the index. sortorder : int or None Level of sortedness (must be lexicographically sorted by that level). names : list / sequence of str, optional Names for the levels in the index. .. versionchanged:: 1.0.0 If not explicitly provided, names will be inferred from the elements of iterables if an element has a name attribute Returns ------- MultiIndex See Also -------- MultiIndex.from_arrays : Convert list of arrays to MultiIndex. MultiIndex.from_tuples : Convert list of tuples to MultiIndex. MultiIndex.from_frame : Make a MultiIndex from a DataFrame. Examples -------- >>> numbers = [0, 1, 2] >>> colors = ['green', 'purple'] >>> pd.MultiIndex.from_product([numbers, colors], ... names=['number', 'color']) MultiIndex([(0, 'green'), (0, 'purple'), (1, 'green'), (1, 'purple'), (2, 'green'), (2, 'purple')], names=['number', 'color']) """ from my_happy_pandas.core.reshape.util import cartesian_product if not is_list_like(iterables): raise TypeError("Input must be a list / sequence of iterables.") elif is_iterator(iterables): iterables = list(iterables) codes, levels = factorize_from_iterables(iterables) if names is lib.no_default: names = [getattr(it, "name", None) for it in iterables] # codes are all ndarrays, so cartesian_product is lossless codes = cartesian_product(codes) return MultiIndex(levels, codes, sortorder=sortorder, names=names) @classmethod def from_frame(cls, df, sortorder=None, names=None): """ Make a MultiIndex from a DataFrame. .. versionadded:: 0.24.0 Parameters ---------- df : DataFrame DataFrame to be converted to MultiIndex. sortorder : int, optional Level of sortedness (must be lexicographically sorted by that level). names : list-like, optional If no names are provided, use the column names, or tuple of column names if the columns is a MultiIndex. If a sequence, overwrite names with the given sequence. Returns ------- MultiIndex The MultiIndex representation of the given DataFrame. See Also -------- MultiIndex.from_arrays : Convert list of arrays to MultiIndex. MultiIndex.from_tuples : Convert list of tuples to MultiIndex. MultiIndex.from_product : Make a MultiIndex from cartesian product of iterables. Examples -------- >>> df = pd.DataFrame([['HI', 'Temp'], ['HI', 'Precip'], ... ['NJ', 'Temp'], ['NJ', 'Precip']], ... columns=['a', 'b']) >>> df a b 0 HI Temp 1 HI Precip 2 NJ Temp 3 NJ Precip >>> pd.MultiIndex.from_frame(df) MultiIndex([('HI', 'Temp'), ('HI', 'Precip'), ('NJ', 'Temp'), ('NJ', 'Precip')], names=['a', 'b']) Using explicit names, instead of the column names >>> pd.MultiIndex.from_frame(df, names=['state', 'observation']) MultiIndex([('HI', 'Temp'), ('HI', 'Precip'), ('NJ', 'Temp'), ('NJ', 'Precip')], names=['state', 'observation']) """ if not isinstance(df, ABCDataFrame): raise TypeError("Input must be a DataFrame") column_names, columns = zip(df.items()) names = column_names if names is None else names return cls.from_arrays(columns, sortorder=sortorder, names=names) # -------------------------------------------------------------------- @property def _values(self): # We override here, since our parent uses _data, which we don't use. return self.values @property def values(self): if self._tuples is not None: return self._tuples values = [] for i in range(self.nlevels): vals = self._get_level_values(i) if is_categorical_dtype(vals.dtype): vals = vals._internal_get_values() if isinstance(vals.dtype, ExtensionDtype) or isinstance( vals, (ABCDatetimeIndex, ABCTimedeltaIndex) ): vals = vals.astype(object) vals = np.array(vals, copy=False) values.append(vals) self._tuples = lib.fast_zip(values) return self._tuples @property def array(self): """ Raises a ValueError for `MultiIndex` because there's no single array backing a MultiIndex. Raises ------ ValueError """ raise ValueError( "MultiIndex has no single backing array. Use " "'MultiIndex.to_numpy()' to get a NumPy array of tuples." ) @property def shape(self): """ Return a tuple of the shape of the underlying data. """ # overriding the base Index.shape definition to avoid materializing # the values (GH-27384, GH-27775) return (len(self),) def __len__(self) -> int: return len(self.codes[0]) # -------------------------------------------------------------------- # Levels Methods @cache_readonly def levels(self): # Use cache_readonly to ensure that self.get_locs doesn't repeatedly # create new IndexEngine # https://github.com/pandas-dev/pandas/issues/31648 result = [ x._shallow_copy(name=name) for x, name in zip(self._levels, self._names) ] for level in result: # disallow midx.levels[0].name = "foo" level._no_setting_name = True return FrozenList(result) def _set_levels( self, levels, level=None, copy=False, validate=True, verify_integrity=False ): # This is NOT part of the levels property because it should be # externally not allowed to set levels. User beware if you change # _levels directly if validate: if len(levels) == 0: raise ValueError("Must set non-zero number of levels.") if level is None and len(levels) != self.nlevels: raise ValueError("Length of levels must match number of levels.") if level is not None and len(levels) != len(level): raise ValueError("Length of levels must match length of level.") if level is None: new_levels = FrozenList( ensure_index(lev, copy=copy)._shallow_copy() for lev in levels ) else: level_numbers = [self._get_level_number(lev) for lev in level] new_levels = list(self._levels) for lev_num, lev in zip(level_numbers, levels): new_levels[lev_num] = ensure_index(lev, copy=copy)._shallow_copy() new_levels = FrozenList(new_levels) if verify_integrity: new_codes = self._verify_integrity(levels=new_levels) self._codes = new_codes names = self.names self._levels = new_levels if any(names): self._set_names(names) self._tuples = None self._reset_cache() def set_levels(self, levels, level=None, inplace=False, verify_integrity=True): """ Set new levels on MultiIndex. Defaults to returning new index. Parameters ---------- levels : sequence or list of sequence New level(s) to apply. level : int, level name, or sequence of int/level names (default None) Level(s) to set (None for all levels). inplace : bool If True, mutates in place. verify_integrity : bool, default True If True, checks that levels and codes are compatible. Returns ------- new index (of same type and class...etc) Examples -------- >>> idx = pd.MultiIndex.from_tuples( ... [ ... (1, "one"), ... (1, "two"), ... (2, "one"), ... (2, "two"), ... (3, "one"), ... (3, "two") ... ], ... names=["foo", "bar"] ... ) >>> idx MultiIndex([(1, 'one'), (1, 'two'), (2, 'one'), (2, 'two'), (3, 'one'), (3, 'two')], names=['foo', 'bar']) >>> idx.set_levels([['a', 'b', 'c'], [1, 2]]) MultiIndex([('a', 1), ('a', 2), ('b', 1), ('b', 2), ('c', 1), ('c', 2)], names=['foo', 'bar']) >>> idx.set_levels(['a', 'b', 'c'], level=0) MultiIndex([('a', 'one'), ('a', 'two'), ('b', 'one'), ('b', 'two'), ('c', 'one'), ('c', 'two')], names=['foo', 'bar']) >>> idx.set_levels(['a', 'b'], level='bar') MultiIndex([(1, 'a'), (1, 'b'), (2, 'a'), (2, 'b'), (3, 'a'), (3, 'b')], names=['foo', 'bar']) If any of the levels passed to ``set_levels()`` exceeds the existing length, all of the values from that argument will be stored in the MultiIndex levels, though the values will be truncated in the MultiIndex output. >>> idx.set_levels([['a', 'b', 'c'], [1, 2, 3, 4]], level=[0, 1]) MultiIndex([('a', 1), ('a', 2), ('b', 1), ('b', 2), ('c', 1), ('c', 2)], names=['foo', 'bar']) >>> idx.set_levels([['a', 'b', 'c'], [1, 2, 3, 4]], level=[0, 1]).levels FrozenList([['a', 'b', 'c'], [1, 2, 3, 4]]) """ if is_list_like(levels) and not isinstance(levels, Index): levels = list(levels) if level is not None and not is_list_like(level): if not is_list_like(levels): raise TypeError("Levels must be list-like") if is_list_like(levels[0]): raise TypeError("Levels must be list-like") level = [level] levels = [levels] elif level is None or is_list_like(level): if not is_list_like(levels) or not is_list_like(levels[0]): raise TypeError("Levels must be list of lists-like") if inplace: idx = self else: idx = self._shallow_copy() idx._reset_identity() idx._set_levels( levels, level=level, validate=True, verify_integrity=verify_integrity ) if not inplace: return idx @property def nlevels(self) -> int: """ Integer number of levels in this MultiIndex. """ return len(self._levels) @property def levshape(self): """ A tuple with the length of each level. """ return tuple(len(x) for x in self.levels) # -------------------------------------------------------------------- # Codes Methods @property def codes(self): return self._codes def _set_codes( self, codes, level=None, copy=False, validate=True, verify_integrity=False ): if validate: if level is None and len(codes) != self.nlevels: raise ValueError("Length of codes must match number of levels") if level is not None and len(codes) != len(level): raise ValueError("Length of codes must match length of levels.") if level is None: new_codes = FrozenList( _coerce_indexer_frozen(level_codes, lev, copy=copy).view() for lev, level_codes in zip(self._levels, codes) ) else: level_numbers = [self._get_level_number(lev) for lev in level] new_codes = list(self._codes) for lev_num, level_codes in zip(level_numbers, codes): lev = self.levels[lev_num] new_codes[lev_num] = _coerce_indexer_frozen(level_codes, lev, copy=copy) new_codes = FrozenList(new_codes) if verify_integrity: new_codes = self._verify_integrity(codes=new_codes) self._codes = new_codes self._tuples = None self._reset_cache() def set_codes(self, codes, level=None, inplace=False, verify_integrity=True): """ Set new codes on MultiIndex. Defaults to returning new index. .. versionadded:: 0.24.0 New name for deprecated method `set_labels`. Parameters ---------- codes : sequence or list of sequence New codes to apply. level : int, level name, or sequence of int/level names (default None) Level(s) to set (None for all levels). inplace : bool If True, mutates in place. verify_integrity : bool (default True) If True, checks that levels and codes are compatible. Returns ------- new index (of same type and class...etc) Examples -------- >>> idx = pd.MultiIndex.from_tuples( ... [(1, "one"), (1, "two"), (2, "one"), (2, "two")], names=["foo", "bar"] ... ) >>> idx MultiIndex([(1, 'one'), (1, 'two'), (2, 'one'), (2, 'two')], names=['foo', 'bar']) >>> idx.set_codes([[1, 0, 1, 0], [0, 0, 1, 1]]) MultiIndex([(2, 'one'), (1, 'one'), (2, 'two'), (1, 'two')], names=['foo', 'bar']) >>> idx.set_codes([1, 0, 1, 0], level=0) MultiIndex([(2, 'one'), (1, 'two'), (2, 'one'), (1, 'two')], names=['foo', 'bar']) >>> idx.set_codes([0, 0, 1, 1], level='bar') MultiIndex([(1, 'one'), (1, 'one'), (2, 'two'), (2, 'two')], names=['foo', 'bar']) >>> idx.set_codes([[1, 0, 1, 0], [0, 0, 1, 1]], level=[0, 1]) MultiIndex([(2, 'one'), (1, 'one'), (2, 'two'), (1, 'two')], names=['foo', 'bar']) """ if level is not None and not is_list_like(level): if not is_list_like(codes): raise TypeError("Codes must be list-like") if is_list_like(codes[0]): raise TypeError("Codes must be list-like") level = [level] codes = [codes] elif level is None or is_list_like(level): if not is_list_like(codes) or not is_list_like(codes[0]): raise TypeError("Codes must be list of lists-like") if inplace: idx = self else: idx = self._shallow_copy() idx._reset_identity() idx._set_codes(codes, level=level, verify_integrity=verify_integrity) if not inplace: return idx # -------------------------------------------------------------------- # Index Internals @cache_readonly def _engine(self): # Calculate the number of bits needed to represent labels in each # level, as log2 of their sizes (including -1 for NaN): sizes = np.ceil(np.log2([len(l) + 1 for l in self.levels])) # Sum bit counts, starting from the _right_.... lev_bits = np.cumsum(sizes[::-1])[::-1] # ... in order to obtain offsets such that sorting the combination of # shifted codes (one for each level, resulting in a unique integer) is # equivalent to sorting lexicographically the codes themselves. Notice # that each level needs to be shifted by the number of bits needed to # represent the _previous_ ones: offsets = np.concatenate([lev_bits[1:], [0]]).astype("uint64") # Check the total number of bits needed for our representation: if lev_bits[0] > 64: # The levels would overflow a 64 bit uint - use Python integers: return MultiIndexPyIntEngine(self.levels, self.codes, offsets) return MultiIndexUIntEngine(self.levels, self.codes, offsets) @property def _constructor(self): return MultiIndex.from_tuples @doc(Index._shallow_copy) def _shallow_copy( self, values=None, name=lib.no_default, levels=None, codes=None, dtype=None, sortorder=None, names=lib.no_default, _set_identity: bool = True, ): if names is not lib.no_default and name is not lib.no_default: raise TypeError("Can only provide one of `names` and `name`") elif names is lib.no_default: names = name if name is not lib.no_default else self.names if values is not None: assert levels is None and codes is None and dtype is None return MultiIndex.from_tuples(values, sortorder=sortorder, names=names) levels = levels if levels is not None else self.levels codes = codes if codes is not None else self.codes result = MultiIndex( levels=levels, codes=codes, dtype=dtype, sortorder=sortorder, names=names, verify_integrity=False, _set_identity=_set_identity, ) result._cache = self._cache.copy() result._cache.pop("levels", None) # GH32669 return result def symmetric_difference(self, other, result_name=None, sort=None): # On equal symmetric_difference MultiIndexes the difference is empty. # Therefore, an empty MultiIndex is returned GH13490 tups = Index.symmetric_difference(self, other, result_name, sort) if len(tups) == 0: return MultiIndex( levels=[[] for _ in range(self.nlevels)], codes=[[] for _ in range(self.nlevels)], names=tups.name, ) return type(self).from_tuples(tups, names=tups.name) # -------------------------------------------------------------------- def copy( self, names=None, dtype=None, levels=None, codes=None, deep=False, name=None, _set_identity=False, ): """ Make a copy of this object. Names, dtype, levels and codes can be passed and will be set on new copy. Parameters ---------- names : sequence, optional dtype : numpy dtype or pandas type, optional levels : sequence, optional codes : sequence, optional deep : bool, default False name : Label Kept for compatibility with 1-dimensional Index. Should not be used. Returns ------- MultiIndex Notes ----- In most cases, there should be no functional difference from using ``deep``, but if ``deep`` is passed it will attempt to deepcopy. This could be potentially expensive on large MultiIndex objects. """ names = self._validate_names(name=name, names=names, deep=deep) if deep: from copy import deepcopy if levels is None: levels = deepcopy(self.levels) if codes is None: codes = deepcopy(self.codes) return self._shallow_copy( levels=levels, codes=codes, names=names, dtype=dtype, sortorder=self.sortorder, _set_identity=_set_identity, ) def __array__(self, dtype=None) -> np.ndarray: """ the array interface, return my values """ return self.values def view(self, cls=None): """ this is defined as a copy with the same identity """ result = self.copy() result._id = self._id return result @doc(Index.__contains__) def __contains__(self, key: Any) -> bool: hash(key) try: self.get_loc(key) return True except (LookupError, TypeError, ValueError): return False @cache_readonly def dtype(self) -> np.dtype: return np.dtype("O") def _is_memory_usage_qualified(self) -> bool: """ return a boolean if we need a qualified .info display """ def f(l): return "mixed" in l or "string" in l or "unicode" in l return any(f(l) for l in self._inferred_type_levels) @doc(Index.memory_usage) def memory_usage(self, deep: bool = False) -> int: # we are overwriting our base class to avoid # computing .values here which could materialize # a tuple representation unnecessarily return self._nbytes(deep) @cache_readonly def nbytes(self) -> int: """ return the number of bytes in the underlying data """ return self._nbytes(False) def _nbytes(self, deep: bool = False) -> int: """ return the number of bytes in the underlying data deeply introspect the level data if deep=True include the engine hashtable this is in internal routine """ # for implementations with no useful getsizeof (PyPy) objsize = 24 level_nbytes = sum(i.memory_usage(deep=deep) for i in self.levels) label_nbytes = sum(i.nbytes for i in self.codes) names_nbytes = sum(getsizeof(i, objsize) for i in self.names) result = level_nbytes + label_nbytes + names_nbytes # include our engine hashtable result += self._engine.sizeof(deep=deep) return result # -------------------------------------------------------------------- # Rendering Methods def _formatter_func(self, tup): """ Formats each item in tup according to its level's formatter function. """ formatter_funcs = [level._formatter_func for level in self.levels] return tuple(func(val) for func, val in zip(formatter_funcs, tup)) def _format_data(self, name=None): """ Return the formatted data as a unicode string """ return format_object_summary( self, self._formatter_func, name=name, line_break_each_value=True ) def _format_attrs(self): """ Return a list of tuples of the (attr,formatted_value). """ return format_object_attrs(self, include_dtype=False) def _format_native_types(self, na_rep="nan", kwargs): new_levels = [] new_codes = [] # go through the levels and format them for level, level_codes in zip(self.levels, self.codes): level = level._format_native_types(na_rep=na_rep, kwargs) # add nan values, if there are any mask = level_codes == -1 if mask.any(): nan_index = len(level) level = np.append(level, na_rep) assert not level_codes.flags.writeable # i.e. copy is needed level_codes = level_codes.copy() # make writeable level_codes[mask] = nan_index new_levels.append(level) new_codes.append(level_codes) if len(new_levels) == 1: # a single-level multi-index return Index(new_levels[0].take(new_codes[0]))._format_native_types() else: # reconstruct the multi-index mi = MultiIndex( levels=new_levels, codes=new_codes, names=self.names, sortorder=self.sortorder, verify_integrity=False, ) return mi._values def format( self, name: Optional[bool] = None, formatter: Optional[Callable] = None, na_rep: Optional[str] = None, names: bool = False, space: int = 2, sparsify=None, adjoin: bool = True, ) -> List: if name is not None: names = name if len(self) == 0: return [] stringified_levels = [] for lev, level_codes in zip(self.levels, self.codes): na = na_rep if na_rep is not None else _get_na_rep(lev.dtype.type) if len(lev) > 0: formatted = lev.take(level_codes).format(formatter=formatter) # we have some NA mask = level_codes == -1 if mask.any(): formatted = np.array(formatted, dtype=object) formatted[mask] = na formatted = formatted.tolist() else: # weird all NA case formatted = [ pprint_thing(na if isna(x) else x, escape_chars=("\t", "\r", "\n")) for x in algos.take_1d(lev._values, level_codes) ] stringified_levels.append(formatted) result_levels = [] for lev, lev_name in zip(stringified_levels, self.names): level = [] if names: level.append( pprint_thing(lev_name, escape_chars=("\t", "\r", "\n")) if lev_name is not None else "" ) level.extend(np.array(lev, dtype=object)) result_levels.append(level) if sparsify is None: sparsify = get_option("display.multi_sparse") if sparsify: sentinel = "" # GH3547 use value of sparsify as sentinel if it's "Falsey" assert isinstance(sparsify, bool) or sparsify is lib.no_default if sparsify in [False, lib.no_default]: sentinel = sparsify # little bit of a kludge job for #1217 result_levels = _sparsify( result_levels, start=int(names), sentinel=sentinel ) if adjoin: from my_happy_pandas.io.formats.format import _get_adjustment adj = _get_adjustment() return adj.adjoin(space, result_levels).split("\n") else: return result_levels # -------------------------------------------------------------------- # Names Methods def _get_names(self): return FrozenList(self._names) def _set_names(self, names, level=None, validate=True): """ Set new names on index. Each name has to be a hashable type. Parameters ---------- values : str or sequence name(s) to set level : int, level name, or sequence of int/level names (default None) If the index is a MultiIndex (hierarchical), level(s) to set (None for all levels). Otherwise level must be None validate : boolean, default True validate that the names match level lengths Raises ------ TypeError if each name is not hashable. Notes ----- sets names on levels. WARNING: mutates! Note that you generally want to set this after* changing levels, so that it only acts on copies """ # GH 15110 # Don't allow a single string for names in a MultiIndex if names is not None and not is_list_like(names): raise ValueError("Names should be list-like for a MultiIndex") names = list(names) if validate: if level is not None and len(names) != len(level): raise ValueError("Length of names must match length of level.") if level is None and len(names) != self.nlevels: raise ValueError( "Length of names must match number of levels in MultiIndex." ) if level is None: level = range(self.nlevels) else: level = [self._get_level_number(lev) for lev in level] # set the name for lev, name in zip(level, names): if name is not None: # GH 20527 # All items in 'names' need to be hashable: if not is_hashable(name): raise TypeError( f"{type(self).__name__}.name must be a hashable type" ) self._names[lev] = name # If .levels has been accessed, the names in our cache will be stale. self._reset_cache() names = property( fset=_set_names, fget=_get_names, doc="""\nNames of levels in MultiIndex.\n""" ) # -------------------------------------------------------------------- @doc(Index._get_grouper_for_level) def _get_grouper_for_level(self, mapper, level): indexer = self.codes[level] level_index = self.levels[level] if mapper is not None: # Handle group mapping function and return level_values = self.levels[level].take(indexer) grouper = level_values.map(mapper) return grouper, None, None codes, uniques = algos.factorize(indexer, sort=True) if len(uniques) > 0 and uniques[0] == -1: # Handle NAs mask = indexer != -1 ok_codes, uniques = algos.factorize(indexer[mask], sort=True) codes = np.empty(len(indexer), dtype=indexer.dtype) codes[mask] = ok_codes codes[~mask] = -1 if len(uniques) < len(level_index): # Remove unobserved levels from level_index level_index = level_index.take(uniques) else: # break references back to us so that setting the name # on the output of a groupby doesn't reflect back here. level_index = level_index.copy() if level_index._can_hold_na: grouper = level_index.take(codes, fill_value=True) else: grouper = level_index.take(codes) return grouper, codes, level_index @cache_readonly def inferred_type(self) -> str: return "mixed" def _get_level_number(self, level) -> int: count = self.names.count(level) if (count > 1) and not is_integer(level): raise ValueError( f"The name {level} occurs multiple times, use a level number" ) try: level = self.names.index(level) except ValueError as err: if not is_integer(level): raise KeyError(f"Level {level} not found") from err elif level < 0: level += self.nlevels if level < 0: orig_level = level - self.nlevels raise IndexError( f"Too many levels: Index has only {self.nlevels} levels, " f"{orig_level} is not a valid level number" ) from err # Note: levels are zero-based elif level >= self.nlevels: raise IndexError( f"Too many levels: Index has only {self.nlevels} levels, " f"not {level + 1}" ) from err return level @property def _has_complex_internals(self) -> bool: # used to avoid libreduction code paths, which raise or require conversion return True @cache_readonly def is_monotonic_increasing(self) -> bool: """ return if the index is monotonic increasing (only equal or increasing) values. """ if any(-1 in code for code in self.codes): return False if all(level.is_monotonic for level in self.levels): # If each level is sorted, we can operate on the codes directly. GH27495 return libalgos.is_lexsorted( [x.astype("int64", copy=False) for x in self.codes] ) # reversed() because lexsort() wants the most significant key last. values = [ self._get_level_values(i)._values for i in reversed(range(len(self.levels))) ] try: sort_order = np.lexsort(values) return Index(sort_order).is_monotonic except TypeError: # we have mixed types and np.lexsort is not happy return Index(self._values).is_monotonic @cache_readonly def is_monotonic_decreasing(self) -> bool: """ return if the index is monotonic decreasing (only equal or decreasing) values. """ # monotonic decreasing if and only if reverse is monotonic increasing return self[::-1].is_monotonic_increasing @cache_readonly def _inferred_type_levels(self): """ return a list of the inferred types, one for each level """ return [i.inferred_type for i in self.levels] @doc(Index.duplicated) def duplicated(self, keep="first"): shape = map(len, self.levels) ids = get_group_index(self.codes, shape, sort=False, xnull=False) return duplicated_int64(ids, keep) def fillna(self, value=None, downcast=None): """ fillna is not implemented for MultiIndex """ raise NotImplementedError("isna is not defined for MultiIndex") @doc(Index.dropna) def dropna(self, how="any"): nans = [level_codes == -1 for level_codes in self.codes] if how == "any": indexer = np.any(nans, axis=0) elif how == "all": indexer = np.all(nans, axis=0) else: raise ValueError(f"invalid how option: {how}") new_codes = [level_codes[~indexer] for level_codes in self.codes] return self.copy(codes=new_codes, deep=True) def _get_level_values(self, level, unique=False): """ Return vector of label values for requested level, equal to the length of the index this is an internal method Parameters ---------- level : int level unique : bool, default False if True, drop duplicated values Returns ------- values : ndarray """ lev = self.levels[level] level_codes = self.codes[level] name = self._names[level] if unique: level_codes = algos.unique(level_codes) filled = algos.take_1d(lev._values, level_codes, fill_value=lev._na_value) return lev._shallow_copy(filled, name=name) def get_level_values(self, level): """ Return vector of label values for requested level. Length of returned vector is equal to the length of the index. Parameters ---------- level : int or str ``level`` is either the integer position of the level in the MultiIndex, or the name of the level. Returns ------- values : Index Values is a level of this MultiIndex converted to a single :class:`Index` (or subclass thereof). Examples -------- Create a MultiIndex: >>> mi = pd.MultiIndex.from_arrays((list('abc'), list('def'))) >>> mi.names = ['level_1', 'level_2'] Get level values by supplying level as either integer or name: >>> mi.get_level_values(0) Index(['a', 'b', 'c'], dtype='object', name='level_1') >>> mi.get_level_values('level_2') Index(['d', 'e', 'f'], dtype='object', name='level_2') """ level = self._get_level_number(level) values = self._get_level_values(level) return values @doc(Index.unique) def unique(self, level=None): if level is None: return super().unique() else: level = self._get_level_number(level) return self._get_level_values(level=level, unique=True) def _to_safe_for_reshape(self): """ convert to object if we are a categorical """ return self.set_levels([i._to_safe_for_reshape() for i in self.levels]) def to_frame(self, index=True, name=None): """ Create a DataFrame with the levels of the MultiIndex as columns. Column ordering is determined by the DataFrame constructor with data as a dict. .. versionadded:: 0.24.0 Parameters ---------- index : bool, default True Set the index of the returned DataFrame as the original MultiIndex. name : list / sequence of str, optional The passed names should substitute index level names. Returns ------- DataFrame : a DataFrame containing the original MultiIndex data. See Also -------- DataFrame : Two-dimensional, size-mutable, potentially heterogeneous tabular data. """ from my_happy_pandas import DataFrame if name is not None: if not is_list_like(name): raise TypeError("'name' must be a list / sequence of column names.") if len(name) != len(self.levels): raise ValueError( "'name' should have same length as number of levels on index." ) idx_names = name else: idx_names = self.names # Guarantee resulting column order - PY36+ dict maintains insertion order result = DataFrame( { (level if lvlname is None else lvlname): self._get_level_values(level) for lvlname, level in zip(idx_names, range(len(self.levels))) }, copy=False, ) if index: result.index = self return result def to_flat_index(self): """ Convert a MultiIndex to an Index of Tuples containing the level values. .. versionadded:: 0.24.0 Returns ------- pd.Index Index with the MultiIndex data represented in Tuples. Notes ----- This method will simply return the caller if called by anything other than a MultiIndex. Examples -------- >>> index = pd.MultiIndex.from_product( ... [['foo', 'bar'], ['baz', 'qux']], ... names=['a', 'b']) >>> index.to_flat_index() Index([('foo', 'baz'), ('foo', 'qux'), ('bar', 'baz'), ('bar', 'qux')], dtype='object') """ return Index(self._values, tupleize_cols=False) @property def is_all_dates(self) -> bool: return False def is_lexsorted(self) -> bool: """ Return True if the codes are lexicographically sorted. Returns ------- bool Examples -------- In the below examples, the first level of the MultiIndex is sorted because a<b<c, so there is no need to look at the next level. >>> pd.MultiIndex.from_arrays([['a', 'b', 'c'], ['d', 'e', 'f']]).is_lexsorted() True >>> pd.MultiIndex.from_arrays([['a', 'b', 'c'], ['d', 'f', 'e']]).is_lexsorted() True In case there is a tie, the lexicographical sorting looks at the next level of the MultiIndex. >>> pd.MultiIndex.from_arrays([[0, 1, 1], ['a', 'b', 'c']]).is_lexsorted() True >>> pd.MultiIndex.from_arrays([[0, 1, 1], ['a', 'c', 'b']]).is_lexsorted() False >>> pd.MultiIndex.from_arrays([['a', 'a', 'b', 'b'], ... ['aa', 'bb', 'aa', 'bb']]).is_lexsorted() True >>> pd.MultiIndex.from_arrays([['a', 'a', 'b', 'b'], ... ['bb', 'aa', 'aa', 'bb']]).is_lexsorted() False """ return self.lexsort_depth == self.nlevels @cache_readonly def lexsort_depth(self): if self.sortorder is not None: return self.sortorder return self._lexsort_depth() def _lexsort_depth(self) -> int: """ Compute and return the lexsort_depth, the number of levels of the MultiIndex that are sorted lexically Returns ------- int """ int64_codes = [ensure_int64(level_codes) for level_codes in self.codes] for k in range(self.nlevels, 0, -1): if libalgos.is_lexsorted(int64_codes[:k]): return k return 0 def _sort_levels_monotonic(self): """ This is an internal function. Create a new MultiIndex from the current to monotonically sorted items IN the levels. This does not actually make the entire MultiIndex monotonic, JUST the levels. The resulting MultiIndex will have the same outward appearance, meaning the same .values and ordering. It will also be .equals() to the original. Returns ------- MultiIndex Examples -------- >>> mi = pd.MultiIndex(levels=[['a', 'b'], ['bb', 'aa']], ... codes=[[0, 0, 1, 1], [0, 1, 0, 1]]) >>> mi MultiIndex([('a', 'bb'), ('a', 'aa'), ('b', 'bb'), ('b', 'aa')], ) >>> mi.sort_values() MultiIndex([('a', 'aa'), ('a', 'bb'), ('b', 'aa'), ('b', 'bb')], ) """ if self.is_lexsorted() and self.is_monotonic: return self new_levels = [] new_codes = [] for lev, level_codes in zip(self.levels, self.codes): if not lev.is_monotonic: try: # indexer to reorder the levels indexer = lev.argsort() except TypeError: pass else: lev = lev.take(indexer) # indexer to reorder the level codes indexer = ensure_int64(indexer) ri = lib.get_reverse_indexer(indexer, len(indexer)) level_codes = algos.take_1d(ri, level_codes) new_levels.append(lev) new_codes.append(level_codes) return MultiIndex( new_levels, new_codes, names=self.names, sortorder=self.sortorder, verify_integrity=False, ) def remove_unused_levels(self): """ Create new MultiIndex from current that removes unused levels. Unused level(s) means levels that are not expressed in the labels. The resulting MultiIndex will have the same outward appearance, meaning the same .values and ordering. It will also be .equals() to the original. Returns ------- MultiIndex Examples -------- >>> mi = pd.MultiIndex.from_product([range(2), list('ab')]) >>> mi MultiIndex([(0, 'a'), (0, 'b'), (1, 'a'), (1, 'b')], ) >>> mi[2:] MultiIndex([(1, 'a'), (1, 'b')], ) The 0 from the first level is not represented and can be removed >>> mi2 = mi[2:].remove_unused_levels() >>> mi2.levels FrozenList([[1], ['a', 'b']]) """ new_levels = [] new_codes = [] changed = False for lev, level_codes in zip(self.levels, self.codes): # Since few levels are typically unused, bincount() is more # efficient than unique() - however it only accepts positive values # (and drops order): uniques = np.where(np.bincount(level_codes + 1) > 0)[0] - 1 has_na = int(len(uniques) and (uniques[0] == -1)) if len(uniques) != len(lev) + has_na: # We have unused levels changed = True # Recalculate uniques, now preserving order. # Can easily be cythonized by exploiting the already existing # "uniques" and stop parsing "level_codes" when all items # are found: uniques = algos.unique(level_codes) if has_na: na_idx = np.where(uniques == -1)[0] # Just ensure that -1 is in first position: uniques[[0, na_idx[0]]] = uniques[[na_idx[0], 0]] # codes get mapped from uniques to 0:len(uniques) # -1 (if present) is mapped to last position code_mapping = np.zeros(len(lev) + has_na) # ... and reassigned value -1: code_mapping[uniques] = np.arange(len(uniques)) - has_na level_codes = code_mapping[level_codes] # new levels are simple lev = lev.take(uniques[has_na:]) new_levels.append(lev) new_codes.append(level_codes) result = self.view() if changed: result._reset_identity() result._set_levels(new_levels, validate=False) result._set_codes(new_codes, validate=False) return result # -------------------------------------------------------------------- # Pickling Methods def __reduce__(self): """Necessary for making this object picklable""" d = dict( levels=list(self.levels), codes=list(self.codes), sortorder=self.sortorder, names=list(self.names), ) return ibase._new_Index, (type(self), d), None # -------------------------------------------------------------------- def __getitem__(self, key): if is_scalar(key): key = com.cast_scalar_indexer(key, warn_float=True) retval = [] for lev, level_codes in zip(self.levels, self.codes): if level_codes[key] == -1: retval.append(np.nan) else: retval.append(lev[level_codes[key]]) return tuple(retval) else: if com.is_bool_indexer(key): key = np.asarray(key, dtype=bool) sortorder = self.sortorder else: # cannot be sure whether the result will be sorted sortorder = None if isinstance(key, Index): key = np.asarray(key) new_codes = [level_codes[key] for level_codes in self.codes] return MultiIndex( levels=self.levels, codes=new_codes, names=self.names, sortorder=sortorder, verify_integrity=False, ) @Appender(_index_shared_docs["take"] % _index_doc_kwargs) def take(self, indices, axis=0, allow_fill=True, fill_value=None, *kwargs): nv.validate_take(tuple(), kwargs) indices = ensure_platform_int(indices) taken = self._assert_take_fillable( self.codes, indices, allow_fill=allow_fill, fill_value=fill_value, na_value=-1, ) return MultiIndex( levels=self.levels, codes=taken, names=self.names, verify_integrity=False ) def _assert_take_fillable( self, values, indices, allow_fill=True, fill_value=None, na_value=None ): """ Internal method to handle NA filling of take """ # only fill if we are passing a non-None fill_value if allow_fill and fill_value is not None: if (indices < -1).any(): msg = ( "When allow_fill=True and fill_value is not None, " "all indices must be >= -1" ) raise ValueError(msg) taken = [lab.take(indices) for lab in self.codes] mask = indices == -1 if mask.any(): masked = [] for new_label in taken: label_values = new_label label_values[mask] = na_value masked.append(np.asarray(label_values)) taken = masked else: taken = [lab.take(indices) for lab in self.codes] return taken def append(self, other): """ Append a collection of Index options together Parameters ---------- other : Index or list/tuple of indices Returns ------- appended : Index """ if not isinstance(other, (list, tuple)): other = [other] if all( (isinstance(o, MultiIndex) and o.nlevels >= self.nlevels) for o in other ): arrays = [] for i in range(self.nlevels): label = self._get_level_values(i) appended = [o._get_level_values(i) for o in other] arrays.append(label.append(appended)) return MultiIndex.from_arrays(arrays, names=self.names) to_concat = (self._values,) + tuple(k._values for k in other) new_tuples = np.concatenate(to_concat) # if all(isinstance(x, MultiIndex) for x in other): try: return MultiIndex.from_tuples(new_tuples, names=self.names) except (TypeError, IndexError): return Index(new_tuples) def argsort(self, args, *kwargs) -> np.ndarray: return self._values.argsort(args, **kwargs) @Appender(_index_shared_docs["repeat"] % _index_doc_kwargs) def repeat(self, repeats, axis=None): nv.validate_repeat(tuple(), dict(axis=axis)) repeats = ensure_platform_int(repeats) return MultiIndex( levels=self.levels, codes=[ level_codes.view(np.ndarray).astype(np.intp).repeat(repeats) for level_codes in self.codes ], names=self.names, sortorder=self.sortorder, verify_integrity=False, ) def where(self, cond, other=None): raise NotImplementedError(".where is not supported for MultiIndex operations") def drop(self, codes, level=None, errors="raise"): """ Make new MultiIndex with passed list of codes deleted Parameters ---------- codes : array-like Must be a list of tuples level : int or level name, default None errors : str, default 'raise' Returns ------- dropped : MultiIndex """ if level is not None: return self._drop_from_level(codes, level, errors) if not isinstance(codes, (np.ndarray, Index)): try: codes = com.index_labels_to_array(codes, dtype=object) except ValueError: pass inds = [] for level_codes in codes: try: loc = self.get_loc(level_codes) # get_loc returns either an integer, a slice, or a boolean # mask if isinstance(loc, int): inds.append(loc) elif isinstance(loc, slice): inds.extend(range(loc.start, loc.stop)) elif com.is_bool_indexer(loc): if self.lexsort_depth == 0: warnings.warn( "dropping on a non-lexsorted multi-index " "without a level parameter may impact performance.", PerformanceWarning, stacklevel=3, ) loc = loc.nonzero()[0] inds.extend(loc) else: msg = f"unsupported indexer of type {type(loc)}" raise AssertionError(msg) except KeyError: if errors != "ignore": raise return self.delete(inds) def _drop_from_level(self, codes, level, errors="raise"): codes = com.index_labels_to_array(codes) i = self._get_level_number(level) index = self.levels[i] values = index.get_indexer(codes) mask = ~algos.isin(self.codes[i], values) if mask.all() and errors != "ignore": raise KeyError(f"labels {codes} not found in level") return self[mask] def swaplevel(self, i=-2, j=-1): """ Swap level i with level j. Calling this method does not change the ordering of the values. Parameters ---------- i : int, str, default -2 First level of index to be swapped. Can pass level name as string. Type of parameters can be mixed. j : int, str, default -1 Second level of index to be swapped. Can pass level name as string. Type of parameters can be mixed. Returns ------- MultiIndex A new MultiIndex. See Also -------- Series.swaplevel : Swap levels i and j in a MultiIndex. Dataframe.swaplevel : Swap levels i and j in a MultiIndex on a particular axis. Examples -------- >>> mi = pd.MultiIndex(levels=[['a', 'b'], ['bb', 'aa']], ... codes=[[0, 0, 1, 1], [0, 1, 0, 1]]) >>> mi MultiIndex([('a', 'bb'), ('a', 'aa'), ('b', 'bb'), ('b', 'aa')], ) >>> mi.swaplevel(0, 1) MultiIndex([('bb', 'a'), ('aa', 'a'), ('bb', 'b'), ('aa', 'b')], ) """ new_levels = list(self.levels) new_codes = list(self.codes) new_names = list(self.names) i = self._get_level_number(i) j = self._get_level_number(j) new_levels[i], new_levels[j] = new_levels[j], new_levels[i] new_codes[i], new_codes[j] = new_codes[j], new_codes[i] new_names[i], new_names[j] = new_names[j], new_names[i] return MultiIndex( levels=new_levels, codes=new_codes, names=new_names, verify_integrity=False ) def reorder_levels(self, order): """ Rearrange levels using input order. May not drop or duplicate levels. Parameters ---------- order : list of int or list of str List representing new level order. Reference level by number (position) or by key (label). Returns ------- MultiIndex """ order = [self._get_level_number(i) for i in order] if len(order) != self.nlevels: raise AssertionError( f"Length of order must be same as number of levels ({self.nlevels}), " f"got {len(order)}" ) new_levels = [self.levels[i] for i in order] new_codes = [self.codes[i] for i in order] new_names = [self.names[i] for i in order] return MultiIndex( levels=new_levels, codes=new_codes, names=new_names, verify_integrity=False ) def _get_codes_for_sorting(self): """ we categorizing our codes by using the available categories (all, not just observed) excluding any missing ones (-1); this is in preparation for sorting, where we need to disambiguate that -1 is not a valid valid """ def cats(level_codes): return np.arange(	np.array(level_codes)	numpy.array
#! /usr/bin/env python import sys import time import random import argparse import itertools import numpy as np import baldor as br import raveutils as ru import robotsp as rtsp import openravepy as orpy from scipy.spatial import ConvexHull from lenny_openrave.manager import EnvironmentManager from lenny_openrave.scheduler import PDPScheduler from lenny_openrave.bimanual import BimanualPlanner def parse_args(): # Remove extra IPython notebook args clean_argv = sys.argv if "-f" in clean_argv: clean_argv = clean_argv[1:] # Parse format_class = argparse.RawDescriptionHelpFormatter parser = argparse.ArgumentParser(description="Lenny RoboTSP bimanual") parser.add_argument("-r", "--reachability", action="store_true", help="If set, will only show reachability") parser.add_argument("-s", "--seed", type=int, default=123, help="Seed for the random yaw of the cubes") parser.add_argument("-v", "--viewer", action="store_true", help="If set, will show the qtcoin viewer") parser.add_argument("--ik", action="store_true", help="If set, will only show the found IK solutions") return parser.parse_args() args = parse_args() np.set_printoptions(precision=6, suppress=True) # Load the environment env = orpy.Environment() world_xml = "worlds/bimanual_pick_and_place.env.xml" if not env.Load(world_xml): raise Exception("Failed to load world: {}".format(world_xml)) robot = env.GetRobot("robot") robot.SetDOFValues(np.zeros(robot.GetDOF())) # Environment manager eman = EnvironmentManager(env, num_cubes=8, seed=args.seed) cubes = eman.get_cubes() bins = eman.get_bins() # Initialize the bimanual planner bimanual = BimanualPlanner(robot) bimanual.set_left_manipulator("arm_left_tool0") bimanual.set_right_manipulator("arm_right_tool0") bimanual.set_torso_joint("torso_joint_b1") if not bimanual.load_ikfast(freeinc=np.pi / 6.): print("Failed to load IKFast. Run the generate_robot_databases.sh script.") exit(0) # Start and configure the viewer if args.viewer: viewer_name = "qtcoin" print("Starting viewer: {0}".format(viewer_name)) eman.start_viewer(viewer_name) if args.reachability: # Reachability. One arm is enough due to symmetry print ("Computing reachable workspace...") indices = np.zeros(3) indices[1:] = bimanual.left_indices[:2] manip = bimanual.left_manip Toffset =	np.eye(4)	numpy.eye
import os, glob import subprocess from os import listdir from os.path import isfile, join import time import traceback import shutil import numpy as np import csv import time def checkForUpdate(count, lastUpdate): sn = os.environ['SERVERNUM'] hdfs = os.environ['HDFS'] updateCount = -1 print("UPDATE CHECK: SERVER") print([count, lastUpdate]) while(updateCount == -1): time.sleep(10) print('Checking') for i in range(lastUpdate+1, count): print([i,count]) print("In Check "+str(i)) out = os.popen('/opt/hadoop/bin/hadoop fs -test -e hdfs://'+hdfs+':9000/server_'+ sn+'/run_'+str(i)+'/knndata && echo $?').read() try: if(int(out) == 0): updateCount = i print("Update Ready: "+str(i)) except: traceback.print_exc() print("Update Not Ready") break; if(updateCount > -1): try: os.remove('knndatasetGI') except: pass out = os.popen('/opt/hadoop/bin/hadoop fs -copyToLocal hdfs://'+hdfs+':9000/server_'+ sn+'/run_'+str(updateCount)+'/knndata knndatasetGI').read() return updateCount def updateLocal(): pwd = os.getcwd() print(pwd) knndata = np.genfromtxt('knndatasetGI',delimiter=',') os.chdir(pwd+'/tmp/') for f in glob.glob(''): print(f) for f in glob.glob('.JPG'): fname = f.split('.')[0] #cmd = 'bash '+pwd+'/Parser/runParser.sh '+pwd+'/tmp/'+str(i)+'/'+f #print(cmd) #out = os.popen(cmd).read().rstrip()[1:-1].split(',') #line = [] #for feat in out: # line.append(float(feat.split('=')[1])) data = [] with open(pwd+'/tmp/'+fname+'.csv') as csvf: reader = csv.reader(csvf) data = list(reader)[0] line = [] for d in data: line.append(float(d)) #print(line) npl =	np.asarray(line)	numpy.asarray
"""Unit tests for probsevere_io.py.""" import copy import unittest import numpy import pandas from gewittergefahr.gg_io import probsevere_io from gewittergefahr.gg_utils import storm_tracking_utils as tracking_utils TOP_DIRECTORY_NAME = 'foo' FTP_DIRECTORY_NAME = 'bar' VALID_TIME_UNIX_SEC = 1507181187 # 052627 5 Oct 2017 PATHLESS_JSON_FILE_NAME = 'SSEC_AWIPS_PROBSEVERE_20171005_052627.json' PATHLESS_ASCII_FILE_NAME = 'SSEC_AWIPS_PROBSEVERE_20171005_052627.ascii' JSON_FILE_NAME = ( 'foo/201710/20171005/SSEC_AWIPS_PROBSEVERE_20171005_052627.json' ) ASCII_FILE_NAME = ( 'foo/201710/20171005/SSEC_AWIPS_PROBSEVERE_20171005_052627.ascii' ) ALTERNATIVE_JSON_FILE_NAME = ( 'foo/201710/20171005/SSEC_AWIPS_CONVECTPROB_20171005_052627.json' ) ALTERNATIVE_ASCII_FILE_NAME = ( 'foo/201710/20171005/SSEC_AWIPS_CONVECTPROB_20171005_052627.ascii' ) JSON_FILE_NAME_ON_FTP = 'bar/SSEC_AWIPS_PROBSEVERE_20171005_052627.json' # The following constants are used to test # _get_dates_needed_for_renaming_storms. NUM_DATES_IN_PERIOD = 20 WORKING_DATE_INDEX_MIDDLE = 10 DATE_NEEDED_INDICES_START = numpy.array([0, 1], dtype=int) DATE_NEEDED_INDICES_END = numpy.array([18, 19], dtype=int) DATE_NEEDED_INDICES_MIDDLE = numpy.array([9, 10, 11], dtype=int) # The following constants are used to test _rename_storms_one_original_id. STORM_TIMES_UNIX_SEC = numpy.array( [0, 1, 2, 3, 6, 7, 8, 9, 12, 15], dtype=int ) NEXT_ID_NUMBER = 5 MAX_DROPOUT_TIME_SECONDS = 2 STORM_ID_STRINGS = [ '5probSevere', '5probSevere', '5probSevere', '5probSevere', '6probSevere', '6probSevere', '6probSevere', '6probSevere', '7probSevere', '8probSevere' ] NEXT_ID_NUMBER_AFTER_ONE_ORIG_ID = 9 # The following constants are used to test _rename_storms_one_table. WORKING_DATE_INDEX_FOR_TABLE = 1 THESE_ID_STRINGS = [ 'a', 'b', 'c', 'b', 'd', 'a', 'b', 'd', 'a', 'b', 'c' ] THESE_TIMES_UNIX_SEC =	numpy.array([0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3], dtype=int)	numpy.array
""" Copyright (C) 2018-2020 Intel Corporation Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. """ import numpy as np from mo.front.common.partial_infer.utils import int64_array from mo.front.extractor import FrontExtractorOp from mo.ops.pooling import Pooling from extensions.ops.adaptive_avg_pooling import AdaptiveAvgPooling from mo.utils.error import Error from .common import get_pads class MaxPool2dFrontExtractor(FrontExtractorOp): op = 'MaxPool2d' enabled = True @classmethod def extract(cls, node): # Extract pads attribute final_pads = get_pads(node.module) # Extract strides attribute strides = [node.module.stride, node.module.stride] final_strides = np.array([1, 1, strides], dtype=np.int64) kernel_shape = [node.module.kernel_size, node.module.kernel_size] final_kernel_shape = np.array([1, 1, kernel_shape], dtype=np.int64) attrs = { 'op': node.op, 'window': final_kernel_shape, 'stride': final_strides, 'pad': final_pads, 'pool_method': 'max', 'channel_dims': np.array([1], dtype=np.int64), 'batch_dims': np.array([0], dtype=np.int64), 'layout': 'NCHW', } if (node.module.ceil_mode): attrs['rounding_type'] = 'ceil' # update the attributes of the node Pooling.update_node_stat(node, attrs) return cls.enabled class AdaptiveAvgPool2dFrontExtractor(FrontExtractorOp): op = 'AdaptiveAvgPool2d' enabled = True @classmethod def extract(cls, node): output_size = node.module.output_size # If a single integer but not a tuple or list if not hasattr(output_size, '__contains__'): output_size = [output_size, output_size] data = { 'output_size': output_size, } AdaptiveAvgPooling.update_node_stat(node, data) return cls.enabled class AvgPool2dFrontExtractor(FrontExtractorOp): op = 'AvgPool2d' enabled = True @classmethod def extract(cls, node): # Extract pads attribute final_pads = get_pads(node.module) # Extract strides attribute strides = [node.module.stride, node.module.stride] final_strides = np.array([1, 1, *strides], dtype=np.int64) kernel_shape = [node.module.kernel_size, node.module.kernel_size] final_kernel_shape =	np.array([1, 1, *kernel_shape], dtype=np.int64)	numpy.array
# ---------------------------------------------------------------------------- # Copyright 2014-2016 Nervana Systems Inc. # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ---------------------------------------------------------------------------- """ Our CPU based backend interface and tensor data structure. Our implementation wraps :mod:`numpy` ndarray and related operations """ from __future__ import division from builtins import object, round, str, zip import numpy as np import logging import time from neon.backends.backend import Tensor, Backend, OpTreeNode, OpCollection from neon.backends.layer_cpu import ConvLayer, DeconvLayer, PoolLayer from neon.util.compat import xrange _none_slice = slice(None, None, None) logger = logging.getLogger(__name__) # TODO: enable this flag to find numerical problems # np.seterr(all='raise') class CPUTensor(Tensor): """ The n-dimensional array data structure that resides in host memory, and is meant to be manipulated on the CPU. wrapped `numpy.ndarray` tensor. Arguments: dtype (numpy.ndtype, optional): underlying data type of the elements. ary (data array, optional): optionally it can be instantiated with a data array persist_values (bool, optional): If set to True (the default), the values assigned to this Tensor will persist across multiple begin and end calls. Setting to False may provide a performance increase if values do not need to be maintained across such calls See also: :class:`NervanaCPU` class """ _tensor = None def __init__(self, backend, shape=None, dtype=np.float32, ary=None, name=None, persist_values=True, base=None): super(CPUTensor, self).__init__(backend, shape, dtype, name, persist_values) # supported dtypes assert dtype in (np.float16, np.float32, np.float64, np.uint8, np.int8, np.uint16, np.int16, np.uint32, np.int32) dtype = np.dtype(dtype) if type(ary) != np.ndarray: self._tensor = np.array(ary, dtype) elif ary.dtype != dtype: self._tensor = ary.astype(dtype) else: self._tensor = ary while self._tensor.ndim < self._min_dims: self._tensor = self._tensor.reshape(self._tensor.shape + (1, )) if shape is not None and len(shape) < self._min_dims: self.shape = shape + (1, )(self._min_dims - len(shape)) else: self.shape = self._tensor.shape shape_ = [] size = 1 for dim in self.shape: if int(dim) != dim: raise TypeError('shape dims must be integer values [%s]' % str(dim)) dim = int(dim) shape_.append(dim) size = dim self.shape = tuple(shape_) self.size = size self.base = base self.dtype = dtype self.is_contiguous = self._tensor.flags.c_contiguous def __str__(self): """ Returns a string representation of this Tensor. Returns: str: the representation. """ if self._tensor.base is not None: base_id = id(self._tensor.base) else: base_id = id(self._tensor) return ("CPUTensor(base 0x%x) name:%s shape:%s dtype:%s strides:%s" " is_c_contiguous:%s" % (base_id, self.name, self.shape, self.dtype, self._tensor.strides, self._tensor.flags.c_contiguous)) def __repr__(self): """ Returns a more unambiguous string representation of the Tensor. Returns: str: the representation. """ return self.__str__() def __len__(self): """ Return the size of the leading dimension of self. """ if len(self.shape): return self.shape[0] else: return 0 def __setitem__(self, key, value): """ Assign the specified value to a subset of elements found via slice style indexing along each dimension. e.g. A[5:10, :] = 4.5. Each slice consists of start_idx:stop_idx:step_size triplets. If step_size isn't specified it defaults to 1. If start_idx isn't specified it defaults to 0. If stop_idx isn't specified it defaults to the total number of elements along that dimension. As such a slice value of ':' allows one to select all elements along that dimension. Arguments: key (int, slice, tuple): indices of each dimension's slice. value (numeric array, CPUTensor): values to be assigned to the extracted element subset. If an array it should be the same shape as what key indexes (or be broadcastable as such). """ self.__getitem__(key)._assign(value) return self def __getitem__(self, key): """ Extract a subset view of the items via slice style indexing along each dimension. e.g. A[5:10, :]. Each slice consists of start_idx:stop_idx:step_size triplets. If step_size isn't specified it defaults to 1. If start_idx isn't specified it defaults to 0. If stop_idx isn't specified it defaults to the total number of elements along that dimension. As such a slice value of ':' allows one to select all elements along that dimension. To be consistent with GPU Tensors, CPU Tensors remove the axis that has size 1 unless it needs to maintain 2D. Arguments: key (int, slice, tuple): indices of each dimension's slice. Returns: CPUTensor: view of self corresponding to the subset items. """ # speed up common case of [:] if not isinstance(key, tuple): if key == _none_slice: return self key = (key,) # ensure we return a view # exact same behavior as cpu # let a.shape = (3,4) # a[1,1] = 10 # cpu, gpu and numpy # type(a[1,1]) # for cpu and gpu type is Tensor; for numpy type is float key_list = list(key) for idx, k in enumerate(key): if type(k) is int: k = self.shape[idx] + k if k < 0 else k key_list[idx] = slice(k, k + 1, None) key = tuple(key_list) new_shape = list(self._tensor[key].shape) for idx, k in enumerate(new_shape): if len(new_shape) > 2 and k is 1: new_shape.remove(k) # return a view of the tensor return self.__class__( backend=self.backend, ary=self._tensor[key].reshape(new_shape), dtype=self._tensor.dtype, base=self) def _assign(self, value): """ Assign an input value to the CPU tensor. The NervanaCPU does clipping for int and uint types, when overflow happens Arguments: value (CPUTensor, OpTreeNode, numeric): the value to be assigned. """ if isinstance(value, (CPUTensor, OpTreeNode)): OpTreeNode.build("assign", self, value) elif isinstance(value, (int, float, np.ndarray)): self.set(value) else: raise TypeError("Invalid type for assignment: %s" % type(value)) return self def set(self, value): """ Wrap the value into NervanaCPU tensor. Arguments: value: Array or single input. If it is array, check and Convert the dtype and shape. If it is single value, broadcast to the memory Returns: self """ if isinstance(value, np.ndarray): if value.dtype is not self.dtype: value = value.astype(self.dtype) assert value.size == self.size if value.ndim < self._min_dims: value = value.reshape(self.shape) self._tensor[:] = value return self def get(self): """ Return the array. """ return self._tensor.copy() def raw(self): """ Access the raw buffer. Returns: pointer: A device specific pointer """ return self._tensor.ctypes.data def asnumpyarray(self): """ Deprecated. Scheduled to be removed in 2.0. Use get() instead. """ return self._tensor def take(self, indices, axis=None): """ Select a subset of elements from an array across an axis. Arguments: indices (Tensor, numpy ndarray): indicies of elements to select axis (int): axis across which to select the values Returns: Tensor: Tensor with selected values """ if type(indices) == self.__class__: indices = indices._tensor # if indices are nx1 or 1xn, much of our code assumes these dims are # collapsed, hence the squeeze call. if type(indices) == np.ndarray: indices = indices.squeeze() new_shape = list(self.shape) new_shape[axis] = indices.size return self.__class__( backend=self.backend, ary=self._tensor.take(indices, axis).reshape(new_shape), dtype=self._tensor.dtype, base=self) def fill(self, value): """ Assign specified value to each element of this CPUTensor. Arguments: value (numeric): The value to be assigned to each element. Return: CPUTensor: updated view of the data. """ self._tensor.fill(value) return self def copy(self, a): """ Construct and return a deep copy of the Tensor passed. Arguments: a (Tensor): the object to copy Returns: Tensor: new array object with the same values as input tensor """ return self._assign(a) def copy_from(self, a): """ Alias of copy. Arguments: a (Tensor): the object to copy Returns: Tensor: new array object with the same values as input tensor """ return self._assign(a) def reshape(self, *shape): """ Return a reshaped view. """ if isinstance(shape[0], (tuple, list)): shape = tuple(shape[0]) if shape == self.shape: return self return self.__class__( backend=self.backend, ary=self._tensor.reshape(shape), dtype=self._tensor.dtype, base=self) @property def T(self): """ Return a transposed view. For 2D tensor, will do a normal transpose For 3D tensor, will keep the 0 dim, swap the 1 and 2 dimensions """ if len(self.shape) <= 2: ary = self._tensor.transpose() else: # support for batched dot. # perserve outer dimension but reverse inner dims # shape = np.concatenate((shape[-1:], shape[:-1]) ary = self._tensor.swapaxes(1, 2) return self.__class__( backend=self.backend, ary=ary, dtype=self._tensor.dtype, base=self) def transpose(self, out=None): """ Return a transposed view of the data. Alias of .T property """ if out: return OpTreeNode.build("assign", out, self.T) return self.T def share(self, shape, dtype=None, name=None): """ Return a view: ary, where ary.size <= self.size. Allows easy sharing of temporary memory This is mostly provided for compatibility, -- dtype is ignored """ size =	np.prod(shape)	numpy.prod
from typing import Dict, Tuple import pandas as pd import numpy as np import attr from itertools import chain @attr.s(slots=True) class MScanLineValidator: sig_val = attr.ib() # SignalValidator def __getattr__(self, item): return getattr(self.sig_val, item) def run(self) -> Tuple[Dict, np.uint64]: """ Interpolate MScan-specific line signals :return: Dictionary containing the data and the mean difference between subsequent lines """ lines = self.dict_of_data["Lines"].loc[:, "abs_time"].copy() rel_idx, delta = self.__calc_line_parameters(lines=lines) lines, rel_idx, delta = self.__filter_extra_lines(lines=lines, delta=delta) if len(rel_idx) > 0: # missing lines, not just extra theo_lines = self.__gen_line_model(lines=lines, m=delta) lines = self.__diff_vec_analysis(lines=lines, y=theo_lines, delta=delta) lines = self.__finalize_lines(lines=lines, delta=delta) if self.bidir: lines = self.sig_val.add_phase_to_bidir_lines(lines=lines) self.dict_of_data["Lines"] = pd.DataFrame( lines, dtype=np.uint64, columns=["abs_time"] ) return self.dict_of_data, delta def __calc_line_parameters(self, lines: pd.Series) -> Tuple[np.ndarray, np.uint64]: """ Generate general parameters of the given acquisition """ rel_idx = np.where( np.abs(lines.diff().pct_change(periods=1)) > self.change_thresh )[0] delta = np.uint64( lines.drop(rel_idx) .reindex(np.arange(len(lines))) .interpolate() .diff() .mean() ) return rel_idx[::2], delta def __filter_extra_lines( self, lines: pd.Series, delta: np.uint64 ) -> Tuple[pd.Series, pd.Series, np.uint64]: """ Kick out excess line signals :param lines: :param delta: :return: Tuple of valid lines, missing lines and new delta of lines """ diffs = lines.diff() rel_idx = np.where(np.abs(diffs.pct_change(periods=1)) > self.change_thresh)[0] recurring = np.where(np.diff(rel_idx) == 1)[0] idx_to_keep = np.ones_like(rel_idx, dtype=bool) for idx, _ in enumerate(recurring[1:], 1): try: if recurring[idx] - recurring[idx - 1] == 1: idx_to_keep[recurring[idx] + 1] = False except IndexError: pass rel_idx_new = pd.Series(rel_idx[idx_to_keep][::2], dtype=np.uint64) missing_lines = [] extra_lines = [] for idx in rel_idx_new: if diffs[idx] < (delta / 2): # excess lines extra_lines.append(idx) else: missing_lines.append(idx) valid_lines = lines.drop(extra_lines).reset_index(drop=True) delta = np.uint64(valid_lines.drop(missing_lines).diff().mean()) # Get rid of lines that came after the last frame num_of_extra_lines = len(valid_lines) % self.num_of_lines valid_lines = valid_lines[:-num_of_extra_lines] return valid_lines, pd.Series(missing_lines), delta def __gen_line_model(self, lines: pd.Series, m: np.uint64) -> np.ndarray: """ Using linear approximation generate a model for the "correct" line signal """ const = lines.iloc[0] x = np.arange(start=0, stop=len(lines), dtype=np.uint64) y = m * x + const if len(lines) > 1500: # correct simulated lines idx_range = np.arange(1500, len(lines), step=1500, dtype=np.uint64) for idx in idx_range: x = np.arange(0, len(lines) - idx, dtype=np.uint64) y[idx:] = m * x + lines.iloc[idx] # MScan's lines are evenly separated first_diff = np.uint64(lines.iloc[2:110].diff()[1::2].median()) delta_diff = np.int32((m - first_diff) / 2) if first_diff < m: y[1::2] -= delta_diff y[::2] += delta_diff else: y[1::2] += delta_diff y[::2] -= delta_diff return y def __diff_vec_analysis( self, y: np.ndarray, lines: pd.Series, delta: np.uint64 ) -> pd.Series: diff_vec = np.abs(np.subtract(y, lines, dtype=np.int64)) missing_val = np.where(diff_vec > delta / 20)[0] while missing_val.shape[0] > 0: if np.abs(diff_vec[missing_val[0]] - delta) / delta < 0.1: # double line lines = np.concatenate( (lines[: missing_val[0]], lines[missing_val[0] + 1 :]) ) else: lines = np.concatenate( ( lines[: missing_val[0]], np.atleast_1d(y[missing_val[0]]), lines[missing_val[0] :], ) ) # Restart the loop y = self.__gen_line_model(pd.Series(lines), delta) diff_vec = np.abs(	np.subtract(y, lines, dtype=np.int64)	numpy.subtract
from pathlib import Path from typing import Optional import numpy as np from cclib.io import ccopen from cclib.parser.utils import convertor import pyscf from pyresponse import cphf, operators, solvers, utils from pyresponse.core import AO2MOTransformationType, Hamiltonian, Spin from pyresponse.dalton.utils import dalton_label_to_operator from pyresponse.pyscf.ao2mo import AO2MOpyscf try: from daltools import mol as dalmol from daltools import sirifc except: pass def calculate_disk_rhf( testcasedir: Path, hamiltonian: str, spin: str, frequency: str, label_1: str, label_2: str, ) -> float: occupations = utils.read_file_occupations(testcasedir / "occupations") nocc_alph, nvirt_alph, nocc_beta, nvirt_beta = occupations assert nocc_alph == nocc_beta assert nvirt_alph == nvirt_beta norb = nocc_alph + nvirt_alph C = utils.read_file_3(testcasedir / "C") assert C.shape[0] == 1 assert C.shape[2] == norb nbasis = C.shape[1] moene = utils.read_file_2(testcasedir / "moene") assert moene.shape == (norb, 1) moints_iajb_aaaa = utils.read_file_4(testcasedir / "moints_iajb_aaaa") moints_ijab_aaaa = utils.read_file_4(testcasedir / "moints_ijab_aaaa") assert moints_iajb_aaaa.shape == (nocc_alph, nvirt_alph, nocc_alph, nvirt_alph) assert moints_ijab_aaaa.shape == (nocc_alph, nocc_alph, nvirt_alph, nvirt_alph) operator_1 = dalton_label_to_operator(label_1) operator_2 = dalton_label_to_operator(label_2) operator_1_integrals_mn = utils.read_file_3(testcasedir / f"operator_mn_{operator_1.label}") operator_2_integrals_mn = utils.read_file_3(testcasedir / f"operator_mn_{operator_2.label}") # The first dimension can"t be checked since there may be multiple # components. assert operator_1_integrals_mn.shape[1:] == (nbasis, nbasis) assert operator_2_integrals_mn.shape[1:] == (nbasis, nbasis) # Only take the component/slice from the integral as determined # from the DALTON operator label. operator_1_integrals_mn = operator_1_integrals_mn[operator_1.slice_idx] operator_2_integrals_mn = operator_2_integrals_mn[operator_2.slice_idx] # However, this eliminates an axis, which needs to be added back. operator_1_integrals_mn = operator_1_integrals_mn[np.newaxis, ...] operator_2_integrals_mn = operator_2_integrals_mn[np.newaxis, ...] operator_1.ao_integrals = operator_1_integrals_mn operator_2.ao_integrals = operator_2_integrals_mn moene = np.diag(moene[:, 0])[np.newaxis, ...] assert moene.shape == (1, norb, norb) solver = solvers.ExactInv(C, moene, occupations) solver.tei_mo = (moints_iajb_aaaa, moints_ijab_aaaa) solver.tei_mo_type = AO2MOTransformationType.partial driver = cphf.CPHF(solver) driver.add_operator(operator_1) driver.add_operator(operator_2) driver.set_frequencies([float(frequency)]) driver.run( hamiltonian=Hamiltonian[hamiltonian.upper()], spin=Spin[spin], program=None, program_obj=None, ) assert len(driver.frequencies) == len(driver.results) == 1 res = driver.results[0] assert res.shape == (2, 2) bl = res[1, 0] tr = res[0, 1] diff = abs(abs(bl) - abs(tr)) # Results should be symmetric w.r.t. interchange between operators # in the LR equations. thresh = 1.0e-13 assert diff < thresh return bl def calculate_disk_uhf( testcasedir: Path, hamiltonian: str, spin: str, frequency: str, label_1: str, label_2: str, ) -> float: occupations = utils.read_file_occupations(testcasedir / "occupations") nocc_alph, nvirt_alph, nocc_beta, nvirt_beta = occupations norb = nocc_alph + nvirt_alph C = utils.read_file_3(testcasedir / "C") assert C.shape[0] == 2 assert C.shape[2] == norb nbasis = C.shape[1] moene = utils.read_file_2(testcasedir / "moene") assert moene.shape == (norb, 2) moints_iajb_aaaa = utils.read_file_4(testcasedir / "moints_iajb_aaaa") moints_iajb_aabb = utils.read_file_4(testcasedir / "moints_iajb_aabb") moints_iajb_bbaa = utils.read_file_4(testcasedir / "moints_iajb_bbaa") moints_iajb_bbbb = utils.read_file_4(testcasedir / "moints_iajb_bbbb") moints_ijab_aaaa = utils.read_file_4(testcasedir / "moints_ijab_aaaa") moints_ijab_bbbb = utils.read_file_4(testcasedir / "moints_ijab_bbbb") assert moints_iajb_aaaa.shape == (nocc_alph, nvirt_alph, nocc_alph, nvirt_alph) assert moints_iajb_aabb.shape == (nocc_alph, nvirt_alph, nocc_beta, nvirt_beta) assert moints_iajb_bbaa.shape == (nocc_beta, nvirt_beta, nocc_alph, nvirt_alph) assert moints_iajb_bbbb.shape == (nocc_beta, nvirt_beta, nocc_beta, nvirt_beta) assert moints_ijab_aaaa.shape == (nocc_alph, nocc_alph, nvirt_alph, nvirt_alph) assert moints_ijab_bbbb.shape == (nocc_beta, nocc_beta, nvirt_beta, nvirt_beta) operator_1 = dalton_label_to_operator(label_1) operator_2 = dalton_label_to_operator(label_2) operator_1_integrals_mn = utils.read_file_3(testcasedir / f"operator_mn_{operator_1.label}") operator_2_integrals_mn = utils.read_file_3(testcasedir / f"operator_mn_{operator_2.label}") # The first dimension can"t be checked since there may be multiple # components. assert operator_1_integrals_mn.shape[1:] == (nbasis, nbasis) assert operator_2_integrals_mn.shape[1:] == (nbasis, nbasis) # Only take the component/slice from the integral as determined # from the DALTON operator label. operator_1_integrals_mn = operator_1_integrals_mn[operator_1.slice_idx] operator_2_integrals_mn = operator_2_integrals_mn[operator_2.slice_idx] # However, this eliminates an axis, which needs to be added back. operator_1_integrals_mn = operator_1_integrals_mn[np.newaxis, ...] operator_2_integrals_mn = operator_2_integrals_mn[np.newaxis, ...] operator_1.ao_integrals = operator_1_integrals_mn operator_2.ao_integrals = operator_2_integrals_mn moene_alph =	np.diag(moene[:, 0])	numpy.diag
# This module has been generated automatically from space group information # obtained from the Computational Crystallography Toolbox # """ Space groups This module contains a list of all the 230 space groups that can occur in a crystal. The variable space_groups contains a dictionary that maps space group numbers and space group names to the corresponding space group objects. .. moduleauthor:: <NAME> <<EMAIL>> """ #----------------------------------------------------------------------------- # Copyright (C) 2013 The Mosaic Development Team # # Distributed under the terms of the BSD License. The full license is in # the file LICENSE.txt, distributed as part of this software. #----------------------------------------------------------------------------- import numpy as N class SpaceGroup(object): """ Space group All possible space group objects are created in this module. Other modules should access these objects through the dictionary space_groups rather than create their own space group objects. """ def __init__(self, number, symbol, transformations): """ :param number: the number assigned to the space group by international convention :type number: int :param symbol: the Hermann-Mauguin space-group symbol as used in PDB and mmCIF files :type symbol: str :param transformations: a list of space group transformations, each consisting of a tuple of three integer arrays (rot, tn, td), where rot is the rotation matrix and tn/td are the numerator and denominator of the translation vector. The transformations are defined in fractional coordinates. :type transformations: list """ self.number = number self.symbol = symbol self.transformations = transformations self.transposed_rotations = N.array([N.transpose(t[0]) for t in transformations]) self.phase_factors = N.exp(N.array([(-2jN.pit[1])/t[2] for t in transformations])) def __repr__(self): return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol)) def __len__(self): """ :return: the number of space group transformations :rtype: int """ return len(self.transformations) def symmetryEquivalentMillerIndices(self, hkl): """ :param hkl: a set of Miller indices :type hkl: Scientific.N.array_type :return: a tuple (miller_indices, phase_factor) of two arrays of length equal to the number of space group transformations. miller_indices contains the Miller indices of each reflection equivalent by symmetry to the reflection hkl (including hkl itself as the first element). phase_factor contains the phase factors that must be applied to the structure factor of reflection hkl to obtain the structure factor of the symmetry equivalent reflection. :rtype: tuple """ hkls = N.dot(self.transposed_rotations, hkl) p = N.multiply.reduce(self.phase_factors**hkl, -1) return hkls, p space_groups = {} transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(1, 'P 1', transformations) space_groups[1] = sg space_groups['P 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(2, 'P -1', transformations) space_groups[2] = sg space_groups['P -1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(3, 'P 1 2 1', transformations) space_groups[3] = sg space_groups['P 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(4, 'P 1 21 1', transformations) space_groups[4] = sg space_groups['P 1 21 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(5, 'C 1 2 1', transformations) space_groups[5] = sg space_groups['C 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(6, 'P 1 m 1', transformations) space_groups[6] = sg space_groups['P 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(7, 'P 1 c 1', transformations) space_groups[7] = sg space_groups['P 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(8, 'C 1 m 1', transformations) space_groups[8] = sg space_groups['C 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(9, 'C 1 c 1', transformations) space_groups[9] = sg space_groups['C 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(10, 'P 1 2/m 1', transformations) space_groups[10] = sg space_groups['P 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(11, 'P 1 21/m 1', transformations) space_groups[11] = sg space_groups['P 1 21/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(12, 'C 1 2/m 1', transformations) space_groups[12] = sg space_groups['C 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(13, 'P 1 2/c 1', transformations) space_groups[13] = sg space_groups['P 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(14, 'P 1 21/c 1', transformations) space_groups[14] = sg space_groups['P 1 21/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(15, 'C 1 2/c 1', transformations) space_groups[15] = sg space_groups['C 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(16, 'P 2 2 2', transformations) space_groups[16] = sg space_groups['P 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(17, 'P 2 2 21', transformations) space_groups[17] = sg space_groups['P 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(18, 'P 21 21 2', transformations) space_groups[18] = sg space_groups['P 21 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(19, 'P 21 21 21', transformations) space_groups[19] = sg space_groups['P 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(20, 'C 2 2 21', transformations) space_groups[20] = sg space_groups['C 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(21, 'C 2 2 2', transformations) space_groups[21] = sg space_groups['C 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(22, 'F 2 2 2', transformations) space_groups[22] = sg space_groups['F 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(23, 'I 2 2 2', transformations) space_groups[23] = sg space_groups['I 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(24, 'I 21 21 21', transformations) space_groups[24] = sg space_groups['I 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(25, 'P m m 2', transformations) space_groups[25] = sg space_groups['P m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(26, 'P m c 21', transformations) space_groups[26] = sg space_groups['P m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(27, 'P c c 2', transformations) space_groups[27] = sg space_groups['P c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(28, 'P m a 2', transformations) space_groups[28] = sg space_groups['P m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(29, 'P c a 21', transformations) space_groups[29] = sg space_groups['P c a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(30, 'P n c 2', transformations) space_groups[30] = sg space_groups['P n c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(31, 'P m n 21', transformations) space_groups[31] = sg space_groups['P m n 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(32, 'P b a 2', transformations) space_groups[32] = sg space_groups['P b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(33, 'P n a 21', transformations) space_groups[33] = sg space_groups['P n a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(34, 'P n n 2', transformations) space_groups[34] = sg space_groups['P n n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(35, 'C m m 2', transformations) space_groups[35] = sg space_groups['C m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(36, 'C m c 21', transformations) space_groups[36] = sg space_groups['C m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(37, 'C c c 2', transformations) space_groups[37] = sg space_groups['C c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(38, 'A m m 2', transformations) space_groups[38] = sg space_groups['A m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(39, 'A b m 2', transformations) space_groups[39] = sg space_groups['A b m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(40, 'A m a 2', transformations) space_groups[40] = sg space_groups['A m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(41, 'A b a 2', transformations) space_groups[41] = sg space_groups['A b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(42, 'F m m 2', transformations) space_groups[42] = sg space_groups['F m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(43, 'F d d 2', transformations) space_groups[43] = sg space_groups['F d d 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(44, 'I m m 2', transformations) space_groups[44] = sg space_groups['I m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(45, 'I b a 2', transformations) space_groups[45] = sg space_groups['I b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(46, 'I m a 2', transformations) space_groups[46] = sg space_groups['I m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(47, 'P m m m', transformations) space_groups[47] = sg space_groups['P m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(48, 'P n n n :2', transformations) space_groups[48] = sg space_groups['P n n n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(49, 'P c c m', transformations) space_groups[49] = sg space_groups['P c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(50, 'P b a n :2', transformations) space_groups[50] = sg space_groups['P b a n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(51, 'P m m a', transformations) space_groups[51] = sg space_groups['P m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(52, 'P n n a', transformations) space_groups[52] = sg space_groups['P n n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(53, 'P m n a', transformations) space_groups[53] = sg space_groups['P m n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(54, 'P c c a', transformations) space_groups[54] = sg space_groups['P c c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(55, 'P b a m', transformations) space_groups[55] = sg space_groups['P b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(56, 'P c c n', transformations) space_groups[56] = sg space_groups['P c c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(57, 'P b c m', transformations) space_groups[57] = sg space_groups['P b c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(58, 'P n n m', transformations) space_groups[58] = sg space_groups['P n n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(59, 'P m m n :2', transformations) space_groups[59] = sg space_groups['P m m n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(60, 'P b c n', transformations) space_groups[60] = sg space_groups['P b c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(61, 'P b c a', transformations) space_groups[61] = sg space_groups['P b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(62, 'P n m a', transformations) space_groups[62] = sg space_groups['P n m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(63, 'C m c m', transformations) space_groups[63] = sg space_groups['C m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(64, 'C m c a', transformations) space_groups[64] = sg space_groups['C m c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(65, 'C m m m', transformations) space_groups[65] = sg space_groups['C m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(66, 'C c c m', transformations) space_groups[66] = sg space_groups['C c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(67, 'C m m a', transformations) space_groups[67] = sg space_groups['C m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(68, 'C c c a :2', transformations) space_groups[68] = sg space_groups['C c c a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(69, 'F m m m', transformations) space_groups[69] = sg space_groups['F m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(70, 'F d d d :2', transformations) space_groups[70] = sg space_groups['F d d d :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(71, 'I m m m', transformations) space_groups[71] = sg space_groups['I m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(72, 'I b a m', transformations) space_groups[72] = sg space_groups['I b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(73, 'I b c a', transformations) space_groups[73] = sg space_groups['I b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(74, 'I m m a', transformations) space_groups[74] = sg space_groups['I m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(75, 'P 4', transformations) space_groups[75] = sg space_groups['P 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(76, 'P 41', transformations) space_groups[76] = sg space_groups['P 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(77, 'P 42', transformations) space_groups[77] = sg space_groups['P 42'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(78, 'P 43', transformations) space_groups[78] = sg space_groups['P 43'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(79, 'I 4', transformations) space_groups[79] = sg space_groups['I 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(80, 'I 41', transformations) space_groups[80] = sg space_groups['I 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(81, 'P -4', transformations) space_groups[81] = sg space_groups['P -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(82, 'I -4', transformations) space_groups[82] = sg space_groups['I -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(83, 'P 4/m', transformations) space_groups[83] = sg space_groups['P 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(84, 'P 42/m', transformations) space_groups[84] = sg space_groups['P 42/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(85, 'P 4/n :2', transformations) space_groups[85] = sg space_groups['P 4/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(86, 'P 42/n :2', transformations) space_groups[86] = sg space_groups['P 42/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(87, 'I 4/m', transformations) space_groups[87] = sg space_groups['I 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(88, 'I 41/a :2', transformations) space_groups[88] = sg space_groups['I 41/a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(89, 'P 4 2 2', transformations) space_groups[89] = sg space_groups['P 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(90, 'P 4 21 2', transformations) space_groups[90] = sg space_groups['P 4 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(91, 'P 41 2 2', transformations) space_groups[91] = sg space_groups['P 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(92, 'P 41 21 2', transformations) space_groups[92] = sg space_groups['P 41 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(93, 'P 42 2 2', transformations) space_groups[93] = sg space_groups['P 42 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(94, 'P 42 21 2', transformations) space_groups[94] = sg space_groups['P 42 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(95, 'P 43 2 2', transformations) space_groups[95] = sg space_groups['P 43 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(96, 'P 43 21 2', transformations) space_groups[96] = sg space_groups['P 43 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(97, 'I 4 2 2', transformations) space_groups[97] = sg space_groups['I 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(98, 'I 41 2 2', transformations) space_groups[98] = sg space_groups['I 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(99, 'P 4 m m', transformations) space_groups[99] = sg space_groups['P 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(100, 'P 4 b m', transformations) space_groups[100] = sg space_groups['P 4 b m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(101, 'P 42 c m', transformations) space_groups[101] = sg space_groups['P 42 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(102, 'P 42 n m', transformations) space_groups[102] = sg space_groups['P 42 n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(103, 'P 4 c c', transformations) space_groups[103] = sg space_groups['P 4 c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(104, 'P 4 n c', transformations) space_groups[104] = sg space_groups['P 4 n c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(105, 'P 42 m c', transformations) space_groups[105] = sg space_groups['P 42 m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(106, 'P 42 b c', transformations) space_groups[106] = sg space_groups['P 42 b c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(107, 'I 4 m m', transformations) space_groups[107] = sg space_groups['I 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(108, 'I 4 c m', transformations) space_groups[108] = sg space_groups['I 4 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(109, 'I 41 m d', transformations) space_groups[109] = sg space_groups['I 41 m d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(110, 'I 41 c d', transformations) space_groups[110] = sg space_groups['I 41 c d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(111, 'P -4 2 m', transformations) space_groups[111] = sg space_groups['P -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(112, 'P -4 2 c', transformations) space_groups[112] = sg space_groups['P -4 2 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(113, 'P -4 21 m', transformations) space_groups[113] = sg space_groups['P -4 21 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(114, 'P -4 21 c', transformations) space_groups[114] = sg space_groups['P -4 21 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(115, 'P -4 m 2', transformations) space_groups[115] = sg space_groups['P -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(116, 'P -4 c 2', transformations) space_groups[116] = sg space_groups['P -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(117, 'P -4 b 2', transformations) space_groups[117] = sg space_groups['P -4 b 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(118, 'P -4 n 2', transformations) space_groups[118] = sg space_groups['P -4 n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(119, 'I -4 m 2', transformations) space_groups[119] = sg space_groups['I -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(120, 'I -4 c 2', transformations) space_groups[120] = sg space_groups['I -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(121, 'I -4 2 m', transformations) space_groups[121] = sg space_groups['I -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(122, 'I -4 2 d', transformations) space_groups[122] = sg space_groups['I -4 2 d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(123, 'P 4/m m m', transformations) space_groups[123] = sg space_groups['P 4/m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(124, 'P 4/m c c', transformations) space_groups[124] = sg space_groups['P 4/m c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(125, 'P 4/n b m :2', transformations) space_groups[125] = sg space_groups['P 4/n b m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot =	N.array([-1,0,0,0,-1,0,0,0,-1])	numpy.array
import geopandas as gpd import numpy as np import pygeos import pytest from xugrid import conversion as cv @pytest.fixture(scope="function") def line(): x = np.array([0.0, 1.0, 2.0]) y = np.array([0.0, 0.0, 0.0]) edge_node_connectivity = np.array( [ [0, 1], [1, 2], ] ) return x, y, edge_node_connectivity @pytest.fixture(scope="function") def line_gdf(): x = np.array([0.0, 1.0, 2.0]) y = np.array([0.0, 0.0, 0.0]) gdf = gpd.GeoDataFrame(geometry=[pygeos.creation.linestrings(x, y)]) return gdf @pytest.fixture(scope="function") def triangle_mesh(): x = np.array([0.0, 1.0, 1.0, 2.0]) y =	np.array([0.0, 0.0, 1.0, 0.0])	numpy.array
import jax.numpy as jnp from jax import grad, vmap, hessian, jit import jax.ops as jop from jax.config import config; config.update("jax_enable_x64", True) # numpy import numpy as onp from numpy import random import scipy.io import argparse import logging import datetime from time import time import os def get_parser(): parser = argparse.ArgumentParser(description='Allen Cahn equation GP solver') parser.add_argument("--nu", type=float, default = 1e-4) parser.add_argument("--kernel", type=str, default="gaussian", choices=["gaussian","inv_quadratics"]) parser.add_argument("--sigma", type = float, default = 0.02) parser.add_argument("--dt", type = float, default = 0.04) parser.add_argument("--T", type = float, default = 1.0) parser.add_argument("--N_domain", type = int, default = 512) parser.add_argument("--nugget", type = float, default = 1e-13) parser.add_argument("--GNsteps", type = int, default = 2) parser.add_argument("--logroot", type=str, default='./logs/') parser.add_argument("--randomseed", type=int, default=9999) args = parser.parse_args() return args def sample_points(num_pts, dt, T, option = 'grid'): Nt = int(T/dt)+1 X_domain = onp.zeros((Nt,num_pts,2)) if option == 'grid': for i in range(Nt): X_domain[i,:,0] = idt X_domain[i,:,1] = onp.linspace(-1.0,1.0, num_pts) return X_domain def assembly_Theta(X_domain, sigma): N_domain = onp.shape(X_domain)[0] N_boundary = 0 Theta = onp.zeros((3N_domain+N_boundary, 3N_domain+N_boundary)) # auxiliary vector for construncting Theta # domain-domain XdXd = onp.tile(X_domain, (N_domain,1)) XdXd_T = onp.transpose(XdXd) XdXb1 = onp.transpose(onp.tile(X_domain,(N_domain+N_boundary,1))) X_all = X_domain XdXb2 = onp.tile(X_all,(N_domain,1)) XdbXdb = onp.tile(X_all,(N_domain+N_boundary,1)) XdbXdb_T = onp.transpose(XdbXdb) val = vmap(lambda x1,y1: Delta_x1_Delta_y1_kappa(x1,y1, sigma))(XdXd_T.flatten(), XdXd.flatten()) Theta[:N_domain,:N_domain] = onp.reshape(val, (N_domain,N_domain)) val = vmap(lambda x1,y1: Delta_x1_D_y1_kappa(x1,y1, sigma))(XdXd_T.flatten(), XdXd.flatten()) Theta[:N_domain,N_domain:2N_domain] = onp.reshape(val, (N_domain,N_domain)) Theta[N_domain:2N_domain,:N_domain] = onp.transpose(onp.reshape(val, (N_domain,N_domain))) val = vmap(lambda x1,y1: Delta_x1_kappa(x1,y1, sigma))(XdXb1.flatten(), XdXb2.flatten()) Theta[:N_domain,2N_domain:] = onp.reshape(val,(N_domain,N_domain+N_boundary)) Theta[2N_domain:,:N_domain] = onp.transpose(onp.reshape(val,(N_domain,N_domain+N_boundary))) val = vmap(lambda x1,y1: D_x1_D_y1_kappa(x1,y1, sigma))(XdXd_T.flatten(), XdXd.flatten()) Theta[N_domain:2N_domain,N_domain:2N_domain] = onp.reshape(val, (N_domain,N_domain)) val = vmap(lambda x1,y1: D_x1_kappa(x1,y1, sigma))(XdXb1.flatten(), XdXb2.flatten()) Theta[N_domain:2N_domain,2N_domain:] = onp.reshape(val,(N_domain,N_domain+N_boundary)) Theta[2N_domain:,N_domain:2N_domain] = onp.transpose(onp.reshape(val,(N_domain,N_domain+N_boundary))) val = vmap(lambda x1,y1: kappa(x1,y1, sigma))(XdbXdb_T.flatten(), XdbXdb.flatten()) Theta[2N_domain:,2N_domain:] = onp.reshape(val, (N_domain+N_boundary,N_domain+N_boundary)) return Theta @jit def J_loss(v, rhs_f, L,dt): N_domain = onp.shape(rhs_f)[0] vec_u = jnp.append(v[:N_domain-1],v[0]) vec_u_x = jnp.append(v[N_domain-1:],v[N_domain-1]) vec_u_xx = (2/dtvec_u+5vec_u3-5vec_u-rhs_f)/nu vv = jnp.append(vec_u_xx,vec_u_x) vv = jnp.append(vv,vec_u) temp = jnp.linalg.solve(L,vv) return jnp.dot(temp, temp) grad_J = grad(J_loss) @jit def GN_J(v, rhs_f, L, dt, v_old): N_domain = onp.shape(rhs_f)[0] vec_u_old = jnp.append(v_old[:N_domain-1],v_old[0]) vec_u = jnp.append(v[:N_domain-1],v[0]) vec_u_x = jnp.append(v[N_domain-1:],v[N_domain-1]) vec_u_xx = (2/dtvec_u+15vec_u_old*2vec_u-5*vec_u-rhs_f)/nu vv = jnp.append(vec_u_xx,vec_u_x) vv = jnp.append(vv,vec_u) temp = jnp.linalg.solve(L,vv) return jnp.dot(temp, temp) Hessian_GN=jit(hessian(GN_J)) def time_steping_solve(X_domain, dt,T,num_pts, step_size = 1, nugget = 1e-10, sigma=0.2, GN_iteration = 4): Nt = int(T/dt)+1 sol_u = onp.zeros((Nt,num_pts)) sol_u_x = onp.zeros((Nt,num_pts)) sol_u_xx =	onp.zeros((Nt,num_pts))	numpy.zeros
# -- coding: utf-8 -- """ Created on Tue Mar 16 11:13:37 2021 @author: dv516 """ import numpy as np import pickle import pyro pyro.enable_validation(True) # can help with debugging pyro.set_rng_seed(1) from algorithms.PyBobyqa_wrapped.Wrapper_for_pybobyqa import PyBobyqaWrapper from algorithms.Bayesian_opt_Pyro.utilities_full import BayesOpt from algorithms.nesterov_random.nesterov_random import nesterov_random from algorithms.simplex.simplex_method import simplex_method from algorithms.CUATRO.CUATRO import CUATRO from algorithms.Finite_differences.Finite_differences import finite_Diff_Newton from algorithms.Finite_differences.Finite_differences import Adam_optimizer from algorithms.Finite_differences.Finite_differences import BFGS_optimizer from algorithms.SQSnobfit_wrapped.Wrapper_for_SQSnobfit import SQSnobFitWrapper from algorithms.DIRECT_wrapped.Wrapper_for_Direct import DIRECTWrapper from test_functions import rosenbrock_constrained, quadratic_constrained import matplotlib.pyplot as plt import pickle def trust_fig(oracle, bounds): N = 200 lim = 2 x = np.linspace(-lim, lim, N) y = np.linspace(-lim, lim, N) X,Y = np.meshgrid(x, y) Z = oracle.sample_obj(X,Y) constr = oracle.sample_constr(X,Y) level_list = np.logspace(-0.5, 4, 10) fig = plt.figure(figsize = (6,4)) ax = fig.add_subplot() ax.contour(X,Y,Z*constr, levels = level_list) ax.plot([bounds[0,0], bounds[0, 1]], [bounds[1,0], bounds[1, 0]], c = 'k') ax.plot([bounds[0,0], bounds[0, 1]], [bounds[1,1], bounds[1, 1]], c = 'k') ax.plot([bounds[0,0], bounds[0, 0]], [bounds[1,0], bounds[1, 1]], c = 'k') ax.plot([bounds[0,1], bounds[0, 1]], [bounds[1,0], bounds[1, 1]], c = 'k') return ax, fig def average_from_list(solutions_list): N = len(solutions_list) f_best_all = np.zeros((N, 100)) for i in range(N): f_best = np.array(solutions_list[i]['f_best_so_far']) x_ind = np.array(solutions_list[i]['samples_at_iteration']) for j in range(100): ind = np.where(x_ind <= j+1) if len(ind[0]) == 0: f_best_all[i, j] = f_best[0] else: f_best_all[i, j] = f_best[ind][-1] f_median = np.median(f_best_all, axis = 0) # f_av = np.average(f_best_all, axis = 0) # f_std = np.std(f_best_all, axis = 0) f_min = np.min(f_best_all, axis = 0) f_max = np.max(f_best_all, axis = 0) return f_best_all, f_median, f_min, f_max class RB: def __init__(self, objective, ineq = []): self.obj = objective ; self.ieq = ineq def sample_obj(self, x, y): return self.obj(x, y) def sample_constr(self, x, y): if self.ieq == []: if (type(x) == float) or (type(x) == int): return 1 else: return np.ones(len(x)) elif (type(x) == float) or (type(x) == int): temporary = [int(g(x, y)) for g in self.ieq] return np.product(	np.array(temporary)	numpy.array
import theano import theano.tensor as T import numpy as np from util import * class Autoencoder_1obj(): # each render_var gets its own l2 layer def __init__(self, scene, n_visible, n_hidden_l1, n_hidden_l2, n_hidden_l3): self.scene = scene self.n_visible = n_visible self.n_hidden_l1 = n_hidden_l1 self.n_hidden_l2 = n_hidden_l2 self.l1_biases = theano.shared(np.zeros(n_hidden_l1), borrow=True) self.l2_biases = theano.shared(np.zeros(n_hidden_l2), borrow=True) self.l3_biases = theano.shared(np.zeros(n_hidden_l3), borrow=True) numpy_rng = np.random.RandomState(1234) self.vis_to_l1 = initialize_weight(n_visible, n_hidden_l1, "vis_to_l1", numpy_rng, 'uniform') self.l1_to_l2 = initialize_weight(n_hidden_l1, n_hidden_l2, "vis_to_l1", numpy_rng, 'uniform') self.l2_to_l3 = initialize_weight(n_hidden_l2, n_hidden_l3, "vis_to_l1", numpy_rng, 'uniform') self.params0 = [self.vis_to_l1, self.l1_to_l2, self.l2_to_l3, self.l1_biases, self.l2_biases,self.l3_biases] #Adding Capsules self.l3_to_rvar1 = theano.shared(self.init_capsule_param(n_hidden_l3),borrow=True) self.rvar1_biases = theano.shared(np.asarray([0,0,2.5,1,1,1]), borrow=True) self.params1 = [self.l3_to_rvar1, self.rvar1_biases] #self.l3_to_rvar2, self.rvar2_biases] self.params= self.params0+self.params1 def init_capsule_param(self, n_hidden_l3): #return 0.07np.asarray( np.random.uniform(\ # low=-4 np.sqrt(6. / 6+n_hidden_l3), # high=4 * np.sqrt(6. / 6+n_hidden_l3), # size=(n_hidden_l3, 6)), dtype=theano.config.floatX) l3_to_center = 0.07np.asarray( np.random.uniform( low=-4 np.sqrt(6. / 6+n_hidden_l3), high=4 *	np.sqrt(6. / 6+n_hidden_l3)	numpy.sqrt
import numpy as onp import jax import jax.numpy as np import random import os import scipy.interpolate import astropy.io.fits as pyfits from redrock.templates import Template from redrock.archetypes import Archetype from chex import assert_shape key = jax.random.PRNGKey(42) mask_std_val = 1e2 def create_mask(x, x_var, indices, val=0.0): mask = onp.ones(x.shape) # mask[x == 0] = val ind = np.where(np.logical_or(x_var <= 0, x_var == mask_std_val ** 2.0)) mask[ind] = val fullindices = onp.asarray(indices)[:, None] + onp.arange(x.shape[1])[None, :] mask[fullindices < 0] = val # offs = - np.maximum(indices, np.zeros_like(indices)) # for io, off in enumerate(offs): # mask[io, 0:off] = 0 return np.asarray(mask) def interp(x_new, x, y): return scipy.interpolate.interp1d( x, y, fill_value="extrapolate", kind="linear", bounds_error=False )(x_new) def draw_uniform(samples, bins, desired_size): """ Draw uniform set of samples """ hist, bin_edges = np.histogram(samples, bins=bins) avg_nb = int(desired_size / float(bins)) numbers = np.repeat(avg_nb, bins) for j in range(4): numbers[hist <= numbers] = hist[hist <= numbers] nb_rest = desired_size - np.sum(numbers[hist <= numbers]) # * bins avg_nb = round(nb_rest / np.sum(hist > numbers)) numbers[hist > numbers] = avg_nb result = [] count = 0 for i in range(bin_edges.size - 1): ind = samples >= bin_edges[i] ind &= samples <= bin_edges[i + 1] if ind.sum() > 0: positions = np.where(ind)[0] nb = min([numbers[i], ind.sum()]) result.append(jax.random.choice(positions, nb, replace=False)) return np.concatenate(result) class DataPipeline: """ Pipeline for loading data """ def load_spectrophotometry( self, input_dir="./", write_subset=False, use_subset=False, subsampling=1, spec=True, phot=True, ): if use_subset: suffix = "2.npy" else: suffix = ".npy" self.input_dir = input_dir self.lamgrid = onp.load(self.input_dir + "lamgrid.npy") self.lam_phot_eff = onp.load(self.input_dir + "lam_phot_eff.npy") self.lam_phot_size_eff = onp.load(self.input_dir + "lam_phot_size_eff.npy") self.redshifts = onp.load(self.input_dir + "redshifts" + suffix) n_obj = self.redshifts.size self.n_obj = n_obj assert_shape(self.redshifts, (n_obj,)) if phot: self.transferfunctions = ( onp.load(self.input_dir + "transferfunctions.npy") * 1e-16 ) self.transferfunctions_zgrid = onp.load( self.input_dir + "transferfunctions_zgrid.npy" ) assert self.transferfunctions.shape[0] == self.transferfunctions_zgrid.size assert self.transferfunctions.shape[1] == self.lamgrid.size self.index_transfer_redshift = onp.load( self.input_dir + "index_transfer_redshift" + suffix ) self.interprightindices_transfer = onp.load( self.input_dir + "interprightindices_transfer" + suffix ) self.interpweights_transfer = onp.load( self.input_dir + "interpweights_transfer" + suffix ) self.phot = fluxes = onp.load(self.input_dir + "phot" + suffix) self.phot_invvar = flux_ivars = onp.load( self.input_dir + "phot_invvar" + suffix ) assert_shape(self.index_transfer_redshift, (n_obj,)) assert_shape(self.interprightindices_transfer, (n_obj,)) assert_shape(self.interpweights_transfer, (n_obj,)) n_pix_phot = self.phot.shape[1] assert_shape(self.phot, (n_obj, n_pix_phot)) assert_shape(self.phot_invvar, (n_obj, n_pix_phot)) self.n_pix_phot = self.phot.shape[1] if spec: self.chi2s_sdss = onp.load(self.input_dir + "chi2s_sdss" + suffix) self.lamspec_waveoffset = int( onp.load(self.input_dir + "lamspec_waveoffset" + suffix) ) self.index_wave = onp.load(self.input_dir + "index_wave" + suffix) self.interprightindices = onp.load( self.input_dir + "interprightindices" + suffix ) self.interpweights = onp.load(self.input_dir + "interpweights" + suffix) self.specmod_sdss = onp.load(self.input_dir + "spec_mod" + suffix) if True: self.spec = onp.load(self.input_dir + "spec" + suffix) self.spec_invvar = onp.load(self.input_dir + "spec_invvar" + suffix) else: self.spec = onp.load(self.input_dir + "spec_mod" + suffix) self.spec_invvar = ( onp.load(self.input_dir + "spec_invvar" + suffix) * 0 + 1 ) self.n_pix_spec = self.spec.shape[1] assert_shape(self.chi2s_sdss, (n_obj,)) assert_shape(self.index_wave, (n_obj,)) n_pix_spec = self.spec.shape[1] assert_shape(self.spec, (n_obj, n_pix_spec)) assert_shape(self.specmod_sdss, (n_obj, n_pix_spec)) assert_shape(self.spec_invvar, (n_obj, n_pix_spec)) if write_subset: M = 50000 suffix = "2.npy" self.index_wave = self.index_wave[:M] self.redshifts = self.redshifts[:M] self.chi2s_sdss = self.chi2s_sdss[:M] self.phot_invvar = self.phot_invvar[:M, :] self.index_transfer_redshift = self.index_transfer_redshift[:M] np.save(self.input_dir + "index_wave" + suffix, self.index_wave[:M]) np.save( self.input_dir + "interprightindices_transfer" + suffix, self.interprightindices_transfer[:M, :], ) np.save( self.input_dir + "interpweights_transfer" + suffix, self.interpweights_transfer[:M, :], ) np.save( self.input_dir + "index_transfer_redshift2.npy", self.index_transfer_redshift, ) np.save(self.input_dir + "redshifts" + suffix, self.redshifts) np.save(self.input_dir + "spec" + suffix, self.spec) np.save(self.input_dir + "chi2s_sdss" + suffix, self.chi2s_sdss) np.save(self.input_dir + "spec_invvar" + suffix, self.spec_invvar) np.save(self.input_dir + "phot" + suffix, self.phot) np.save(self.input_dir + "phot_invvar" + suffix, self.phot_invvar) np.save(self.input_dir + "spec_mod" + suffix, self.specmod_sdss) if subsampling > 1: self.lamgrid = self.lamgrid[::subsampling] self.transferfunctions = self.transferfunctions[:, ::subsampling, :][ ::subsampling, :, : ] self.transferfunctions_zgrid = self.transferfunctions_zgrid[::subsampling] self.lamspec_waveoffset = self.lamspec_waveoffset // subsampling self.spec = self.spec[:, ::subsampling] self.specmod_sdss = self.specmod_sdss[:, ::subsampling] self.spec_invvar = self.spec_invvar[:, ::subsampling] self.index_wave = self.index_wave // subsampling self.index_transfer_redshift = self.index_transfer_redshift // subsampling self.interprightindices = ( self.interprightindices[:, ::subsampling] // subsampling ) self.interpweights = ( self.interpweights[:, ::subsampling] / subsampling ) # dilution self.interprightindices_transfer = ( self.interprightindices_transfer // subsampling ) # is it correct? self.interpweights_transfer = ( self.interpweights_transfer / subsampling ) # is it correct? @staticmethod def save_fake_data(n_obj, n_pix_sed, n_pix_spec, n_pix_phot, n_pix_transfer): root = "data/fake/fake_" from jax.random import uniform, randint np.save(root + "lamgrid.npy", 8.1e2 + np.arange(n_pix_sed)) np.save(root + "lam_phot_eff.npy", np.arange(n_pix_phot)) np.save(root + "lam_phot_size_eff.npy", np.arange(n_pix_phot)) np.save( root + "transferfunctions.npy", uniform(key, (n_pix_transfer, n_pix_sed, n_pix_phot)), ) np.save(root + "transferfunctions_zgrid.npy", np.arange(n_pix_transfer)) np.save(root + "chi2s_sdss.npy", uniform(key, (n_obj,))) np.save( root + "lamspec_waveoffset.npy", randint(key, (1,), 0, n_pix_sed - n_pix_spec - 1), ) np.save( root + "index_wave.npy", randint(key, (n_obj,), 0, n_pix_sed - n_pix_spec - 1), ) np.save( root + "index_transfer_redshift.npy", randint(key, (n_obj,), 0, n_pix_transfer), ) np.save( root + "interprightindices.npy", randint(key, (n_obj, n_pix_spec), 0, n_pix_transfer), ) np.save( root + "interpweights.npy", uniform(key, (n_obj, n_pix_spec)), ) np.save( root + "interprightindices_transfer.npy", randint(key, (n_obj,), 0, n_pix_transfer), ) np.save( root + "interpweights_transfer.npy", uniform(key, (n_obj,)), ) np.save(root + "spec.npy", uniform(key, (n_obj, n_pix_spec))) np.save(root + "spec_mod.npy", uniform(key, (n_obj, n_pix_spec))) np.save(root + "spec_invvar.npy", uniform(key, (n_obj, n_pix_spec))) np.save(root + "phot.npy", uniform(key, (n_obj, n_pix_phot))) np.save(root + "phot_invvar.npy", uniform(key, (n_obj, n_pix_phot))) np.save(root + "redshifts.npy", uniform(key, (n_obj,))) def __init__( self, input_dir="./", subsampling=1, npix_min=1, write_subset=False, use_subset=False, spec=True, phot=True, ): self.load_spectrophotometry( input_dir=input_dir, write_subset=write_subset, use_subset=use_subset, subsampling=subsampling, spec=spec, phot=phot, ) self.indices = np.arange(self.n_obj) self.batch = 0 self.subsampling = subsampling self.npix_min = npix_min if phot: # Multiplying by delta lambda in preparation for integral over lambda xbounds = onp.zeros(self.lamgrid.size + 1) xbounds[1:-1] = (self.lamgrid[1:] + self.lamgrid[:-1]) / 2 xbounds[0] = self.lamgrid[0] - (xbounds[1] - self.lamgrid[0]) xbounds[-1] = self.lamgrid[-1] + (self.lamgrid[-1] - xbounds[-2]) xsizes = np.asarray(np.diff(xbounds)) self.transferfunctions = self.transferfunctions * xsizes[None, :, None] print("Initial lamgrid shape:", self.lamgrid.shape) if spec: print("Initial spec shape:", self.spec.shape) # spec[spec <= 0] = np.nan self.spec_invvar[~onp.isfinite(self.spec)] = 0 self.spec_invvar[self.spec == 0] = 0 self.spec_invvar[~onp.isfinite(self.spec_invvar)] = 0 self.spec_invvar[self.spec_invvar < 0] = 0 self.spec_invvar[self.interpweights < 0] = 0 self.spec_invvar[self.interprightindices < 0] = 0 self.spec[~onp.isfinite(self.spec)] = 0 # Masking sky lines lamsize_spec = self.spec.shape[1] print( "lamspec_waveoffset", self.lamspec_waveoffset, self.lamgrid[self.lamspec_waveoffset], ) print("lamsize_spec", lamsize_spec) print("lamgrid", self.lamgrid.size) # Floor spectroscopic errors ind = self.spec_invvar ** -0.5 < 1e-4 * np.abs(self.spec) # ind &= self.spec_invvar != 0 # ind &= self.spec != 0 print("How many spec errors are floored?", np.sum(ind), "out of", ind.size) # ind = np.where(ind)[0] self.spec_invvar[ind] = (1e-4 * np.abs(self.spec)[ind]) -2.0 if ( np.sum(~np.isfinite(self.spec)) > 0 or np.sum(~np.isfinite(self.spec_invvar)) > 0 ): print( "nans?", np.sum(~np.isfinite(self.spec)), np.sum(~np.isfinite(self.spec_invvar)), ) stop # Calculated after changing the data self.chi2s_sdss = np.sum( (self.specmod_sdss - self.spec) 2 * self.spec_invvar, axis=-1 ) print("Revised data shape:", self.spec.shape) # masks = create_mask(self.spec, self.spec_invvar, self.index_wave) masks = ~(self.spec_invvar == 0) npix = np.sum(masks, axis=1) print("Number of objects with 0 valid pixels:", np.sum(npix == 0)) print("Number of objects with <10 valid pixels:", np.sum(npix <= 10)) print("Number of objects with <100 valid pixels:", np.sum(npix <= 100)) self.indices = onp.where(npix > npix_min)[0] onp.random.shuffle(self.indices) print("Number of objects with valid pixels:", self.indices.size) self.specphotscalings = np.ones((self.spec.shape[0],)) if phot: ind = ~np.isfinite(self.phot_invvar) ind \|= self.phot_invvar < 0 # ind = np.where(ind)[0] self.phot_invvar[ind] = 0 print("Initial phot shape:", self.phot.shape) # Floor photometric errors ind = self.phot_invvar ** -0.5 < 1e-2 * self.phot print("How many phot errors are floored?", np.sum(ind), "out of", ind.size) # ind = np.where(ind)[0] self.phot_invvar[ind] = (1e-2 * self.phot[ind]) ** -2.0 print("Finished pre-processing data.") def get_grids(self): n_pix_sed = self.lamgrid.size n_pix_spec = self.spec.shape[1] n_pix_phot = self.phot.shape[1] # lamgrid_spec = self.lamgrid[ # self.lamspec_waveoffset : self.lamspec_waveoffset + n_pix_spec # ] return ( self.lamgrid, self.lam_phot_eff, self.lam_phot_size_eff, self.transferfunctions, self.transferfunctions_zgrid, n_pix_sed, n_pix_spec, n_pix_phot, ) def next_batch_specandphot(self, indices, batchsize): length = indices.size startindex = self.batch * batchsize batch_indices = indices[startindex : startindex + batchsize] # print('batch_indices', batch_indices.size, batch_indices[0], batch_indices[-1]) batch_index_wave = np.take(self.index_wave, batch_indices) batch_index_transfer_redshift = np.take( self.index_transfer_redshift, batch_indices ) batch_spec = np.take(self.spec, batch_indices, axis=0) batch_spec_invvar = np.take(self.spec_invvar, batch_indices, axis=0) # batch_sed_mask = create_mask(batch_spec, batch_spec_invvar, batch_index_wave) batch_phot = np.take(self.phot, batch_indices, axis=0) batch_phot_invvar = np.take(self.phot_invvar, batch_indices, axis=0) batch_redshifts = np.take(self.redshifts, batch_indices) batch_specphotscaling = np.take(self.specphotscalings, batch_indices) batch_interpweights = np.take(self.interpweights, batch_indices, axis=0) batch_interprightindices = np.take( self.interprightindices, batch_indices, axis=0 ) self.batch += 1 nextbatch_startindex = self.batch * batchsize if nextbatch_startindex >= length: self.batch = 0 actualbatchsize = min([batchsize, length - startindex]) # si, _ = startindex, batchsize # sh = (batch_spec.shape[0], wavesize) # batch_transferfunctions = np.zeros((batch_spec.shape[0], wavesize, batch_phot.shape[1])) batch_transferfunctions = self.transferfunctions[ batch_index_transfer_redshift, :, : ] batch_index_wave_ext = batch_index_wave[:, None] + np.arange( batch_spec.shape[1] ) if np.sum(batch_index_wave_ext < 0) > 0: print( "Number of negative wave indices:", np.sum(batch_index_wave < 0), np.sum(batch_index_wave_ext < 0), ) exit(1) # batch_index_wave_ext[batch_index_wave_ext < 0] = 0 batch_spec_loginvvar = np.where( batch_spec_invvar == 0, 0, np.log(batch_spec_invvar) ) batch_phot_loginvvar = np.where( batch_phot_invvar == 0, 0, np.log(batch_phot_invvar) ) if ( np.sum(~np.isfinite(batch_spec)) > 0 or np.sum(~np.isfinite(batch_spec_invvar)) > 0 or np.sum(~np.isfinite(batch_spec_loginvvar)) > 0 ): print( "nans?", np.sum(~np.isfinite(batch_spec)), np.sum(~np.isfinite(batch_spec_invvar)), np.sum(~np.isfinite(batch_spec_loginvvar)), ) exit(1) return ( startindex, actualbatchsize, batch_index_wave, batch_index_transfer_redshift, batch_spec, batch_spec_invvar, batch_spec_loginvvar, # batch_sed_mask, batch_specphotscaling, batch_phot, batch_phot_invvar, batch_phot_loginvvar, batch_redshifts, batch_transferfunctions, batch_index_wave_ext, batch_interprightindices, batch_interpweights, ) def next_batch_photonly(self, indices, batchsize): length = indices.size startindex = self.batch * batchsize batch_indices = indices[startindex : startindex + batchsize] batch_phot = np.take(self.phot, batch_indices, axis=0) batch_phot_invvar = np.take(self.phot_invvar, batch_indices, axis=0) batch_redshifts = np.take(self.redshifts, batch_indices) batch_interpweights_transfer = np.take( self.interpweights_transfer, batch_indices, axis=0 ) batch_interprightindices_transfer = np.take( self.interprightindices_transfer, batch_indices, axis=0 ) self.batch += 1 nextbatch_startindex = self.batch * batchsize if nextbatch_startindex >= length: self.batch = 0 actualbatchsize = min([batchsize, length - startindex]) batch_phot_loginvvar = np.where( batch_phot_invvar == 0, 0, np.log(batch_phot_invvar) ) return ( startindex, actualbatchsize, batch_phot, batch_phot_invvar, batch_phot_loginvvar, batch_redshifts, self.transferfunctions, batch_interprightindices_transfer, batch_interpweights_transfer, ) def get_nbatches(self, indices, batchsize): self.batchsize = batchsize return (indices.shape[0] // self.batchsize) + 1 def change_redshift(self, iz, zstep, data_batch): ( si, bs, batch_index_wave, batch_index_transfer_redshift, spec, spec_invvar, spec_loginvvar, # batch_spec_mask, specphotscaling, phot, phot_invvar, phot_loginvvar, batch_redshifts, batch_transferfunctions, batch_index_wave_ext, batch_interprightindices, batch_interpweights, ) = data_batch batch_transferfunctions = self.transferfunctions[ None, iz * zstep, :, : ] * onp.ones((bs, 1, 1)) # batch_index_wave = np.repeat(self.lamspec_waveoffset - iz * zstep, bs) # not correct with new arrays batch_index_wave_z0 = batch_index_wave + batch_index_transfer_redshift batch_interprightindices_z0 = ( batch_interprightindices + batch_index_transfer_redshift[:, None] ) batch_index_wave = batch_index_wave_z0 - iz * zstep batch_interprightindices = batch_interprightindices_z0 - iz * zstep batch_index_wave_ext = batch_index_wave[:, None] + onp.arange(spec.shape[1]) # batch_index_wave_ext[batch_index_wave_ext < 0] = 0 # TODO: is this a problem? # TODO: something to do about the specphotscaling? return ( si, bs, batch_index_wave, batch_index_transfer_redshift, spec, spec_invvar, spec_loginvvar, # batch_spec_mask, specphotscaling, phot, phot_invvar, phot_loginvvar, batch_redshifts, batch_transferfunctions, batch_index_wave_ext, batch_interprightindices, batch_interpweights, ) class ResultsPipeline: def __init__( self, prefix, suffix, n_archetypes, n_components, dataPipeline, indices=None ): n_pix_sed = dataPipeline.lamgrid.size n_pix_spec = dataPipeline.spec.shape[1] n_pix_phot = dataPipeline.phot.shape[1] self.dataPipeline = dataPipeline self.prefix = prefix self.suffix = suffix if indices is not None: n_obj = indices.size self.indices = indices self.logfml = onp.zeros((n_obj, n_archetypes)) self.specmod = onp.zeros((n_obj, n_pix_spec)) self.photmod = onp.zeros((n_obj, n_pix_phot)) self.thetamap = onp.zeros((n_obj, n_archetypes, n_components)) self.thetastd = onp.zeros((n_obj, n_archetypes, n_components)) self.ellfactors = onp.zeros((n_obj, n_archetypes)) def write_batch( self, data_batch, logfml, thetamap, thetastd, specmod, photmod, ellfactors ): si, bs = data_batch[0], data_batch[1] best = np.argmax(logfml, axis=1) fac = np.ones((bs, specmod.shape[2]), dtype=int) i0 = np.arange(bs, dtype=int)[:, None] * fac i1 = best[:, None] * fac i2 = fac * np.arange(specmod.shape[2], dtype=int)[None, :] self.specmod[si : si + bs, :] = specmod[i0, i1, i2] fac = np.ones((bs, photmod.shape[2]), dtype=int) i0 = np.arange(bs, dtype=int)[:, None] * fac i1 = best[:, None] * fac i2 = fac * np.arange(photmod.shape[2], dtype=int)[None, :] self.photmod[si : si + bs, :] = photmod[i0, i1, i2] self.logfml[si : si + bs, :] = logfml self.thetamap[si : si + bs, :, :] = thetamap self.thetastd[si : si + bs, :, :] = thetastd self.ellfactors[si : si + bs, :] = ellfactors def load_reconstructions(self): self.indices = onp.load(self.prefix + "indices" + self.suffix + ".npy") self.logfml =	onp.load(self.prefix + "logfml" + self.suffix + ".npy")	numpy.load
#!/usr/bin/env python ############################################################################# ## # This file is part of Taurus ## # http://taurus-scada.org ## # Copyright 2011 CELLS / ALBA Synchrotron, Bellaterra, Spain ## # Taurus is free software: you can redistribute it and/or modify # it under the terms of the GNU Lesser General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. ## # Taurus is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU Lesser General Public License for more details. ## # You should have received a copy of the GNU Lesser General Public License # along with Taurus. If not, see <http://www.gnu.org/licenses/>. ## ############################################################################# """ arrayedit.py: Widget for editing a spectrum/array via control points """ from __future__ import absolute_import from builtins import range import numpy from taurus.external.qt import Qt, Qwt5 from taurus.qt.qtgui.util.ui import UILoadable from .curvesAppearanceChooserDlg import CurveAppearanceProperties @UILoadable class ControllerBox(Qt.QWidget): selected = Qt.pyqtSignal(int) def __init__(self, parent=None, x=0, y=0, corr=0): Qt.QWidget.__init__(self, parent) self.loadUi() self._x = x self.setY(y) self.box.setTitle('x=%6g' % self._x) self.corrSB.setValue(corr) self.ctrlObj = self.corrSB.ctrlObj = self.lCopyBT.ctrlObj = self.rCopyBT.ctrlObj = self.lScaleBT.ctrlObj = self.rScaleBT.ctrlObj = self # reimplementing the focusInEvent method for the spinbox self.corrSB.focusInEvent = self.corrSB_focusInEvent self.box.mousePressEvent = self.mousePressEvent #self.connect(self.corrSB, Qt.SIGNAL('valueChanged(double)'), self.enableScale) def mousePressEvent(self, event): self.selected.emit(self._x) # print 'SELECTED', self #Qt.QDoubleSpinBox.focusInEvent(self.corrSB, event) def corrSB_focusInEvent(self, event): self.selected.emit(self._x) # print 'GOT FOCUS', self Qt.QDoubleSpinBox.focusInEvent(self.corrSB, event) def setY(self, y): self._y = y self.enableScale() def enableScale(self, args): enable = (self._y + self.corrSB.value()) != 0 self.lScaleBT.setEnabled(enable) self.rScaleBT.setEnabled(enable) @UILoadable class EditCPointsDialog(Qt.QDialog): def __init__(self, parent=None, x=0): Qt.QDialog.__init__(self, parent) self.loadUi() @UILoadable class AddCPointsDialog(Qt.QDialog): def __init__(self, parent=None, x=0): Qt.QDialog.__init__(self, parent) self.loadUi() @UILoadable class ArrayEditor(Qt.QWidget): def __init__(self, parent=None): Qt.QWidget.__init__(self, parent) self.loadUi() self._controllers = [] # construct the layout for controllers container self.ctrlLayout = Qt.QHBoxLayout(self.controllersContainer) self.ctrlLayout.setContentsMargins(5, 0, 5, 0) self.ctrlLayout.setSpacing(1) # implement scroll bars for the controllers container self.scrollArea = Qt.QScrollArea(self) self.scrollArea.setWidget(self.controllersContainer) self.scrollArea.setVerticalScrollBarPolicy(Qt.Qt.ScrollBarAlwaysOff) self.scrollArea.setWidgetResizable(True) self.cpointsGroupBox.layout().insertWidget(0, self.scrollArea) # initialize data cpoints = 2 self.x = numpy.arange(256, dtype='double') self.y = numpy.zeros(256, dtype='double') self.xp = numpy.linspace(self.x[0], self.x[-1], cpoints) self.corrp = numpy.zeros(cpoints) self.yp = numpy.interp(self.xp, self.x, self.y) self.corr = numpy.zeros(self.x.size) # markers self.markerPos = self.xp[0] self.marker1 = Qwt5.QwtPlotMarker() self.marker1.setSymbol(Qwt5.QwtSymbol(Qwt5.QwtSymbol.Rect, Qt.QBrush(Qt.Qt.NoBrush), Qt.QPen(Qt.Qt.green), Qt.QSize(8, 8))) self.marker1.attach(self.plot1) self.marker2 = Qwt5.QwtPlotMarker() self.marker2.setSymbol(Qwt5.QwtSymbol(Qwt5.QwtSymbol.Rect, Qt.QBrush(Qt.Qt.NoBrush), Qt.QPen(Qt.Qt.green), Qt.QSize(8, 8))) self.marker2.attach(self.plot2) # cpointsPickers self._cpointMovingIndex = None self._cpointsPicker1 = Qwt5.QwtPicker(self.plot1.canvas()) self._cpointsPicker1.setSelectionFlags(Qwt5.QwtPicker.PointSelection) self._cpointsPicker2 = Qwt5.QwtPicker(self.plot2.canvas()) self._cpointsPicker2.setSelectionFlags(Qwt5.QwtPicker.PointSelection) self._cpointsPicker1.widgetMousePressEvent = self.plot1MousePressEvent self._cpointsPicker1.widgetMouseReleaseEvent = self.plot1MouseReleaseEvent self._cpointsPicker2.widgetMousePressEvent = self.plot2MousePressEvent self._cpointsPicker2.widgetMouseReleaseEvent = self.plot2MouseReleaseEvent self._cpointsPicker1.widgetMouseDoubleClickEvent = self.plot1MouseDoubleClickEvent self._cpointsPicker2.widgetMouseDoubleClickEvent = self.plot2MouseDoubleClickEvent self._populatePlots() self.resetCorrection() self._selectedController = self._controllers[0] self._addCPointsDialog = AddCPointsDialog(self) # Launch low-priority initializations (to speed up load time) # Qt.QTimer.singleShot(0, <method>) # connections self.addCPointsBT.clicked.connect(self._addCPointsDialog.show) self._addCPointsDialog.editBT.clicked.connect(self.showEditCPointsDialog) self._addCPointsDialog.cleanBT.clicked.connect(self.resetCorrection) self._addCPointsDialog.addSingleCPointBT.clicked.connect(self.onAddSingleCPointBT) self._addCPointsDialog.addRegEspCPointsBT.clicked.connect(self.onAddRegEspCPointsBT) def plot1MousePressEvent(self, event): self.plotMousePressEvent(event, self.plot1) def plot2MousePressEvent(self, event): self.plotMousePressEvent(event, self.plot2) def plotMousePressEvent(self, event, taurusplot): picked, pickedCurveName, pickedIndex = taurusplot.pickDataPoint( event.pos(), scope=20, showMarker=False, targetCurveNames=['Control Points']) if picked is not None: self.changeCPointSelection(picked.x()) self.makeControllerVisible(self._controllers[pickedIndex]) self._cpointMovingIndex = pickedIndex self._movingStartYPos = event.y() taurusplot.canvas().setCursor(Qt.Qt.SizeVerCursor) def plot1MouseReleaseEvent(self, event): self.plotMouseReleaseEvent(event, self.plot1) def plot2MouseReleaseEvent(self, event): self.plotMouseReleaseEvent(event, self.plot2) def plotMouseReleaseEvent(self, event, taurusplot): if self._cpointMovingIndex is None: return # if no cpoint was picked, do nothing on release # no motion s performed if the y position is unchanged or if the mouse # release is out of the canvas validMotion = (self._movingStartYPos != event.pos().y() ) and taurusplot.canvas().rect().contains(event.pos()) if validMotion: # calculate the new correction newCorr = taurusplot.invTransform( taurusplot.getCurve('Control Points').yAxis(), event.y()) if taurusplot is self.plot1: newCorr -= self.yp[self._cpointMovingIndex] # apply new correction self._controllers[self._cpointMovingIndex].corrSB.setValue(newCorr) # reset the moving state self._cpointMovingIndex = None taurusplot.canvas().setCursor(Qt.Qt.CrossCursor) def plot1MouseDoubleClickEvent(self, event): self.plotMouseDoubleClickEvent(event, self.plot1) def plot2MouseDoubleClickEvent(self, event): self.plotMouseDoubleClickEvent(event, self.plot2) def plotMouseDoubleClickEvent(self, event, taurusplot): picked, pickedCurveName, pickedIndex = taurusplot.pickDataPoint( event.pos(), scope=20, showMarker=False, targetCurveNames=['Control Points']) if picked is not None: return # we dont want to create a control point too close of an existing one xp = taurusplot.invTransform(taurusplot.getCurve( 'Control Points').xAxis(), event.x()) if xp < self.xp[0] or xp > self.xp[-1]: return # we dont want to create control points out of the curve range if Qt.QMessageBox.question(self, 'Create Control Point?', 'Insert a new control point at x=%g?' % xp, 'Yes', 'No') == 0: self.insertController(xp) self.changeCPointSelection(xp) # singleshot is used as a hack to get out of the eventhandler Qt.QTimer.singleShot(1, self.makeControllerVisible) def makeControllerVisible(self, ctrl=None): if ctrl is None: ctrl = self._selectedController self.scrollArea.ensureWidgetVisible(ctrl) def connectToController(self, ctrl): ctrl.selected.connect(self.changeCPointSelection) ctrl.corrSB.valueChanged.connect(self.onCorrSBChanged) ctrl.lCopyBT.clicked.connect(self.onLCopy) ctrl.rCopyBT.clicked.connect(self.onRCopy) ctrl.lScaleBT.clicked.connect(self.onLScale) ctrl.rScaleBT.clicked.connect(self.onRScale) def onAddSingleCPointBT(self): x = self._addCPointsDialog.singleCPointXSB.value() self.insertController(x) def onAddRegEspCPointsBT(self): cpoints = self._addCPointsDialog.regEspCPointsSB.value() positions = numpy.linspace(self.x[0], self.x[-1], cpoints + 2)[1:-1] for xp in positions: self.insertController(xp) def showEditCPointsDialog(self): dialog = EditCPointsDialog(self) table = dialog.tableTW table.setRowCount(self.xp.size) for i, (xp, corrp) in enumerate(zip(self.xp, self.corrp)): table.setItem(i, 0, Qt.QTableWidgetItem(str(xp))) table.setItem(i, 1, Qt.QTableWidgetItem(str(corrp))) # show dialog and update values if it is accepted if dialog.exec_(): # delete previous controllers for c in self._controllers: c.setParent(None) c.deleteLater() self._controllers = [] # and create them anew new_xp = numpy.zeros(table.rowCount()) new_corrp = numpy.zeros(table.rowCount()) try: for i in range(table.rowCount()): new_xp[i] = float(table.item(i, 0).text()) new_corrp[i] = float(table.item(i, 1).text()) self.setCorrection(new_xp, new_corrp) except: Qt.QMessageBox.warning( self, 'Invalid data', 'Some values were not valid. Edition is ignored.') def _getInsertionIndex(self, xp): i = 0 while (self.xp[i] < xp): i += 1 return i def insertControllers(self, xplist): for xp in xplist: self.insertController(xp) def insertController(self, xp, index=None): if xp in self.xp: return None if index is None: index = self._getInsertionIndex(xp) # updating data (not in the most efficient way, but at least is clean) old_xp = self.xp self.xp = numpy.concatenate((self.xp[:index], (xp,), self.xp[index:])) self.yp = numpy.interp(self.xp, self.x, self.y) # the new correction is obtained by interpolation from the neighbouring # ones self.corrp = numpy.interp(self.xp, old_xp, self.corrp) # creating the controller ctrl = ControllerBox(parent=None, x=xp, y=self.yp[ index], corr=self.corrp[index]) self.ctrlLayout.insertWidget(index, ctrl) self._controllers.insert(index, ctrl) self.connectToController(ctrl) self.updatePlots() return index def delController(self, index): c = self._controllers.pop(index) c.setParent(None) c.deleteLater() self.xp = numpy.concatenate((self.xp[:index], self.xp[index + 1:])) self.yp = numpy.interp(self.xp, self.x, self.y) self.corrp = numpy.concatenate( (self.corrp[:index], self.corrp[index + 1:])) def _populatePlots(self): # Curves appearance self._yAppearance = CurveAppearanceProperties( sStyle=Qwt5.QwtSymbol.NoSymbol, lStyle=Qt.Qt.SolidLine, lWidth=2, lColor='black', cStyle=Qwt5.QwtPlotCurve.Lines, yAxis=Qwt5.QwtPlot.yLeft) self._correctedAppearance = CurveAppearanceProperties( sStyle=Qwt5.QwtSymbol.NoSymbol, lStyle=Qt.Qt.DashLine, lWidth=1, lColor='blue', cStyle=Qwt5.QwtPlotCurve.Lines, yAxis=Qwt5.QwtPlot.yLeft) self._cpointsAppearance = CurveAppearanceProperties( sStyle=Qwt5.QwtSymbol.Rect, sSize=5, sColor='blue', sFill=True, lStyle=Qt.Qt.NoPen, yAxis=Qwt5.QwtPlot.yLeft) self._corrAppearance = CurveAppearanceProperties( sStyle=Qwt5.QwtSymbol.NoSymbol, lStyle=Qt.Qt.SolidLine, lWidth=1, lColor='blue', cStyle=Qwt5.QwtPlotCurve.Lines, yAxis=Qwt5.QwtPlot.yLeft) self.plot1.attachRawData({'x': self.x, 'y': self.y, 'title': 'Master'}) self.plot1.setCurveAppearanceProperties({'Master': self._yAppearance}) self.plot1.attachRawData( {'x': self.xp, 'y': self.yp + self.corrp, 'title': 'Control Points'}) self.plot1.setCurveAppearanceProperties( {'Control Points': self._cpointsAppearance}) self.plot1.attachRawData( {'x': self.x, 'y': self.y + self.corr, 'title': 'Corrected'}) self.plot1.setCurveAppearanceProperties( {'Corrected': self._correctedAppearance}) self.plot2.attachRawData( {'x': self.x, 'y': self.corr, 'title': 'Correction'}) self.plot2.setCurveAppearanceProperties( {'Correction': self._corrAppearance}) self.plot2.attachRawData( {'x': self.xp, 'y': self.corrp, 'title': 'Control Points'}) self.plot2.setCurveAppearanceProperties( {'Control Points': self._cpointsAppearance}) def updatePlots(self): self.plot1.getCurve('Control Points').setData( self.xp, self.yp + self.corrp) self.plot1.getCurve('Corrected').setData(self.x, self.y + self.corr) self.plot2.getCurve('Correction').setData(self.x, self.corr) self.plot2.getCurve('Control Points').setData(self.xp, self.corrp) index = self._getInsertionIndex(self.markerPos) self.marker1.setValue(self.xp[index], self.yp[ index] + self.corrp[index]) self.marker2.setValue(self.xp[index], self.corrp[index]) self.plot1.replot() self.plot2.replot() def onLCopy(self, checked): sender = self.sender().ctrlObj index = self._getInsertionIndex(sender._x) v = sender.corrSB.value() for ctrl in self._controllers[:index]: ctrl.corrSB.setValue(v) def onRCopy(self, checked): sender = self.sender().ctrlObj index = self._getInsertionIndex(sender._x) v = sender.corrSB.value() for ctrl in self._controllers[index + 1:]: ctrl.corrSB.setValue(v) def onLScale(self, checked): sender = self.sender().ctrlObj index = self._getInsertionIndex(sender._x) # y=numpy.interp(self.xp, self.x, self.y) #values of the master at the # control points if self.yp[index] == 0: Qt.QMessageBox.warning( self, 'Scaling Error', 'The master at this control point is zero-valued. This point cannot be used as reference for scaling') return v = sender.corrSB.value() / (self.yp[index]) for i in range(0, index): self._controllers[i].corrSB.setValue(v self.yp[i]) def onRScale(self, checked): sender = self.sender().ctrlObj index = self._getInsertionIndex(sender._x) # y=numpy.interp(self.xp, self.x, self.y) #values of the master at the # control points if self.yp[index] == 0: Qt.QMessageBox.warning( self, 'Scaling Error', 'The master at this control point is zero-valued. This point cannot be used as reference for scaling') return v = sender.corrSB.value() / (self.yp[index]) for i in range(index + 1, self.xp.size): self._controllers[i].corrSB.setValue(v * self.yp[i]) def changeCPointSelection(self, newpos): index = self._getInsertionIndex(newpos) old_index = self._getInsertionIndex(self.markerPos) self.markerPos = self.xp[index] self.marker1.setValue(self.xp[index], self.yp[ index] + self.corrp[index]) self.marker2.setValue(self.xp[index], self.corrp[index]) self.plot1.replot() self.plot2.replot() self._controllers[old_index].corrSB.setStyleSheet('') self._controllers[index].corrSB.setStyleSheet('background:lightgreen') self._selectedController = self._controllers[index] def onCorrSBChanged(self, value=None): '''recalculates the position and value of the control points (self.xp and self.corrp) as well as the correction curve (self.corr)''' ctrl = self.sender().ctrlObj self.corrp[self._getInsertionIndex(ctrl._x)] = value # recalculate the correction curve self.corr = numpy.interp(self.x, self.xp, self.corrp) self.updatePlots() def setMaster(self, x, y, keepCP=False, keepCorr=False): # make sure that x,y are numpy arrays and that the values are sorted # for x x, y = numpy.array(x), numpy.array(y) if x.shape != y.shape or x.size == 0 or y.size == 0: raise ValueError('The master curve is not valid') sortedindexes =	numpy.argsort(x)	numpy.argsort
import os import pickle import numpy as np from tqdm import tqdm import torch from self_supervised.data.io import loadmat FILENAMES = { ('mihi', 1): 'full-mihi-03032014', ('mihi', 2): 'full-mihi-03062014', ('chewie', 1): 'full-chewie-10032013', ('chewie', 2): 'full-chewie-12192013', } class ReachNeuralDataset: def __init__(self, path, primate='mihi', day=1, binning_period=0.1, binning_overlap=0.0, train_split=0.8, scale_firing_rates=False, scale_velocity=False, sort_by_reach=True): self.path = path # get path to data assert primate in ['mihi', 'chewie'] assert day in [1, 2] self.primate = primate self.filename = FILENAMES[(self.primate, day)] self.raw_path = os.path.join(self.path, 'raw/%s.mat') % self.filename self.processed_path = os.path.join(self.path, 'processed/%s.pkl') % (self.filename + '-%.2f' % binning_period) # get binning parameters self.binning_period = binning_period self.binning_overlap = binning_overlap if self.binning_overlap != 0: raise NotImplemented # train/val split self.train_split = train_split # initialize some parameters self.dataset_ = {} self.subset = 'train' # default selected subset ### Process data # load data if not os.path.exists(self.processed_path): data_train_test = self._process_data() else: data_train_test = self._load_processed_data() # split data data_train, data_test = self._split_data(data_train_test) self._num_trials = {'train': len(data_train['firing_rates']), 'test': len(data_test['firing_rates'])} # compute mean and std of firing rates self.mean, self.std = self._compute_mean_std(data_train, feature='firing_rates') # remove neurons with no variance data_train, data_test = self._remove_static_neurons(data_train, data_test) # scale data if scale_firing_rates: data_train, data_test = self._scale_data(data_train, data_test, feature='firing_rates') if scale_velocity: data_train, data_test = self._scale_data(data_train, data_test, feature='velocity') # sort by reach direction if sort_by_reach: data_train = self._sort_by_reach_direction(data_train) data_test = self._sort_by_reach_direction(data_test) # build sequences trial_lengths_train = [seq.shape[0] for seq in data_train['firing_rates']] # merge everything for feature in data_train.keys(): data_train[feature] = np.concatenate(data_train[feature]).squeeze() data_test[feature] = np.concatenate(data_test[feature]).squeeze() data_train['trial_lengths'] = trial_lengths_train data_train['reach_directions'] = np.unique(data_train['labels']).tolist() data_train['reach_lengths'] = [np.sum(data_train['labels'] == reach_id) for reach_id in data_train['reach_directions']] # map labels to 0 .. N-1 for training data_train['raw_labels'] = data_train['labels'].copy() data_test['raw_labels'] = data_test['labels'].copy() data_train['labels'] = self._map_labels(data_train) data_test['labels'] = self._map_labels(data_test) self.dataset_['train'] = data_train self.dataset_['test'] = data_test @property def dataset(self): return self.dataset_[self.subset] def __getattr__(self, item): return self.dataset[item] def train(self): self.subset = 'train' def test(self): self.subset = 'test' @property def num_trials(self): return self._num_trials[self.subset] @property def num_neurons(self): return self[0]['firing_rates'].shape[1] def _process_data(self): print('Preparing dataset: Binning data.') # load data mat_dict = loadmat(self.raw_path) # bin data data = self._bin_data(mat_dict) self._save_processed_data(data) return data def _save_processed_data(self, data): with open(self.processed_path, 'wb') as output: pickle.dump({'data': data}, output) def _load_processed_data(self): with open(self.processed_path, "rb") as fp: data = pickle.load(fp)['data'] return data def _bin_data(self, mat_dict): # load matrix trialtable = mat_dict['trial_table'] neurons = mat_dict['out_struct']['units'] pos = np.array(mat_dict['out_struct']['pos']) vel = np.array(mat_dict['out_struct']['vel']) acc = np.array(mat_dict['out_struct']['acc']) force =	np.array(mat_dict['out_struct']['force'])	numpy.array
# Copyright 2018 <NAME> # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. from typed_python import ( Bool, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Float32, Float64, NoneType, TupleOf, ListOf, OneOf, Tuple, NamedTuple, Dict, ConstDict, Alternative, serialize, deserialize, Value, Class, Member, TypeFilter, UndefinedBehaviorException, Function ) from typed_python.test_util import currentMemUsageMb import typed_python._types as _types import psutil import unittest import traceback import time import numpy import os import sys def typeFor(t): assert not isinstance(t, list), t return type(t) def typeForSeveral(t): ts = set(typeFor(a) for a in t) if len(ts) == 1: return list(ts)[0] return OneOf(ts) def makeTupleOf(args): if not args: return TupleOf(int)() return TupleOf(typeForSeveral(args))(args) def makeNamedTuple(kwargs): if not kwargs: return NamedTuple()() return NamedTuple({k:typeFor(v) for k,v in kwargs.items()})(*kwargs) def makeTuple(args): if not args: return Tuple()() return Tuple([typeFor(v) for v in args])(args) def makeDict(d): if not d: return ConstDict(int,int)() return ConstDict(typeForSeveral(d.keys()), typeForSeveral(d.values()))(d) def makeAlternative(severalDicts): types = list( set( tuple( (k,typeFor(v)) for k,v in ntDict.items() ) for ntDict in severalDicts ) ) alt = Alternative("Alt", { "a_%s" % i: dict(types[i]) for i in range(len(types)) }) res = [] for thing in severalDicts: did = False for i in range(len(types)): try: res.append(getattr(alt,"a_%s" % i)(thing)) did = True except Exception: pass if did: break assert len(res) == len(severalDicts) return res def choice(x): #numpy.random.choice([1,(1,2)]) blows up because it looks 'multidimensional' #so we have to pick from a list of indices if not isinstance(x,list): x = list(x) return x[numpy.random.choice(list(range(len(x))))] class RandomValueProducer: def __init__(self): self.levels = {0: [b'1', b'', '2', '', 0, 1, 0.0, 1.0, None, False, True, "a ", "a string", "b string", "b str"]} def addEvenly(self, levels, count): for level in range(1, levels+1): self.addValues(level, count) def all(self): res = [] for valueList in self.levels.values(): res.extend(valueList) return res def addValues(self, level, count, sublevels = None): assert level > 0 if sublevels is None: sublevels = list(range(level)) sublevels = [x for x in sublevels if x in self.levels] assert sublevels def picker(): whichLevel = choice(sublevels) try: return choice(self.levels[whichLevel]) except Exception: print(self.levels[whichLevel]) raise for _ in range(count): val = self.randomValue(picker) if not isinstance(val,list): val = [val] self.levels.setdefault(level, []).extend(val) def randomValue(self, picker): def randomTuple(): return makeTuple([picker() for i in range(choice([0,1,2,3,4]))]) def randomNamedTupleDict(): return {"x_%s" % i: picker() for i in range(choice([0,1,2,3,4]))} def randomNamedTuple(): return makeNamedTuple(*randomNamedTupleDict()) def randomDict(): return makeDict({picker():picker() for i in range(choice([0,1,2,3,4]))}) def randomTupleOf(): return makeTupleOf([picker() for i in range(choice([0,1,2,3,4]))]) def randomAlternative(): return makeAlternative([randomNamedTupleDict() for i in range(choice([1,2,3,4]))]) return choice([randomTuple,randomNamedTuple,randomDict,randomTupleOf,randomAlternative,picker])() def pickRandomly(self): return choice(self.levels[choice(list(self.levels))]) class NativeTypesTests(unittest.TestCase): def check_expected_performance(self, elapsed, expected=1.0): if os.environ.get('TRAVIS_CI', None) is not None: expected = 2 * expected self.assertTrue( elapsed < expected, "Slow Performance: expected to take {expected} sec, but took {elapsed}" .format(expected=expected, elapsed=elapsed) ) def test_objects_are_singletons(self): self.assertTrue(Int8 is Int8) self.assertTrue(NoneType is NoneType) def test_object_binary_compatibility(self): ibc = _types.isBinaryCompatible self.assertTrue(ibc(NoneType, NoneType)) self.assertTrue(ibc(Int8, Int8)) NT = NamedTuple(a=int,b=int) class X(NamedTuple(a=int,b=int)): pass class Y(NamedTuple(a=int,b=int)): pass self.assertTrue(ibc(X, X)) self.assertTrue(ibc(X, Y)) self.assertTrue(ibc(X, NT)) self.assertTrue(ibc(Y, NT)) self.assertTrue(ibc(NT, Y)) self.assertFalse(ibc(OneOf(int, float), OneOf(float, int))) self.assertTrue(ibc(OneOf(int, X), OneOf(int, Y))) self.assertIsInstance(OneOf(None, X)(Y()), X) self.assertIsInstance(NamedTuple(x=OneOf(None, X))(x=Y()).x, X) def test_binary_compatibility_incompatible_alternatives(self): ibc = _types.isBinaryCompatible A1 = Alternative("A1", X={'a': int}, Y={'b': float}) A2 = Alternative("A2", X={'a': int}, Y={'b': str}) self.assertTrue(ibc(A1, A1.X)) self.assertTrue(ibc(A1, A1.Y)) self.assertTrue(ibc(A1.Y, A1.Y)) self.assertTrue(ibc(A1.Y, A1)) self.assertTrue(ibc(A1.X, A1)) self.assertFalse(ibc(A1.X, A1.Y)) self.assertFalse(ibc(A1, A2)) self.assertFalse(ibc(A1.X, A2.X)) self.assertFalse(ibc(A1.Y, A2.Y)) def test_binary_compatibility_compatible_alternatives(self): ibc = _types.isBinaryCompatible A1 = Alternative("A1", X={'a': int}, Y={'b': float}) A2 = Alternative("A2", X={'a': int}, Y={'b': float}) self.assertTrue(ibc(A1.X, A2.X)) self.assertTrue(ibc(A1.Y, A2.Y)) self.assertFalse(ibc(A1.X, A2.Y)) self.assertFalse(ibc(A1.Y, A2.X)) def test_object_bytecounts(self): self.assertEqual(_types.bytecount(NoneType), 0) self.assertEqual(_types.bytecount(Int8), 1) self.assertEqual(_types.bytecount(Int64), 8) def test_type_stringification(self): for t in ['Int8', 'NoneType']: self.assertEqual(str(getattr(_types,t)()), "<class '%s'>" % t) def test_tuple_of(self): tupleOfInt = TupleOf(int) i = tupleOfInt(()) i = tupleOfInt((1,2,3)) self.assertEqual(len(i), 3) self.assertEqual(tuple(i), (1,2,3)) for x in range(10): self.assertEqual( tuple(tupleOfInt(tuple(range(x)))), tuple(range(x)) ) with self.assertRaisesRegex(AttributeError, "do not accept attributes"): tupleOfInt((1,2,3)).x = 2 def test_one_of_alternative(self): X = Alternative("X", V={'a': int}) O = OneOf(None, X) self.assertEqual(O(X.V(a=10)), X.V(a=10)) def test_one_of_py_subclass(self): class X(NamedTuple(x=int)): def f(self): return self.x O = OneOf(None, X) self.assertEqual(NamedTuple(x=int)(x=10).x, 10) self.assertEqual(X(x=10).f(), 10) self.assertEqual(O(X(x=10)).f(), 10) def test_tuple_of_tuple_of(self): tupleOfInt = TupleOf(int) tupleOfTupleOfInt = TupleOf(tupleOfInt) pyVersion = (1,2,3),(1,2,3,4) nativeVersion = tupleOfTupleOfInt(pyVersion) self.assertEqual(len(nativeVersion), 2) self.assertEqual(len(nativeVersion[0]), 3) self.assertEqual(tuple(tuple(x) for x in nativeVersion), pyVersion) bigTup = tupleOfInt(list(range(1000))) t0 = time.time() t = (bigTup,bigTup,bigTup,bigTup,bigTup) for i in range(1000000): tupleOfTupleOfInt(t) elapsed = time.time() - t0 print("Took ", elapsed, " to do 1mm") self.check_expected_performance(elapsed) def test_default_initializer_oneof(self): x = OneOf(None, int) self.assertTrue(x() is None, repr(x())) def test_tuple_of_various_things(self): for thing, typeOfThing in [("hi", str), (b"somebytes", bytes), (1.0, float), (2, int), (None, type(None)) ]: tupleType = TupleOf(typeOfThing) t = tupleType((thing,)) self.assertTrue(type(t[0]) is typeOfThing) self.assertEqual(t[0], thing) def test_tuple_assign_fails(self): with self.assertRaisesRegex(TypeError, "does not support item assignment"): (1,2,3)[10] = 20 with self.assertRaisesRegex(TypeError, "does not support item assignment"): TupleOf(int)((1,2,3))[10] = 20 def test_list_of(self): L = ListOf(int) self.assertEqual(L.__qualname__, "ListOf(Int64)") l = L([1,2,3,4]) self.assertEqual(l[0], 1) self.assertEqual(l[-1], 4) l[0] = 10 self.assertEqual(l[0], 10) l[-1] = 11 self.assertEqual(l[3], 11) with self.assertRaisesRegex(IndexError, "index out of range"): l[100] = 20 l2 = L((10,2,3,11)) self.assertEqual(l,l2) self.assertNotEqual(l,(10,2,3,11)) self.assertEqual(l,[10,2,3,11]) self.assertEqual(str(l),str([10,2,3,11])) l3 = l + l2 self.assertEqual(l3, [10,2,3,11,10,2,3,11]) l3.append(23) self.assertEqual(l3, [10,2,3,11,10,2,3,11, 23]) def test_list_resize(self): l = ListOf(TupleOf(int))() l.resize(10) self.assertEqual(l.reserved(), 10) self.assertEqual(len(l), 10) emptyTup = TupleOf(int)() aTup = TupleOf(int)((1,2,3)) self.assertEqual(list(l), [emptyTup] * 10) l.resize(20, aTup) self.assertEqual(list(l), [emptyTup] * 10 + [aTup] * 10) self.assertEqual(_types.refcount(aTup), 11) self.assertEqual(l.pop(15), aTup) self.assertEqual(l.pop(5), emptyTup) self.assertEqual(_types.refcount(aTup), 10) l.resize(15) with self.assertRaises(IndexError): l.pop(100) self.assertEqual(_types.refcount(aTup), 7) #6 in the list because we popped at '5' l.pop() self.assertEqual(_types.refcount(aTup), 6) #this pops one of the empty tuples l.pop(-10) self.assertEqual(_types.refcount(aTup), 6) l.clear() self.assertEqual(len(l), 0) def test_one_of(self): o = OneOf(None, str) self.assertEqual(o("hi"), "hi") self.assertTrue(o(None) is None) o = OneOf(None, "hi", 1.5, 1, True, b"hi2") self.assertTrue(o(None) is None) self.assertTrue(o("hi") == "hi") self.assertTrue(o(b"hi2") == b"hi2") self.assertTrue(o(1.5) == 1.5) self.assertTrue(o(1) is 1) self.assertIs(o(True), True) with self.assertRaises(TypeError): o("hi2") with self.assertRaises(TypeError): o(b"hi") with self.assertRaises(TypeError): o(3) with self.assertRaises(TypeError): o(False) def test_ordering(self): o = OneOf(None, "hi", 1.5, 1, True, b"hi2") self.assertIs(o(True), True) def test_one_of_flattening(self): self.assertEqual(OneOf(OneOf(None, 1.0), OneOf(2.0, 3.0)), OneOf(None, 1.0, 2.0, 3.0)) def test_one_of_order_matters(self): self.assertNotEqual(OneOf(1.0, 2.0), OneOf(2.0, 1.0)) def test_type_filter(self): EvenInt = TypeFilter(int, lambda i: i % 2 == 0) self.assertTrue(isinstance(2, EvenInt)) self.assertFalse(isinstance(1, EvenInt)) self.assertFalse(isinstance(2.0, EvenInt)) EvenIntegers = TupleOf(EvenInt) e = EvenIntegers(()) e2 = e + (2,4,0) with self.assertRaises(TypeError): EvenIntegers((1,)) with self.assertRaises(TypeError): e2 + (1,) def test_tuple_of_one_of_fixed_size(self): t = TupleOf(OneOf(0,1,2,3,4)) ints = tuple([x % 5 for x in range(1000000)]) typedInts = t(ints) self.assertEqual(len(serialize(t, typedInts)), len(ints) + 8) #4 bytes for size of list, 4 bytes for frame size self.assertEqual(tuple(typedInts), ints) def test_tuple_of_one_of_multi(self): t = TupleOf(OneOf(int, bool)) someThings = tuple([100 + x % 5 if x % 17 != 0 else bool(x%19) for x in range(1000000)]) typedThings = t(someThings) self.assertEqual( len(serialize(t, typedThings)), sum(2 if isinstance(t,bool) else 9 for t in someThings) + 8 ) self.assertEqual(tuple(typedThings), someThings) def test_compound_oneof(self): producer = RandomValueProducer() producer.addEvenly(1000, 2) for _ in range(1000): vals = (producer.pickRandomly(), producer.pickRandomly(), producer.pickRandomly()) a = OneOf(vals[0], vals[1], type(vals[2])) for v in vals: self.assertEqual(a(v), v, (a(v),v)) tup = TupleOf(a) tupInst = tup(vals) for i in range(len(vals)): self.assertEqual(tupInst[i], vals[i], vals) def test_one_of_conversion_failure(self): o = OneOf(None, str) with self.assertRaises(TypeError): o(b"bytes") def test_one_of_in_tuple(self): t = Tuple(OneOf(None, str), str) self.assertEqual(t(("hi","hi2"))[0], "hi") self.assertEqual(t(("hi","hi2"))[1], "hi2") self.assertEqual(t((None,"hi2"))[1], "hi2") self.assertEqual(t((None,"hi2"))[0], None) with self.assertRaises(TypeError): t((None,None)) with self.assertRaises(IndexError): t((None,"hi2"))[2] def test_one_of_composite(self): t = OneOf(TupleOf(str), TupleOf(float)) self.assertIsInstance(t((1.0,2.0)), TupleOf(float)) self.assertIsInstance(t(("1.0","2.0")), TupleOf(str)) with self.assertRaises(TypeError): t((1.0,"2.0")) def test_named_tuple(self): t = NamedTuple(a=int, b=int) with self.assertRaisesRegex(AttributeError, "object has no attribute"): t().asdf with self.assertRaisesRegex(AttributeError, "immutable"): t().a = 1 self.assertEqual(t()[0], 0) self.assertEqual(t().a, 0) self.assertEqual(t()[1], 0) self.assertEqual(t(a=1,b=2).a, 1) self.assertEqual(t(a=1,b=2).b, 2) def test_named_tuple_construction(self): t = NamedTuple(a=int, b=int) self.assertEqual(t(a=10).a, 10) self.assertEqual(t(a=10).b, 0) self.assertEqual(t(a=10,b=2).a, 10) self.assertEqual(t(a=10,b=2).b, 2) self.assertEqual(t({'a': 10,'b':2}).a, 10) self.assertEqual(t({'a': 10,'b':2}).b, 2) self.assertEqual(t({'b':2}).a, 0) self.assertEqual(t({'b':2}).b, 2) with self.assertRaises(TypeError): t({'c':10}) with self.assertRaises(TypeError): t(c=10) def test_named_tuple_str(self): t = NamedTuple(a=str, b=str) self.assertEqual(t(a='1',b='2').a, '1') self.assertEqual(t(a='1',b='2').b, '2') self.assertEqual(t(b='2').a, '') self.assertEqual(t(b='2').b, '2') self.assertEqual(t().a, '') self.assertEqual(t().b, '') def test_tuple_of_string_perf(self): t = NamedTuple(a=str, b=str) t0 = time.time() for i in range(1000000): t(a="a", b="b").a elapsed = time.time() - t0 print("Took ", elapsed, " to do 1mm") self.check_expected_performance(elapsed) def test_comparisons_in_one_of(self): t = OneOf(None, float) def map(x): if x is None: return -1000000.0 else: return x lt = lambda a,b: map(a) < map(b) le = lambda a,b: map(a) <= map(b) eq = lambda a,b: map(a) == map(b) ne = lambda a,b: map(a) != map(b) gt = lambda a,b: map(a) > map(b) ge = lambda a,b: map(a) >= map(b) funcs = [lt,le,eq,ne,gt,ge] ts = [None,1.0,2.0,3.0] for f in funcs: for t1 in ts: for t2 in ts: self.assertTrue(f(t1,t2) is f(t(t1),t(t2))) def test_comparisons_equivalence(self): t = TupleOf(OneOf(None, str, bytes, float, int, bool, TupleOf(int)),) def lt(a,b): return a < b def le(a,b): return a <= b def eq(a,b): return a == b def ne(a,b): return a != b def gt(a,b): return a > b def ge(a,b): return a >= b funcs = [lt,le,eq,ne,gt,ge] tgroups = [ [1.0,2.0,3.0], [1,2,3], [True,False], ["a","b","ab","bb","ba","aaaaaaa","","asdf"], ["1","2","3","12","13","23","24","123123", "0", ""], [b"a",b"b",b"ab",b"bb",b"ba",b"aaaaaaa",b"",b"asdf"], [(1,2),(1,2,3),(),(1,1),(1,)] ] for ts in tgroups: for f in funcs: for t1 in ts: for t2 in ts: self.assertTrue(f(t1,t2) is f(t((t1,)),t((t2,))), (f, t1,t2, f(t1,t2), f(t((t1,)),t((t2,)))) ) def test_const_dict(self): t = ConstDict(str,str) self.assertEqual(len(t()), 0) self.assertEqual(len(t({})), 0) self.assertEqual(len(t({'a':'b'})), 1) self.assertEqual(t({'a':'b'})['a'], 'b') self.assertEqual(t({'a':'b','b':'c'})['b'], 'c') self.assertTrue("a" in deserialize(t,serialize(t, t({'a':'b'})))) self.assertTrue("a" in deserialize(t,serialize(t, t({'a':'b','b':'c'})))) self.assertTrue("a" in deserialize(t,serialize(t, t({'a':'b','b':'c','c':'d'})))) self.assertTrue("a" in deserialize(t,serialize(t, t({'a':'b','b':'c','c':'d','d':'e'})))) self.assertTrue("c" in deserialize(t,serialize(t, t({'a':'b','b':'c','c':'d','def':'e'})))) self.assertTrue("def" in deserialize(t,serialize(t, t({'a':'b','b':'c','c':'d','def':'e'})))) def test_const_dict_get(self): a = ConstDict(str,str)({'a':'b','c':'d'}) self.assertEqual(a.get('a'),'b') self.assertEqual(a.get('asdf'),None) self.assertEqual(a.get('asdf',20),20) def test_const_dict_items_keys_and_values(self): a = ConstDict(str,str)({'a':'b','c':'d'}) self.assertEqual(sorted(a.items()), [('a','b'),('c','d')]) self.assertEqual(sorted(a.keys()), ['a','c']) self.assertEqual(sorted(a.values()), ['b','d']) def test_empty_string(self): a = ConstDict(str,str)({'a':''}) print(a['a']) def test_dict_to_oneof(self): t = ConstDict(str,OneOf("A","B","ABCDEF")) a = t({'a':'A','b':'ABCDEF'}) self.assertEqual(a['a'], "A") self.assertEqual(a['b'], "ABCDEF") self.assertEqual(a, deserialize(t,serialize(t,a))) def test_deserialize_primitive(self): x = deserialize(str, serialize(str, "a")) self.assertTrue(isinstance(x,str)) def test_dict_containment(self): for _ in range(100): producer = RandomValueProducer() producer.addEvenly(20, 2) values = producer.all() for v in values: if str(type(v))[:17] == "<class 'ConstDict": v = deserialize(type(v), serialize(type(v), v)) for k in v: self.assertTrue(k in v) def test_named_tuple_from_dict(self): N = NamedTuple(x=int, y=str,z=OneOf(None,"hihi")) self.assertEqual(N().x, 0) self.assertEqual(N().y, "") self.assertEqual(N().z, None) self.assertEqual(N({}).x, 0) self.assertEqual(N({}).y, "") self.assertEqual(N({}).z, None) self.assertEqual(N({'x': 20}).x, 20) self.assertEqual(N({'x': 20, 'y': "30"}).y, "30") self.assertEqual(N({'y': "30", 'x': 20}).y, "30") self.assertEqual(N({'z': "hihi"}).z, "hihi") with self.assertRaises(Exception): N({'r': 'hi'}) N({'y': 'hi', 'z': "not hihi"}) N({'a': 0, 'b': 0, 'c': 0, 'd': 0}) def test_const_dict_mixed(self): t = ConstDict(str,int) self.assertTrue(t({"a":10})["a"] == 10) t = ConstDict(int, str) self.assertTrue(t({10:"a"})[10] == "a") def test_const_dict_comparison(self): t = ConstDict(str,str) self.assertEqual(t({'a':'b'}), t({'a':'b'})) self.assertLess(t({}), t({'a':'b'})) def test_const_dict_lookup(self): for type_to_use, vals in [ (int, list(range(20))), (bytes, [b'1', b'2', b'3', b'4', b'5']) ]: t = ConstDict(type_to_use, type_to_use) for _ in range(10): ks = list(vals) vs = list(vals) numpy.random.shuffle(ks) numpy.random.shuffle(vs) py_d = {} for i in range(len(ks)): py_d[ks[i]] = vs[i] typed_d = t(py_d) for k in py_d: self.assertEqual(py_d[k], typed_d[k]) last_k = None for k in typed_d: assert last_k is None or k > last_k, (k,last_k) last_k = k def test_const_dict_lookup_time(self): int_dict = ConstDict(int, int) d = int_dict({k:k for k in range(1000000)}) for k in range(1000000): self.assertTrue(k in d) self.assertTrue(d[k] == k) def test_const_dict_of_dict(self): int_dict = ConstDict(int, int) int_dict_2 = ConstDict(int_dict,int_dict) d = int_dict({1:2}) d2 = int_dict({1:2,3:4}) big = int_dict_2({d:d2}) self.assertTrue(d in big) self.assertTrue(d2 not in big) self.assertTrue(big[d] == d2) def test_dict_hash_perf(self): str_dict = ConstDict(str, str) s = str_dict({'a' * 1000000: 'b' * 1000000}) t0 = time.time() for k in range(1000000): hash(s) elapsed = time.time() - t0 print(elapsed, " to do 1mm") self.check_expected_performance(elapsed) def test_const_dict_str_perf(self): t = ConstDict(str,str) t0 = time.time() for i in range(100000): t({str(k): str(k+1) for k in range(10)}) elapsed = time.time() - t0 print("Took ", elapsed, " to do 1mm") self.check_expected_performance(elapsed) def test_const_dict_int_perf(self): t = ConstDict(int,int) t0 = time.time() for i in range(100000): t({k:k+1 for k in range(10)}) elapsed = time.time() - t0 print("Took ", elapsed, " to do 1mm") self.check_expected_performance(elapsed) def test_const_dict_iter_int(self): t = ConstDict(int,int) aDict = t({k:k+1 for k in range(100)}) for k in aDict: self.assertEqual(aDict[k], k+1) def test_const_dict_iter_str(self): t = ConstDict(str,str) aDict = t({str(k):str(k+1) for k in range(100)}) for k in aDict: self.assertEqual(aDict[str(k)], str(int(k)+1)) def test_alternatives_with_Bytes(self): alt = Alternative( "Alt", x_0={'a':bytes} ) self.assertEqual(alt.x_0(a=b''), alt.x_0(a=b'')) def test_alternatives_with_str_func(self): alt = Alternative( "Alt", x_0={'a':bytes}, f=lambda self: 1, __str__=lambda self: "not_your_usual_str" ) self.assertEqual(alt.x_0().f(), 1) self.assertEqual(str(alt.x_0()), "not_your_usual_str") def test_named_tuple_subclass_magic_methods(self): class X(NamedTuple(x=int,y=int)): def __str__(self): return "str override" def __repr__(self): return "repr override" self.assertEqual(repr(X()), "repr override") self.assertEqual(str(X()), "str override") def test_empty_alternatives(self): a = Alternative( "Alt", A={}, B={} ) self.assertEqual(a.A(), a.A()) self.assertIsInstance(deserialize(a, serialize(a, a.A())), a.A) self.assertEqual(a.A(), deserialize(a, serialize(a, a.A()))) self.assertEqual(a.B(), a.B()) self.assertNotEqual(a.A(), a.B()) self.assertNotEqual(a.B(), a.A()) def test_extracted_alternatives_have_correct_type(self): Alt = Alternative( "Alt", A={}, B={} ) tOfAlt = TupleOf(Alt) a = Alt.A() aTup = tOfAlt((a,)) self.assertEqual(a, aTup[0]) self.assertTrue(type(a) is type(aTup[0])) def test_alternatives(self): alt = Alternative( "Alt", child_ints={'x': int, 'y': int}, child_strings={'x': str, 'y': str} ) self.assertTrue(issubclass(alt.child_ints, alt)) self.assertTrue(issubclass(alt.child_strings, alt)) a = alt.child_ints(x=10,y=20) a2 = alt.child_ints(x=10,y=20) self.assertEqual(a,a2) self.assertTrue(isinstance(a, alt)) self.assertTrue(isinstance(a, alt.child_ints)) self.assertEqual(a.x, 10) self.assertEqual(a.y, 20) self.assertTrue(a.matches.child_ints) self.assertFalse(a.matches.child_strings) with self.assertRaisesRegex(AttributeError, "immutable"): a.x = 20 def test_alternatives_comparison(self): empty = Alternative("X", A={}, B={}) self.assertEqual(empty.A(), empty.A()) self.assertEqual(empty.B(), empty.B()) self.assertNotEqual(empty.A(), empty.B()) a = Alternative("X", A={'a': int}, B={'b': int}, C={'c': str}, D={'d': bytes}, ) self.assertEqual(a.A(a=10), a.A(a=10)) self.assertNotEqual(a.A(a=10), a.A(a=11)) self.assertNotEqual(a.C(c=""), a.C(c="hi")) self.assertFalse(a.C(c="") == a.C(c="hi")) self.assertNotEqual(a.D(d=b""), a.D(d=b"hi")) def test_alternatives_add_operator(self): alt = Alternative( "Alt", child_ints={'x': int, 'y': int}, __add__=lambda l,r: (l,r) ) a = alt.child_ints(x=0,y=2) self.assertEqual(a+a,(a,a)) def test_alternatives_perf(self): alt = Alternative( "Alt", child_ints={'x': int, 'y': int}, child_strings={'x': str, 'y': str} ) t0 = time.time() for i in range(1000000): a = alt.child_ints(x=10,y=20) a.matches.child_ints a.x elapsed = time.time() - t0 print("Took ", elapsed, " to do 1mm") self.check_expected_performance(elapsed, expected=2.0) def test_object_hashing_and_equality(self): for _ in range(100): producer = RandomValueProducer() producer.addEvenly(20, 2) values = producer.all() for v1 in values: for v2 in values: if hash(v1) != hash(v2) and v1 == v2: print(v1,v2, type(v1), type(v2)) for v1 in values: for v2 in values: if type(v1) == type(v2) and v1 == v2: self.assertEqual(hash(v1), hash(v2), (v1, v2)) if type(v1) is type(v2): self.assertEqual(repr(v1), repr(v2), (v1, v2, type(v1),type(v2))) values = sorted([makeTuple(v) for v in values]) for i in range(len(values)-1): self.assertTrue(values[i] <= values[i+1]) self.assertTrue(values[i+1] >= values[i]) def test_bytes_repr(self): for _ in range(100000): #always start with a '"' because otherwise python keeps chosing different #initial characters. someBytes = b'"' + numpy.random.uniform(size=2).tostring() self.assertEqual(repr(makeTuple(someBytes)), repr((someBytes,))) def test_equality_with_native_python_objects(self): tups = [(1,2,3), (), ("2",), (b"2",), (1,2,3, "b"), (2,), (None,)] for tup1 in tups: self.assertEqual( makeTuple(tup1), tup1 ) for tup2 in tups: if tup1 != tup2: self.assertNotEqual( makeTuple(tup1), tup2 ) for tup1 in tups: self.assertEqual( makeTupleOf(tup1), tup1 ) for tup2 in tups: if tup1 != tup2: self.assertNotEqual( makeTupleOf(tup1), tup2 ) def test_add_tuple_of(self): tupleOfInt = TupleOf(int) tups = [(),(1,2),(1,),(1,2,3,4)] for tup1 in tups: for tup2 in tups: self.assertEqual(tupleOfInt(tup1) + tupleOfInt(tup2), tupleOfInt(tup1+tup2)) self.assertEqual(tupleOfInt(tup1) + tup2, tupleOfInt(tup1+tup2)) def test_slice_tuple_of(self): tupleOfInt = TupleOf(int) ints = tuple(range(20)) aTuple = tupleOfInt(ints); for i in range(-21,21): for i2 in range(-21, 21): for step in range(-3, 3): if step != 0: self.assertEqual(aTuple[i:i2:step], ints[i:i2:step]) try: ints[i] self.assertEqual(aTuple[i], ints[i]) except IndexError: with self.assertRaises(IndexError): aTuple[i] def test_dictionary_subtraction_basic(self): intDict = ConstDict(int,int) self.assertEqual(intDict({1:2}) - (1,), intDict({})) self.assertEqual(intDict({1:2, 3:4}) - (1,), intDict({3:4})) self.assertEqual(intDict({1:2, 3:4}) - (3,), intDict({1:2})) def test_dictionary_addition_and_subtraction(self): someDicts = [{i:choice([1,2,3,4,5]) for i in range(choice([4,6,10,20]))} for _ in range(20)] intDict = ConstDict(int,int) for d1 in someDicts: for d2 in someDicts: addResult = dict(d1) addResult.update(d2) self.assertEqual(intDict(d1) + intDict(d2), intDict(addResult)) res = intDict(addResult) while len(res): toRemove = [] for i in range(choice(list(range(len(res))))+1): key = choice(list(addResult)) del addResult[key] toRemove.append(key) res = res - toRemove self.assertEqual(res, intDict(addResult)) def test_subclassing(self): BaseTuple = NamedTuple(x=int,y=float) class NTSubclass(BaseTuple): def f(self): return self.x + self.y def __repr__(self): return "ASDF" inst = NTSubclass(x=10,y=20) self.assertTrue(isinstance(inst, BaseTuple)) self.assertTrue(isinstance(inst, NTSubclass)) self.assertTrue(type(inst) is NTSubclass) self.assertEqual(repr(inst), "ASDF") self.assertNotEqual(BaseTuple.__repr__(inst), "ASDF") self.assertEqual(inst.x, 10) self.assertEqual(inst.f(), 30) TupleOfSubclass = TupleOf(NTSubclass) instTup = TupleOfSubclass((inst,BaseTuple(x=20,y=20.0))) self.assertTrue(isinstance(instTup[0], NTSubclass)) self.assertTrue(isinstance(instTup[1], NTSubclass)) self.assertEqual(instTup[0].f(), 30) self.assertEqual(instTup[1].f(), 40) self.assertEqual(BaseTuple(inst).x, 10) self.assertTrue(OneOf(None, NTSubclass)(None) is None) self.assertTrue(OneOf(None, NTSubclass)(inst) == inst) def test_serialization(self): ints = TupleOf(int)((1,2,3,4)) self.assertEqual( len(serialize(TupleOf(int), ints)), 40 ) while len(ints) < 1000000: ints = ints + ints t0 = time.time() self.assertEqual(len(serialize(TupleOf(int), ints)), len(ints) * 8 + 8) print(time.time() - t0, " for ", len(ints)) def test_serialization_roundtrip(self): badlen = None for _ in range(100): producer = RandomValueProducer() producer.addEvenly(30, 3) values = producer.all() for v in values: ser = serialize(type(v), v) v2 = deserialize(type(v), ser) ser2 = serialize(type(v), v2) self.assertTrue(type(v2) is type(v)) self.assertEqual(ser,ser2) self.assertEqual(str(v), str(v2)) self.assertEqual(v, v2) def test_serialize_doesnt_leak(self): T = TupleOf(int) def getMem(): return psutil.Process().memory_info().rss / 1024 ** 2 m0 = getMem() for passIx in range(100): for i in range(1000): t = T(list(range(i))) deserialize(T, serialize(T,t)) self.assertTrue(getMem() < m0 + 100) def test_const_dict_of_tuple(self): K = NamedTuple(a=OneOf(float, int), b=OneOf(float, int)) someKs = [K(a=0,b=0), K(a=1), K(a=10), K(b=10), K()] T = ConstDict(K, K) indexDict = {} x = T() numpy.random.seed(42) for _ in range(100): i1 = numpy.random.choice(len(someKs)) i2 = numpy.random.choice(len(someKs)) add = numpy.random.choice([False, True]) if add: indexDict[i1] = i2 x = x + {someKs[i1]: someKs[i2]} else: if i1 in indexDict: del indexDict[i1] x = x - (someKs[i1],) self.assertEqual(x, T({someKs[i]:someKs[v] for i,v in indexDict.items()})) for k in x: self.assertTrue(k in x) x[k] def test_conversion_of_binary_compatible(self): class T1(NamedTuple(a=int)): pass class T2(NamedTuple(a=int)): pass class T1Comp(NamedTuple(d=ConstDict(str, T1))): pass class T2Comp(NamedTuple(d=ConstDict(str, T1))): pass aT1C = T1Comp(d={'a': T1(a=10)}) self.assertEqual(T2Comp(aT1C).d['a'].a, 10) self.assertEqual(aT1C, deserialize(T1Comp, serialize(T2Comp, aT1C))) def test_conversion_of_binary_compatible_nested(self): def make(): class Interior(NamedTuple(a=int)): pass class Exterior(NamedTuple(a=Interior)): pass return Exterior E1 = make() E2 = make() OneOf(None, E2)(E1()) def test_python_objects_in_tuples(self): class NormalPyClass(object): pass class NormalPySubclass(NormalPyClass): pass NT = NamedTuple(x=NormalPyClass, y=NormalPySubclass) nt = NT(x=NormalPyClass(),y=NormalPySubclass()) self.assertIsInstance(nt.x, NormalPyClass) self.assertIsInstance(nt.y, NormalPySubclass) def test_construct_alternatives_with_positional_arguments(self): a = Alternative("A", HasOne = {'a': str}, HasTwo = {'a': str, 'b': str}) with self.assertRaises(TypeError): a.HasTwo("hi") self.assertEqual(a.HasOne("hi"), a.HasOne(a="hi")) hasOne = a.HasOne("hi") self.assertEqual(a.HasOne(hasOne), hasOne) with self.assertRaises(TypeError): a.HasOne(a.HasTwo(a='1',b='b')) def test_recursive_classes_repr(self): class ASelfRecursiveClass(Class): x = Member(OneOf(None, lambda: ASelfRecursiveClass)) a = ASelfRecursiveClass() a.x = a b = ASelfRecursiveClass() b.x = b print(repr(a)) def test_unsafe_pointers_to_list_internals(self): x = ListOf(int)() x.resize(100) for i in range(len(x)): x[i] = i aPointer = x.pointerUnsafe(0) self.assertTrue(str(aPointer).startswith("(Int64*)0x")) self.assertEqual(aPointer.get(), x[0]) aPointer.set(100) self.assertEqual(aPointer.get(), 100) self.assertEqual(x[0], 100) aPointer = aPointer + 10 self.assertEqual(aPointer.get(), x[10]) self.assertEqual(aPointer[10], x[20]) aPointer.set(20) self.assertEqual(aPointer.get(), 20) self.assertEqual(x[10], 20) #this is OK because ints are POD. aPointer.initialize(30) self.assertEqual(x[10], 30) def test_unsafe_pointers_to_uninitialized_list_items(self): #because this is testing unsafe operations, the test is #really just that we don't segfault! for _ in range(100): x = ListOf(TupleOf(int))() x.reserve(10) for i in range(x.reserved()): x.pointerUnsafe(i).initialize((i,)) x.setSizeUnsafe(10) #now check that if we fail to set the size we'll leak the tuple aLeakedTuple = TupleOf(int)((1,2,3)) x = ListOf(TupleOf(int))() x.reserve(1) x.pointerUnsafe(0).initialize(aLeakedTuple) x = None self.assertEqual(_types.refcount(aLeakedTuple), 2) def test_list_copy_operation_duplicates_list(self): T = ListOf(int) x = T([1,2,3]) y = T(x) x[0] = 100 self.assertNotEqual(y[0], 100) def test_list_and_tuple_conversion_to_numpy(self): for T in [ListOf(bool), TupleOf(bool)]: for arr in [	numpy.array([])	numpy.array
#!/usr/bin/python ''' Improved Minima Controlled Recursive Averaging (IMCRA) single channel noise estmation after [1] Israel Cohen, Noise Spectrum estimation in Adverse Environments: Improved Minima Controlled Recursive Averaging. IEEE. Trans. Acoust. Speech Signal Process. VOL. 11, NO. 5, Sep 2003. <NAME> Feb2015 ''' import numpy as np import sys import os # Add the path of the toolbox root # from ns import MMSE_LSA # For debugging purposes #import ipdb #np.seterr(divide='ignore',invalid='raise') def post_speech_prob(Y_l, q, Gamma, xi): ''' Posterior speech probability given prior speech absence and the complex Gaussian model of speech distortion Input: Y_l [K, 1] STFT frame Input: q [K, 1] a priori speech presence Input: Gamma [K, 1] A posteriori SNR Input: xi [K, 1] A priori SNR ''' nu = Gammaxi/(1+xi) p = np.zeros(Y_l.shape) p[q < 1] = 1./(1+(q[q < 1]/(1-q[q < 1]))(1+xi[q < 1])np.exp(-nu[q < 1])) return p def sym_hanning(n): ''' Same Hanning as the matlab default ''' # to float n = float(n) if np.mod(n, 2) == 0: # Even length window half = n/2; else: # Odd length window half = (n+1)/2; w = .5(1 - np.cos(2np.pinp.arange(1,half+1)/(n+1))) return np.concatenate((w, w[:-1])); # Default buffer size L_MAX = 1000 class imcra_se(): ''' Simple class for enhancement using IMCRA ''' def __init__(self, nfft, Lambda_D=None, Bmin=3.2, alpha =0.92, xi_min=10*(-25./20), IS=10): # Decision directed smoothing factor self.alpha = alpha # Decision directed a priori SNR floor self.xi_min = xi_min self.nfft = int(nfft/2+1) # self.store = {} self.store['Lambda_D'] = np.zeros((self.nfft, L_MAX)) self.store['p'] = np.zeros((self.nfft, L_MAX)) self.store['xi'] = np.zeros((self.nfft, L_MAX)) self.store['MSE'] = np.zeros((self.nfft, L_MAX)) self.l = 0 # IMCRA initial background segment (frames) # Initialization self.imcra = imcra(nfft, IS=IS, Bmin=Bmin) self.G = 1 self.p = np.zeros([self.nfft, 1]) # Initial noise estimate if Lambda_D is None: self.Lambda_D = 1e-6np.ones([self.nfft, 1]) else: self.Lambda_D = Lambda_D def update(self, Y): hat_X = np.zeros(Y.shape, dtype=complex) G = self.G Gamma = G Lambda_D = self.Lambda_D p = self.p K, L = Y.shape if self.l + L > L_MAX: # If maximum size surpassed, add a new batch of zeroes self.store['Lambda_D'] = np.concatenate((self.store['Lambda_D'], np.zeros((K, L_MAX))), 1) self.store['p'] = np.concatenate((self.store['p'], np.zeros((K, L_MAX))), 1) self.store['xi'] = np.concatenate((self.store['xi'], np.zeros((K, L_MAX))), 1) self.store['MSE'] = np.concatenate((self.store['MSE'], np.zeros((K, L_MAX))), 1) for l in np.arange(0, L): # A priori SNR, stationary parameter estimate (uses last Gamma) xi_G = (G*2)Gamma # A posterori SNR Gamma = (np.abs(Y[:, l:l+1])*2)/Lambda_D # A priori SNR, maximum likelihood estimate xi_ML = Gamma - 1 xi_ML[xi_ML<1e-6] = 1e-6 # Decision directed rule xi = self.alphaxi_G + (1-self.alpha)xi_ML # Flooring xi[xi<self.xi_min] = self.xi_min # MMSE-LSA # Get Wiener gain G = xi/(1 + xi) hat_X[:, l:l+1] = MMSE_LSA(GY[:, l:l+1], GLambda_D) # Residual MSE of Wiener filter MSE = GLambda_D # TODO: Store additional variables if solicited self.store['Lambda_D'][:, self.l:self.l+1] = Lambda_D self.store['p'][:, self.l:self.l+1] = p self.store['xi'][:, self.l:self.l+1] = xi self.store['MSE'][:, self.l:self.l+1] = MSE self.l += 1 # IMCRA noise estimate and posterior speech probability for the # next iteration Lambda_D, p = self.imcra.update(Y[:, l:l+1], Gamma, xi) # Keep these for the next iteration self.G = G self.Lambda_D = Lambda_D[:, -2:] self.p = p return hat_X def get_param(self, param_list): ''' Return stored parameters ''' val_list = [] for par in param_list: if par not in self.store: raise(ValueError, "Parameter %s was not recorded" % par) val_list.append(self.store[par][:, :self.l]) return val_list class imcra(): ''' IMCRA class ''' def __init__(self, nfft, Bmin=None, *kwargs): # IMCRA DEFAULT CONFIGURATION # Consult [1] on how to set the parameters # Number of initial frames of the signal assumed to be noise self.IS = 15 # How many adjacent bins (before and after bin k) are used to smooth # spectrogram in frecuency (S_f[k,l]) self.w = 1 # Adaptation rate for the spectrogram smoothing in time self.alpha_s = 0.9 # Adaptation rate for speech probability dependent time smoothing # paramater self.alpha_d = 0.85 # U spectrogram values are stored to perform minimum tracking self.U = 8 # 8 # Each V frames minimum tracking will take place self.V = 15 # 15 # Number of frames before the actual frame considered in minimum # traking. (Irrelevant its included in Bmin) self.D = self.Uself.V # Significance levels # Significance level for the first VAD self.epsilon = 0.01 # Significance level for the second VAD self.epsilon1 = 0.05 # Overload defaults for par in kwargs.keys(): # If parameter is one of the defaults, overload it if par in self.__dict__: setattr(self, par, kwargs[par]) else: raise ValueError("%s is not an imcra parameter" % par) # If the standard significance levels and smoothing parameters not used # we need to recompute everything if ((self.epsilon == 0.01) & (self.epsilon1 == 0.05) & (self.alpha_s == 0.9) & (self.w == 1)): # VAD is attained through hypothesis test assuming distributions # for ratios related to the minimum statistics, these are the # parameteres # Treshold to achieve 0.01 significance in first VAD speech absence # hypothesis test self.Gamma0 = 4.6 # Treshold to achieve 0.05 significance in second VAD speech # presence hypothesis test self.Gamma1 = 3 # Treshold to achieve 0.05 significance in second VAD speech # presence hypothesis test self.zeta0 = 1.67 # Noise variance estimate bias for speech absence (depends only # on the last three parameters though [1, Eq. 31]) self.beta = 1.47 else: # Note: This STILL assumes that we use the posterior probability # as defined by [1, Eq. 7], see [1, App. II] # This will need SCIPY! import scipy.stats.chi2 as chi2 # Approx degrees of freedom of Eq. 20, see App. II mu = (1+self.alpha_s)/(1-self.alha_s)(1 + 0.7w) # Treshold to achieve 0.01 significance in first VAD speech absence # hypothesis test self.Gamma0 = -np.log(epsilon) self.zeta0 = chi2.ppf(1-epsilon,mu)/mu self.Gamma1 = -np.log(epsilon1) # Treshold to achieve 0.05 significance in second VAD speech # presence hypothesis test [1, Eq. 31]) self.beta = ((gamma1 - 1 -np.exp(-1) + np.exp(-gamma1))/ (gamma1 -1 - 3np.exp(-1) + (gamma1+2)np.exp(-gamma1))) # Check for smoothed spectrogram bias set if Bmin is None: import warnings warnings.warn("Minimum statistic bias Bmin is not set. Run " "imcra.setBmin(), until then 2.1 used.", DeprecationWarning) self.Bmin = 2.1 # This is for my config! else: self.Bmin = Bmin self.K = int(nfft/2+1) # Number of frequency bins under Nyquist self.l = -1 # Set frame index. -1 is no frame processed self.j = 0 # Set counter for the buffer update self.u = 0 # Set copunter for buffer last filled position # To do the smoothing in frequency fast, we create indices to expand # each frame (column) to a matrix with that column on the center and # neighbouring frequencies on each row. Thay way we can smooth with # One single loop # Create matrix of indices self.sm_idx = np.arange(0,self.K)[:,None] + np.arange(-self.w,self.w+1)[None,:] # Create coresponding matrix of hamming windows self.sm_win = np.tile(sym_hanning(2self.w+1),(self.K,1)) # Ignore indices out of bounds self.sm_win[self.sm_idx<0] = 0 self.sm_win[self.sm_idx>self.K-1] = 0 self.sm_idx[self.sm_idx<0] = 0 self.sm_idx[self.sm_idx>self.K-1] = self.K-1 # Normalize self.sm_win = self.sm_win/np.sum(self.sm_win, 1, keepdims=True) # BUFFERS # They will be propperly initialized when the first frame is processed # Smoothed Spectrogram first iteration self.S = np.zeros([self.K, 1]) # Smoothed Spectrogram minimum first iteration self.Smin = np.zeros([self.K, 1]) # Smoothed Spectrogram second iteration self.tilde_S = np.zeros([self.K, 1]) # Smoothed Spectrogram second iteration self.tilde_Smin = np.zeros([self.K, 1]) # Smoothed Spectrogram minimum running minimum self.Smin_sw = np.zeros([self.K, 1]) # Second smoothed Spectrogram minimum running minimum self.tilde_Smin_sw = np.zeros([self.K, 1]) # Smoothed Spectrogram minimum first iteration store buffer self.Storing = np.zeros([self.K, self.U]) # Smoothed Spectrogram minimum second iteration store buffer self.tilde_Storing = np.zeros([self.K, self.U]) # Biased noise variance estimate self.ov_Lambda_D = np.zeros([self.K, 1]) # Unbiased noise variance estimate self.Lambda_D = np.zeros([self.K, 1]) # A posteriori speech presence probability self.q = np.ones([self.K, 1]) # A posteriori speech presence probability self.p = np.zeros([self.K, 1]) # Speech presence prob upbound self.p_upthr = 0.9 def reset(self, nfft=512, Bmin=3.2): self.__init__(self, nfft, Bmin) def setBmin(self, N): ''' Computes Bmin given the stft of a white noise signal as obtained e.g n = np.random.randn(1e5) N = stft(n, windowsize, shift, nfft) Bmin = imcra.computeBmin(N) ''' # SANITY CHECK: Enough samples if N.shape[1] < 3self.Uself.V: raise ValueError("Not enough samples, pick a langer white noise signal") Bmin = np.zeros(N.shape) for l in np.arange(0,N.shape[1]): # Init if l == 0: self.init_params(N[:,l:l+1]) # Get minimum statistics Bmin = (np.abs(N[:,l:l+1])2)/self.Smin # [3,eq.18] #zeta[:,l:l+1] = imcra.S/(imcra.Bminimcra.Smin) # [3,eq.21] #tilde_Gamma_min[:,l:l+1] = (np.abs(Y[:,l:l+1])*2)/(imcra.Bminimcra.tilde_Smin) # [3,eq.18] #tilde_zeta[:,l:l+1] = imcra.S/(imcra.Bminimcra.tilde_Smin) # [3,eq.21] # Compute mean as average self.Bmin = np.mean(Bmin) return self.Bmin ''' Fast frequency smoothing ''' def fsmooth(self, P_l): return np.sum(self.sm_winP_l[self.sm_idx][:, :, 0], 1)[:,None] def init_params(self,Y_l): # Smoothed spectrograms # Smoothed Spectrogram first iteration self.S = self.fsmooth(np.abs(Y_l)2) # Smoothed Spectrogram second iteration self.tilde_S = self.S.copy() # Smoothed Spectrogram minimum first iteration self.Smin = self.S.copy() # Smoothed Spectrogram minimum first second iteration self.tilde_Smin = self.S.copy() # Smoothed Spectrogram minimum running minimum self.Smin_sw = self.S.copy() # Second smoothed Spectrogram minimum running minimum self.tilde_Smin_sw = self.S.copy() # Other parameters # Biased noise variance estimate self.ov_Lambda_D = np.abs(Y_l)2 # Unbiased noise variance estimate self.Lambda_D = self.ov_Lambda_D # A posteriori speech presence probability self.p = np.zeros(Y_l.shape) def update(self, Y_l, Gamma, xi): ''' This calls the components of IMCRA as in the original paper. These are A priori speech absence probability estimator A posteriori speech probability estimator Probabilistic recursive smoothing For the initialization period (only noise assumed) it uses normal smoothing ''' # Increase frame counter self.l += 1 # If in first frame, initialize buffers with observed frame if self.l == 0: # print('first frame!') self.init_params(Y_l) # If in initialization segment, update noise stats only # Note: Keep in mind that IS might be zero if self.l < self.IS: # Frequency smoothing [3,eq.14] Sf = self.fsmooth(np.abs(Y_l)*2) # Frequency and time smoothing [3,eqs.15] self.S = self.alpha_sself.S + (1-self.alpha_s)Sf # Update running minimum self.Smin = np.min(np.concatenate((self.Smin,self.S),1),1)[:,None] self.Smin_sw = np.min(np.concatenate((self.Smin_sw,self.S),1),1)[:,None] # Compute smoothed spectrogram for p = 0 self.Lambda_D = self.alpha_dself.Lambda_D + (1-self.alpha_d)np.abs(Y_l)2 # Set a priori background probability to one self.q[:] = 1 # Set a posteriori speech probability to zero self.p[:] = 0 else: # FIRST MINIMA CONTROLLED VAD # This provides a rough VAD to eliminate relatively strong speech # components towards the second power spectrum estimation Sf = self.fsmooth(np.abs(Y_l)2) # [3,eq.14] # Time smoothing self.S = self.alpha_sself.S+(1-self.alpha_s)Sf # [3,eq.15] # update running minimum self.Smin = np.min(np.concatenate((self.Smin,self.S),1),1)[:,None] self.Smin_sw = np.min(np.concatenate((self.Smin_sw,self.S),1),1)[:,None] # Indicator function for VAD Gamma_min = (np.abs(Y_l)2)/(self.Bminself.Smin) # [3,eq.18] zeta = self.S/(self.Bminself.Smin) # [3,eq.21] I = np.zeros([self.K, 1]) I[(Gamma_min < self.Gamma0 ) & (zeta < self.zeta0)] = 1 # [3,eq.21] # SECOND MINIMA CONTROLLED VAD # This provides the speech probability needed to compute the final # noise estimation. The hard VAD index I, computed in the previous # estimation, is here used to exclude strong speech components. norm = self.fsmooth(I) self.tilde_Sf = self.fsmooth(Inp.abs(Y_l)*2) self.tilde_Sf[norm>0] = self.tilde_Sf[norm>0]/norm[norm>0] # Time smoothing self.tilde_S = self.alpha_sself.tilde_S+(1-self.alpha_s)self.tilde_Sf # [3,eq.27] # Update running minimum self.tilde_Smin = np.min(np.concatenate((self.tilde_Smin,self.tilde_S),1),1)[:,None] # [3,eq.26] self.tilde_Smin_sw = np.min(np.concatenate((self.tilde_Smin_sw,self.tilde_S),1),1)[:,None] # [3,eq.27] # A PRIORI SPEECH ABSENCE tilde_Gamma_min = (np.abs(Y_l)2)/(self.Bminself.tilde_Smin) tilde_zeta = self.S/(self.Bminself.tilde_Smin) # [3,eq.28] # Speech absence self.q = np.zeros(Y_l.shape) self.q[(tilde_Gamma_min <= 1) & (tilde_zeta < self.zeta0)] = 1 # [3,eq.29] self.q[(1 < tilde_Gamma_min) & (tilde_Gamma_min < self.Gamma1) & (tilde_zeta < self.zeta0)] = (self.Gamma1 - tilde_Gamma_min[(1 < tilde_Gamma_min) & (tilde_Gamma_min < self.Gamma1) & (tilde_zeta < self.zeta0)])/(self.Gamma1-1) # [3,Eq.29] # self.q[:] = 1 # A POSTERIORI SPEECH PROBABILITY self.p = post_speech_prob(Y_l,self.q,Gamma,xi) self.p[self.p>self.p_upthr] = self.p_upthr # PROBABILITY DRIVEN RECURSIVE SMOOTHING # Smoothing parameter tilde_alpha_d = self.alpha_d+(1-self.alpha_d)self.p # [3,eq.11] # UPDATE NOISE SPECTRUM ESTIMATE self.ov_Lambda_D = tilde_alpha_dself.ov_Lambda_D + (1-tilde_alpha_d)np.abs(Y_l)*2 # [3,eq.10] # Bias correction self.Lambda_D = self.betaself.ov_Lambda_D # [3,eq.12] # UPDATE MINIMUM TRACKING self.j += 1 if self.j == self.V: # Minimum tracking for the first estimation if self.u < self.U: self.Storing[:,self.u:self.u+1] = self.Smin_sw else: self.Storing =	np.roll(self.Storing,-1,axis=1)	numpy.roll
from typing import Any, Set, Tuple, Union, Optional from pathlib import Path from collections import defaultdict from html.parser import HTMLParser import pytest from anndata import AnnData import numpy as np import xarray as xr from imageio import imread, imsave import tifffile from squidpy.im import ImageContainer from squidpy.im._utils import CropCoords, CropPadding, _NULL_COORDS from squidpy._constants._pkg_constants import Key class SimpleHTMLValidator(HTMLParser): # modified from CellRank def __init__(self, n_expected_rows: int, expected_tags: Set[str], kwargs: Any): super().__init__(kwargs) self._cnt = defaultdict(int) self._n_rows = 0 self._n_expected_rows = n_expected_rows self._expected_tags = expected_tags def handle_starttag(self, tag: str, attrs: Any) -> None: self._cnt[tag] += 1 self._n_rows += tag == "strong" def handle_endtag(self, tag: str) -> None: self._cnt[tag] -= 1 def validate(self) -> None: assert self._n_rows == self._n_expected_rows assert set(self._cnt.keys()) == self._expected_tags if len(self._cnt): assert set(self._cnt.values()) == {0} class TestContainerIO: def test_empty_initialization(self): img = ImageContainer() assert not len(img) assert isinstance(img.data, xr.Dataset) assert img.shape == (0, 0) assert str(img) assert repr(img) def _test_initialize_from_dataset(self): dataset = xr.Dataset({"foo": xr.DataArray(np.zeros((100, 100, 3)))}, attrs={"foo": "bar"}) img = ImageContainer._from_dataset(data=dataset) assert img.data is not dataset assert "foo" in img assert img.shape == (100, 100) np.testing.assert_array_equal(img.data.values(), dataset.values) assert img.data.attrs == dataset.attrs def test_save_load_zarr(self, tmpdir): img = ImageContainer(np.random.normal(size=(100, 100, 1))) img.data.attrs["scale"] = 42 img.save(Path(tmpdir) / "foo") img2 = ImageContainer.load(Path(tmpdir) / "foo") np.testing.assert_array_equal(img["image"].values, img2["image"].values) np.testing.assert_array_equal(img.data.dims, img2.data.dims) np.testing.assert_array_equal(sorted(img.data.attrs.keys()), sorted(img2.data.attrs.keys())) for k, v in img.data.attrs.items(): assert type(v) == type(img2.data.attrs[k]) # noqa: E721 assert v == img2.data.attrs[k] def test_load_zarr_2_objects_can_overwrite_store(self, tmpdir): img = ImageContainer(np.random.normal(size=(100, 100, 1))) img.data.attrs["scale"] = 42 img.save(Path(tmpdir) / "foo") img2 = ImageContainer.load(Path(tmpdir) / "foo") img2.data.attrs["sentinel"] = "foobar" img2["image"].values += 42 img2.save(Path(tmpdir) / "foo") img3 = ImageContainer.load(Path(tmpdir) / "foo") assert "sentinel" in img3.data.attrs assert img3.data.attrs["sentinel"] == "foobar" np.testing.assert_array_equal(img3["image"].values, img2["image"].values) np.testing.assert_allclose(img3["image"].values - 42, img["image"].values) @pytest.mark.parametrize( ("shape1", "shape2"), [ ((100, 200, 3), (100, 200, 1)), ((100, 200, 3), (100, 200)), ], ) def test_add_img(self, shape1: Tuple[int, ...], shape2: Tuple[int, ...]): img_orig = np.random.randint(low=0, high=255, size=shape1, dtype=np.uint8) cont = ImageContainer(img_orig, layer="img_orig") img_new = np.random.randint(low=0, high=255, size=shape2, dtype=np.uint8) cont.add_img(img_new, layer="img_new", channel_dim="mask") assert "img_orig" in cont assert "img_new" in cont np.testing.assert_array_equal(np.squeeze(cont.data["img_new"]), np.squeeze(img_new)) @pytest.mark.parametrize("shape", [(100, 200, 3), (100, 200, 1)]) def test_load_jpeg(self, shape: Tuple[int, ...], tmpdir): img_orig = np.random.randint(low=0, high=255, size=shape, dtype=np.uint8) fname = tmpdir / "tmp.jpeg" imsave(str(fname), img_orig) gt = imread(str(fname)) # because of compression, we load again cont = ImageContainer(str(fname)) np.testing.assert_array_equal(cont["image"].values.squeeze(), gt.squeeze()) @pytest.mark.parametrize("shape", [(100, 200, 3), (100, 200, 1), (10, 100, 200, 1)]) def test_load_tiff(self, shape: Tuple[int, ...], tmpdir): img_orig = np.random.randint(low=0, high=255, size=shape, dtype=np.uint8) fname = tmpdir / "tmp.tiff" tifffile.imsave(fname, img_orig) cont = ImageContainer(str(fname)) if len(shape) > 3: # multi-channel tiff np.testing.assert_array_equal(cont["image"], img_orig[..., 0].transpose(1, 2, 0)) else:	np.testing.assert_array_equal(cont["image"], img_orig)	numpy.testing.assert_array_equal

import matplotlib import matplotlib.collections import matplotlib.pyplot as plt import numpy as np from .entropy_approximate import entropy_approximate from .optim_complexity_delay import ( _embedding_delay_metric, _embedding_delay_plot, _embedding_delay_select, ) from .optim_complexity_dimension import ( _embedding_dimension_afn, _embedding_dimension_ffn, _embedding_dimension_plot, ) from .optim_complexity_tolerance import _optimize_tolerance_plot def complexity_optimize( signal, delay_max=50, delay_method="fraser1986", dimension_max=10, dimension_method="afnn", tolerance_method="maxApEn", show=False, **kwargs ): """**Joint-estimation of optimal complexity parameters** The selection of the parameters *Dimension* and *Delay* is a challenge. One approach is to select them (semi) independently (as dimension selection often requires the delay) from each other, using :func:`complexity_delay` and :func:`complexity_dimension`. Estimate optimal complexity parameters Dimension (m), Time Delay (tau) and tolerance (r). Parameters ---------- signal : Union[list, np.array, pd.Series] The signal (i.e., a time series) in the form of a vector of values. delay_max : int See :func:`complexity_delay`. delay_method : str See :func:`complexity_delay`. dimension_max : int See :func:`complexity_dimension`. dimension_method : str See :func:`complexity_dimension`. tolerance_method : str See :func:`complexity_tolerance`. show : bool Defaults to ``False``. Returns ------- optimal_dimension : int Optimal dimension. optimal_delay : int Optimal time delay. optimal_tolerance : int Optimal tolerance See Also ------------ complexity_delay, complexity_dimension, complexity_tolerance Examples --------- .. ipython:: python import neurokit2 as nk signal = nk.signal_simulate(duration=10, frequency=[5, 7], noise=0.01) parameters = nk.complexity_optimize(signal, show=True) parameters References ----------- * <NAME>., <NAME>., & <NAME>. (2003, April). A differential entropy based method for determining the optimal embedding parameters of a signal. In 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP'03). (Vol. 6, pp. VI-29). IEEE. * <NAME>., & <NAME>. (2009). The role of the embedding dimension and time delay in time series forecasting. IFAC Proceedings Volumes, 42(7), 316-320. * <NAME>., <NAME>., & <NAME>. (1994). Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physica-Section D, 73(1), 82-98. * <NAME>. (1997). Practical method for determining the minimum embedding dimension of a scalar time series. Physica D: Nonlinear Phenomena, 110(1-2), 43-50. * <NAME>., <NAME>., <NAME>., <NAME>., & <NAME>. (2008). Automatic selection of the threshold value r for approximate entropy. IEEE Transactions on Biomedical Engineering, 55(8), 1966-1972. """ out = {} # Optimize delay tau_sequence, metric, metric_values, out["Delay"] = _complexity_delay( signal, delay_max=delay_max, method=delay_method ) # Optimize dimension dimension_seq, optimize_indices, out["Dimension"] = _complexity_dimension( signal, delay=out["Delay"], dimension_max=dimension_max, method=dimension_method, **kwargs ) # Optimize r tolerance_method = tolerance_method.lower() if tolerance_method in ["traditional"]: out["Tolerance"] = 0.2 * np.std(signal, ddof=1) if tolerance_method in ["maxapen", "optimize"]: r_range, ApEn, out["Tolerance"] = _complexity_tolerance( signal, delay=out["Delay"], dimension=out["Dimension"] ) if show is True: if tolerance_method in ["traditional"]: raise ValueError( "NeuroKit error: complexity_optimize():" "show is not available for current tolerance_method" ) if tolerance_method in ["maxapen", "optimize"]: _complexity_plot( signal, out, tau_sequence, metric, metric_values, dimension_seq[:-1], optimize_indices, r_range, ApEn, dimension_method=dimension_method, ) return out # ============================================================================= # Plot # ============================================================================= def _complexity_plot( signal, out, tau_sequence, metric, metric_values, dimension_seq, optimize_indices, r_range, ApEn, dimension_method="afnn", ): # Prepare figure fig = plt.figure(constrained_layout=False) spec = matplotlib.gridspec.GridSpec( ncols=2, nrows=3, height_ratios=[1, 1, 1], width_ratios=[1 - 1.2 / np.pi, 1.2 / np.pi] ) ax_tau = fig.add_subplot(spec[0, :-1]) ax_dim = fig.add_subplot(spec[1, :-1]) ax_r = fig.add_subplot(spec[2, :-1]) if out["Dimension"] > 2: plot_type = "3D" ax_attractor = fig.add_subplot(spec[:, -1], projection="3d") else: plot_type = "2D" ax_attractor = fig.add_subplot(spec[:, -1]) fig.suptitle("Otimization of Complexity Parameters", fontweight="bold", fontsize=16) plt.subplots_adjust(hspace=0.4, wspace=0.05) # Plot tau optimization # Plot Attractor _embedding_delay_plot( signal, metric_values=metric_values, tau_sequence=tau_sequence, tau=out["Delay"], metric=metric, ax0=ax_tau, ax1=ax_attractor, plot=plot_type, ) # Plot dimension optimization if dimension_method.lower() in ["afnn"]: _embedding_dimension_plot( method=dimension_method, dimension_seq=dimension_seq, min_dimension=out["Dimension"], E1=optimize_indices[0], E2=optimize_indices[1], ax=ax_dim, ) if dimension_method.lower() in ["fnn"]: _embedding_dimension_plot( method=dimension_method, dimension_seq=dimension_seq, min_dimension=out["Dimension"], f1=optimize_indices[0], f2=optimize_indices[1], f3=optimize_indices[2], ax=ax_dim, ) # Plot r optimization _optimize_tolerance_plot(out["Tolerance"], {"Values": r_range, "Scores": ApEn}, ax=ax_r) return fig # ============================================================================= # Internals # ============================================================================== def _complexity_delay(signal, delay_max=100, method="fraser1986"): # Initalize vectors if isinstance(delay_max, int): tau_sequence = np.arange(1, delay_max) else: tau_sequence = np.array(delay_max) # Get metric # Method method = method.lower() if method in ["fraser", "fraser1986", "tdmi"]: metric = "Mutual Information" algorithm = "first local minimum" elif method in ["theiler", "theiler1990"]: metric = "Autocorrelation" algorithm = "first 1/e crossing" elif method in ["casdagli", "casdagli1991"]: metric = "Autocorrelation" algorithm = "first zero crossing" elif method in ["rosenstein", "rosenstein1993", "adfd"]: metric = "Displacement" algorithm = "closest to 40% of the slope" else: raise ValueError("NeuroKit error: complexity_delay(): 'method' not recognized.") metric_values = _embedding_delay_metric(signal, tau_sequence, metric=metric) # Get optimal tau optimal = _embedding_delay_select(metric_values, algorithm=algorithm) if ~

np.isnan(optimal)

numpy.isnan

# coding: utf-8 import os import sys sys.path.append(os.path.abspath(os.path.join(sys.path[0], '../'))) from model.model import ResNetLayer3Feat, ResNetLayer4Feat import torch import torch.nn.functional as F from torchvision import transforms import numpy as np from dataloader import TrainDataLoader from torch.autograd import Variable import outils from tqdm import tqdm import json import argparse parser = argparse.ArgumentParser() parser.add_argument( '--outDir', type=str , help='output model directory') ##---- Loss Parameter ----#### parser.add_argument( '--tripleLossThreshold', type=float , default = 1.0, help='threshold for triple loss') ##---- Search, Train, Validate Region ----#### parser.add_argument( '--searchRegion', type=int, default=1, help='feat size') ##---- Training parameters ----#### parser.add_argument( '--modelPth', type=str, default = '../model/net98_8.pth', help='finetune model weight path') parser.add_argument( '--searchDir', type=str, default= '../data/watermark/C_cross_domain/trainBG2/', help='searching directory') parser.add_argument( '--queryDir', type=str, default= '../data/watermark/C_cross_domain/trainBG2/', help='query image directory') parser.add_argument( '--nbEpoch', type=int , default = 300, help='Number of training epochs') parser.add_argument( '--lr', type=float , default = 1e-5, help='learning rate') parser.add_argument( '--batchSize', type=int , default = 8, help='batch size') parser.add_argument( '--cuda', action='store_true', help='cuda setting') parser.add_argument( '--nbSearchImgEpoch', type=int, default = 2000, help='maximum number of searching image in one epoch') parser.add_argument( '--featScaleBase', type=int, default= 22, help='median # of features in the scale list ') parser.add_argument( '--stepNbFeat', type=int, default= 3, help='difference nb feature in adjacent scales ') parser.add_argument( '--nbscale', type=int, default= 2, help='# of octaves') parser.add_argument( '--featLayer', type = str, default='conv4', choices=['conv4', 'conv5'], help='which feature, conv4 or conv5') parser.add_argument( '--labelInfo', type = str, default='../data/crossDomainTraining.json', help='label category') parser.add_argument( '--tmpTrainDir', type = str, default='./trainPair', help='temporal image directory to store training pairs') parser.add_argument( '--eta', type = float, default=1e-7, help='eta for calculate norm') parser.add_argument( '--margin', type = int, default=3, help='keep top K ') parser.add_argument( '--tolerance', type = float, default=4, help='tolerance') parser.add_argument( '--valK', type = int, default=300, help='keep top K for validation') parser.add_argument( '--K', type = int, default=300, help='keep top K ') parser.add_argument( '--dataset', type = str, default='watermark', choices = ['watermark', 'sketch'], help='running on which dataset') args = parser.parse_args() tqdm.monitor_interval = 0 print (args) if os.path.exists(args.tmpTrainDir) : cmd = 'rm -r {}'.format(args.tmpTrainDir) os.system(cmd) os.mkdir(args.tmpTrainDir) ## Dataset, Minimum dimension, Total patch during the training with open(args.labelInfo, 'r') as f : label = json.load(f) QueryImgList = sorted(label['queryImg']) SearchImgList = sorted(label['searchImg']) labelCategory = label['annotation'] nbPatchTotal = args.nbSearchImgEpoch imgFeatMin = args.searchRegion + 2 * args.margin + 1 ## Minimum dimension of feature map in a image tolerance = args.tolerance / float(args.featScaleBase) ## Loading model if args.dataset == 'watermark': normalize = transforms.Normalize(mean = [ 0.75, 0.70, 0.65 ], std = [ 0.14,0.15,0.16 ]) ## watermark classification normalization if args.featLayer == 'conv4' : net = ResNetLayer3Feat( None ) msg = 'loading weight from {}'.format(args.modelPth) print (msg) modelParams = torch.load(args.modelPth) for key in list(modelParams.keys()) : if 'layer4' in key or 'fc.fc1' in key: modelParams.pop(key, None) else : net = ResNetLayer4Feat( None ) msg = 'loading weight from {}'.format(args.modelPth) print (msg) for key in list(modelParams.keys()) : if 'fc.fc1' in key: modelParams.pop(key, None) modelParams = torch.load(args.modelPth) net.load_state_dict( modelParams ) else : normalize = transforms.Normalize(mean = [ 0.485, 0.456, 0.406 ], std = [ 0.229, 0.224, 0.225 ]) ## imagenet classification normalization if args.featLayer == 'conv4' : net = ResNetLayer3Feat( None ) msg = 'loading weight from {}'.format(args.modelPth) print (msg) modelParams = torch.load(args.modelPth) for key in list(modelParams.keys()) : if 'layer4' in key or 'fc' in key: modelParams.pop(key, None) else : net = ResNetLayer4Feat( None ) msg = 'loading weight from {}'.format(args.modelPth) print (msg) for key in list(modelParams.keys()) : if 'fc' in key: modelParams.pop(key, None) modelParams = torch.load(args.modelPth) net.load_state_dict( modelParams ) if args.cuda : net.cuda() featChannel = 256 if args.featLayer == 'conv4' else 512 ## stride size, min input size, channel of feature strideNet = 16 minNet = 15 PATIENCE = 10 # 10 epochs no improved, training will be stopped optimizer = torch.optim.Adam(net.parameters(), lr=args.lr, betas=(0.5, 0.999)) transform = transforms.Compose([ transforms.ToTensor(), normalize, ]) ## Scales scales = [args.featScaleBase - args.stepNbFeat * i for i in range(args.nbscale, 0, -1)] + [args.featScaleBase] + [args.featScaleBase + args.stepNbFeat * i for i in range(1, args.nbscale + 1)] msg = 'We search to match in {:d} scales, the max dimensions in the feature maps are:'.format(len(scales)) print (msg) print (scales) print ('\n\n') ## Output if not os.path.exists(args.outDir) : os.mkdir(args.outDir) history = {'posLoss':[], 'negaLoss':[], 'nbPos':[]} nbEpochNoImproved = 0 bestNbPos = 0 outHistory = os.path.join(args.outDir, 'history.json') if len(QueryImgList) <= args.nbSearchImgEpoch : valQueryImgList = QueryImgList valSearchImgList = SearchImgList else : index = np.linspace(0, len(QueryImgList)-1, args.nbSearchImgEpoch).astype(np.int64) valQueryImgList = [QueryImgList[i] for i in index] valSearchImgList = [SearchImgList[i] for i in index] ## Main Loop for i_ in range(args.nbEpoch) : logPosLoss = [] logNegaLoss = [] print ('Training Epoch {:d}'.format(i_)) print ('---> Get query...') net.eval() if len(QueryImgList) <= args.nbSearchImgEpoch : queryImgList = QueryImgList else : index = np.random.permutation(np.arange(len(QueryImgList)))[:args.nbSearchImgEpoch] queryImgList = [QueryImgList[i] for i in index] if len(SearchImgList) <= args.nbSearchImgEpoch : searchImgList = SearchImgList else : index = np.random.permutation(np.arange(len(SearchImgList)))[:args.nbSearchImgEpoch] searchImgList = [SearchImgList[i] for i in index] featQuery, queryNameList = outils.RandomQueryFeat(nbPatchTotal, featChannel, args.searchRegion, imgFeatMin, minNet, strideNet, transform, net, args.searchDir, args.margin, queryImgList, args.cuda, args.featScaleBase) print ('---> Get topK patches matching to query...') topkImg, topkScale, topkValue, topkW, topkH = outils.RetrievalRes(nbPatchTotal, searchImgList, args.searchDir, args.margin, args.searchRegion, scales, minNet, strideNet, transform, net, featQuery, args.cuda, min(len(searchImgList), args.K)) print ('---> Get training pairs...') posPair, negPair = outils.TrainPair(args.searchDir, searchImgList, topkImg, topkScale, topkW, topkH, transform, net, args.margin, args.cuda, featChannel, args.searchRegion, minNet, strideNet, labelCategory, min(len(searchImgList), args.K), queryNameList, tolerance) outils.saveTrainImgPair(posPair, negPair, args.tmpTrainDir, args.margin, args.searchDir, searchImgList, topkImg, topkScale, topkW, topkH, minNet, strideNet, args.searchRegion) msg = 'NB Pos Train Pair : {:d}, NB Neg Train Pair : {:d}'.format(len(posPair), len(negPair)) print (msg) if len(posPair) < args.batchSize : continue trainloader = TrainDataLoader(args.tmpTrainDir, len(posPair), transform, args.batchSize) ## Calculate Loss net.train() # switch to train mode net.trainFreezeBN() for batch in trainloader : p1, p2, n1, n2 = batch['posI1'], batch['posI2'], batch['negI1'], batch['negI2'] if args.cuda : p1, p2, n1, n2 = p1.cuda(), p2.cuda(), n1.cuda(), n2.cuda() optimizer.zero_grad() p1, p2, n1, n2 = net(p1), net(p2), net(n1), net(n2) posSimilarityBatch, negaSimilarityBatch = outils.CosSimilarity(p1, p2, n1, n2, args.margin, args.eta) ## Triplet Loss loss = torch.clamp(negaSimilarityBatch + args.tripleLossThreshold - 1, min=0) + torch.clamp(args.tripleLossThreshold - posSimilarityBatch, min=0) ## make sure that gradient is not zero if (loss > 0).any() : loss = loss.mean() loss.backward() optimizer.step() logPosLoss.append( posSimilarityBatch.mean().item() ) logNegaLoss.append( negaSimilarityBatch.mean().item() ) # Save model, training history; print loss msg = 'EPOCH {:d}, positive pairs similarity: {:.4f}, negative pairs similarity: {:.4f}'.format(i_, np.mean(logPosLoss), np.mean(logNegaLoss)) print (msg) history['posLoss'].append(np.mean(logPosLoss)) history['negaLoss'].append(

np.mean(logNegaLoss)

numpy.mean

# Lint as: python3 # Copyright 2021 The TensorFlow Authors. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ============================================================================== """Tests for whitening module.""" import numpy as np import tensorflow as tf from delf.python import whiten class WhitenTest(tf.test.TestCase): def testApplyWhitening(self): # Testing the application of the learned whitening. vectors = np.array([[0.14022471, 0.96360618], [0.37601032, 0.25528411]]) # Learn whitening for the `vectors`. First element in the `vectors` is # viewed is the example query and the second element is the corresponding # positive. mean_vector, projection = whiten.learn_whitening(vectors, [0], [1]) # Apply the computed whitening. whitened_vectors = whiten.apply_whitening(vectors, mean_vector, projection) expected_whitened_vectors = np.array([[0., 9.99999000e-01], [0., -2.81240452e-13]]) # Compare the obtained whitened vectors with the expected result. self.assertAllClose(whitened_vectors, expected_whitened_vectors) def testLearnWhitening(self): # Testing whitening learning function. input = np.array([[0.14022471, 0.96360618], [0.37601032, 0.25528411]]) # Obtain the mean descriptor vector and the projection matrix. mean_vector, projection = whiten.learn_whitening(input, [0], [1]) expected_mean_vector = np.array([[0.14022471], [0.37601032]]) expected_projection = np.array([[1.18894378e+00, -1.74326044e-01], [1.45071361e+04, 9.89421193e+04]]) # Check that the both calculated values are close to the expected values. self.assertAllClose(mean_vector, expected_mean_vector) self.assertAllClose(projection, expected_projection) def testCholeskyPositiveDefinite(self): # Testing the Cholesky decomposition for the positive definite matrix. input = np.array([[1, -2j], [2j, 5]]) output = whiten.cholesky(input) expected_output = np.array([[1. + 0.j, 0. + 0.j], [0. + 2.j, 1. + 0.j]]) # Check that the expected output is obtained. self.assertAllClose(output, expected_output) # Check that the properties of the Cholesky decomposition are satisfied. self.assertAllClose(np.matmul(output, output.T.conj()), input) def testCholeskyNonPositiveDefinite(self): # Testing the Cholesky decomposition for a non-positive definite matrix. input_matrix = np.array([[1., 2.], [-2., 1.]]) decomposition = whiten.cholesky(input_matrix) expected_output =

np.array([[2., -2.], [-2., 2.]])

numpy.array

from __future__ import division, print_function import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt from matplotlib.backends.backend_pdf import PdfPages from mpl_toolkits.axes_grid1 import make_axes_locatable from mpl_toolkits.mplot3d import Axes3D import streakline #import streakline2 import myutils import ffwd from streams import load_stream, vcirc_potential, store_progparams, wrap_angles, progenitor_prior #import streams import astropy import astropy.units as u from astropy.constants import G from astropy.table import Table import astropy.coordinates as coord import gala.coordinates as gc import scipy.linalg as la import scipy.interpolate import scipy.optimize import zscale import itertools import copy import pickle # observers # defaults taken as in astropy v2.0 icrs mw_observer = {'z_sun': 27.*u.pc, 'galcen_distance': 8.3*u.kpc, 'roll': 0*u.deg, 'galcen_coord': coord.SkyCoord(ra=266.4051*u.deg, dec=-28.936175*u.deg, frame='icrs')} vsun = {'vcirc': 237.8*u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]*u.km/u.s} vsun0 = {'vcirc': 237.8*u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]*u.km/u.s} gc_observer = {'z_sun': 27.*u.pc, 'galcen_distance': 0.1*u.kpc, 'roll': 0*u.deg, 'galcen_coord': coord.SkyCoord(ra=266.4051*u.deg, dec=-28.936175*u.deg, frame='icrs')} vgc = {'vcirc': 0*u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]*u.km/u.s} vgc0 = {'vcirc': 0*u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]*u.km/u.s} MASK = -9999 pparams_fid = [np.log10(0.5e10)*u.Msun, 0.7*u.kpc, np.log10(6.8e10)*u.Msun, 3*u.kpc, 0.28*u.kpc, 430*u.km/u.s, 30*u.kpc, 1.57*u.rad, 1*u.Unit(1), 1*u.Unit(1), 1*u.Unit(1), 0.*u.pc/u.Myr**2, 0.*u.pc/u.Myr**2, 0.*u.pc/u.Myr**2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0.*u.Gyr**-2*u.kpc**-1, 0*u.deg, 0*u.deg, 0*u.kpc, 0*u.km/u.s, 0*u.mas/u.yr, 0*u.mas/u.yr] #pparams_fid = [0.5e-5*u.Msun, 0.7*u.kpc, 6.8e-5*u.Msun, 3*u.kpc, 0.28*u.kpc, 430*u.km/u.s, 30*u.kpc, 1.57*u.rad, 1*u.Unit(1), 1*u.Unit(1), 1*u.Unit(1), 0.*u.pc/u.Myr**2, 0.*u.pc/u.Myr**2, 0.*u.pc/u.Myr**2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0.*u.Gyr**-2, 0*u.deg, 0*u.deg, 0*u.kpc, 0*u.km/u.s, 0*u.mas/u.yr, 0*u.mas/u.yr] class Stream(): def __init__(self, x0=[]*u.kpc, v0=[]*u.km/u.s, progenitor={'coords': 'galactocentric', 'observer': {}, 'pm_polar': False}, potential='nfw', pparams=[], minit=2e4*u.Msun, mfinal=2e4*u.Msun, rcl=20*u.pc, dr=0.5, dv=2*u.km/u.s, dt=1*u.Myr, age=6*u.Gyr, nstars=600, integrator='lf'): """Initialize """ setup = {} if progenitor['coords']=='galactocentric': setup['x0'] = x0 setup['v0'] = v0 elif (progenitor['coords']=='equatorial') & (len(progenitor['observer'])!=0): if progenitor['pm_polar']: a = v0[1].value phi = v0[2].value v0[1] = a*np.sin(phi)*u.mas/u.yr v0[2] = a*np.cos(phi)*u.mas/u.yr # convert positions xeq = coord.SkyCoord(x0[0], x0[1], x0[2], **progenitor['observer']) xgal = xeq.transform_to(coord.Galactocentric) setup['x0'] = [xgal.x.to(u.kpc), xgal.y.to(u.kpc), xgal.z.to(u.kpc)]*u.kpc # convert velocities setup['v0'] = gc.vhel_to_gal(xeq.icrs, rv=v0[0], pm=v0[1:], **vsun) #setup['v0'] = [v.to(u.km/u.s) for v in vgal]*u.km/u.s else: raise ValueError('Observer position needed!') setup['dr'] = dr setup['dv'] = dv setup['minit'] = minit setup['mfinal'] = mfinal setup['rcl'] = rcl setup['dt'] = dt setup['age'] = age setup['nstars'] = nstars setup['integrator'] = integrator setup['potential'] = potential setup['pparams'] = pparams self.setup = setup self.setup_aux = {} self.fill_intid() self.fill_potid() self.st_params = self.format_input() def fill_intid(self): """Assign integrator ID for a given integrator choice Assumes setup dictionary has an 'integrator' key""" if self.setup['integrator']=='lf': self.setup_aux['iaux'] = 0 elif self.setup['integrator']=='rk': self.setup_aux['iaux'] = 1 def fill_potid(self): """Assign potential ID for a given potential choice Assumes d has a 'potential' key""" if self.setup['potential']=='nfw': self.setup_aux['paux'] = 3 elif self.setup['potential']=='log': self.setup_aux['paux'] = 2 elif self.setup['potential']=='point': self.setup_aux['paux'] = 0 elif self.setup['potential']=='gal': self.setup_aux['paux'] = 4 elif self.setup['potential']=='lmc': self.setup_aux['paux'] = 6 elif self.setup['potential']=='dipole': self.setup_aux['paux'] = 8 elif self.setup['potential']=='quad': self.setup_aux['paux'] = 9 elif self.setup['potential']=='octu': self.setup_aux['paux'] = 10 def format_input(self): """Format input parameters for streakline.stream""" p = [None]*12 # progenitor position p[0] = self.setup['x0'].si.value p[1] = self.setup['v0'].si.value # potential parameters p[2] = [x.si.value for x in self.setup['pparams']] # stream smoothing offsets p[3] = [self.setup['dr'], self.setup['dv'].si.value] # potential and integrator choice p[4] = self.setup_aux['paux'] p[5] = self.setup_aux['iaux'] # number of steps and stream stars p[6] = int(self.setup['age']/self.setup['dt']) p[7] = int(p[6]/self.setup['nstars']) # cluster properties p[8] = self.setup['minit'].si.value p[9] = self.setup['mfinal'].si.value p[10] = self.setup['rcl'].si.value # time step p[11] = self.setup['dt'].si.value return p def generate(self): """Create streakline model for a stream of set parameters""" #xm1, xm2, xm3, xp1, xp2, xp3, vm1, vm2, vm3, vp1, vp2, vp3 = streakline.stream(*p) stream = streakline.stream(*self.st_params) self.leading = {} self.leading['x'] = stream[:3]*u.m self.leading['v'] = stream[6:9]*u.m/u.s self.trailing = {} self.trailing['x'] = stream[3:6]*u.m self.trailing['v'] = stream[9:12]*u.m/u.s def observe(self, mode='cartesian', wangle=0*u.deg, units=[], errors=[], nstars=-1, sequential=False, present=[], logerr=False, observer={'z_sun': 0.*u.pc, 'galcen_distance': 8.3*u.kpc, 'roll': 0*u.deg, 'galcen_ra': 300*u.deg, 'galcen_dec': 20*u.deg}, vobs={'vcirc': 237.8*u.km/u.s, 'vlsr': [11.1, 12.2, 7.3]*u.km/u.s}, footprint='none', rotmatrix=None): """Observe the stream stream.obs holds all observations stream.err holds all errors""" x = np.concatenate((self.leading['x'].to(u.kpc).value, self.trailing['x'].to(u.kpc).value), axis=1) * u.kpc v = np.concatenate((self.leading['v'].to(u.km/u.s).value, self.trailing['v'].to(u.km/u.s).value), axis=1) * u.km/u.s if mode=='cartesian': # returns coordinates in following order # x(x, y, z), v(vx, vy, vz) if len(units)<2: units.append(self.trailing['x'].unit) units.append(self.trailing['v'].unit) if len(errors)<2: errors.append(0.2*u.kpc) errors.append(2*u.km/u.s) # positions x = x.to(units[0]) ex = np.ones(np.shape(x))*errors[0] ex = ex.to(units[0]) # velocities v = v.to(units[1]) ev = np.ones(np.shape(v))*errors[1] ev = ev.to(units[1]) self.obs = np.concatenate([x,v]).value self.err = np.concatenate([ex,ev]).value elif mode=='equatorial': # assumes coordinates in the following order: # ra, dec, distance, vrad, mualpha, mudelta if len(units)!=6: units = [u.deg, u.deg, u.kpc, u.km/u.s, u.mas/u.yr, u.mas/u.yr] if len(errors)!=6: errors = [0.2*u.deg, 0.2*u.deg, 0.5*u.kpc, 1*u.km/u.s, 0.2*u.mas/u.yr, 0.2*u.mas/u.yr] # define reference frame xgal = coord.Galactocentric(x, **observer) #frame = coord.Galactocentric(**observer) # convert xeq = xgal.transform_to(coord.ICRS) veq = gc.vgal_to_hel(xeq, v, **vobs) # store coordinates ra, dec, dist = [xeq.ra.to(units[0]).wrap_at(wangle), xeq.dec.to(units[1]), xeq.distance.to(units[2])] vr, mua, mud = [veq[2].to(units[3]), veq[0].to(units[4]), veq[1].to(units[5])] obs = np.hstack([ra, dec, dist, vr, mua, mud]).value obs = np.reshape(obs,(6,-1)) if footprint=='sdss': infoot = dec > -2.5*u.deg obs = obs[:,infoot] if np.allclose(rotmatrix, np.eye(3))!=1: xi, eta = myutils.rotate_angles(obs[0], obs[1], rotmatrix) obs[0] = xi obs[1] = eta self.obs = obs # store errors err = np.ones(np.shape(self.obs)) if logerr: for i in range(6): err[i] *= np.exp(errors[i].to(units[i]).value) else: for i in range(6): err[i] *= errors[i].to(units[i]).value self.err = err self.obsunit = units self.obserror = errors # randomly select nstars from the stream if nstars>-1: if sequential: select = np.linspace(0, np.shape(self.obs)[1], nstars, endpoint=False, dtype=int) else: select = np.random.randint(low=0, high=np.shape(self.obs)[1], size=nstars) self.obs = self.obs[:,select] self.err = self.err[:,select] # include only designated dimensions if len(present)>0: self.obs = self.obs[present] self.err = self.err[present] self.obsunit = [ self.obsunit[x] for x in present ] self.obserror = [ self.obserror[x] for x in present ] def prog_orbit(self): """Generate progenitor orbital history""" orbit = streakline.orbit(self.st_params[0], self.st_params[1], self.st_params[2], self.st_params[4], self.st_params[5], self.st_params[6], self.st_params[11], -1) self.orbit = {} self.orbit['x'] = orbit[:3]*u.m self.orbit['v'] = orbit[3:]*u.m/u.s def project(self, name, N=1000, nbatch=-1): """Project the stream from observed to native coordinates""" poly = np.loadtxt("../data/{0:s}_all.txt".format(name)) self.streak = np.poly1d(poly) self.streak_x = np.linspace(np.min(self.obs[0])-2, np.max(self.obs[0])+2, N) self.streak_y = np.polyval(self.streak, self.streak_x) self.streak_b = np.zeros(N) self.streak_l = np.zeros(N) pdot = np.polyder(poly) for i in range(N): length = scipy.integrate.quad(self._delta_path, self.streak_x[0], self.streak_x[i], args=(pdot,)) self.streak_l[i] = length[0] XB = np.transpose(np.vstack([self.streak_x, self.streak_y])) n = np.shape(self.obs)[1] if nbatch<0: nstep = 0 nbatch = -1 else: nstep = np.int(n/nbatch) i1 = 0 i2 = nbatch for i in range(nstep): XA = np.transpose(np.vstack([np.array(self.obs[0][i1:i2]), np.array(self.obs[1][i1:i2])])) self.emdist(XA, XB, i1=i1, i2=i2) i1 += nbatch i2 += nbatch XA = np.transpose(np.vstack([np.array(self.catalog['ra'][i1:]), np.array(self.catalog['dec'][i1:])])) self.emdist(XA, XB, i1=i1, i2=n) #self.catalog.write("../data/{0:s}_footprint_catalog.txt".format(self.name), format='ascii.commented_header') def emdist(self, XA, XB, i1=0, i2=-1): """""" distances = scipy.spatial.distance.cdist(XA, XB) self.catalog['b'][i1:i2] = np.min(distances, axis=1) imin = np.argmin(distances, axis=1) self.catalog['b'][i1:i2][self.catalog['dec'][i1:i2]<self.streak_y[imin]] *= -1 self.catalog['l'][i1:i2] = self.streak_l[imin] def _delta_path(self, x, pdot): """Return integrand for calculating length of a path along a polynomial""" return np.sqrt(1 + np.polyval(pdot, x)**2) def plot(self, mode='native', fig=None, color='k', **kwargs): """Plot stream""" # Plotting if fig==None: plt.close() plt.figure() ax = plt.axes([0.12,0.1,0.8,0.8]) if mode=='native': # Color setup cindices = np.arange(self.setup['nstars']) # colors of stream particles nor = mpl.colors.Normalize(vmin=0, vmax=self.setup['nstars']) # colormap normalization plt.plot(self.setup['x0'][0].to(u.kpc).value, self.setup['x0'][2].to(u.kpc).value, 'wo', ms=10, mew=2, zorder=3) plt.scatter(self.trailing['x'][0].to(u.kpc).value, self.trailing['x'][2].to(u.kpc).value, s=30, c=cindices, cmap='winter', norm=nor, marker='o', edgecolor='none', lw=0, alpha=0.1) plt.scatter(self.leading['x'][0].to(u.kpc).value, self.leading['x'][2].to(u.kpc).value, s=30, c=cindices, cmap='autumn', norm=nor, marker='o', edgecolor='none', lw=0, alpha=0.1) plt.xlabel("X (kpc)") plt.ylabel("Z (kpc)") elif mode=='observed': plt.subplot(221) plt.plot(self.obs[0], self.obs[1], 'o', color=color, **kwargs) plt.xlabel("RA") plt.ylabel("Dec") plt.subplot(223) plt.plot(self.obs[0], self.obs[2], 'o', color=color, **kwargs) plt.xlabel("RA") plt.ylabel("Distance") plt.subplot(222) plt.plot(self.obs[3], self.obs[4], 'o', color=color, **kwargs) plt.xlabel("V$_r$") plt.ylabel("$\mu\\alpha$") plt.subplot(224) plt.plot(self.obs[3], self.obs[5], 'o', color=color, **kwargs) plt.xlabel("V$_r$") plt.ylabel("$\mu\delta$") plt.tight_layout() #plt.minorticks_on() def read(self, fname, units={'x': u.kpc, 'v': u.km/u.s}): """Read stream star positions from a file""" t = np.loadtxt(fname).T n = np.shape(t)[1] ns = int((n-1)/2) self.setup['nstars'] = ns # progenitor self.setup['x0'] = t[:3,0] * units['x'] self.setup['v0'] = t[3:,0] * units['v'] # leading tail self.leading = {} self.leading['x'] = t[:3,1:ns+1] * units['x'] self.leading['v'] = t[3:,1:ns+1] * units['v'] # trailing tail self.trailing = {} self.trailing['x'] = t[:3,ns+1:] * units['x'] self.trailing['v'] = t[3:,ns+1:] * units['v'] def save(self, fname): """Save stream star positions to a file""" # define table t = Table(names=('x', 'y', 'z', 'vx', 'vy', 'vz')) # add progenitor info t.add_row(np.ravel([self.setup['x0'].to(u.kpc).value, self.setup['v0'].to(u.km/u.s).value])) # add leading tail infoobsmode tt = Table(np.concatenate((self.leading['x'].to(u.kpc).value, self.leading['v'].to(u.km/u.s).value)).T, names=('x', 'y', 'z', 'vx', 'vy', 'vz')) t = astropy.table.vstack([t,tt]) # add trailing tail info tt = Table(np.concatenate((self.trailing['x'].to(u.kpc).value, self.trailing['v'].to(u.km/u.s).value)).T, names=('x', 'y', 'z', 'vx', 'vy', 'vz')) t = astropy.table.vstack([t,tt]) # save to file t.write(fname, format='ascii.commented_header') # make a streakline model of a stream def stream_model(name='gd1', pparams0=pparams_fid, dt=0.2*u.Myr, rotmatrix=np.eye(3), graph=False, graphsave=False, observer=mw_observer, vobs=vsun, footprint='', obsmode='equatorial'): """Create a streakline model of a stream baryonic component as in kupper+2015: 3.4e10*u.Msun, 0.7*u.kpc, 1e11*u.Msun, 6.5*u.kpc, 0.26*u.kpc""" # vary progenitor parameters mock = pickle.load(open('../data/mock_{}.params'.format(name), 'rb')) for i in range(3): mock['x0'][i] += pparams0[26+i] mock['v0'][i] += pparams0[29+i] # vary potential parameters potential = 'octu' pparams = pparams0[:26] #print(pparams[0]) pparams[0] = (10**pparams0[0].value)*pparams0[0].unit pparams[2] = (10**pparams0[2].value)*pparams0[2].unit #pparams[0] = pparams0[0]*1e15 #pparams[2] = pparams0[2]*1e15 #print(pparams[0]) # adjust circular velocity in this halo vobs['vcirc'] = vcirc_potential(observer['galcen_distance'], pparams=pparams) # create a model stream with these parameters params = {'generate': {'x0': mock['x0'], 'v0': mock['v0'], 'progenitor': {'coords': 'equatorial', 'observer': mock['observer'], 'pm_polar': False}, 'potential': potential, 'pparams': pparams, 'minit': mock['mi'], 'mfinal': mock['mf'], 'rcl': 20*u.pc, 'dr': 0., 'dv': 0*u.km/u.s, 'dt': dt, 'age': mock['age'], 'nstars': 400, 'integrator': 'lf'}, 'observe': {'mode': mock['obsmode'], 'wangle': mock['wangle'], 'nstars':-1, 'sequential':True, 'errors': [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc, 5*u.km/u.s, 0.5*u.mas/u.yr, 0.5*u.mas/u.yr], 'present': [0,1,2,3,4,5], 'observer': mock['observer'], 'vobs': mock['vobs'], 'footprint': mock['footprint'], 'rotmatrix': rotmatrix}} stream = Stream(**params['generate']) stream.generate() stream.observe(**params['observe']) ################################ # Plot observed stream and model if graph: observed = load_stream(name) Ndim = np.shape(observed.obs)[0] modcol = 'k' obscol = 'orange' ylabel = ['Dec (deg)', 'Distance (kpc)', 'Radial velocity (km/s)'] plt.close() fig, ax = plt.subplots(1, 3, figsize=(12,4)) for i in range(3): plt.sca(ax[i]) plt.gca().invert_xaxis() plt.xlabel('R.A. (deg)') plt.ylabel(ylabel[i]) plt.plot(observed.obs[0], observed.obs[i+1], 's', color=obscol, mec='none', ms=8, label='Observed stream') plt.plot(stream.obs[0], stream.obs[i+1], 'o', color=modcol, mec='none', ms=4, label='Fiducial model') if i==0: plt.legend(frameon=False, handlelength=0.5, fontsize='small') plt.tight_layout() if graphsave: plt.savefig('../plots/mock_observables_{}_p{}.png'.format(name, potential), dpi=150) return stream def progenitor_params(n): """Return progenitor parameters for a given stream""" if n==-1: age = 1.6*u.Gyr mi = 1e4*u.Msun mf = 2e-1*u.Msun x0, v0 = gd1_coordinates(observer=mw_observer) elif n==-2: age = 2.7*u.Gyr mi = 1e5*u.Msun mf = 2e4*u.Msun x0, v0 = pal5_coordinates(observer=mw_observer, vobs=vsun0) elif n==-3: age = 3.5*u.Gyr mi = 5e4*u.Msun mf = 2e-1*u.Msun x0, v0 = tri_coordinates(observer=mw_observer) elif n==-4: age = 2*u.Gyr mi = 2e4*u.Msun mf = 2e-1*u.Msun x0, v0 = atlas_coordinates(observer=mw_observer) out = {'x0': x0, 'v0': v0, 'age': age, 'mi': mi, 'mf': mf} return out def gal2eq(x, v, observer=mw_observer, vobs=vsun0): """""" # define reference frame xgal = coord.Galactocentric(np.array(x)[:,np.newaxis]*u.kpc, **observer) # convert xeq = xgal.transform_to(coord.ICRS) veq = gc.vgal_to_hel(xeq, np.array(v)[:,np.newaxis]*u.km/u.s, **vobs) # store coordinates units = [u.deg, u.deg, u.kpc, u.km/u.s, u.mas/u.yr, u.mas/u.yr] xobs = [xeq.ra.to(units[0]), xeq.dec.to(units[1]), xeq.distance.to(units[2])] vobs = [veq[2].to(units[3]), veq[0].to(units[4]), veq[1].to(units[5])] return(xobs, vobs) def gd1_coordinates(observer=mw_observer): """Approximate GD-1 progenitor coordinates""" x = coord.SkyCoord(ra=154.377*u.deg, dec=41.5309*u.deg, distance=8.2*u.kpc, **observer) x_ = x.galactocentric x0 = [x_.x.value, x_.y.value, x_.z.value] v0 = [-90, -250, -120] return (x0, v0) def pal5_coordinates(observer=mw_observer, vobs=vsun0): """Pal5 coordinates""" # sdss ra = 229.0128*u.deg dec = -0.1082*u.deg # bob's rrlyrae d = 21.7*u.kpc # harris #d = 23.2*u.kpc # odenkirchen 2002 vr = -58.7*u.km/u.s # fritz & kallivayalil 2015 mua = -2.296*u.mas/u.yr mud = -2.257*u.mas/u.yr d = 24*u.kpc x = coord.SkyCoord(ra=ra, dec=dec, distance=d, **observer) x0 = x.galactocentric v0 = gc.vhel_to_gal(x.icrs, rv=vr, pm=[mua, mud], **vobs).to(u.km/u.s) return ([x0.x.value, x0.y.value, x0.z.value], v0.value.tolist()) def tri_coordinates(observer=mw_observer): """Approximate Triangulum progenitor coordinates""" x = coord.SkyCoord(ra=22.38*u.deg, dec=30.26*u.deg, distance=33*u.kpc, **observer) x_ = x.galactocentric x0 = [x_.x.value, x_.y.value, x_.z.value] v0 = [-40, 155, 155] return (x0, v0) def atlas_coordinates(observer=mw_observer): """Approximate ATLAS progenitor coordinates""" x = coord.SkyCoord(ra=20*u.deg, dec=-27*u.deg, distance=20*u.kpc, **observer) x_ = x.galactocentric x0 = [x_.x.value, x_.y.value, x_.z.value] v0 = [40, 150, -120] return (x0, v0) # great circle orientation def find_greatcircle(stream=None, name='gd1', pparams=pparams_fid, dt=0.2*u.Myr, save=True, graph=True): """Save rotation matrix for a stream model""" if stream==None: stream = stream_model(name, pparams0=pparams, dt=dt) # find the pole ra = np.radians(stream.obs[0]) dec = np.radians(stream.obs[1]) rx = np.cos(ra) * np.cos(dec) ry = np.sin(ra) * np.cos(dec) rz = np.sin(dec) r = np.column_stack((rx, ry, rz)) # fit the plane x0 = np.array([0, 1, 0]) lsq = scipy.optimize.minimize(wfit_plane, x0, args=(r,)) x0 = lsq.x/np.linalg.norm(lsq.x) ra0 = np.arctan2(x0[1], x0[0]) dec0 = np.arcsin(x0[2]) ra0 += np.pi dec0 = np.pi/2 - dec0 # euler rotations R0 = myutils.rotmatrix(np.degrees(-ra0), 2) R1 = myutils.rotmatrix(np.degrees(dec0), 1) R2 = myutils.rotmatrix(0, 2) R = np.dot(R2, np.matmul(R1, R0)) xi, eta = myutils.rotate_angles(stream.obs[0], stream.obs[1], R) # put xi = 50 at the beginning of the stream xi[xi>180] -= 360 xi += 360 xi0 = np.min(xi) - 50 R2 = myutils.rotmatrix(-xi0, 2) R = np.dot(R2, np.matmul(R1, R0)) xi, eta = myutils.rotate_angles(stream.obs[0], stream.obs[1], R) if save: np.save('../data/rotmatrix_{}'.format(name), R) f = open('../data/mock_{}.params'.format(name), 'rb') mock = pickle.load(f) mock['rotmatrix'] = R f.close() f = open('../data/mock_{}.params'.format(name), 'wb') pickle.dump(mock, f) f.close() if graph: plt.close() fig, ax = plt.subplots(1,2,figsize=(10,5)) plt.sca(ax[0]) plt.plot(stream.obs[0], stream.obs[1], 'ko') plt.xlabel('R.A. (deg)') plt.ylabel('Dec (deg)') plt.sca(ax[1]) plt.plot(xi, eta, 'ko') plt.xlabel('$\\xi$ (deg)') plt.ylabel('$\\eta$ (deg)') plt.ylim(-5, 5) plt.tight_layout() plt.savefig('../plots/gc_orientation_{}.png'.format(name)) return R def wfit_plane(x, r, p=None): """Fit a plane to a set of 3d points""" Np = np.shape(r)[0] if np.any(p)==None: p = np.ones(Np) Q = np.zeros((3,3)) for i in range(Np): Q += p[i]**2 * np.outer(r[i], r[i]) x = x/np.linalg.norm(x) lsq = np.inner(x, np.inner(Q, x)) return lsq # observed streams #def load_stream(n): #"""Load stream observations""" #if n==-1: #observed = load_gd1(present=[0,1,2,3]) #elif n==-2: #observed = load_pal5(present=[0,1,2,3]) #elif n==-3: #observed = load_tri(present=[0,1,2,3]) #elif n==-4: #observed = load_atlas(present=[0,1,2,3]) #return observed def endpoints(name): """""" stream = load_stream(name) # find endpoints amin = np.argmin(stream.obs[0]) amax = np.argmax(stream.obs[0]) ra = np.array([stream.obs[0][i] for i in [amin, amax]]) dec = np.array([stream.obs[1][i] for i in [amin, amax]]) f = open('../data/mock_{}.params'.format(name), 'rb') mock = pickle.load(f) # rotate endpoints R = mock['rotmatrix'] xi, eta = myutils.rotate_angles(ra, dec, R) #xi, eta = myutils.rotate_angles(stream.obs[0], stream.obs[1], R) mock['ra_range'] = ra mock['xi_range'] = xi #np.percentile(xi, [10,90]) f.close() f = open('../data/mock_{}.params'.format(name), 'wb') pickle.dump(mock, f) f.close() def load_pal5(present, nobs=50, potential='gal'): """""" if len(present)==2: t = Table.read('../data/pal5_members.txt', format='ascii.commented_header') dist = 21.7 deltadist = 0.7 np.random.seed(34) t = t[np.random.randint(0, high=len(t), size=nobs)] nobs = len(t) d = np.random.randn(nobs)*deltadist + dist obs = np.array([t['ra'], t['dec'], d]) obsunit = [u.deg, u.deg, u.kpc] err = np.repeat( np.array([2e-4, 2e-4, 0.7]), nobs ).reshape(3, -1) obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc] if len(present)==3: #t = Table.read('../data/pal5_kinematic.txt', format='ascii.commented_header') t = Table.read('../data/pal5_allmembers.txt', format='ascii.commented_header') obs = np.array([t['ra'], t['dec'], t['d']]) obsunit = [u.deg, u.deg, u.kpc] err = np.array([t['err_ra'], t['err_dec'], t['err_d']]) obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc] if len(present)==4: #t = Table.read('../data/pal5_kinematic.txt', format='ascii.commented_header') t = Table.read('../data/pal5_allmembers.txt', format='ascii.commented_header') obs = np.array([t['ra'], t['dec'], t['d'], t['vr']]) obsunit = [u.deg, u.deg, u.kpc, u.km/u.s] err = np.array([t['err_ra'], t['err_dec'], t['err_d'], t['err_vr']]) obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc, 5*u.km/u.s] observed = Stream(potential=potential) observed.obs = obs observed.obsunit = obsunit observed.err = err observed.obserror = obserr return observed def load_gd1(present, nobs=50, potential='gal'): """""" if len(present)==3: t = Table.read('../data/gd1_members.txt', format='ascii.commented_header') dist = 0 deltadist = 0.5 np.random.seed(34) t = t[np.random.randint(0, high=len(t), size=nobs)] nobs = len(t) d = np.random.randn(nobs)*deltadist + dist d += t['l']*0.04836 + 9.86 obs = np.array([t['ra'], t['dec'], d]) obsunit = [u.deg, u.deg, u.kpc] err = np.repeat( np.array([2e-4, 2e-4, 0.5]), nobs ).reshape(3, -1) obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc] if len(present)==4: #t = Table.read('../data/gd1_kinematic.txt', format='ascii.commented_header') t = Table.read('../data/gd1_allmembers.txt', format='ascii.commented_header') obs = np.array([t['ra'], t['dec'], t['d'], t['vr']]) obsunit = [u.deg, u.deg, u.kpc, u.km/u.s] err = np.array([t['err_ra'], t['err_dec'], t['err_d'], t['err_vr']]) obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc, 5*u.km/u.s] ind = np.all(obs!=MASK, axis=0) observed = Stream(potential=potential) observed.obs = obs#[np.array(present)] observed.obsunit = obsunit observed.err = err#[np.array(present)] observed.obserror = obserr return observed def load_tri(present, nobs=50, potential='gal'): """""" if len(present)==4: t = Table.read('../data/tri_allmembers.txt', format='ascii.commented_header') obs = np.array([t['ra'], t['dec'], t['d'], t['vr']]) obsunit = [u.deg, u.deg, u.kpc, u.km/u.s] err = np.array([t['err_ra'], t['err_dec'], t['err_d'], t['err_vr']]) obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc, 5*u.km/u.s] if len(present)==3: t = Table.read('../data/tri_allmembers.txt', format='ascii.commented_header') obs = np.array([t['ra'], t['dec'], t['d']]) obsunit = [u.deg, u.deg, u.kpc] err = np.array([t['err_ra'], t['err_dec'], t['err_d']]) obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc] ind = np.all(obs!=MASK, axis=0) observed = Stream(potential=potential) observed.obs = obs observed.obsunit = obsunit observed.err = err observed.obserror = obserr return observed def load_atlas(present, nobs=50, potential='gal'): """""" ra, dec = atlas_track() n = np.size(ra) d = np.random.randn(n)*2 + 20 obs = np.array([ra, dec, d]) obsunit = [u.deg, u.deg, u.kpc] err = np.array([np.ones(n)*0.05, np.ones(n)*0.05, np.ones(n)*2]) obserr = [2e-4*u.deg, 2e-4*u.deg, 0.5*u.kpc, 5*u.km/u.s] observed = Stream(potential=potential) observed.obs = obs observed.obsunit = obsunit observed.err = err observed.obserror = obserr return observed def atlas_track(): """""" ra0, dec0 = np.radians(77.16), np.radians(46.92 - 90) # euler rotations D = np.array([[np.cos(ra0), np.sin(ra0), 0], [-np.sin(ra0), np.cos(ra0), 0], [0, 0, 1]]) C = np.array([[np.cos(dec0), 0, np.sin(dec0)], [0, 1, 0], [-np.sin(dec0), 0, np.cos(dec0)]]) B = np.diag(np.ones(3)) R = np.dot(B, np.dot(C, D)) Rinv = np.linalg.inv(R) l0 = np.linspace(0, 2*np.pi, 500) b0 = np.zeros(500) xeq, yeq, zeq = myutils.eq2car(l0, b0) eq = np.column_stack((xeq, yeq, zeq)) eq_rot = np.zeros(np.shape(eq)) for i in range(np.size(l0)): eq_rot[i] = np.dot(Rinv, eq[i]) l0_rot, b0_rot = myutils.car2eq(eq_rot[:, 0], eq_rot[:, 1], eq_rot[:, 2]) ra_s, dec_s = np.degrees(l0_rot), np.degrees(b0_rot) ind_s = (ra_s>17) & (ra_s<30) ra_s = ra_s[ind_s] dec_s = dec_s[ind_s] return (ra_s, dec_s) def fancy_name(n): """Return nicely formatted stream name""" names = {-1: 'GD-1', -2: 'Palomar 5', -3: 'Triangulum', -4: 'ATLAS'} return names[n] # model parameters def get_varied_pars(vary): """Return indices and steps for a preset of varied parameters, and a label for varied parameters Parameters: vary - string setting the parameter combination to be varied, options: 'potential', 'progenitor', 'halo', or a list thereof""" if type(vary) is not list: vary = [vary] Nt = len(vary) vlabel = '_'.join(vary) pid = [] dp = [] for v in vary: o1, o2 = get_varied_bytype(v) pid += o1 dp += o2 return (pid, dp, vlabel) def get_varied_bytype(vary): """Get varied parameter of a particular type""" if vary=='potential': pid = [5,6,8,10,11] dp = [20*u.km/u.s, 2*u.kpc, 0.05*u.Unit(1), 0.05*u.Unit(1), 0.4e11*u.Msun] elif vary=='bary': pid = [0,1,2,3,4] # gd1 dp = [1e-1*u.Msun, 0.005*u.kpc, 1e-1*u.Msun, 0.002*u.kpc, 0.002*u.kpc] ## atlas & triangulum #dp = [0.4e5*u.Msun, 0.0005*u.kpc, 0.5e6*u.Msun, 0.0002*u.kpc, 0.002*u.kpc] # pal5 dp = [1e-2*u.Msun, 0.000005*u.kpc, 1e-2*u.Msun, 0.000002*u.kpc, 0.00002*u.kpc] dp = [1e-7*u.Msun, 0.5*u.kpc, 1e-7*u.Msun, 0.5*u.kpc, 0.5*u.kpc] dp = [1e-2*u.Msun, 0.5*u.kpc, 1e-2*u.Msun, 0.5*u.kpc, 0.5*u.kpc] elif vary=='halo': pid = [5,6,8,10] dp = [20*u.km/u.s, 2*u.kpc, 0.05*u.Unit(1), 0.05*u.Unit(1)] dp = [35*u.km/u.s, 2.9*u.kpc, 0.05*u.Unit(1), 0.05*u.Unit(1)] elif vary=='progenitor': pid = [26,27,28,29,30,31] dp = [1*u.deg, 1*u.deg, 0.5*u.kpc, 20*u.km/u.s, 0.3*u.mas/u.yr, 0.3*u.mas/u.yr] elif vary=='dipole': pid = [11,12,13] #dp = [1e-11*u.Unit(1), 1e-11*u.Unit(1), 1e-11*u.Unit(1)] dp = [0.05*u.pc/u.Myr**2, 0.05*u.pc/u.Myr**2, 0.05*u.pc/u.Myr**2] elif vary=='quad': pid = [14,15,16,17,18] dp = [0.5*u.Gyr**-2 for x in range(5)] elif vary=='octu': pid = [19,20,21,22,23,24,25] dp = [0.001*u.Gyr**-2*u.kpc**-1 for x in range(7)] else: pid = [] dp = [] return (pid, dp) def get_parlabel(pid): """Return label for a list of parameter ids Parameter: pid - list of parameter ids""" master = ['log $M_b$', '$a_b$', 'log $M_d$', '$a_d$', '$b_d$', '$V_h$', '$R_h$', '$\phi$', '$q_x$', '$q_y$', '$q_z$', '$a_{1,-1}$', '$a_{1,0}$', '$a_{1,1}$', '$a_{2,-2}$', '$a_{2,-1}$', '$a_{2,0}$', '$a_{2,1}$', '$a_{2,2}$', '$a_{3,-3}$', '$a_{3,-2}$', '$a_{3,-1}$', '$a_{3,0}$', '$a_{3,1}$', '$a_{3,2}$', '$a_{3,3}$', '$RA_p$', '$Dec_p$', '$d_p$', '$V_{r_p}$', '$\mu_{\\alpha_p}$', '$\mu_{\delta_p}$', ] master_units = ['dex', 'kpc', 'dex', 'kpc', 'kpc', 'km/s', 'kpc', 'rad', '', '', '', 'pc/Myr$^2$', 'pc/Myr$^2$', 'pc/Myr$^2$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'Gyr$^{-2}$ kpc$^{-1}$', 'deg', 'deg', 'kpc', 'km/s', 'mas/yr', 'mas/yr', ] if type(pid) is list: labels = [] units = [] for i in pid: labels += [master[i]] units += [master_units[i]] else: labels = master[pid] units = master_units[pid] return (labels, units) def get_steps(Nstep=50, log=False): """Return deltax steps in both directions Paramerets: Nstep - number of steps in one direction (default: 50) log - if True, steps are logarithmically spaced (default: False)""" if log: step = np.logspace(-10, 1, Nstep) else: step = np.linspace(0.1, 10, Nstep) step = np.concatenate([-step[::-1], step]) return (Nstep, step) def lmc_position(): """""" ra = 80.8939*u.deg dec = -69.7561*u.deg dm = 18.48 d = 10**(1 + dm/5)*u.pc x = coord.SkyCoord(ra=ra, dec=dec, distance=d) xgal = [x.galactocentric.x.si, x.galactocentric.y.si, x.galactocentric.z.si] print(xgal) def lmc_properties(): """""" # penarrubia 2016 mass = 2.5e11*u.Msun ra = 80.8939*u.deg dec = -69.7561*u.deg dm = 18.48 d = 10**(1 + dm/5)*u.pc c1 = coord.SkyCoord(ra=ra, dec=dec, distance=d) cgal1 = c1.transform_to(coord.Galactocentric) xgal = np.array([cgal1.x.to(u.kpc).value, cgal1.y.to(u.kpc).value, cgal1.z.to(u.kpc).value])*u.kpc return (mass, xgal) # fit bspline to a stream model def fit_bspline(n, pparams=pparams_fid, dt=0.2*u.Myr, align=False, save='', graph=False, graphsave='', fiducial=False): """Fit bspline to a stream model and save to file""" Ndim = 6 fits = [None]*(Ndim-1) if align: rotmatrix = np.load('../data/rotmatrix_{}.npy'.format(n)) else: rotmatrix = None stream = stream_model(n, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) Nobs = 10 k = 3 isort = np.argsort(stream.obs[0]) ra = np.linspace(np.min(stream.obs[0])*1.05, np.max(stream.obs[0])*0.95, Nobs) t = np.r_[(stream.obs[0][isort][0],)*(k+1), ra, (stream.obs[0][isort][-1],)*(k+1)] for j in range(Ndim-1): fits[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][isort], stream.obs[j+1][isort], t, k=k) if len(save)>0: np.savez('../data/{:s}'.format(save), fits=fits) if graph: xlims, ylims = get_stream_limits(n, align) ylabel = ['R.A. (deg)', 'Dec (deg)', 'd (kpc)', '$V_r$ (km/s)', '$\mu_\\alpha$ (mas/yr)', '$\mu_\delta$ (mas/yr)'] if align: ylabel[:2] = ['$\\xi$ (deg)', '$\\eta$ (deg)'] if fiducial: stream_fid = stream_model(n, pparams0=pparams_fid, dt=dt, rotmatrix=rotmatrix) fidsort = np.argsort(stream_fid.obs[0]) ra = np.linspace(np.min(stream_fid.obs[0])*1.05, np.max(stream_fid.obs[0])*0.95, Nobs) tfid = np.r_[(stream_fid.obs[0][fidsort][0],)*(k+1), ra, (stream_fid.obs[0][fidsort][-1],)*(k+1)] llabel = 'b-spline fit' else: llabel = '' plt.close() fig, ax = plt.subplots(2,5,figsize=(20,5), sharex=True, gridspec_kw = {'height_ratios':[3, 1]}) for i in range(Ndim-1): plt.sca(ax[0][i]) plt.plot(stream.obs[0], stream.obs[i+1], 'ko') plt.plot(stream.obs[0][isort], fits[i](stream.obs[0][isort]), 'r-', lw=2, label=llabel) if fiducial: fits_fid = scipy.interpolate.make_lsq_spline(stream_fid.obs[0][fidsort], stream_fid.obs[i+1][fidsort], tfid, k=k) plt.plot(stream_fid.obs[0], stream_fid.obs[i+1], 'wo', mec='k', alpha=0.1) plt.plot(stream_fid.obs[0][fidsort], fits_fid(stream_fid.obs[0][fidsort]), 'b-', lw=2, label='Fiducial') plt.ylabel(ylabel[i+1]) plt.xlim(xlims[0], xlims[1]) plt.ylim(ylims[i][0], ylims[i][1]) plt.sca(ax[1][i]) if fiducial: yref = fits_fid(stream.obs[0]) ycolor = 'b' else: yref = fits[i](stream.obs[0]) ycolor = 'r' plt.axhline(0, color=ycolor, lw=2) if fiducial: plt.plot(stream.obs[0][isort], stream.obs[i+1][isort] - stream_fid.obs[i+1][fidsort], 'wo', mec='k', alpha=0.1) plt.plot(stream.obs[0], stream.obs[i+1] - yref, 'ko') if fiducial: fits_diff = scipy.interpolate.make_lsq_spline(stream.obs[0][isort], stream.obs[i+1][isort] - stream_fid.obs[i+1][fidsort], t, k=k) plt.plot(stream.obs[0][isort], fits_diff(stream.obs[0][isort]), 'r--') plt.plot(stream.obs[0][isort], fits[i](stream.obs[0][isort]) - yref[isort], 'r-', lw=2, label=llabel) plt.xlabel(ylabel[0]) plt.ylabel('$\Delta$ {}'.format(ylabel[i+1].split(' ')[0])) if fiducial: plt.sca(ax[0][Ndim-2]) plt.legend(fontsize='small') plt.tight_layout() if len(graphsave)>0: plt.savefig('../plots/{:s}.png'.format(graphsave)) def fitbyt_bspline(n, pparams=pparams_fid, dt=0.2*u.Myr, align=False, save='', graph=False, graphsave='', fiducial=False): """Fit each tail individually""" Ndim = 6 fits = [None]*(Ndim-1) if align: rotmatrix = np.load('../data/rotmatrix_{}.npy'.format(n)) else: rotmatrix = None stream = stream_model(n, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) Nobs = 10 k = 3 isort = np.argsort(stream.obs[0]) ra = np.linspace(np.min(stream.obs[0])*1.05, np.max(stream.obs[0])*0.95, Nobs) t = np.r_[(stream.obs[0][isort][0],)*(k+1), ra, (stream.obs[0][isort][-1],)*(k+1)] for j in range(Ndim-1): fits[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][isort], stream.obs[j+1][isort], t, k=k) if len(save)>0: np.savez('../data/{:s}'.format(save), fits=fits) if graph: xlims, ylims = get_stream_limits(n, align) ylabel = ['R.A. (deg)', 'Dec (deg)', 'd (kpc)', '$V_r$ (km/s)', '$\mu_\\alpha$ (mas/yr)', '$\mu_\delta$ (mas/yr)'] if align: ylabel[:2] = ['$\\xi$ (deg)', '$\\eta$ (deg)'] if fiducial: stream_fid = stream_model(n, pparams0=pparams_fid, dt=dt, rotmatrix=rotmatrix) plt.close() fig, ax = plt.subplots(2,Ndim,figsize=(20,4), sharex=True, gridspec_kw = {'height_ratios':[3, 1]}) for i in range(Ndim): plt.sca(ax[0][i]) Nhalf = int(0.5*np.size(stream.obs[i])) plt.plot(stream.obs[i][:Nhalf], 'o') plt.plot(stream.obs[i][Nhalf:], 'o') if fiducial: plt.plot(stream_fid.obs[i][:Nhalf], 'wo', mec='k', mew=0.2, alpha=0.5) plt.plot(stream_fid.obs[i][Nhalf:], 'wo', mec='k', mew=0.2, alpha=0.5) plt.ylabel(ylabel[i]) plt.sca(ax[1][i]) if fiducial: plt.plot(stream.obs[i][:Nhalf] - stream_fid.obs[i][:Nhalf], 'o') plt.plot(stream.obs[i][Nhalf:] - stream_fid.obs[i][Nhalf:], 'o') if fiducial: plt.sca(ax[0][Ndim-1]) plt.legend(fontsize='small') plt.tight_layout() if len(graphsave)>0: plt.savefig('../plots/{:s}.png'.format(graphsave)) else: return fig def get_stream_limits(n, align=False): """Return lists with limiting values in different dimensions""" if n==-1: xlims = [260, 100] ylims = [[-20, 70], [5, 15], [-400, 400], [-15,5], [-15, 5]] elif n==-2: xlims = [250, 210] ylims = [[-20, 15], [17, 27], [-80, -20], [-5,0], [-5, 0]] elif n==-3: xlims = [27, 17] ylims = [[10, 50], [34, 36], [-175, -50], [0.45, 1], [0.1, 0.7]] elif n==-4: xlims = [35, 10] ylims = [[-40, -20], [15, 25], [50, 200], [-0.5,0.5], [-1.5, -0.5]] if align: ylims[0] = [-5, 5] xup = [110, 110, 80, 80] xlims = [xup[np.abs(n)-1], 40] return (xlims, ylims) # step sizes for derivatives def iterate_steps(n): """Calculate derivatives for different parameter classes, and plot""" for vary in ['bary', 'halo', 'progenitor']: print(n, vary) step_convergence(n, Nstep=10, vary=vary) choose_step(n, Nstep=10, vary=vary) def iterate_plotsteps(n): """Plot stream models for a variety of model parameters""" for vary in ['bary', 'halo', 'progenitor']: print(n, vary) pid, dp, vlabel = get_varied_pars(vary) for p in range(len(pid)): plot_steps(n, p=p, Nstep=5, vary=vary, log=False) def plot_steps(n, p=0, Nstep=20, log=True, dt=0.2*u.Myr, vary='halo', verbose=False, align=True, observer=mw_observer, vobs=vsun): """Plot stream for different values of a potential parameter""" if align: rotmatrix = np.load('../data/rotmatrix_{}.npy'.format(n)) else: rotmatrix = None pparams0 = pparams_fid pid, dp, vlabel = get_varied_pars(vary) plabel, punit = get_parlabel(pid[p]) Nstep, step = get_steps(Nstep=Nstep, log=log) plt.close() fig, ax = plt.subplots(5,5,figsize=(20,10), sharex=True, gridspec_kw = {'height_ratios':[3, 1, 1, 1, 1]}) # fiducial model stream0 = stream_model(n, pparams0=pparams0, dt=dt, rotmatrix=rotmatrix, observer=observer, vobs=vobs) Nobs = 10 k = 3 isort = np.argsort(stream0.obs[0]) ra = np.linspace(np.min(stream0.obs[0])*1.05, np.max(stream0.obs[0])*0.95, Nobs) t = np.r_[(stream0.obs[0][isort][0],)*(k+1), ra, (stream0.obs[0][isort][-1],)*(k+1)] fits = [None]*5 for j in range(5): fits[j] = scipy.interpolate.make_lsq_spline(stream0.obs[0][isort], stream0.obs[j+1][isort], t, k=k) # excursions stream_fits = [[None] * 5 for x in range(2 * Nstep)] for i, s in enumerate(step[:]): pparams = [x for x in pparams0] pparams[pid[p]] = pparams[pid[p]] + s*dp[p] stream = stream_model(n, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) color = mpl.cm.RdBu(i/(2*Nstep-1)) #print(i, dp[p], pparams) # fits iexsort = np.argsort(stream.obs[0]) raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs) tex = np.r_[(stream.obs[0][iexsort][0],)*(k+1), raex, (stream.obs[0][iexsort][-1],)*(k+1)] fits_ex = [None]*5 for j in range(5): fits_ex[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[j+1][iexsort], tex, k=k) stream_fits[i][j] = fits_ex[j] plt.sca(ax[0][j]) plt.plot(stream.obs[0], stream.obs[j+1], 'o', color=color, ms=2) plt.sca(ax[1][j]) plt.plot(stream.obs[0], stream.obs[j+1] - fits[j](stream.obs[0]), 'o', color=color, ms=2) plt.sca(ax[2][j]) plt.plot(stream.obs[0], fits_ex[j](stream.obs[0]) - fits[j](stream.obs[0]), 'o', color=color, ms=2) plt.sca(ax[3][j]) plt.plot(stream.obs[0], (fits_ex[j](stream.obs[0]) - fits[j](stream.obs[0]))/(s*dp[p]), 'o', color=color, ms=2) # symmetric derivatives ra_der = np.linspace(np.min(stream0.obs[0])*1.05, np.max(stream0.obs[0])*0.95, 100) for i in range(Nstep): color = mpl.cm.Greys_r(i/Nstep) for j in range(5): dy = stream_fits[i][j](ra_der) - stream_fits[-i-1][j](ra_der) dydx = -dy / np.abs(2*step[i]*dp[p]) plt.sca(ax[4][j]) plt.plot(ra_der, dydx, '-', color=color, lw=2, zorder=Nstep-i) # labels, limits xlims, ylims = get_stream_limits(n, align) ylabel = ['R.A. (deg)', 'Dec (deg)', 'd (kpc)', '$V_r$ (km/s)', '$\mu_\\alpha$ (mas/yr)', '$\mu_\delta$ (mas/yr)'] if align: ylabel[:2] = ['$\\xi$ (deg)', '$\\eta$ (deg)'] for j in range(5): plt.sca(ax[0][j]) plt.ylabel(ylabel[j+1]) plt.xlim(xlims[0], xlims[1]) plt.ylim(ylims[j][0], ylims[j][1]) plt.sca(ax[1][j]) plt.ylabel('$\Delta$ {}'.format(ylabel[j+1].split(' ')[0])) plt.sca(ax[2][j]) plt.ylabel('$\Delta$ {}'.format(ylabel[j+1].split(' ')[0])) plt.sca(ax[3][j]) plt.ylabel('$\Delta${}/$\Delta${}'.format(ylabel[j+1].split(' ')[0], plabel)) plt.sca(ax[4][j]) plt.xlabel(ylabel[0]) plt.ylabel('$\langle$$\Delta${}/$\Delta${}$\\rangle$'.format(ylabel[j+1].split(' ')[0], plabel)) #plt.suptitle('Varying {}'.format(plabel), fontsize='small') plt.tight_layout() plt.savefig('../plots/observable_steps_{:d}_{:s}_p{:d}_Ns{:d}.png'.format(n, vlabel, p, Nstep)) def step_convergence(name='gd1', Nstep=20, log=True, layer=1, dt=0.2*u.Myr, vary='halo', align=True, graph=False, verbose=False, Nobs=10, k=3, ra_der=np.nan, Nra=50): """Check deviations in numerical derivatives for consecutive step sizes""" mock = pickle.load(open('../data/mock_{}.params'.format(name),'rb')) if align: rotmatrix = mock['rotmatrix'] xmm = mock['xi_range'] else: rotmatrix = np.eye(3) xmm = mock['ra_range'] # fiducial model pparams0 = pparams_fid stream0 = stream_model(name=name, pparams0=pparams0, dt=dt, rotmatrix=rotmatrix) if np.any(~np.isfinite(ra_der)): ra_der = np.linspace(xmm[0]*1.05, xmm[1]*0.95, Nra) Nra = np.size(ra_der) # parameters to vary pid, dp, vlabel = get_varied_pars(vary) Np = len(pid) dpvec = np.array([x.value for x in dp]) Nstep, step = get_steps(Nstep=Nstep, log=log) dydx_all = np.empty((Np, Nstep, 5, Nra)) dev_der = np.empty((Np, Nstep-2*layer)) step_der = np.empty((Np, Nstep-2*layer)) for p in range(Np): plabel = get_parlabel(pid[p]) if verbose: print(p, plabel) # excursions stream_fits = [[None] * 5 for x in range(2 * Nstep)] for i, s in enumerate(step[:]): if verbose: print(i, s) pparams = [x for x in pparams0] pparams[pid[p]] = pparams[pid[p]] + s*dp[p] stream = stream_model(name=name, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) # fits iexsort = np.argsort(stream.obs[0]) raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs) tex = np.r_[(stream.obs[0][iexsort][0],)*(k+1), raex, (stream.obs[0][iexsort][-1],)*(k+1)] fits_ex = [None]*5 for j in range(5): fits_ex[j] = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[j+1][iexsort], tex, k=k) stream_fits[i][j] = fits_ex[j] # symmetric derivatives dydx = np.empty((Nstep, 5, Nra)) for i in range(Nstep): color = mpl.cm.Greys_r(i/Nstep) for j in range(5): dy = stream_fits[i][j](ra_der) - stream_fits[-i-1][j](ra_der) dydx[i][j] = -dy / np.abs(2*step[i]*dp[p]) dydx_all[p] = dydx # deviations from adjacent steps step_der[p] = -step[layer:Nstep-layer] * dp[p] for i in range(layer, Nstep-layer): dev_der[p][i-layer] = 0 for j in range(5): for l in range(layer): dev_der[p][i-layer] += np.sum((dydx[i][j] - dydx[i-l-1][j])**2) dev_der[p][i-layer] += np.sum((dydx[i][j] - dydx[i+l+1][j])**2) np.savez('../data/step_convergence_{}_{}_Ns{}_log{}_l{}'.format(name, vlabel, Nstep, log, layer), step=step_der, dev=dev_der, ders=dydx_all, steps_all=np.outer(dpvec,step[Nstep:])) if graph: plt.close() fig, ax = plt.subplots(1,Np,figsize=(4*Np,4)) for p in range(Np): plt.sca(ax[p]) plt.plot(step_der[p], dev_der[p], 'ko') #plabel = get_parlabel(pid[p]) #plt.xlabel('$\Delta$ {}'.format(plabel)) plt.ylabel('D') plt.gca().set_yscale('log') plt.tight_layout() plt.savefig('../plots/step_convergence_{}_{}_Ns{}_log{}_l{}.png'.format(name, vlabel, Nstep, log, layer)) def choose_step(name='gd1', tolerance=2, Nstep=20, log=True, layer=1, vary='halo'): """""" pid, dp, vlabel = get_varied_pars(vary) Np = len(pid) plabels, units = get_parlabel(pid) punits = ['({})'.format(x) if len(x) else '' for x in units] t = np.load('../data/step_convergence_{}_{}_Ns{}_log{}_l{}.npz'.format(name, vlabel, Nstep, log, layer)) dev = t['dev'] step = t['step'] dydx = t['ders'] steps_all = t['steps_all'][:,::-1] Nra = np.shape(dydx)[-1] best = np.empty(Np) # plot setup da = 4 nrow = 2 ncol = Np plt.close() fig, ax = plt.subplots(nrow, ncol, figsize=(da*ncol, da*1.3), squeeze=False, sharex='col', gridspec_kw = {'height_ratios':[1.2, 3]}) for p in range(Np): # choose step dmin = np.min(dev[p]) dtol = tolerance * dmin opt_step = np.min(step[p][dev[p]<dtol]) opt_id = step[p]==opt_step best[p] = opt_step ## largest step w deviation smaller than 1e-4 #opt_step = np.max(step[p][dev[p]<1e-4]) #opt_id = step[p]==opt_step #best[p] = opt_step plt.sca(ax[0][p]) for i in range(5): for j in range(10): plt.plot(steps_all[p], np.tanh(dydx[p,:,i,np.int64(j*Nra/10)]), '-', color='{}'.format(i/5), lw=0.5, alpha=0.5) plt.axvline(opt_step, ls='-', color='r', lw=2) plt.ylim(-1,1) plt.ylabel('Derivative') plt.title('{}'.format(plabels[p])+'$_{best}$ = '+'{:2.2g}'.format(opt_step), fontsize='small') plt.sca(ax[1][p]) plt.plot(step[p], dev[p], 'ko') plt.axvline(opt_step, ls='-', color='r', lw=2) plt.plot(step[p][opt_id], dev[p][opt_id], 'ro') plt.axhline(dtol, ls='-', color='orange', lw=1) y0, y1 = plt.gca().get_ylim() plt.axhspan(y0, dtol, color='orange', alpha=0.3, zorder=0) plt.gca().set_yscale('log') plt.gca().set_xscale('log') plt.xlabel('$\Delta$ {} {}'.format(plabels[p], punits[p])) plt.ylabel('Derivative deviation') np.save('../data/optimal_step_{}_{}'.format(name, vlabel), best) plt.tight_layout(h_pad=0) plt.savefig('../plots/step_convergence_{}_{}_Ns{}_log{}_l{}.png'.format(name, vlabel, Nstep, log, layer)) def read_optimal_step(name, vary, equal=False): """Return optimal steps for a range of parameter types""" if type(vary) is not list: vary = [vary] dp = np.empty(0) for v in vary: dp_opt = np.load('../data/optimal_step_{}_{}.npy'.format(name, v)) dp = np.concatenate([dp, dp_opt]) if equal: dp = np.array([0.05, 0.05, 0.2, 1, 0.01, 0.01, 0.05, 0.1, 0.05, 0.1, 0.1, 10, 1, 0.01, 0.01]) return dp def visualize_optimal_steps(name='gd1', vary=['progenitor', 'bary', 'halo'], align=True, dt=0.2*u.Myr, Nobs=50, k=3): """""" mock = pickle.load(open('../data/mock_{}.params'.format(name),'rb')) if align: rotmatrix = mock['rotmatrix'] xmm = mock['xi_range'] else: rotmatrix = np.eye(3) xmm = mock['ra_range'] # varied parameters pparams0 = pparams_fid pid, dp_fid, vlabel = get_varied_pars(vary) Np = len(pid) dp_opt = read_optimal_step(name, vary) dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)] fiducial = stream_model(name=name, pparams0=pparams0, dt=dt, rotmatrix=rotmatrix) iexsort = np.argsort(fiducial.obs[0]) raex = np.linspace(np.percentile(fiducial.obs[0], 10), np.percentile(fiducial.obs[0], 90), Nobs) tex = np.r_[(fiducial.obs[0][iexsort][0],)*(k+1), raex, (fiducial.obs[0][iexsort][-1],)*(k+1)] fit = scipy.interpolate.make_lsq_spline(fiducial.obs[0][iexsort], fiducial.obs[1][iexsort], tex, k=k) nrow = 2 ncol = np.int64((Np+1)/nrow) da = 4 c = ['b', 'b', 'b', 'r', 'r', 'r'] plt.close() fig, ax = plt.subplots(nrow, ncol, figsize=(ncol*da, nrow*da), squeeze=False) for p in range(Np): plt.sca(ax[p%2][int(p/2)]) for i, s in enumerate([-1.1, -1, -0.9, 0.9, 1, 1.1]): pparams = [x for x in pparams0] pparams[pid[p]] = pparams[pid[p]] + s*dp[p] stream = stream_model(name=name, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) # bspline fits to stream centerline iexsort = np.argsort(stream.obs[0]) raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs) tex = np.r_[(stream.obs[0][iexsort][0],)*(k+1), raex, (stream.obs[0][iexsort][-1],)*(k+1)] fitex = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[1][iexsort], tex, k=k) plt.plot(raex, fitex(raex) - fit(raex), '-', color=c[i]) plt.xlabel('R.A. (deg)') plt.ylabel('Dec (deg)') #print(get_parlabel(p)) plt.title('$\Delta$ {} = {:.2g}'.format(get_parlabel(p)[0], dp[p]), fontsize='medium') plt.tight_layout() plt.savefig('../plots/{}_optimal_steps.png'.format(name), dpi=200) # observing modes def define_obsmodes(): """Output a pickled dictionary with typical uncertainties and dimensionality of data for a number of observing modes""" obsmodes = {} obsmodes['fiducial'] = {'sig_obs': np.array([0.1, 2, 5, 0.1, 0.1]), 'Ndim': [3,4,6]} obsmodes['binospec'] = {'sig_obs': np.array([0.1, 2, 10, 0.1, 0.1]), 'Ndim': [3,4,6]} obsmodes['hectochelle'] = {'sig_obs': np.array([0.1, 2, 1, 0.1, 0.1]), 'Ndim': [3,4,6]} obsmodes['desi'] = {'sig_obs': np.array([0.1, 2, 10, np.nan, np.nan]), 'Ndim': [4,]} obsmodes['gaia'] = {'sig_obs': np.array([0.1, 0.2, 10, 0.2, 0.2]), 'Ndim': [6,]} obsmodes['exgal'] = {'sig_obs': np.array([0.5, np.nan, 20, np.nan, np.nan]), 'Ndim': [3,]} pickle.dump(obsmodes, open('../data/observing_modes.info','wb')) def obsmode_name(mode): """Return full name of the observing mode""" if type(mode) is not list: mode = [mode] full_names = {'fiducial': 'Fiducial', 'binospec': 'Binospec', 'hectochelle': 'Hectochelle', 'desi': 'DESI-like', 'gaia': 'Gaia-like', 'exgal': 'Extragalactic'} keys = full_names.keys() names = [] for m in mode: if m in keys: name = full_names[m] else: name = m names += [name] return names # crbs using bspline def calculate_crb(name='gd1', dt=0.2*u.Myr, vary=['progenitor', 'bary', 'halo'], ra=np.nan, dd=0.5, Nmin=15, verbose=False, align=True, scale=False, errmode='fiducial', k=3): """""" mock = pickle.load(open('../data/mock_{}.params'.format(name),'rb')) if align: rotmatrix = mock['rotmatrix'] xmm = np.sort(mock['xi_range']) else: rotmatrix = np.eye(3) xmm = np.sort(mock['ra_range']) # typical uncertainties and data availability obsmodes = pickle.load(open('../data/observing_modes.info', 'rb')) if errmode not in obsmodes.keys(): errmode = 'fiducial' sig_obs = obsmodes[errmode]['sig_obs'] data_dim = obsmodes[errmode]['Ndim'] # mock observations if np.any(~np.isfinite(ra)): if (np.int64((xmm[1]-xmm[0])/dd + 1) < Nmin): dd = (xmm[1]-xmm[0])/Nmin ra = np.arange(xmm[0], xmm[1]+dd, dd) #ra = np.linspace(xmm[0]*1.05, xmm[1]*0.95, Nobs) #else: Nobs = np.size(ra) print(name, Nobs) err = np.tile(sig_obs, Nobs).reshape(Nobs,-1) # varied parameters pparams0 = pparams_fid pid, dp_fid, vlabel = get_varied_pars(vary) Np = len(pid) dp_opt = read_optimal_step(name, vary) dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)] fits_ex = [[[None]*5 for x in range(2)] for y in range(Np)] if scale: dp_unit = unity_scale(dp) dps = [x*y for x,y in zip(dp, dp_unit)] # calculate derivatives for all parameters for p in range(Np): for i, s in enumerate([-1, 1]): pparams = [x for x in pparams0] pparams[pid[p]] = pparams[pid[p]] + s*dp[p] stream = stream_model(name=name, pparams0=pparams, dt=dt, rotmatrix=rotmatrix) # bspline fits to stream centerline iexsort = np.argsort(stream.obs[0]) raex = np.linspace(np.percentile(stream.obs[0], 10), np.percentile(stream.obs[0], 90), Nobs) tex = np.r_[(stream.obs[0][iexsort][0],)*(k+1), raex, (stream.obs[0][iexsort][-1],)*(k+1)] for j in range(5): fits_ex[p][i][j] = scipy.interpolate.make_lsq_spline(stream.obs[0][iexsort], stream.obs[j+1][iexsort], tex, k=k) # populate matrix of derivatives and calculate CRB for Ndim in data_dim: #for Ndim in [6,]: Ndata = Nobs * (Ndim - 1) cyd = np.empty(Ndata) dydx = np.empty((Np, Ndata)) dy2 = np.empty((2, Np, Ndata)) for j in range(1, Ndim): for p in range(Np): dy = fits_ex[p][0][j-1](ra) - fits_ex[p][1][j-1](ra) dy2[0][p][(j-1)*Nobs:j*Nobs] = fits_ex[p][0][j-1](ra) dy2[1][p][(j-1)*Nobs:j*Nobs] = fits_ex[p][1][j-1](ra) #positive = np.abs(dy)>0 #if verbose: print('{:d},{:d} {:s} min{:.1e} max{:1e} med{:.1e}'.format(j, p, get_parlabel(pid[p])[0], np.min(np.abs(dy[positive])), np.max(np.abs(dy)), np.median(np.abs(dy)))) if scale: dydx[p][(j-1)*Nobs:j*Nobs] = -dy / np.abs(2*dps[p].value) else: dydx[p][(j-1)*Nobs:j*Nobs] = -dy / np.abs(2*dp[p].value) #if verbose: print('{:d},{:d} {:s} min{:.1e} max{:1e} med{:.1e}'.format(j, p, get_parlabel(pid[p])[0], np.min(np.abs(dydx[p][(j-1)*Nobs:j*Nobs][positive])), np.max(np.abs(dydx[p][(j-1)*Nobs:j*Nobs])), np.median(np.abs(dydx[p][(j-1)*Nobs:j*Nobs])))) #print(j, p, get_parlabel(pid[p])[0], dp[p], np.min(np.abs(dy)), np.max(np.abs(dy)), np.median(dydx[p][(j-1)*Nobs:j*Nobs])) cyd[(j-1)*Nobs:j*Nobs] = err[:,j-1]**2 np.savez('../data/crb/components_{:s}{:1d}_{:s}_a{:1d}_{:s}'.format(errmode, Ndim, name, align, vlabel), dydx=dydx, y=dy2, cyd=cyd, dp=dp_opt) # data component of the Fisher matrix cy = np.diag(cyd) cyi = np.diag(1. / cyd) caux = np.matmul(cyi, dydx.T) dxi = np.matmul(dydx, caux) # component based on prior knowledge of model parameters pxi = priors(name, vary) # full Fisher matrix cxi = dxi + pxi if verbose: cx = np.linalg.inv(cxi) cx = np.matmul(np.linalg.inv(np.matmul(cx, cxi)), cx) # iteration to improve inverse at large cond numbers sx = np.sqrt(np.diag(cx)) print('CRB', sx) print('condition {:g}'.format(np.linalg.cond(cxi))) print('standard inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0]))) cx = stable_inverse(cxi) print('stable inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0]))) np.savez('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}'.format(errmode, Ndim, name, align, vlabel), cxi=cxi, dxi=dxi, pxi=pxi) def priors(name, vary): """Return covariance matrix with prior knowledge about parameters""" mock = pickle.load(open('../data/mock_{}.params'.format(name), 'rb')) cprog = mock['prog_prior'] cbary = np.array([0.1*x.value for x in pparams_fid[:5]])**-2 chalo = np.zeros(4) cdipole = np.zeros(3) cquad = np.zeros(5) coctu = np.zeros(7) priors = {'progenitor': cprog, 'bary': cbary, 'halo': chalo, 'dipole': cdipole, 'quad': cquad, 'octu': coctu} cprior = np.empty(0) for v in vary: cprior = np.concatenate([cprior, priors[v]]) pxi = np.diag(cprior) return pxi def scale2invert(name='gd1', Ndim=6, vary=['progenitor', 'bary', 'halo'], verbose=False, align=True, errmode='fiducial'): """""" pid, dp_fid, vlabel = get_varied_pars(vary) #dp = read_optimal_step(name, vary) d = np.load('../data/crb/components_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel)) dydx = d['dydx'] cyd = d['cyd'] y = d['y'] dp = d['dp'] dy = (y[1,:,:] - y[0,:,:]) dydx = (y[1,:,:] - y[0,:,:]) / (2*dp[:,np.newaxis]) scaling_par = np.median(np.abs(dydx), axis=1) dydx = dydx / scaling_par[:,np.newaxis] dydx_ = np.reshape(dydx, (len(dp), Ndim-1, -1)) scaling_dim = np.median(np.abs(dydx_), axis=(2,0)) dydx_ = dydx_ / scaling_dim[np.newaxis,:,np.newaxis] cyd_ = np.reshape(cyd, (Ndim-1, -1)) cyd_ = cyd_ / scaling_dim[:,np.newaxis] cyd = np.reshape(cyd_, (-1)) dydx = np.reshape(dydx_, (len(dp), -1)) mmin = np.min(np.abs(dy), axis=0) mmax = np.max(np.abs(dy), axis=0) mmed = np.median(np.abs(dydx), axis=1) dyn_range = mmax/mmin #print(dyn_range) print(np.min(dyn_range), np.max(dyn_range), np.std(dyn_range)) cy = np.diag(cyd) cyi = np.diag(1. / cyd) caux = np.matmul(cyi, dydx.T) cxi = np.matmul(dydx, caux) print('condition {:e}'.format(np.linalg.cond(cxi))) cx = np.linalg.inv(cxi) cx = np.matmul(np.linalg.inv(np.matmul(cx, cxi)), cx) # iteration to improve inverse at large cond numbers print('standard inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0]))) cx = stable_inverse(cxi, maxiter=30) print('stable inverse', np.allclose(cxi, cxi.T), np.allclose(cx, cx.T), np.allclose(np.matmul(cx,cxi), np.eye(np.shape(cx)[0]))) def unity_scale(dp): """""" dim_scale = 10**np.array([2, 3, 3, 2, 4, 3, 7, 7, 5, 7, 7, 4, 4, 4, 4, 3, 3, 3, 4, 3, 4, 4, 4]) dim_scale = 10**np.array([3, 2, 3, 4, 0, 2, 2, 3, 2, 2, 2, 4, 3, 2, 2, 3]) #dim_scale = 10**np.array([2, 3, 3, 1, 3, 2, 5, 5, 3, 5, 5, 2, 2, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3]) #dim_scale = 10**np.array([2, 3, 3, 1, 3, 2, 5, 5, 3, 5, 5, 2, 2, 4, 4, 3, 3, 3]) dp_unit = [(dp[x].value*dim_scale[x])**-1 for x in range(len(dp))] return dp_unit def test_inversion(name='gd1', Ndim=6, vary=['progenitor', 'bary', 'halo'], align=True, errmode='fiducial'): """""" pid, dp, vlabel = get_varied_pars(vary) d = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel)) cxi = d['cxi'] N = np.shape(cxi)[0] cx_ = np.linalg.inv(cxi) cx = stable_inverse(cxi, verbose=True, maxiter=100) #cx_ii = stable_inverse(cx, verbose=True, maxiter=50) print('condition {:g}'.format(np.linalg.cond(cxi))) print('linalg inverse', np.allclose(np.matmul(cx_,cxi), np.eye(N))) print('stable inverse', np.allclose(np.matmul(cx,cxi), np.eye(N))) #print(np.matmul(cx,cxi)) #print('inverse inverse', np.allclose(cx_ii, cxi)) def stable_inverse(a, maxiter=20, verbose=False): """Invert a matrix with a bad condition number""" N = np.shape(a)[0] # guess q = np.linalg.inv(a) qa = np.matmul(q,a) # iterate for i in range(maxiter): if verbose: print(i, np.sqrt(np.sum((qa - np.eye(N))**2)), np.allclose(qa, np.eye(N))) if np.allclose(qa, np.eye(N)): return q qai = np.linalg.inv(qa) q = np.matmul(qai,q) qa = np.matmul(q,a) return q def crb_triangle(n, vary, Ndim=6, align=True, plot='all', fast=False): """""" pid, dp, vlabel = get_varied_pars(vary) plabels, units = get_parlabel(pid) params = ['$\Delta$' + x + '({})'.format(y) for x,y in zip(plabels, units)] if align: alabel = '_align' else: alabel = '' fm = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel)) cxi = fm['cxi'] if fast: cx = np.linalg.inv(cxi) else: cx = stable_inverse(cxi) #print(cx[0][0]) if plot=='halo': cx = cx[:4, :4] params = params[:4] elif plot=='bary': cx = cx[4:9, 4:9] params = params[4:9] elif plot=='progenitor': cx = cx[9:, 9:] params = params[9:] Nvar = len(params) plt.close() dax = 2 fig, ax = plt.subplots(Nvar-1, Nvar-1, figsize=(dax*Nvar, dax*Nvar), sharex='col', sharey='row') for i in range(0,Nvar-1): for j in range(i+1,Nvar): plt.sca(ax[j-1][i]) cx_2d = np.array([[cx[i][i], cx[i][j]], [cx[j][i], cx[j][j]]]) w, v = np.linalg.eig(cx_2d) if np.all(np.isreal(v)): theta = np.degrees(np.arccos(v[0][0])) width = np.sqrt(w[0])*2 height = np.sqrt(w[1])*2 e = mpl.patches.Ellipse((0,0), width=width, height=height, angle=theta, fc='none', ec=mpl.cm.bone(0.5), lw=2) plt.gca().add_patch(e) plt.gca().autoscale_view() #plt.xlim(-ylim[i],ylim[i]) #plt.ylim(-ylim[j], ylim[j]) if j==Nvar-1: plt.xlabel(params[i]) if i==0: plt.ylabel(params[j]) # turn off unused axes for i in range(0,Nvar-1): for j in range(i+1,Nvar-1): plt.sca(ax[i][j]) plt.axis('off') plt.tight_layout() plt.savefig('../plots/crb_triangle_{:s}_{:d}_{:s}_{:d}_{:s}.pdf'.format(alabel, n, vlabel, Ndim, plot)) def crb_triangle_alldim(name='gd1', vary=['progenitor', 'bary', 'halo'], align=True, plot='all', fast=False, scale=False, errmode='fiducial'): """Show correlations in CRB between a chosen set of parameters in a triangle plot""" pid, dp_fid, vlabel = get_varied_pars(vary) dp_opt = read_optimal_step(name, vary) dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)] plabels, units = get_parlabel(pid) punits = [' ({})'.format(x) if len(x) else '' for x in units] params = ['$\Delta$ {}{}'.format(x, y) for x,y in zip(plabels, punits)] if plot=='halo': i0 = 11 i1 = 15 elif plot=='bary': i0 = 6 i1 = 11 elif plot=='progenitor': i0 = 0 i1 = 6 elif plot=='dipole': i0 = 15 i1 = len(params) else: i0 = 0 i1 = len(params) Nvar = i1 - i0 params = params[i0:i1] if scale: dp_unit = unity_scale(dp) #print(dp_unit) dp_unit = dp_unit[i0:i1] pid = pid[i0:i1] label = ['RA, Dec, d', 'RA, Dec, d, $V_r$', 'RA, Dec, d, $V_r$, $\mu_\\alpha$, $\mu_\delta$'] plt.close() dax = 2 fig, ax = plt.subplots(Nvar-1, Nvar-1, figsize=(dax*Nvar, dax*Nvar), sharex='col', sharey='row') for l, Ndim in enumerate([3, 4, 6]): fm = np.load('../data/crb/cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npz'.format(errmode, Ndim, name, align, vlabel)) cxi = fm['cxi'] #cxi = np.load('../data/crb/bspline_cxi_{:s}{:1d}_{:s}_a{:1d}_{:s}.npy'.format(errmode, Ndim, name, align, vlabel)) if fast: cx = np.linalg.inv(cxi) else: cx = stable_inverse(cxi) cx = cx[i0:i1,i0:i1] for i in range(0,Nvar-1): for j in range(i+1,Nvar): plt.sca(ax[j-1][i]) if scale: cx_2d = np.array([[cx[i][i]/dp_unit[i]**2, cx[i][j]/(dp_unit[i]*dp_unit[j])], [cx[j][i]/(dp_unit[j]*dp_unit[i]), cx[j][j]/dp_unit[j]**2]]) else: cx_2d = np.array([[cx[i][i], cx[i][j]], [cx[j][i], cx[j][j]]]) w, v = np.linalg.eig(cx_2d) if np.all(np.isreal(v)): theta = np.degrees(np.arctan2(v[1][0], v[0][0])) width = np.sqrt(w[0])*2 height = np.sqrt(w[1])*2 e = mpl.patches.Ellipse((0,0), width=width, height=height, angle=theta, fc='none', ec=mpl.cm.bone(0.1+l/4), lw=2, label=label[l]) plt.gca().add_patch(e) if l==1: plt.gca().autoscale_view() if j==Nvar-1: plt.xlabel(params[i]) if i==0: plt.ylabel(params[j]) # turn off unused axes for i in range(0,Nvar-1): for j in range(i+1,Nvar-1): plt.sca(ax[i][j]) plt.axis('off') plt.sca(ax[int(Nvar/2-1)][int(Nvar/2-1)]) plt.legend(loc=2, bbox_to_anchor=(1,1)) plt.tight_layout() plt.savefig('../plots/cxi_{:s}_{:s}_a{:1d}_{:s}_{:s}.pdf'.format(errmode, name, align, vlabel, plot)) def compare_optimal_steps(): """""" vary = ['progenitor', 'bary', 'halo', 'dipole', 'quad'] vary = ['progenitor', 'bary', 'halo'] for name in ['gd1', 'tri']: print(name) print(read_optimal_step(name, vary)) def get_crb(name, Nstep=10, vary=['progenitor', 'bary', 'halo'], first=True): """""" if first: store_progparams(name) wrap_angles(name, save=True) progenitor_prior(name) find_greatcircle(name=name) endpoints(name) for v in vary: step_convergence(name=name, Nstep=Nstep, vary=v) choose_step(name=name, Nstep=Nstep, vary=v) calculate_crb(name=name, vary=vary, verbose=True) crb_triangle_alldim(name=name, vary=vary) ######################## # cartesian coordinates # accelerations def acc_kepler(x, p=1*u.Msun): """Keplerian acceleration""" r = np.linalg.norm(x)*u.kpc a = -G * p * 1e11 * r**-3 * x return a.to(u.pc*u.Myr**-2) def acc_bulge(x, p=[pparams_fid[j] for j in range(2)]): """""" r = np.linalg.norm(x)*u.kpc a = -(G*p[0]*x/(r * (r + p[1])**2)).to(u.pc*u.Myr**-2) return a def acc_disk(x, p=[pparams_fid[j] for j in range(2,5)]): """""" R = np.linalg.norm(x[:2])*u.kpc z = x[2] a = -(G*p[0]*x * (R**2 + (p[1] + np.sqrt(z**2 + p[2]**2))**2)**-1.5).to(u.pc*u.Myr**-2) a[2] *= (1 + p[2]/np.sqrt(z**2 + p[2]**2)) return a def acc_nfw(x, p=[pparams_fid[j] for j in [5,6,8,10]]): """""" r = np.linalg.norm(x)*u.kpc q = np.array([1*u.Unit(1), p[2], p[3]]) a = (p[0]**2 * p[1] * r**-3 * (1/(1+p[1]/r) - np.log(1+r/p[1])) * x * q**-2).to(u.pc*u.Myr**-2) return a def acc_dipole(x, p=[pparams_fid[j] for j in range(11,14)]): """Acceleration due to outside dipole perturbation""" pv = [x.value for x in p] a = np.sqrt(3/(4*np.pi)) * np.array([pv[2], pv[0], pv[1]])*u.pc*u.Myr**-2 return a def acc_quad(x, p=[pparams_fid[j] for j in range(14,19)]): """Acceleration due to outside quadrupole perturbation""" a = np.zeros(3)*u.pc*u.Myr**-2 f = 0.5*np.sqrt(15/np.pi) a[0] = x[0]*(f*p[4] - f/np.sqrt(3)*p[2]) + x[1]*f*p[0] + x[2]*f*p[3] a[1] = x[0]*f*p[0] - x[1]*(f*p[4] + f/np.sqrt(3)*p[2]) + x[2]*f*p[1] a[2] = x[0]*f*p[3] + x[1]*f*p[1] + x[2]*2*f/np.sqrt(3)*p[2] return a.to(u.pc*u.Myr**-2) def acc_octu(x, p=[pparams_fid[j] for j in range(19,26)]): """Acceleration due to outside octupole perturbation""" a = np.zeros(3)*u.pc*u.Myr**-2 f = np.array([0.25*np.sqrt(35/(2*np.pi)), 0.5*np.sqrt(105/np.pi), 0.25*np.sqrt(21/(2*np.pi)), 0.25*np.sqrt(7/np.pi), 0.25*np.sqrt(21/(2*np.pi)), 0.25*np.sqrt(105/np.pi), 0.25*np.sqrt(35/(2*np.pi))]) xu = x.unit pu = p[0].unit pvec = np.array([i.value for i in p]) * pu dmat = np.ones((3,7)) * f * pvec * xu**2 x = np.array([i.value for i in x]) dmat[0] *= np.array([6*x[0]*x[1], x[1]*x[2], -2*x[0]*x[1], -6*x[0]*x[2], 4*x[2]**2-x[1]**2-3*x[0]**2, 2*x[0]*x[2], 3*x[0]**2-3*x[1]**2]) dmat[1] *= np.array([3*x[0]**2-3*x[1]**2, x[0]*x[2], 4*x[2]**2-x[0]**2-3*x[1]**2, -6*x[1]*x[2], -2*x[0]*x[1], -2*x[1]*x[2], -6*x[0]*x[1]]) dmat[2] *= np.array([0, x[0]*x[1], 8*x[1]*x[2], 6*x[2]**2-3*x[0]**2-3*x[1]**2, 8*x[0]*x[2], x[0]**2-x[1]**2, 0]) a = np.einsum('ij->i', dmat) * dmat.unit return a.to(u.pc*u.Myr**-2) # derivatives def der_kepler(x, p=1*u.Msun): """Derivative of Kepler potential parameters wrt cartesian components of the acceleration""" r = np.linalg.norm(x)*u.kpc dmat = np.zeros((3,1)) * u.pc**-1 * u.Myr**2 * u.Msun dmat[:,0] = (-r**3/(G*x)).to(u.pc**-1 * u.Myr**2 * u.Msun) * 1e-11 return dmat.value def pder_kepler(x, p=1*u.Msun): """Derivative of cartesian components of the acceleration wrt to Kepler potential parameter""" r = np.linalg.norm(x)*u.kpc dmat = np.zeros((3,1)) * u.pc * u.Myr**-2 * u.Msun**-1 dmat[:,0] = (-G*x*r**-3).to(u.pc * u.Myr**-2 * u.Msun**-1) * 1e11 return dmat.value def pder_nfw(x, pu=[pparams_fid[j] for j in [5,6,8,10]]): """Calculate derivatives of cartesian components of the acceleration wrt halo potential parameters""" p = pu q = np.array([1, p[2], p[3]]) # physical quantities r = np.linalg.norm(x)*u.kpc a = acc_nfw(x, p=pu) # derivatives dmat = np.zeros((3, 4)) # Vh dmat[:,0] = 2*a/p[0] # Rh dmat[:,1] = a/p[1] + p[0]**2 * p[1] * r**-3 * (1/(p[1]+p[1]**2/r) - 1/(r*(1+p[1]/r)**2)) * x * q**-2 # qy, qz for i in [1,2]: dmat[i,i+1] = (-2*a[i]/q[i]).value return dmat def pder_bulge(x, pu=[pparams_fid[j] for j in range(2)]): """Calculate derivarives of cartesian components of the acceleration wrt Hernquist bulge potential parameters""" # coordinates r = np.linalg.norm(x)*u.kpc # accelerations ab = acc_bulge(x, p=pu[:2]) # derivatives dmat = np.zeros((3, 2)) # Mb dmat[:,0] = ab/pu[0] # ab dmat[:,1] = 2 * ab / (r + pu[1]) return dmat def pder_disk(x, pu=[pparams_fid[j] for j in range(2,5)]): """Calculate derivarives of cartesian components of the acceleration wrt Miyamoto-Nagai disk potential parameters""" # coordinates R = np.linalg.norm(x[:2])*u.kpc z = x[2] aux = np.sqrt(z**2 + pu[2]**2) # accelerations ad = acc_disk(x, p=pu) # derivatives dmat = np.zeros((3, 3)) # Md dmat[:,0] = ad / pu[0] # ad dmat[:,1] = 3 * ad * (pu[1] + aux) / (R**2 + (pu[1] + aux)**2) # bd dmat[:2,2] = 3 * ad[:2] * (pu[1] + aux) / (R**2 + (pu[1] + aux)**2) * pu[2] / aux dmat[2,2] = (3 * ad[2] * (pu[1] + aux) / (R**2 + (pu[1] + aux)**2) * pu[2] / aux - G * pu[0] * z * (R**2 + (pu[1] + aux)**2)**-1.5 * z**2 * (pu[2]**2 + z**2)**-1.5).value return dmat def der_dipole(x, pu=[pparams_fid[j] for j in range(11,14)]): """Calculate derivatives of dipole potential parameters wrt (Cartesian) components of the acceleration vector a""" # shape: 3, Npar dmat = np.zeros((3,3)) f = np.sqrt((4*np.pi)/3) dmat[0,2] = f dmat[1,0] = f dmat[2,1] = f return dmat def pder_dipole(x, pu=[pparams_fid[j] for j in range(11,14)]): """Calculate derivatives of (Cartesian) components of the acceleration vector a wrt dipole potential parameters""" # shape: 3, Npar dmat = np.zeros((3,3)) f = np.sqrt(3/(4*np.pi)) dmat[0,2] = f dmat[1,0] = f dmat[2,1] = f return dmat def der_quad(x, p=[pparams_fid[j] for j in range(14,19)]): """Caculate derivatives of quadrupole potential parameters wrt (Cartesian) components of the acceleration vector a""" f = 2/np.sqrt(15/np.pi) s = np.sqrt(3) x = [1e-3/i.value for i in x] dmat = np.ones((3,5)) * f dmat[0] = np.array([x[1], 0, -s*x[0], x[2], x[0]]) dmat[1] = np.array([x[0], x[2], -s*x[1], 0, -x[1]]) dmat[2] = np.array([0, x[1], 0.5*s*x[2], x[0], 0]) return dmat def pder_quad(x, p=[pparams_fid[j] for j in range(14,19)]): """Caculate derivatives of (Cartesian) components of the acceleration vector a wrt quadrupole potential parameters""" f = 0.5*np.sqrt(15/np.pi) s = 1/np.sqrt(3) x = [1e-3*i.value for i in x] dmat = np.ones((3,5)) * f dmat[0] *= np.array([x[1], 0, -s*x[0], x[2], x[0]]) dmat[1] *= np.array([x[0], x[2], -s*x[1], 0, -x[1]]) dmat[2] *= np.array([0, x[1], 2*s*x[2], x[0], 0]) return dmat def pder_octu(x, p=[pparams_fid[j] for j in range(19,26)]): """Caculate derivatives of (Cartesian) components of the acceleration vector a wrt octupole potential parameters""" f = np.array([0.25*np.sqrt(35/(2*np.pi)), 0.5*np.sqrt(105/np.pi), 0.25*np.sqrt(21/(2*np.pi)), 0.25*np.sqrt(7/np.pi), 0.25*np.sqrt(21/(2*np.pi)), 0.25*np.sqrt(105/np.pi), 0.25*np.sqrt(35/(2*np.pi))]) x = [1e-3*i.value for i in x] dmat = np.ones((3,7)) * f dmat[0] *= np.array([6*x[0]*x[1], x[1]*x[2], -2*x[0]*x[1], -6*x[0]*x[2], 4*x[2]**2-x[1]**2-3*x[0]**2, 2*x[0]*x[2], 3*x[0]**2-3*x[1]**2]) dmat[1] *= np.array([3*x[0]**2-3*x[1]**2, x[0]*x[2], 4*x[2]**2-x[0]**2-3*x[1]**2, -6*x[1]*x[2], -2*x[0]*x[1], -2*x[1]*x[2], -6*x[0]*x[1]]) dmat[2] *= np.array([0, x[0]*x[1], 8*x[1]*x[2], 6*x[2]**2-3*x[0]**2-3*x[1]**2, 8*x[0]*x[2], x[0]**2-x[1]**2, 0]) return dmat def crb_ax(n, Ndim=6, vary=['halo', 'bary', 'progenitor'], align=True, fast=False): """Calculate CRB inverse matrix for 3D acceleration at position x in a halo potential""" pid, dp, vlabel = get_varied_pars(vary) if align: alabel = '_align' else: alabel = '' # read in full inverse CRB for stream modeling cxi = np.load('../data/crb/bspline_cxi{:s}_{:d}_{:s}_{:d}.npy'.format(alabel, n, vlabel, Ndim)) if fast: cx = np.linalg.inv(cxi) else: cx = stable_inverse(cxi) # subset halo parameters Nhalo = 4 cq = cx[:Nhalo,:Nhalo] if fast: cqi = np.linalg.inv(cq) else: cqi = stable_inverse(cq) xi = np.array([-8.3, 0.1, 0.1])*u.kpc x0, v0 = gd1_coordinates() #xi = np.array(x0)*u.kpc d = 50 Nb = 20 x = np.linspace(x0[0]-d, x0[0]+d, Nb) y = np.linspace(x0[1]-d, x0[1]+d, Nb) x = np.linspace(-d, d, Nb) y = np.linspace(-d, d, Nb) xv, yv = np.meshgrid(x, y) xf = np.ravel(xv) yf = np.ravel(yv) af = np.empty((Nb**2, 3)) plt.close() fig, ax = plt.subplots(3,3,figsize=(11,10)) dimension = ['x', 'y', 'z'] xlabel = ['y', 'x', 'x'] ylabel = ['z', 'z', 'y'] for j in range(3): if j==0: xin = np.array([np.repeat(x0[j], Nb**2), xf, yf]).T elif j==1: xin = np.array([xf, np.repeat(x0[j], Nb**2), yf]).T elif j==2: xin = np.array([xf, yf, np.repeat(x0[j], Nb**2)]).T for i in range(Nb**2): #xi = np.array([xf[i], yf[i], x0[2]])*u.kpc xi = xin[i]*u.kpc a = acc_nfw(xi) dqda = halo_accelerations(xi) cai = np.matmul(dqda, np.matmul(cqi, dqda.T)) if fast: ca = np.linalg.inv(cai) else: ca = stable_inverse(cai) a_crb = (np.sqrt(np.diag(ca)) * u.km**2 * u.kpc**-1 * u.s**-2).to(u.pc*u.Myr**-2) af[i] = np.abs(a_crb/a) af[i] = a_crb for i in range(3): plt.sca(ax[j][i]) im = plt.imshow(af[:,i].reshape(Nb,Nb), extent=[-d, d, -d, d], cmap=mpl.cm.gray) #, norm=mpl.colors.LogNorm(), vmin=1e-2, vmax=0.1) plt.xlabel(xlabel[j]+' (kpc)') plt.ylabel(ylabel[j]+' (kpc)') divider = make_axes_locatable(plt.gca()) cax = divider.append_axes("top", size="4%", pad=0.05) plt.colorbar(im, cax=cax, orientation='horizontal') plt.gca().xaxis.set_ticks_position('top') cax.tick_params(axis='x', labelsize='xx-small') if j==0: plt.title('a$_{}$'.format(dimension[i]), y=4) plt.tight_layout(rect=[0,0,1,0.95]) plt.savefig('../plots/acc_{}_{}_{}.png'.format(n, vlabel, Ndim)) def acc_cart(x, components=['bary', 'halo', 'dipole']): """""" acart = np.zeros(3) * u.pc*u.Myr**-2 dict_acc = {'bary': [acc_bulge, acc_disk], 'halo': [acc_nfw], 'dipole': [acc_dipole], 'quad': [acc_quad], 'octu': [acc_octu], 'point': [acc_kepler]} accelerations = [] for c in components: accelerations += dict_acc[c] for acc in accelerations: a_ = acc(x) acart += a_ return acart def acc_rad(x, components=['bary', 'halo', 'dipole']): """Return radial acceleration""" r = np.linalg.norm(x) * x.unit theta = np.arccos(x[2].value/r.value) phi = np.arctan2(x[1].value, x[0].value) trans = np.array([np.sin(theta)*np.cos(phi), np.sin(theta)*np.sin(phi), np.cos(theta)]) a_cart = acc_cart(x, components=components) a_rad = np.dot(a_cart, trans) return a_rad def ader_cart(x, components=['bary', 'halo', 'dipole']): """""" dacart = np.empty((3,0)) dict_der = {'bary': [der_bulge, der_disk], 'halo': [der_nfw], 'dipole': [der_dipole], 'quad': [der_quad], 'point': [der_kepler]} derivatives = [] for c in components: derivatives += dict_der[c] for ader in derivatives: da_ = ader(x) dacart = np.hstack((dacart, da_)) return dacart def apder_cart(x, components=['bary', 'halo', 'dipole']): """""" dacart = np.empty((3,0)) dict_der = {'bary': [pder_bulge, pder_disk], 'halo': [pder_nfw], 'dipole': [pder_dipole], 'quad': [pder_quad], 'octu': [pder_octu], 'point': [pder_kepler]} derivatives = [] for c in components: derivatives += dict_der[c] for ader in derivatives: da_ = ader(x) dacart = np.hstack((dacart, da_)) return dacart def apder_rad(x, components=['bary', 'halo', 'dipole']): """Return dar/dx_pot (radial acceleration/potential parameters) evaluated at vector x""" r = np.linalg.norm(x) * x.unit theta = np.arccos(x[2].value/r.value) phi = np.arctan2(x[1].value, x[0].value) trans = np.array([np.sin(theta)*np.cos(phi), np.sin(theta)*np.sin(phi), np.cos(theta)]) dadq_cart = apder_cart(x, components=components) dadq_rad = np.einsum('ij,i->j', dadq_cart, trans) return dadq_rad def crb_acart(n, Ndim=6, vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], component='all', align=True, d=20, Nb=50, fast=False, scale=False, relative=True, progenitor=False, errmode='fiducial'): """""" pid, dp_fid, vlabel = get_varied_pars(vary) if align: alabel = '_align' else: alabel = '' if relative: vmin = 1e-2 vmax = 1 rlabel = ' / a' else: vmin = 3e-1 vmax = 1e1 rlabel = ' (pc Myr$^{-2}$)' # read in full inverse CRB for stream modeling cxi = np.load('../data/crb/bspline_cxi{:s}_{:s}_{:d}_{:s}_{:d}.npy'.format(alabel, errmode, n, vlabel, Ndim)) if fast: cx = np.linalg.inv(cxi) else: cx = stable_inverse(cxi) # choose the appropriate components: Nprog, Nbary, Nhalo, Ndipole, Npoint = [6, 5, 4, 3, 1] if 'progenitor' not in vary: Nprog = 0 nstart = {'bary': Nprog, 'halo': Nprog + Nbary, 'dipole': Nprog + Nbary + Nhalo, 'all': Nprog, 'point': 0} nend = {'bary': Nprog + Nbary, 'halo': Nprog + Nbary + Nhalo, 'dipole': Nprog + Nbary + Nhalo + Ndipole, 'all': np.shape(cx)[0], 'point': 1} if 'progenitor' not in vary: nstart['dipole'] = Npoint nend['dipole'] = Npoint + Ndipole if component in ['bary', 'halo', 'dipole', 'point']: components = [component] else: components = [x for x in vary if x!='progenitor'] cq = cx[nstart[component]:nend[component], nstart[component]:nend[component]] Npot = np.shape(cq)[0] if fast: cqi = np.linalg.inv(cq) else: cqi = stable_inverse(cq) if scale: dp_opt = read_optimal_step(n, vary) dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)] scale_vec = np.array([x.value for x in dp[nstart[component]:nend[component]]]) scale_mat = np.outer(scale_vec, scale_vec) cqi *= scale_mat if progenitor: x0, v0 = gd1_coordinates() else: x0 = np.array([4, 4, 0]) Rp = np.linalg.norm(x0[:2]) zp = x0[2] R = np.linspace(-d, d, Nb) k = x0[1]/x0[0] x = R/np.sqrt(1+k**2) y = k * x z = np.linspace(-d, d, Nb) xv, zv = np.meshgrid(x, z) yv, zv = np.meshgrid(y, z) xin = np.array([np.ravel(xv), np.ravel(yv), np.ravel(zv)]).T Npix = np.size(xv) af = np.empty((Npix, 3)) derf = np.empty((Npix, 3, Npot)) for i in range(Npix): xi = xin[i]*u.kpc a = acc_cart(xi, components=components) dadq = apder_cart(xi, components=components) derf[i] = dadq ca = np.matmul(dadq, np.matmul(cq, dadq.T)) a_crb = np.sqrt(np.diag(ca)) * u.pc * u.Myr**-2 if relative: af[i] = np.abs(a_crb/a) else: af[i] = a_crb #print(xi, a_crb) # save np.savez('../data/crb_acart{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}'.format(alabel, errmode, n, vlabel, component, Ndim, d, Nb, relative), acc=af, x=xin, der=derf) plt.close() fig, ax = plt.subplots(1, 3, figsize=(15, 5)) label = ['$\Delta$ $a_X$', '$\Delta$ $a_Y$', '$\Delta$ $a_Z$'] for i in range(3): plt.sca(ax[i]) im = plt.imshow(af[:,i].reshape(Nb, Nb), origin='lower', extent=[-d, d, -d, d], cmap=mpl.cm.gray, vmin=vmin, vmax=vmax, norm=mpl.colors.LogNorm()) if progenitor: plt.plot(Rp, zp, 'r*', ms=10) plt.xlabel('R (kpc)') plt.ylabel('Z (kpc)') divider = make_axes_locatable(plt.gca()) cax = divider.append_axes("right", size="3%", pad=0.1) plt.colorbar(im, cax=cax) plt.ylabel(label[i] + rlabel) plt.tight_layout() plt.savefig('../plots/crb_acc_cart{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}.png'.format(alabel, errmode, n, vlabel, component, Ndim, d, Nb, relative)) def crb_acart_cov(n, Ndim=6, vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], component='all', j=0, align=True, d=20, Nb=30, fast=False, scale=False, relative=True, progenitor=False, batch=False, errmode='fiducial'): """""" pid, dp_fid, vlabel = get_varied_pars(vary) if align: alabel = '_align' else: alabel = '' if relative: vmin = 1e-2 vmax = 1 rlabel = ' / a' else: vmin = -0.005 vmax = 0.005 #vmin = 1e-2 #vmax = 1e0 rlabel = ' (pc Myr$^{-2}$)' # read in full inverse CRB for stream modeling cxi = np.load('../data/crb/bspline_cxi{:s}_{:s}_{:d}_{:s}_{:d}.npy'.format(alabel, errmode, n, vlabel, Ndim)) if fast: cx = np.linalg.inv(cxi) else: cx = stable_inverse(cxi) # choose the appropriate components: Nprog, Nbary, Nhalo, Ndipole, Nquad, Npoint = [6, 5, 4, 3, 5, 1] if 'progenitor' not in vary: Nprog = 0 nstart = {'bary': Nprog, 'halo': Nprog + Nbary, 'dipole': Nprog + Nbary + Nhalo, 'quad': Nprog + Nbary + Nhalo + Ndipole, 'all': Nprog, 'point': 0} nend = {'bary': Nprog + Nbary, 'halo': Nprog + Nbary + Nhalo, 'dipole': Nprog + Nbary + Nhalo + Ndipole, 'quad': Nprog + Nbary + Nhalo + Ndipole + Nquad, 'all': np.shape(cx)[0], 'point': 1} if 'progenitor' not in vary: nstart['dipole'] = Npoint nend['dipole'] = Npoint + Ndipole if component in ['bary', 'halo', 'dipole', 'quad', 'point']: components = [component] else: components = [x for x in vary if x!='progenitor'] cq = cx[nstart[component]:nend[component], nstart[component]:nend[component]] Npot = np.shape(cq)[0] if fast: cqi = np.linalg.inv(cq) else: cqi = stable_inverse(cq) if scale: dp_opt = read_optimal_step(n, vary) dp = [x*y.unit for x,y in zip(dp_opt, dp_fid)] scale_vec = np.array([x.value for x in dp[nstart[component]:nend[component]]]) scale_mat = np.outer(scale_vec, scale_vec) cqi *= scale_mat if progenitor: prog_coords = {-1: gd1_coordinates(), -2: pal5_coordinates(), -3: tri_coordinates(), -4: atlas_coordinates()} x0, v0 = prog_coords[n] print(x0) else: x0 = np.array([4, 4, 0]) Rp = np.linalg.norm(x0[:2]) zp = x0[2] R = np.linspace(-d, d, Nb) k = x0[1]/x0[0] x = R/np.sqrt(1+k**2) y = k * x z = np.linspace(-d, d, Nb) xv, zv = np.meshgrid(x, z) yv, zv = np.meshgrid(y, z) xin = np.array([np.ravel(xv), np.ravel(yv), np.ravel(zv)]).T Npix = np.size(xv) af = np.empty((Npix, 3)) derf = np.empty((Npix*3, Npot)) for i in range(Npix): xi = xin[i]*u.kpc a = acc_cart(xi, components=components) dadq = apder_cart(xi, components=components) derf[i*3:(i+1)*3] = dadq ca = np.matmul(derf, np.matmul(cq, derf.T)) Nx = Npot Nw = Npix*3 vals, vecs = la.eigh(ca, eigvals=(Nw - Nx - 2, Nw - 1)) ## check orthogonality: #for i in range(Npot-1): #for k in range(i+1, Npot): #print(i, k) #print(np.dot(vecs[:,i], vecs[:,k])) #print(np.dot(vecs[::3,i], vecs[::3,k]), np.dot(vecs[1::3,i], vecs[1::3,k]), np.dot(vecs[1::3,i], vecs[1::3,k])) # save np.savez('../data/crb_acart_cov{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}_{:d}'.format(alabel, errmode, n, vlabel, component, Ndim, d, Nb, relative, progenitor), x=xin, der=derf, c=ca) plt.close() fig, ax = plt.subplots(1, 3, figsize=(15, 5)) if j==0: vcomb = np.sqrt(np.sum(vecs**2*vals, axis=1)) label = ['($\Sigma$ Eigval $\\times$ Eigvec$^2$ $a_{}$'.format(x)+')$^{1/2}$' for x in ['X', 'Y', 'Z']] vmin = 1e-2 vmax = 5e0 norm = mpl.colors.LogNorm() else: vcomb = vecs[:,j] label = ['Eig {} $a_{}$'.format(np.abs(j), x) for x in ['X', 'Y', 'Z']] vmin = -0.025 vmax = 0.025 norm = None for i in range(3): plt.sca(ax[i]) #im = plt.imshow(vecs[i::3,j].reshape(Nb, Nb), origin='lower', extent=[-d, d, -d, d], cmap=mpl.cm.gray, vmin=vmin, vmax=vmax) im = plt.imshow(vcomb[i::3].reshape(Nb, Nb), origin='lower', extent=[-d, d, -d, d], cmap=mpl.cm.gray, vmin=vmin, vmax=vmax, norm=norm) if progenitor: plt.plot(Rp, zp, 'r*', ms=10) plt.xlabel('R (kpc)') plt.ylabel('Z (kpc)') divider = make_axes_locatable(plt.gca()) cax = divider.append_axes("right", size="3%", pad=0.1) plt.colorbar(im, cax=cax) plt.ylabel(label[i]) plt.tight_layout() if batch: return fig else: plt.savefig('../plots/crb_acc_cart_cov{:s}_{:s}_{:d}_{:s}_{:s}_{:d}_{:d}_{:d}_{:d}_{:d}_{:d}.png'.format(alabel, errmode, n, vlabel, component, np.abs(j), Ndim, d, Nb, relative, progenitor)) def a_vecfield(vary=['progenitor', 'bary', 'halo', 'dipole', 'quad'], component='all', d=20, Nb=10): """Plot acceleration field in R,z plane""" if component in ['bary', 'halo', 'dipole', 'quad', 'point']: components = [component] else: components = [x for x in vary if x!='progenitor'] x0 = np.array([4, 4, 0]) R = np.linspace(-d, d, Nb) k = x0[1]/x0[0] x = R/np.sqrt(1+k**2) y = k * x z = np.linspace(-d, d, Nb) xv, zv = np.meshgrid(x, z) yv, zv = np.meshgrid(y, z) xin = np.array([np.ravel(xv), np.ravel(yv),

np.ravel(zv)

numpy.ravel

# Copyright 2019 Division of Medical Image Computing, German Cancer Research Center (DKFZ), Heidelberg, Germany # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. import argparse import numpy as np from batchgenerators.augmentations.utils import resize_segmentation from uuunet.experiment_planning.plan_and_preprocess_task import get_caseIDs_from_splitted_dataset_folder from uuunet.inference.segmentation_export import save_segmentation_nifti_from_softmax from batchgenerators.utilities.file_and_folder_operations import * from multiprocessing import Process, Queue import torch import threading import matplotlib import matplotlib.pyplot as plt import matplotlib.animation as animation from mpl_toolkits.mplot3d import Axes3D import SimpleITK as sitk import shutil from multiprocessing import Pool from uuunet.training.model_restore import load_model_and_checkpoint_files from uuunet.training.network_training.nnUNetTrainer import nnUNetTrainer from uuunet.utilities.one_hot_encoding import to_one_hot def plot_images(img, img2=None): """ Plot at most 2 images. Support passing in ndarray or image path string. """ fig = plt.figure(figsize=(20,10)) if isinstance(img, str): img = imread(img) if isinstance(img2, str): img2 = imread(img2) if img2 is None: ax = fig.add_subplot(111) ax.imshow(img) else: height, width = img.shape[0], img.shape[1] if height < width: ax = fig.add_subplot(211) ax2 = fig.add_subplot(212) else: ax = fig.add_subplot(121) ax2 = fig.add_subplot(122) ax.imshow(img) ax2.imshow(img2) plt.show() def view_batch(imgs, lbls, labels=['image', 'label'], stack=False): ''' imgs: [D, H, W, C], the depth or batch dimension should be the first. ''' fig = plt.figure() ax1 = fig.add_subplot(121) ax2 = fig.add_subplot(122) ax1.set_title(labels[0]) ax2.set_title(labels[1]) """ if init with zeros, the animation may not update? seems bug in animation. """ if stack: lbls = np.stack((lbls, imgs, imgs), -1) img1 = ax1.imshow(np.random.rand(*imgs.shape[1:])) img2 = ax2.imshow(np.random.rand(*lbls.shape[1:])) def update(i): plt.suptitle(str(i)) img1.set_data(imgs[i]) img2.set_data(lbls[i]) return img1, img2 ani = animation.FuncAnimation(fig, update, frames=len(imgs), interval=10, blit=False, repeat_delay=0) plt.show() def predict_save_to_queue(preprocess_fn, q, list_of_lists, output_files, segs_from_prev_stage, classes): errors_in = [] for i, l in enumerate(list_of_lists): try: output_file = output_files[i] print("preprocessing", output_file) d, _, dct = preprocess_fn(l) print(output_file, dct) if segs_from_prev_stage[i] is not None: assert isfile(segs_from_prev_stage[i]) and segs_from_prev_stage[i].endswith(".nii.gz"), "segs_from_prev_stage" \ " must point to a " \ "segmentation file" seg_prev = sitk.GetArrayFromImage(sitk.ReadImage(segs_from_prev_stage[i])) # check to see if shapes match img = sitk.GetArrayFromImage(sitk.ReadImage(l[0])) assert all([i == j for i, j in zip(seg_prev.shape, img.shape)]), "image and segmentation from previous " \ "stage don't have the same pixel array " \ "shape! image: %s, seg_prev: %s" % \ (l[0], segs_from_prev_stage[i]) seg_reshaped = resize_segmentation(seg_prev, d.shape[1:], order=1, cval=0) seg_reshaped = to_one_hot(seg_reshaped, classes) d = np.vstack((d, seg_reshaped)).astype(np.float32) """There is a problem with python process communication that prevents us from communicating obejcts larger than 2 GB between processes (basically when the length of the pickle string that will be sent is communicated by the multiprocessing.Pipe object then the placeholder (\%i I think) does not allow for long enough strings (lol). This could be fixed by changing i to l (for long) but that would require manually patching system python code. We circumvent that problem here by saving softmax_pred to a npy file that will then be read (and finally deleted) by the Process. save_segmentation_nifti_from_softmax can take either filename or np.ndarray and will handle this automatically""" print(d.shape) if np.prod(d.shape) > (2e9 / 4 * 0.9): # *0.9 just to be save, 4 because float32 is 4 bytes print( "This output is too large for python process-process communication. " "Saving output temporarily to disk") np.save(output_file[:-7] + ".npy", d) d = output_file[:-7] + ".npy" q.put((output_file, (d, dct))) except KeyboardInterrupt: raise KeyboardInterrupt except Exception as e: print("error in", l) print(e) q.put("end") if len(errors_in) > 0: print("There were some errors in the following cases:", errors_in) print("These cases were ignored.") else: print("This worker has ended successfully, no errors to report") def preprocess_multithreaded(trainer, list_of_lists, output_files, num_processes=2, segs_from_prev_stage=None): if segs_from_prev_stage is None: segs_from_prev_stage = [None] * len(list_of_lists) classes = list(range(1, trainer.num_classes)) assert isinstance(trainer, nnUNetTrainer) q = Queue(1) processes = [] for i in range(num_processes): pr = Process(target=predict_save_to_queue, args=(trainer.preprocess_patient, q, list_of_lists[i::num_processes], output_files[i::num_processes], segs_from_prev_stage[i::num_processes], classes)) pr.start() processes.append(pr) try: end_ctr = 0 while end_ctr != num_processes: item = q.get() if item == "end": end_ctr += 1 continue else: yield item finally: for p in processes: if p.is_alive(): p.terminate() # this should not happen but better safe than sorry right p.join() q.close() def predict_cases(model, list_of_lists, output_filenames, folds, save_npz, num_threads_preprocessing, num_threads_nifti_save, segs_from_prev_stage=None, do_tta=True, overwrite_existing=False, data_type='2d', modality=0): assert len(list_of_lists) == len(output_filenames) if segs_from_prev_stage is not None: assert len(segs_from_prev_stage) == len(output_filenames) prman = Pool(num_threads_nifti_save) results = [] cleaned_output_files = [] for o in output_filenames: dr, f = os.path.split(o) if len(dr) > 0: maybe_mkdir_p(dr) if not f.endswith(".nii.gz"): f, _ = os.path.splitext(f) f = f + ".nii.gz" cleaned_output_files.append(join(dr, f)) if not overwrite_existing: print("number of cases:", len(list_of_lists)) not_done_idx = [i for i, j in enumerate(cleaned_output_files) if not isfile(j)] cleaned_output_files = [cleaned_output_files[i] for i in not_done_idx] list_of_lists = [list_of_lists[i] for i in not_done_idx] if segs_from_prev_stage is not None: segs_from_prev_stage = [segs_from_prev_stage[i] for i in not_done_idx] print("number of cases that still need to be predicted:", len(cleaned_output_files)) print("emptying cuda cache") torch.cuda.empty_cache() ################################## # Damn, finally find the model. print("loading parameters for folds,", folds) trainer, params = load_model_and_checkpoint_files(model, folds) trainer.modality = modality print("starting preprocessing generator") preprocessing = preprocess_multithreaded(trainer, list_of_lists, cleaned_output_files, num_threads_preprocessing, segs_from_prev_stage) print("starting prediction...") for preprocessed in preprocessing: output_filename, (d, dct) = preprocessed if isinstance(d, str): data = np.load(d) os.remove(d) d = data print("predicting", output_filename) softmax = [] for p in params: trainer.load_checkpoint_ram(p, False) softmax.append(trainer.predict_preprocessed_data_return_softmax(d, do_tta, 1, False, 1, trainer.data_aug_params['mirror_axes'], True, True, 2, trainer.patch_size, True, data_type=data_type)[None]) softmax =

np.vstack(softmax)

numpy.vstack

import numpy as np import matplotlib.pyplot as plt from os import makedirs from os.path import isfile, exists from scipy.constants import mu_0 # from numba import njit def calcDipolMomentAnalytical(remanence, volume): """ Calculating the magnetic moment from the remanence in T and the volume in m^3""" m = remanence * volume / mu_0 # [A * m^2] return m def plotSimple(data, FOV, fig, ax, cbar=True, **args): """ Generate simple colorcoded plot of 2D grid data with contour. Returns axes object.""" im = ax.imshow(data, extent=FOV, origin="lower", **args) cs = ax.contour(data, colors="k", extent=FOV, origin="lower", linestyles="dotted") class nf(float): def __repr__(self): s = f"{self:.1f}" return f"{self:.0f}" if s[-1] == "0" else s cs.levels = [nf(val) for val in cs.levels] if plt.rcParams["text.usetex"]: fmt = r"%r" else: fmt = "%r" ax.clabel(cs, cs.levels, inline=True, fmt=fmt, fontsize=10) if cbar == True: fig.colorbar(im, ax=ax) return im def centerCut(field, axis): """return a slice of the data at the center for the specified axis""" dims = np.shape(field) return np.take(field, indices=int(dims[axis] / 2), axis=axis) def isHarmonic(field, sphericalMask, shellMask): """Checks if the extrema of the field are in the shell.""" fullField = np.multiply(field, sphericalMask) # [T] reducedField = np.multiply(field, shellMask) if int(ptpPPM(fullField)) > int(ptpPPM(reducedField)): print( "ptpPPM of field:", ptpPPM(fullField), "ptpPPM on surface", ptpPPM(reducedField), ) print("Masked field is NOT a harmonic function...") return False else: print( "ptpPPM of field:", ptpPPM(fullField), "ptpPPM on surface", ptpPPM(reducedField), ) print("Masked field is harmonic.") sizeSpherical = int(np.nansum(sphericalMask)) sizeShell = int(np.nansum(shellMask)) print( "Reduced size of field from {} to {} ({}%)".format( sizeSpherical, sizeShell, int(100 * sizeShell / sizeSpherical) ) ) return True def genQmesh(field, resolution): """Generate a mesh of quadratic coordinates""" mask = np.zeros(np.shape(field)) xAxis = np.linspace( -(np.size(field, 0) - 1) * resolution / 2, (np.size(field, 0) - 1) * resolution / 2, np.size(field, 0), ) yAxis = np.linspace( -(np.size(field, 1) - 1) * resolution / 2, (np.size(field, 1) - 1) * resolution / 2, np.size(field, 1), ) zAxis = np.linspace( -(np.size(field, 2) - 1) * resolution / 2, (np.size(field, 2) - 1) * resolution / 2, np.size(field, 2), ) xAxis, yAxis, zAxis = np.meshgrid(xAxis, yAxis, zAxis) xAxisSquare = np.square(xAxis) yAxisSquare = np.square(yAxis) zAxisSquare = np.square(zAxis) return mask, xAxisSquare, yAxisSquare, zAxisSquare def genMask( field, resolution, diameter=False, shellThickness=False, axis=False, debug=False ): """Generate a mask for a spherical shell""" mask, xAxisSquare, yAxisSquare, zAxisSquare = genQmesh(field, resolution) if (shellThickness != False) and (diameter != False): if debug == True: print( "Creating shell mask. (resolution = {}, diameter = {}, shellThickness = {})".format( resolution, diameter, shellThickness ) ) print("The shell is added inside the sphere surface!") rAxisSquare = xAxisSquare + yAxisSquare + zAxisSquare innerRadiusSquare = (diameter / 2 - shellThickness) ** 2 outerRadiusSquare = (diameter / 2) ** 2 mask[ (rAxisSquare <= outerRadiusSquare) & (rAxisSquare >= innerRadiusSquare) ] = 1 mask[mask == 0] = "NaN" return mask def genSphericalMask(field, diameter, resolution): """generate spherical mask with >>diameter<< for a >>field<< and a given >>resolution<< """ mask, xAxisSquare, yAxisSquare, zAxisSquare = genQmesh(field, resolution) mask[xAxisSquare + yAxisSquare + zAxisSquare <= (diameter / 2) ** 2] = 1 mask[mask == 0] = "NaN" return mask def genSliceMask(field, diameter, resolution, axis="x"): """generate mask for a circular slice with >>diameter<< for a >>field<< and a given >>resolution<< Every input variable has to have the same unit (mm or m or ...) """ mask, xAxisSquare, yAxisSquare, zAxisSquare = genQmesh(field, resolution) if axis == "z": mask[ (xAxisSquare + yAxisSquare <= (diameter / 2) ** 2) & (zAxisSquare == 0) ] = 1 if axis == "y": mask[ (xAxisSquare + zAxisSquare <= (diameter / 2) ** 2) & (yAxisSquare == 0) ] = 1 if axis == "x": mask[ (yAxisSquare + zAxisSquare <= (diameter / 2) ** 2) & (xAxisSquare == 0) ] = 1 mask[mask == 0] = "NaN" return mask def genEllipseSliceMask(field, a, b, resolution, axis="x"): """generate mask for a circulat slice with >>diameter<< for a >>field<< and a given >>resolution<< Every input variable has to have the same unit (mm or m or ...) """ # generate spherical mask mask, xAxisSquare, yAxisSquare, zAxisSquare = genQmesh(field, resolution) if axis == "z": mask[ (xAxisSquare / (a / 2) ** 2 + yAxisSquare / (b / 2) ** 2 <= 1) & (zAxisSquare == 0) ] = 1 elif axis == "y": mask[ (xAxisSquare / (a / 2) ** 2 + zAxisSquare / (b / 2) ** 2 <= 1) & (yAxisSquare == 0) ] = 1 elif axis == "x": mask[ (yAxisSquare / (a / 2) ** 2 + zAxisSquare / (b / 2) ** 2 <= 1) & (xAxisSquare == 0) ] = 1 mask[mask == 0] = "NaN" return mask def ptpPPM(field): """Calculate the peak-to-peak homogeneity in ppm.""" return 1e6 * (np.nanmax(field) - np.nanmin(field)) / np.nanmean(field) def saveParameters(parameters, folder): """Saving a dict to the file parameters.npy . If the file exist it is beeing updated, if the parameters are not stored already. __future__: Fix usecase: Some parameters are in dict which are identical to the stored ones and some are new! """ try: print("Saving parameters to file...", end=" ") print("\x1b[6;30;42m", *parameters.keys(), "\x1b[0m", end=" ") oldParameters = loadParameters(folder) if parameters.items() <= oldParameters.items(): print(" ... the parameters are already saved and identical.") elif set(parameters).issubset( set(oldParameters) ): # here just keys are compared! print( " ...\x1b[6;37;41m" + " parameters are NOT saved. Other parameters are stored. Please cleanup! " + "\x1b[0m" ) else: oldParameters.update(parameters) np.save(folder + "/parameters", oldParameters) print(" ... added.") except FileNotFoundError or AttributeError: np.save(folder + "/parameters", parameters) oldParameters = parameters # print('The following parameters are currently stored:\n', *oldParameters.keys()) def loadParameters(folder): return np.load(folder + "/parameters.npy", allow_pickle=True).item() def loadParameter(key, folder): return loadParameters(folder)[key] def displayParameters(folder): print(loadParameters(folder)) def createShimfieldsShimRingV2( numMagnets=(32, 44), rings=4, radii=(0.074, 0.097), zRange=(-0.08, -0.039, 0.039, 0.08), resolution=1000, kValue=2, simDimensions=(0.04, 0.04, 0.04), numRotations=2, ): """ Calculating the magnetic field distributions for a single or multiple Halbach Rings. This has to be multiplied with the magnetic moment amplitude of a magnet to get the real distribution For every magnet position we set 4 different rotations: 0°, 45°, 90°, 135°. This has to be considered in the cost function otherwise two magnets are placed in one position resolution is the amount of sample points times data points in one dimension """ mu = mu_0 # positioning of the magnets in a circle if len(zRange) == 2: rings = np.linspace(zRange[0], zRange[1], rings) elif rings == len(zRange): rings = np.array(zRange) else: print("No clear definition how to place shims...") rotation_elements = np.linspace(0, np.pi, numRotations, endpoint=False) # create array to store field data count = 0 if type(numMagnets) in (list, tuple): totalNumMagnets = np.sum(numMagnets) * np.size(rings) * numRotations else: totalNumMagnets = numMagnets * np.size(rings) * numRotations * len(radii) print(totalNumMagnets, numMagnets, np.size(rings), np.size(numRotations)) shimFields = np.zeros( ( int(simDimensions[0] * resolution) + 1, int(simDimensions[1] * resolution) + 1, int(simDimensions[2] * resolution) + 1, 3, totalNumMagnets, ), dtype=np.float32, ) for rotation in rotation_elements: # create halbach array for row in rings: for i, radius in enumerate(radii): angle_elements = np.linspace( -np.pi, np.pi, numMagnets[i], endpoint=False ) for angle in angle_elements: print( "Simulating magnet " + str(count + 1) + " of " + str(totalNumMagnets), end="\t", ) position = (row, radius * np.cos(angle), radius * np.sin(angle)) print( "@ position {:2.2},\t {:2.2},\t {:2.2}".format(*position), end="\r", ) angle = kValue * angle + rotation dip_vec = [0, np.sin(angle), -np.cos(angle)] dip_vec = np.multiply(dip_vec, mu) dip_vec = np.divide(dip_vec, 4 * np.pi) # create mesh coordinates x = np.linspace( -simDimensions[0] / 2 + position[0], simDimensions[0] / 2 + position[0], int(simDimensions[0] * resolution) + 1, dtype=np.float32, ) y = np.linspace( -simDimensions[1] / 2 + position[1], simDimensions[1] / 2 + position[1], int(simDimensions[1] * resolution) + 1, dtype=np.float32, ) z = np.linspace( -simDimensions[2] / 2 + position[2], simDimensions[2] / 2 + position[2], int(simDimensions[2] * resolution) + 1, dtype=np.float32, ) x, y, z = np.meshgrid(x, y, z) vec_dot_dip = 3 * (y * dip_vec[1] + z * dip_vec[2]) # calculate the distance of each mesh point to magnet, optimised for speed # for improved memory performance move in to b0 calculations vec_mag = np.square(x) + np.square(y) + np.square(z) # if the magnet is in the origin, we divide by 0, therefore we set it to nan to # avoid getting and error. if this has any effect on speed just leave it out # as we do not care about the values outside of the FOV and even less inside the magnets vec_mag[(vec_mag <= 1e-15) & (vec_mag >= -1e-15)] = "NaN" vec_mag_3 = np.power(vec_mag, 1.5) vec_mag_5 = np.power(vec_mag, 2.5) del vec_mag # calculate contributions of magnet to total field, dipole always points in yz plane # so second term is zero for the x component shimFields[:, :, :, 0, count] = np.divide( np.multiply(x, vec_dot_dip), vec_mag_5 ) shimFields[:, :, :, 1, count] = np.divide( np.multiply(y, vec_dot_dip), vec_mag_5 ) - np.divide(dip_vec[1], vec_mag_3) shimFields[:, :, :, 2, count] = np.divide(

np.multiply(z, vec_dot_dip)

numpy.multiply

import numpy as np import pandas as pd import plotly.graph_objects as go import toolsClass import multiprocessing import time from scipy.interpolate import interp1d import scipy.integrate as integrate #from tqdm.contrib.concurrent import process_map #for process bar. very slow... tools = toolsClass.tools() import logging log = logging.getLogger(__name__) class GYRO: def __init__(self, rootDir, dataPath): """ rootDir is root location of python modules (where dashGUI.py lives) dataPath is the location where we write all output to """ self.rootDir = rootDir tools.rootDir = self.rootDir self.dataPath = dataPath tools.dataPath = self.dataPath return def allowed_class_vars(self): """ Writes a list of recognized class variables to HEAT object Used for error checking input files and for initialization Here is a list of variables with description: testvar dummy for testing """ self.allowed_vars = [ 'N_gyroSteps', 'gyroDeg', 'gyroT_eV', 'N_vSlice', 'N_vPhase', 'N_gyroPhase', 'ionMassAMU', 'vMode', 'ionFrac' ] return def setTypes(self): """ Set variable types for the stuff that isnt a string from the input file """ integers = [ 'N_gyroSteps', 'gyroDeg', 'N_vSlice', 'N_vPhase', 'N_gyroPhase', ] floats = [ 'ionFrac', 'gyroT_eV', 'ionMassAMU', ] for var in integers: if (getattr(self, var) is not None) and (~np.isnan(float(getattr(self, var)))): try: setattr(self, var, int(getattr(self, var))) except: print("Error with input file var "+var+". Perhaps you have invalid input values?") log.info("Error with input file var "+var+". Perhaps you have invalid input values?") for var in floats: if var is not None: if (getattr(self, var) is not None) and (~np.isnan(float(getattr(self, var)))): try: setattr(self, var, float(getattr(self, var))) except: print("Error with input file var "+var+". Perhaps you have invalid input values?") log.info("Error with input file var "+var+". Perhaps you have invalid input values?") return def setupConstants(self, ionMassAMU=2.014): """ Sets up constants default mass is deuterium 2.014 MeV/c^2 """ #unit conversions self.kg2eV = 5.609e35 #1kg = 5.609e35 eV/c^2 self.eV2K = 1.160e4 #1ev=1.160e4 K #constants self.AMU = 931.494e6 #ev/c^2 self.kB = 8.617e-5 #ev/K self.e = 1.602e-19 # C self.c = 299792458 #m/s self.diamag = -1 #diamagnetism = -1 for ions, 1 for electrons self.mass_eV = ionMassAMU * self.AMU self.Z=1 #assuming isotopes of hydrogen here return def temp2thermalVelocity(self, T_eV): """ Calculates thermal velocity from a temperature, where thermal velocity is defined as the most probable speed T_eV is temperature in eV can also be found with: d/dv( v*f(v) ) = 0 note that this is for v, not vPerp or v|| """ return np.sqrt(2.0*T_eV/(self.mass_eV/self.c**2)) def setupFreqs(self, B): """ Calculates frequencies, periods, that are dependent upon B These definitions follow Freidberg Section 7.7. B is magnetic field magnitude """ self.omegaGyro = self.Z * self.e * B / (self.mass_eV / self.kg2eV) if np.isscalar(self.omegaGyro): self.omegaGyro = np.array([self.omegaGyro]) self.fGyro = np.abs(self.omegaGyro)/(2*np.pi) self.TGyro = 1.0/self.fGyro return def setupRadius(self, vPerp): """ calculates gyro radius. rGyro has a column for each MC run (N_MC columns), and a row for each point on the PFC (N_pts), so it is a matrix of shape: N_pts X N_MC """ N_pts = len(self.omegaGyro) #get number of vPerps if np.isscalar(vPerp): vPerp = np.array([vPerp]) N_MC = 1 else: N_MC = len(vPerp) self.rGyro = np.zeros((N_pts,N_MC)) for i in range(N_MC): self.rGyro[:,i] = vPerp[i] / np.abs(self.omegaGyro) return def setupVelocities(self, N): """ sets up velocities based upon vMode input from GUI N is the number of source mesh elements (ie len(PFC.centers) ) len(self.t1) is number of points in divertor we are calculating HF on """ #get velocity space phase angles self.uniformVelPhaseAngle() if self.vMode == 'single': print("Gyro orbit calculation from single plasma temperature") log.info("Gyro orbit calculation from single plasma temperature") self.T0 = np.ones((N))*self.gyroT_eV #get average velocity for each temperature point self.vThermal = self.temp2thermalVelocity(self.T0) #set upper bound of v*f(v) (note that this cuts off high energy particles) self.vMax = 5 * self.vThermal #get 100 points to initialize functional form of f(v) (note this is a 2D matrix cause vMax is 2D) self.vScan = np.linspace(0,self.vMax,10000).T #get velocity slices for each T0 self.pullEqualProbabilityVelocities() else: #TO ADD THIS YOU WILL NEED TO PASS IN XYZ COORDINATES OF CTRS AND INTERPOLATE print("3D plasma temperature interpolation from file not yet supported. Run gyro orbits in single mode") log.info("3D plasma temperature interpolation from file not yet supported. Run gyro orbits in single mode") return def pullEqualProbabilityVelocities(self): """ creates vSlices: array of velocities indexed to match T0 array (or PFC.centers) each vSlice is positioned at a place in the PDF so it has an equal probability of occuring. ie the area under the PDF curve between each vSlice is equal. in loop, i is mesh element index """ self.vSlices = np.ones((len(self.T0),self.N_vSlice))*np.nan self.energySlices = np.zeros((len(self.T0),self.N_vSlice)) self.energyIntegrals = np.zeros((len(self.T0),self.N_vSlice)) self.energyFracs = np.zeros((len(self.T0),self.N_vSlice)) self.vBounds = np.zeros((len(self.T0),self.N_vSlice+1)) for i in range(len(self.T0)): #get speed range for this T0 v = self.vScan[i,:] #generate the (here maxwellian) velocity vector PDF #pdf = lambda x: (self.mass_eV/self.c**2) / (self.T0[i]) * np.exp(-(self.mass_eV/self.c**2 * x**2) / (2*self.T0[i]) ) pdf = lambda x: ( (self.mass_eV/self.c**2) / (2 * np.pi * self.T0[i]) )**(3.0/2.0) * np.exp(-(self.mass_eV/self.c**2 * x**2) / (2*self.T0[i]) ) #speed pdf (integrate over solid angle) v_pdf = 4*np.pi * v**2 * pdf(v) #generate the CDF v_cdf = np.cumsum(v_pdf[1:])*np.diff(v) v_cdf = np.insert(v_cdf, 0, 0) #create bspline interpolators for the cdf and cdf inverse inverseCDF = interp1d(v_cdf, v, kind='linear') forwardCDF = interp1d(v, v_cdf, kind='linear') #CDF location of vSlices and bin boundaries cdfBounds = np.linspace(0,v_cdf[-1],self.N_vSlice+1) #CDF location of velocity bin bounds omitting 0 and 1 #old method does not make vSlices truly bin centers #cdfBounds = np.linspace(0,1,self.N_vSlice+1)[1:-1] #old method 2 spaces centers uniformly # #calculate N_vSlice velocities for each pdf each with equal area (probability) # cdfMax = v_cdf[-1] # cdfMin = v_cdf[0] # sliceWidth = cdfMax / (self.N_vSlice+1) # #CDF location of vSlices omitting 0 and 1 # cdfSlices = np.linspace(0,1,self.N_vSlice+2)[1:-1] # #CDF location of velocity bin bounds omitting 0 and 1 # #old method does not make vSlices truly bin centers # #cdfBounds = np.linspace(0,1,self.N_vSlice+1)[1:-1] # #new method makes vSlices bin centers, except for the end bins # cdfBounds = np.diff(cdfSlices)/2.0 + cdfSlices[:-1] # #vSlices are Maxwellian distribution sample locations (@ bin centers) # self.vSlices[i,:] = inverseCDF(cdfSlices) # vBounds = inverseCDF(cdfBounds) # vBounds = np.insert(vBounds,0,0) # vBounds = np.append(vBounds,self.vMax[i]) #new method spaces bins uniformly, then makes vSlices center of these bins in CDF space cdfSlices = np.diff(cdfBounds)/2.0 + cdfBounds[:-1] #vSlices are Maxwellian distribution sample locations (@ bin centers) self.vSlices[i,:] = inverseCDF(cdfSlices) vBounds = inverseCDF(cdfBounds) self.vBounds[i,:] = vBounds #print(cdfBounds) #print(cdfSlices) #print(self.vBounds) #print(self.vSlices) #Now find energies that correspond to these vSlices #we integrate: v**2 * f(v) #energy pdf (missing 1/2*mass but that gets divided out later anyways ) #EofV = lambda x: x**2 * pdf(x) #EofV = lambda x: 4*np.pi * x**4 * pdf(x) f_E = lambda x: 2 * np.sqrt(x / np.pi) * (self.T0[i])**(-3.0/2.0) * np.exp(-x / self.T0[i]) #energy slices that correspond to velocity slices self.energySlices[i,:] = f_E(0.5 * (self.mass_eV/self.c**2) * self.vSlices[i,:]**2) #energy integrals for j in range(self.N_vSlice): Elo = 0.5 * (self.mass_eV/self.c**2) * vBounds[j]**2 Ehi = 0.5 * (self.mass_eV/self.c**2) * vBounds[j+1]**2 self.energyIntegrals[i,j] = integrate.quad(f_E, Elo, Ehi)[0] energyTotal = self.energyIntegrals[i,:].sum() #for testing #if i==0: # print("Integral Test===") # print(energyTotal) # print(integrate.quad(f_E, 0.0, self.vMax[i])[0]) #energy fractions for j in range(self.N_vSlice): self.energyFracs[i,j] = self.energyIntegrals[i,j] / energyTotal print("Found N_vPhase velocities of equal probability") log.info("Found N_vPhase velocities of equal probability") return def uniformGyroPhaseAngle(self): """ Uniform sampling of a uniform distribution between 0 and 2pi returns angles in radians """ self.gyroPhases = np.linspace(0,2*np.pi,self.N_gyroPhase+1)[:-1] return def uniformVelPhaseAngle(self): """ Sampling of a uniform distribution between 0 and pi/2 (only forward velocities) vPerp is x-axis of velocity space vParallel is y-axis of velocity space returns angles in radians """ self.vPhases = np.linspace(0.0,np.pi/2,self.N_vPhase+2)[1:-1] return def singleGyroTrace(self,vPerp,vParallel,gyroPhase,N_gyroSteps, BtraceXYZ,controlfilePath,TGyro,rGyro,omegaGyro, verbose=True): """ Calculates the gyro-Orbit path and saves to .csv and .vtk vPerp and vParallel [m/s] are in velocities gyroPhase [degrees] is initial orbit phase angle N_gyroSteps is number of discrete line segments per gyro period BtraceXYZ is the points of the Bfield trace that we will gyrate about """ print("Calculating gyro trace...") #Loop thru B field trace while tracing gyro orbit helixTrace = None for i in range(len(BtraceXYZ)-1): #points in this iteration p0 = BtraceXYZ[i,:] p1 = BtraceXYZ[i+1,:] #vector delP = p1 - p0 #magnitude or length of line segment magP = np.sqrt(delP[0]**2 + delP[1]**2 + delP[2]**2) #time it takes to transit line segment delta_t = magP / (vParallel) #Number of steps in line segment Tsample = self.TGyro / N_gyroSteps Nsteps = int(delta_t / Tsample) #length (in time) along guiding center t = np.linspace(0,delta_t,Nsteps+1) #guiding center location xGC = np.linspace(p0[0],p1[0],Nsteps+1) yGC = np.linspace(p0[1],p1[1],Nsteps+1) zGC = np.linspace(p0[2],p1[2],Nsteps+1) # construct orthogonal system for coordinate transformation w = delP if np.all(w==[0,0,1]): u = np.cross(w,[0,1,0]) #prevent failure if bhat = [0,0,1] else: u = np.cross(w,[0,0,1]) #this would fail if bhat = [0,0,1] (rare) v = np.cross(w,u) #normalize u = u / np.sqrt(u.dot(u)) v = v / np.sqrt(v.dot(v)) w = w / np.sqrt(w.dot(w)) xfm = np.vstack([u,v,w]).T #get helix path along (proxy) z axis reference frame x_helix = self.rGyro*np.cos(self.omegaGyro*t + gyroPhase) y_helix = self.diamag*self.rGyro*np.sin(self.omegaGyro*t + gyroPhase) z_helix = np.zeros((len(t))) #perform rotation to field line reference frame helix = np.vstack([x_helix,y_helix,z_helix]).T helix_rot = np.zeros((len(helix),3)) for j,coord in enumerate(helix): helix_rot[j,:] = helix[j,0]*u + helix[j,1]*v + helix[j,2]*w #perform translation to field line reference frame helix_rot[:,0] += xGC helix_rot[:,1] += yGC helix_rot[:,2] += zGC #update gyroPhase variable so next iteration starts here gyroPhase = self.omegaGyro*t[-1] + gyroPhase #append to helix trace if helixTrace is None: helixTrace = helix_rot else: helixTrace = np.vstack([helixTrace,helix_rot]) helixTrace*=1000.0 #scale for ParaView print("Saving data to CSV and VTK formats") #save data to csv format head = 'X[mm],Y[mm],Z[mm]' np.savetxt(controlfilePath+'helix.csv', helixTrace, delimiter=',', header=head) #save data to vtk format tools.createVTKOutput(controlfilePath+'helix.csv', 'trace', 'Gyro_trace') if verbose==True: print("V_perp = {:f} [m/s]".format(vPerp)) print("V_parallel = {:f} [m/s]".format(vParallel)) print("Cyclotron Freq = {:f} [rad/s]".format(self.omegaGyro[0])) print("Cyclotron Freq = {:f} [Hz]".format(self.fGyro[0])) print("Gyro Radius = {:f} [m]".format(self.rGyro[0][0])) print("Number of gyro points = {:f}".format(len(helixTrace))) print("Longitudinal dist between gyro points = {:f} [m]".format(magP/float(Nsteps))) print("Each line segment length ~ {:f} [m]".format(magP)) return def gyroTraceParallel(self, i, mode='MT'): """ parallelized gyro trace. called by multiprocessing.pool.map() i is index of parallel run from multiprocessing, corresponds to a mesh face we are tracing in the ROI writes helical trace to self.helixTrace[i] in 2D matrix format: columns = X,Y,Z rows = steps up helical trace also updates self.lastPhase for use in next iteration step mode options are: -Signed Volume Loop: 'SigVolLoop' -Signed Volume Matrix: 'SigVolMat' -Moller-Trumbore Algorithm: 'MT' """ #vector delP = self.p1[i] - self.p0[i] #magnitude magP = np.sqrt(delP[0]**2 + delP[1]**2 + delP[2]**2) #time it takes to transit line segment delta_t = magP / (self.vParallelMC[self.GYRO_HLXmap][i]) #Number of steps in line segment Tsample = self.TGyro[self.GYRO_HLXmap][i] / self.N_gyroSteps Nsteps = int(delta_t / Tsample) #length (in time) along guiding center t = np.linspace(0,delta_t,Nsteps+1) #guiding center location xGC = np.linspace(self.p0[i,0],self.p1[i,0],Nsteps+1) yGC = np.linspace(self.p0[i,1],self.p1[i,1],Nsteps+1) zGC = np.linspace(self.p0[i,2],self.p1[i,2],Nsteps+1) arrGC = np.vstack([xGC,yGC,zGC]).T # construct orthogonal system for coordinate transformation w = delP if np.all(w==[0,0,1]): u = np.cross(w,[0,1,0]) #prevent failure if bhat = [0,0,1] else: u = np.cross(w,[0,0,1]) #this would fail if bhat = [0,0,1] (rare) v = np.cross(w,u) #normalize u = u / np.sqrt(u.dot(u)) v = v / np.sqrt(v.dot(v)) w = w / np.sqrt(w.dot(w)) xfm = np.vstack([u,v,w]).T #get helix path along (proxy) z axis reference frame rGyro = self.rGyroMC[self.GYRO_HLXmap][i] omega = self.omegaGyro[self.GYRO_HLXmap][i] theta = self.lastPhase[self.GYRO_HLXmap][i] x_helix = rGyro*np.cos(omega*t + theta) y_helix = self.diamag*rGyro*

np.sin(omega*t + theta)

numpy.sin

""" This module contains the BinMapper class. BinMapper is used for mapping a real-valued dataset into integer-valued bins. Bin thresholds are computed with the quantiles so that each bin contains approximately the same number of samples. """ # Author: <NAME> import numpy as np from ...utils import check_random_state, check_array from ...base import BaseEstimator, TransformerMixin from ...utils.validation import check_is_fitted from ._binning import _map_to_bins from .types import X_DTYPE, X_BINNED_DTYPE def _find_binning_thresholds(data, max_bins, subsample, random_state): """Extract feature-wise quantiles from numerical data. Parameters ---------- data : array-like, shape (n_samples, n_features) The data to bin. max_bins : int The maximum number of bins to use. If for a given feature the number of unique values is less than ``max_bins``, then those unique values will be used to compute the bin thresholds, instead of the quantiles. subsample : int or None If ``n_samples > subsample``, then ``sub_samples`` samples will be randomly choosen to compute the quantiles. If ``None``, the whole data is used. random_state: int or numpy.random.RandomState or None Pseudo-random number generator to control the random sub-sampling. See :term:`random_state`. Return ------ binning_thresholds: list of arrays For each feature, stores the increasing numeric values that can be used to separate the bins. Thus ``len(binning_thresholds) == n_features``. """ if not (2 <= max_bins <= 256): raise ValueError('max_bins={} should be no smaller than 2 ' 'and no larger than 256.'.format(max_bins)) rng = check_random_state(random_state) if subsample is not None and data.shape[0] > subsample: subset = rng.choice(

np.arange(data.shape[0])

numpy.arange

import os import tempfile import numpy as np import scipy.ndimage.measurements as meas from functools import reduce import warnings import sys sys.path.append(os.path.abspath(r'../lib')) import NumCppPy as NumCpp # noqa E402 #################################################################################### def factors(n): return set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))) #################################################################################### def test_seed():

np.random.seed(1)

numpy.random.seed

# This module has been generated automatically from space group information # obtained from the Computational Crystallography Toolbox # """ Space groups This module contains a list of all the 230 space groups that can occur in a crystal. The variable space_groups contains a dictionary that maps space group numbers and space group names to the corresponding space group objects. .. moduleauthor:: <NAME> <<EMAIL>> """ #----------------------------------------------------------------------------- # Copyright (C) 2013 The Mosaic Development Team # # Distributed under the terms of the BSD License. The full license is in # the file LICENSE.txt, distributed as part of this software. #----------------------------------------------------------------------------- import numpy as N class SpaceGroup(object): """ Space group All possible space group objects are created in this module. Other modules should access these objects through the dictionary space_groups rather than create their own space group objects. """ def __init__(self, number, symbol, transformations): """ :param number: the number assigned to the space group by international convention :type number: int :param symbol: the Hermann-Mauguin space-group symbol as used in PDB and mmCIF files :type symbol: str :param transformations: a list of space group transformations, each consisting of a tuple of three integer arrays (rot, tn, td), where rot is the rotation matrix and tn/td are the numerator and denominator of the translation vector. The transformations are defined in fractional coordinates. :type transformations: list """ self.number = number self.symbol = symbol self.transformations = transformations self.transposed_rotations = N.array([N.transpose(t[0]) for t in transformations]) self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2] for t in transformations])) def __repr__(self): return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol)) def __len__(self): """ :return: the number of space group transformations :rtype: int """ return len(self.transformations) def symmetryEquivalentMillerIndices(self, hkl): """ :param hkl: a set of Miller indices :type hkl: Scientific.N.array_type :return: a tuple (miller_indices, phase_factor) of two arrays of length equal to the number of space group transformations. miller_indices contains the Miller indices of each reflection equivalent by symmetry to the reflection hkl (including hkl itself as the first element). phase_factor contains the phase factors that must be applied to the structure factor of reflection hkl to obtain the structure factor of the symmetry equivalent reflection. :rtype: tuple """ hkls = N.dot(self.transposed_rotations, hkl) p = N.multiply.reduce(self.phase_factors**hkl, -1) return hkls, p space_groups = {} transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(1, 'P 1', transformations) space_groups[1] = sg space_groups['P 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(2, 'P -1', transformations) space_groups[2] = sg space_groups['P -1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(3, 'P 1 2 1', transformations) space_groups[3] = sg space_groups['P 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(4, 'P 1 21 1', transformations) space_groups[4] = sg space_groups['P 1 21 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(5, 'C 1 2 1', transformations) space_groups[5] = sg space_groups['C 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(6, 'P 1 m 1', transformations) space_groups[6] = sg space_groups['P 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(7, 'P 1 c 1', transformations) space_groups[7] = sg space_groups['P 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(8, 'C 1 m 1', transformations) space_groups[8] = sg space_groups['C 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(9, 'C 1 c 1', transformations) space_groups[9] = sg space_groups['C 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(10, 'P 1 2/m 1', transformations) space_groups[10] = sg space_groups['P 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(11, 'P 1 21/m 1', transformations) space_groups[11] = sg space_groups['P 1 21/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(12, 'C 1 2/m 1', transformations) space_groups[12] = sg space_groups['C 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(13, 'P 1 2/c 1', transformations) space_groups[13] = sg space_groups['P 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(14, 'P 1 21/c 1', transformations) space_groups[14] = sg space_groups['P 1 21/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(15, 'C 1 2/c 1', transformations) space_groups[15] = sg space_groups['C 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(16, 'P 2 2 2', transformations) space_groups[16] = sg space_groups['P 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(17, 'P 2 2 21', transformations) space_groups[17] = sg space_groups['P 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(18, 'P 21 21 2', transformations) space_groups[18] = sg space_groups['P 21 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(19, 'P 21 21 21', transformations) space_groups[19] = sg space_groups['P 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(20, 'C 2 2 21', transformations) space_groups[20] = sg space_groups['C 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(21, 'C 2 2 2', transformations) space_groups[21] = sg space_groups['C 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(22, 'F 2 2 2', transformations) space_groups[22] = sg space_groups['F 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(23, 'I 2 2 2', transformations) space_groups[23] = sg space_groups['I 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(24, 'I 21 21 21', transformations) space_groups[24] = sg space_groups['I 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(25, 'P m m 2', transformations) space_groups[25] = sg space_groups['P m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(26, 'P m c 21', transformations) space_groups[26] = sg space_groups['P m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(27, 'P c c 2', transformations) space_groups[27] = sg space_groups['P c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(28, 'P m a 2', transformations) space_groups[28] = sg space_groups['P m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(29, 'P c a 21', transformations) space_groups[29] = sg space_groups['P c a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(30, 'P n c 2', transformations) space_groups[30] = sg space_groups['P n c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(31, 'P m n 21', transformations) space_groups[31] = sg space_groups['P m n 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(32, 'P b a 2', transformations) space_groups[32] = sg space_groups['P b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(33, 'P n a 21', transformations) space_groups[33] = sg space_groups['P n a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(34, 'P n n 2', transformations) space_groups[34] = sg space_groups['P n n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(35, 'C m m 2', transformations) space_groups[35] = sg space_groups['C m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(36, 'C m c 21', transformations) space_groups[36] = sg space_groups['C m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(37, 'C c c 2', transformations) space_groups[37] = sg space_groups['C c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(38, 'A m m 2', transformations) space_groups[38] = sg space_groups['A m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(39, 'A b m 2', transformations) space_groups[39] = sg space_groups['A b m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(40, 'A m a 2', transformations) space_groups[40] = sg space_groups['A m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(41, 'A b a 2', transformations) space_groups[41] = sg space_groups['A b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(42, 'F m m 2', transformations) space_groups[42] = sg space_groups['F m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(43, 'F d d 2', transformations) space_groups[43] = sg space_groups['F d d 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(44, 'I m m 2', transformations) space_groups[44] = sg space_groups['I m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(45, 'I b a 2', transformations) space_groups[45] = sg space_groups['I b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(46, 'I m a 2', transformations) space_groups[46] = sg space_groups['I m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(47, 'P m m m', transformations) space_groups[47] = sg space_groups['P m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(48, 'P n n n :2', transformations) space_groups[48] = sg space_groups['P n n n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(49, 'P c c m', transformations) space_groups[49] = sg space_groups['P c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(50, 'P b a n :2', transformations) space_groups[50] = sg space_groups['P b a n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(51, 'P m m a', transformations) space_groups[51] = sg space_groups['P m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(52, 'P n n a', transformations) space_groups[52] = sg space_groups['P n n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(53, 'P m n a', transformations) space_groups[53] = sg space_groups['P m n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(54, 'P c c a', transformations) space_groups[54] = sg space_groups['P c c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(55, 'P b a m', transformations) space_groups[55] = sg space_groups['P b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(56, 'P c c n', transformations) space_groups[56] = sg space_groups['P c c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(57, 'P b c m', transformations) space_groups[57] = sg space_groups['P b c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(58, 'P n n m', transformations) space_groups[58] = sg space_groups['P n n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(59, 'P m m n :2', transformations) space_groups[59] = sg space_groups['P m m n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(60, 'P b c n', transformations) space_groups[60] = sg space_groups['P b c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(61, 'P b c a', transformations) space_groups[61] = sg space_groups['P b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(62, 'P n m a', transformations) space_groups[62] = sg space_groups['P n m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(63, 'C m c m', transformations) space_groups[63] = sg space_groups['C m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(64, 'C m c a', transformations) space_groups[64] = sg space_groups['C m c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(65, 'C m m m', transformations) space_groups[65] = sg space_groups['C m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(66, 'C c c m', transformations) space_groups[66] = sg space_groups['C c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(67, 'C m m a', transformations) space_groups[67] = sg space_groups['C m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(68, 'C c c a :2', transformations) space_groups[68] = sg space_groups['C c c a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(69, 'F m m m', transformations) space_groups[69] = sg space_groups['F m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(70, 'F d d d :2', transformations) space_groups[70] = sg space_groups['F d d d :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(71, 'I m m m', transformations) space_groups[71] = sg space_groups['I m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(72, 'I b a m', transformations) space_groups[72] = sg space_groups['I b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(73, 'I b c a', transformations) space_groups[73] = sg space_groups['I b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(74, 'I m m a', transformations) space_groups[74] = sg space_groups['I m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(75, 'P 4', transformations) space_groups[75] = sg space_groups['P 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(76, 'P 41', transformations) space_groups[76] = sg space_groups['P 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(77, 'P 42', transformations) space_groups[77] = sg space_groups['P 42'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(78, 'P 43', transformations) space_groups[78] = sg space_groups['P 43'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(79, 'I 4', transformations) space_groups[79] = sg space_groups['I 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(80, 'I 41', transformations) space_groups[80] = sg space_groups['I 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(81, 'P -4', transformations) space_groups[81] = sg space_groups['P -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(82, 'I -4', transformations) space_groups[82] = sg space_groups['I -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(83, 'P 4/m', transformations) space_groups[83] = sg space_groups['P 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(84, 'P 42/m', transformations) space_groups[84] = sg space_groups['P 42/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(85, 'P 4/n :2', transformations) space_groups[85] = sg space_groups['P 4/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(86, 'P 42/n :2', transformations) space_groups[86] = sg space_groups['P 42/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(87, 'I 4/m', transformations) space_groups[87] = sg space_groups['I 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(88, 'I 41/a :2', transformations) space_groups[88] = sg space_groups['I 41/a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(89, 'P 4 2 2', transformations) space_groups[89] = sg space_groups['P 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(90, 'P 4 21 2', transformations) space_groups[90] = sg space_groups['P 4 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(91, 'P 41 2 2', transformations) space_groups[91] = sg space_groups['P 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(92, 'P 41 21 2', transformations) space_groups[92] = sg space_groups['P 41 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(93, 'P 42 2 2', transformations) space_groups[93] = sg space_groups['P 42 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(94, 'P 42 21 2', transformations) space_groups[94] = sg space_groups['P 42 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(95, 'P 43 2 2', transformations) space_groups[95] = sg space_groups['P 43 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(96, 'P 43 21 2', transformations) space_groups[96] = sg space_groups['P 43 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(97, 'I 4 2 2', transformations) space_groups[97] = sg space_groups['I 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(98, 'I 41 2 2', transformations) space_groups[98] = sg space_groups['I 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(99, 'P 4 m m', transformations) space_groups[99] = sg space_groups['P 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(100, 'P 4 b m', transformations) space_groups[100] = sg space_groups['P 4 b m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(101, 'P 42 c m', transformations) space_groups[101] = sg space_groups['P 42 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(102, 'P 42 n m', transformations) space_groups[102] = sg space_groups['P 42 n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(103, 'P 4 c c', transformations) space_groups[103] = sg space_groups['P 4 c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(104, 'P 4 n c', transformations) space_groups[104] = sg space_groups['P 4 n c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(105, 'P 42 m c', transformations) space_groups[105] = sg space_groups['P 42 m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(106, 'P 42 b c', transformations) space_groups[106] = sg space_groups['P 42 b c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(107, 'I 4 m m', transformations) space_groups[107] = sg space_groups['I 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(108, 'I 4 c m', transformations) space_groups[108] = sg space_groups['I 4 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(109, 'I 41 m d', transformations) space_groups[109] = sg space_groups['I 41 m d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(110, 'I 41 c d', transformations) space_groups[110] = sg space_groups['I 41 c d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(111, 'P -4 2 m', transformations) space_groups[111] = sg space_groups['P -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(112, 'P -4 2 c', transformations) space_groups[112] = sg space_groups['P -4 2 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(113, 'P -4 21 m', transformations) space_groups[113] = sg space_groups['P -4 21 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(114, 'P -4 21 c', transformations) space_groups[114] = sg space_groups['P -4 21 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(115, 'P -4 m 2', transformations) space_groups[115] = sg space_groups['P -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(116, 'P -4 c 2', transformations) space_groups[116] = sg space_groups['P -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(117, 'P -4 b 2', transformations) space_groups[117] = sg space_groups['P -4 b 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(118, 'P -4 n 2', transformations) space_groups[118] = sg space_groups['P -4 n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(119, 'I -4 m 2', transformations) space_groups[119] = sg space_groups['I -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(120, 'I -4 c 2', transformations) space_groups[120] = sg space_groups['I -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(121, 'I -4 2 m', transformations) space_groups[121] = sg space_groups['I -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(122, 'I -4 2 d', transformations) space_groups[122] = sg space_groups['I -4 2 d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(123, 'P 4/m m m', transformations) space_groups[123] = sg space_groups['P 4/m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(124, 'P 4/m c c', transformations) space_groups[124] = sg space_groups['P 4/m c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(125, 'P 4/n b m :2', transformations) space_groups[125] = sg space_groups['P 4/n b m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(126, 'P 4/n n c :2', transformations) space_groups[126] = sg space_groups['P 4/n n c :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(127, 'P 4/m b m', transformations) space_groups[127] = sg space_groups['P 4/m b m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(128, 'P 4/m n c', transformations) space_groups[128] = sg space_groups['P 4/m n c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(129, 'P 4/n m m :2', transformations) space_groups[129] = sg space_groups['P 4/n m m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(130, 'P 4/n c c :2', transformations) space_groups[130] = sg space_groups['P 4/n c c :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(131, 'P 42/m m c', transformations) space_groups[131] = sg space_groups['P 42/m m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(132, 'P 42/m c m', transformations) space_groups[132] = sg space_groups['P 42/m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(133, 'P 42/n b c :2', transformations) space_groups[133] = sg space_groups['P 42/n b c :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(134, 'P 42/n n m :2', transformations) space_groups[134] = sg space_groups['P 42/n n m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(135, 'P 42/m b c', transformations) space_groups[135] = sg space_groups['P 42/m b c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(136, 'P 42/m n m', transformations) space_groups[136] = sg space_groups['P 42/m n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(137, 'P 42/n m c :2', transformations) space_groups[137] = sg space_groups['P 42/n m c :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(138, 'P 42/n c m :2', transformations) space_groups[138] = sg space_groups['P 42/n c m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(139, 'I 4/m m m', transformations) space_groups[139] = sg space_groups['I 4/m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(140, 'I 4/m c m', transformations) space_groups[140] = sg space_groups['I 4/m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(141, 'I 41/a m d :2', transformations) space_groups[141] = sg space_groups['I 41/a m d :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(142, 'I 41/a c d :2', transformations) space_groups[142] = sg space_groups['I 41/a c d :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(143, 'P 3', transformations) space_groups[143] = sg space_groups['P 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(144, 'P 31', transformations) space_groups[144] = sg space_groups['P 31'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(145, 'P 32', transformations) space_groups[145] = sg space_groups['P 32'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(146, 'R 3 :H', transformations) space_groups[146] = sg space_groups['R 3 :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(147, 'P -3', transformations) space_groups[147] = sg space_groups['P -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(148, 'R -3 :H', transformations) space_groups[148] = sg space_groups['R -3 :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(149, 'P 3 1 2', transformations) space_groups[149] = sg space_groups['P 3 1 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(150, 'P 3 2 1', transformations) space_groups[150] = sg space_groups['P 3 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(151, 'P 31 1 2', transformations) space_groups[151] = sg space_groups['P 31 1 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(152, 'P 31 2 1', transformations) space_groups[152] = sg space_groups['P 31 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(153, 'P 32 1 2', transformations) space_groups[153] = sg space_groups['P 32 1 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(154, 'P 32 2 1', transformations) space_groups[154] = sg space_groups['P 32 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(155, 'R 3 2 :H', transformations) space_groups[155] = sg space_groups['R 3 2 :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(156, 'P 3 m 1', transformations) space_groups[156] = sg space_groups['P 3 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(157, 'P 3 1 m', transformations) space_groups[157] = sg space_groups['P 3 1 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(158, 'P 3 c 1', transformations) space_groups[158] = sg space_groups['P 3 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(159, 'P 3 1 c', transformations) space_groups[159] = sg space_groups['P 3 1 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(160, 'R 3 m :H', transformations) space_groups[160] = sg space_groups['R 3 m :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(161, 'R 3 c :H', transformations) space_groups[161] = sg space_groups['R 3 c :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(162, 'P -3 1 m', transformations) space_groups[162] = sg space_groups['P -3 1 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(163, 'P -3 1 c', transformations) space_groups[163] = sg space_groups['P -3 1 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(164, 'P -3 m 1', transformations) space_groups[164] = sg space_groups['P -3 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(165, 'P -3 c 1', transformations) space_groups[165] = sg space_groups['P -3 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(166, 'R -3 m :H', transformations) space_groups[166] = sg space_groups['R -3 m :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,7]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,2,2]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,2,1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,5]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([2,1,1]) trans_den = N.array([3,3,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,-1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,-1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([2,1,-1]) trans_den = N.array([3,3,6]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(167, 'R -3 c :H', transformations) space_groups[167] = sg space_groups['R -3 c :H'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(168, 'P 6', transformations) space_groups[168] = sg space_groups['P 6'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(169, 'P 61', transformations) space_groups[169] = sg space_groups['P 61'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(170, 'P 65', transformations) space_groups[170] = sg space_groups['P 65'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(171, 'P 62', transformations) space_groups[171] = sg space_groups['P 62'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(172, 'P 64', transformations) space_groups[172] = sg space_groups['P 64'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(173, 'P 63', transformations) space_groups[173] = sg space_groups['P 63'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(174, 'P -6', transformations) space_groups[174] = sg space_groups['P -6'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(175, 'P 6/m', transformations) space_groups[175] = sg space_groups['P 6/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(176, 'P 63/m', transformations) space_groups[176] = sg space_groups['P 63/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(177, 'P 6 2 2', transformations) space_groups[177] = sg space_groups['P 6 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(178, 'P 61 2 2', transformations) space_groups[178] = sg space_groups['P 61 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,5]) trans_den = N.array([1,1,6]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(179, 'P 65 2 2', transformations) space_groups[179] = sg space_groups['P 65 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(180, 'P 62 2 2', transformations) space_groups[180] = sg space_groups['P 62 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,2]) trans_den = N.array([1,1,3]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(181, 'P 64 2 2', transformations) space_groups[181] = sg space_groups['P 64 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(182, 'P 63 2 2', transformations) space_groups[182] = sg space_groups['P 63 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(183, 'P 6 m m', transformations) space_groups[183] = sg space_groups['P 6 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(184, 'P 6 c c', transformations) space_groups[184] = sg space_groups['P 6 c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(185, 'P 63 c m', transformations) space_groups[185] = sg space_groups['P 63 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(186, 'P 63 m c', transformations) space_groups[186] = sg space_groups['P 63 m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(187, 'P -6 m 2', transformations) space_groups[187] = sg space_groups['P -6 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(188, 'P -6 c 2', transformations) space_groups[188] = sg space_groups['P -6 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(189, 'P -6 2 m', transformations) space_groups[189] = sg space_groups['P -6 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(190, 'P -6 2 c', transformations) space_groups[190] = sg space_groups['P -6 2 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(191, 'P 6/m m m', transformations) space_groups[191] = sg space_groups['P 6/m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(192, 'P 6/m c c', transformations) space_groups[192] = sg space_groups['P 6/m c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(193, 'P 63/m c m', transformations) space_groups[193] = sg space_groups['P 63/m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,1,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,1,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,-1,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,-1,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(194, 'P 63/m m c', transformations) space_groups[194] = sg space_groups['P 63/m m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(195, 'P 2 3', transformations) space_groups[195] = sg space_groups['P 2 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(196, 'F 2 3', transformations) space_groups[196] = sg space_groups['F 2 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(197, 'I 2 3', transformations) space_groups[197] = sg space_groups['I 2 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(198, 'P 21 3', transformations) space_groups[198] = sg space_groups['P 21 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(199, 'I 21 3', transformations) space_groups[199] = sg space_groups['I 21 3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(200, 'P m -3', transformations) space_groups[200] = sg space_groups['P m -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(201, 'P n -3 :2', transformations) space_groups[201] = sg space_groups['P n -3 :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(202, 'F m -3', transformations) space_groups[202] = sg space_groups['F m -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(203, 'F d -3 :2', transformations) space_groups[203] = sg space_groups['F d -3 :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(204, 'I m -3', transformations) space_groups[204] = sg space_groups['I m -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(205, 'P a -3', transformations) space_groups[205] = sg space_groups['P a -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(206, 'I a -3', transformations) space_groups[206] = sg space_groups['I a -3'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(207, 'P 4 3 2', transformations) space_groups[207] = sg space_groups['P 4 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(208, 'P 42 3 2', transformations) space_groups[208] = sg space_groups['P 42 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(209, 'F 4 3 2', transformations) space_groups[209] = sg space_groups['F 4 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(210, 'F 41 3 2', transformations) space_groups[210] = sg space_groups['F 41 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(211, 'I 4 3 2', transformations) space_groups[211] = sg space_groups['I 4 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(212, 'P 43 3 2', transformations) space_groups[212] = sg space_groups['P 43 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(213, 'P 41 3 2', transformations) space_groups[213] = sg space_groups['P 41 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(214, 'I 41 3 2', transformations) space_groups[214] = sg space_groups['I 41 3 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(215, 'P -4 3 m', transformations) space_groups[215] = sg space_groups['P -4 3 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(216, 'F -4 3 m', transformations) space_groups[216] = sg space_groups['F -4 3 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(217, 'I -4 3 m', transformations) space_groups[217] = sg space_groups['I -4 3 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(218, 'P -4 3 n', transformations) space_groups[218] = sg space_groups['P -4 3 n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(219, 'F -4 3 c', transformations) space_groups[219] = sg space_groups['F -4 3 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,5,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(220, 'I -4 3 d', transformations) space_groups[220] = sg space_groups['I -4 3 d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(221, 'P m -3 m', transformations) space_groups[221] = sg space_groups['P m -3 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(222, 'P n -3 n :2', transformations) space_groups[222] = sg space_groups['P n -3 n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(223, 'P m -3 n', transformations) space_groups[223] = sg space_groups['P m -3 n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(224, 'P n -3 m :2', transformations) space_groups[224] = sg space_groups['P n -3 m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(225, 'F m -3 m', transformations) space_groups[225] = sg space_groups['F m -3 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(226, 'F m -3 c', transformations) space_groups[226] = sg space_groups['F m -3 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(227, 'F d -3 m :2', transformations) space_groups[227] = sg space_groups['F d -3 m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,1,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,-1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,-1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,-1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,-1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,1,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,0,0,-1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,1,0,0,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,-1,0,0,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,0,0,1,1,0,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,-1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,-3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,1,0,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([0,-1,-3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,-1,0,1,0]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,0,1,0,-1,0]) rot.shape = (3, 3) trans_num = N.array([1,5,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,0,1,0,1,0,-1,0,0]) rot.shape = (3, 3) trans_num = N.array([1,5,1]) trans_den =

N.array([4,4,2])

numpy.array

import numpy as np import pytest from plaguepy import bereken def test_perc_overlap(): """Test de functie perc_overlap in bereken.py.""" assert bereken.perc_overlap(0, 0, 1) == 1.0 assert bereken.perc_overlap(0, 1, 1) == 1.0 assert bereken.perc_overlap(1, 0, 1) == pytest.approx(0.3173105) assert bereken.perc_overlap(1, 1, 1) == pytest.approx(0.3173105) with pytest.raises(ValueError): assert bereken.perc_overlap(0, 1, 0) == ValueError assert bereken.perc_overlap(1, 0, 0) == ValueError assert bereken.perc_overlap(0, 0, 0) == ValueError assert bereken.perc_overlap(1, 1, 0) == ValueError def test_grens(): """Test de functie grens in bereken.py.""" assert bereken.grens(0.025, 0, 1) == pytest.approx(-1.95996398) # -2 SD assert bereken.grens(0.16, 0, 1) == pytest.approx(-0.99445788) # -1 SD assert bereken.grens(0.5, 0, 1) == 0.0 # 50% dus nog op gemiddelde assert bereken.grens(0.84, 0, 1) == pytest.approx(0.99445788) # 1 SD assert bereken.grens(0.975, 0, 1) == pytest.approx(1.95996398) # 2 SD with pytest.raises(ValueError): assert bereken.grens(-0.5, 0, 1) == ValueError assert bereken.grens(0, 0, 1) == ValueError assert bereken.grens(1, 0, 1) == ValueError assert bereken.grens(1.5, 0, 1) == ValueError def test_helling(): """Test de functie helling in bereken.py.""" assert bereken.helling(np.array([0, 0]), np.array([1, 0])) == 0.0 assert bereken.helling(np.array([0, 0]), np.array([1, 1])) == 45.0 assert bereken.helling(np.array([0, 0]), np.array([-1, -1])) == 45.0 assert bereken.helling(np.array([0, 0]), np.array([-1, 1])) == -45.0 assert bereken.helling(np.array([0, 0]), np.array([1, -1])) == -45.0 assert bereken.helling(np.array([0, 0]),

np.array([0, 0])

numpy.array

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 =

np.linspace(maxima_y[-1], minima_y[-1], 101)

numpy.linspace

import os import json import numpy as np import torch from gym import spaces from omegaconf import OmegaConf def available_device() -> torch.device: if torch.cuda.is_available(): return torch.device('cuda') return torch.device('cpu') def format_number(num): return '{:,}'.format(num) def count_parameters(model): return sum(p.numel() for p in model.parameters() if p.requires_grad) def soft_update(target, source, polyak): for target_param, param in zip(target.parameters(), source.parameters()): target_param.data.copy_((1 - polyak) * param.data + polyak * target_param.data) def hard_update(target, source): for target_param, param in zip(target.parameters(), source.parameters()): target_param.data.copy_(param.data) class NumpyArrayEncoder(json.JSONEncoder): def default(self, obj): if isinstance(obj, np.integer): return int(obj) elif isinstance(obj, np.floating): return float(obj) elif isinstance(obj, np.ndarray): return obj.tolist() elif isinstance(obj, object): # NOTE: Ignore classes for now return None else: return super(NumpyArrayEncoder, self).default(obj) def init_storage(cfg): logdir = os.getcwd() model_path = os.path.join(logdir, 'models') if not os.path.exists(model_path): os.mkdir(model_path) video_path = os.path.join(logdir, 'videos') if cfg.log_video and not os.path.exists(video_path): os.mkdir(video_path) with open(os.path.join(logdir, 'omega_config.yaml'), 'w') as file: OmegaConf.save(config=cfg, f=file) return logdir, model_path def is_image_observation(observation_space): if isinstance(observation_space, spaces.Box) and len(observation_space.shape) == 3: # Check the type if observation_space.dtype == np.uint8: return True # Check the value range elif np.any(observation_space.low == 0) or

np.any(observation_space.high == 255)

numpy.any

import numpy as np from joblib import Memory from scipy.optimize import fmin_l_bfgs_b location = './cachedir' memory = Memory(location, verbose=0) def x_to_params(x, p, q, n): A = x[:p * q].reshape(p, q) P = x[p * q: p * q + q * n].reshape(n, q) return A, P def params_to_x(A, P): p, q = A.shape n, _ = P.shape x = np.zeros(p * q + n * q) x[:p * q] = A.ravel() x[p * q: p * q + q * n] = P.ravel() return x def kl(A, B): p, _ = A.shape C = np.dot(A,

np.linalg.inv(B)

numpy.linalg.inv

import numpy from radiomics import base, cMatrices class RadiomicsGLRLM(base.RadiomicsFeaturesBase): r""" A Gray Level Run Length Matrix (GLRLM) quantifies gray level runs, which are defined as the length in number of pixels, of consecutive pixels that have the same gray level value. In a gray level run length matrix :math:`\textbf{P}(i,j|\theta)`, the :math:`(i,j)^{\text{th}}` element describes the number of runs with gray level :math:`i` and length :math:`j` occur in the image (ROI) along angle :math:`\theta`. As a two dimensional example, consider the following 5x5 image, with 5 discrete gray levels: .. math:: \textbf{I} = \begin{bmatrix} 5 & 2 & 5 & 4 & 4\\ 3 & 3 & 3 & 1 & 3\\ 2 & 1 & 1 & 1 & 3\\ 4 & 2 & 2 & 2 & 3\\ 3 & 5 & 3 & 3 & 2 \end{bmatrix} The GLRLM for :math:`\theta = 0`, where 0 degrees is the horizontal direction, then becomes: .. math:: \textbf{P} = \begin{bmatrix} 1 & 0 & 1 & 0 & 0\\ 3 & 0 & 1 & 0 & 0\\ 4 & 1 & 1 & 0 & 0\\ 1 & 1 & 0 & 0 & 0\\ 3 & 0 & 0 & 0 & 0 \end{bmatrix} Let: - :math:`N_g` be the number of discreet intensity values in the image - :math:`N_r` be the number of discreet run lengths in the image - :math:`N_p` be the number of voxels in the image - :math:`N_r(\theta)` be the number of runs in the image along angle :math:`\theta`, which is equal to :math:`\sum^{N_g}_{i=1}\sum^{N_r}_{j=1}{\textbf{P}(i,j|\theta)}` and :math:`1 \leq N_r(\theta) \leq N_p` - :math:`\textbf{P}(i,j|\theta)` be the run length matrix for an arbitrary direction :math:`\theta` - :math:`p(i,j|\theta)` be the normalized run length matrix, defined as :math:`p(i,j|\theta) = \frac{\textbf{P}(i,j|\theta)}{N_r(\theta)}` By default, the value of a feature is calculated on the GLRLM for each angle separately, after which the mean of these values is returned. If distance weighting is enabled, GLRLMs are weighted by the distance between neighbouring voxels and then summed and normalised. Features are then calculated on the resultant matrix. The distance between neighbouring voxels is calculated for each angle using the norm specified in 'weightingNorm'. The following class specific settings are possible: - weightingNorm [None]: string, indicates which norm should be used when applying distance weighting. Enumerated setting, possible values: - 'manhattan': first order norm - 'euclidean': second order norm - 'infinity': infinity norm. - 'no_weighting': GLCMs are weighted by factor 1 and summed - None: Applies no weighting, mean of values calculated on separate matrices is returned. In case of other values, an warning is logged and option 'no_weighting' is used. References - <NAME>. 1975. Texture analysis using gray level run lengths. Computer Graphics and Image Processing, 4(2):172-179. - <NAME>., <NAME>., <NAME>. 1990. Use of gray value distribution of run length for texture analysis. Pattern Recognition Letters, 11(6):415-419 - <NAME>., <NAME>., <NAME>., <NAME>. 2004. Run-Length Encoding For Volumetric Texture. International Conference on Visualization, Imaging and Image Processing (VIIP), p. 452-458 - <NAME>. 1998. Texture information in run-length matrices. IEEE Transactions on Image Processing 7(11):1602-1609. - `<NAME>., <NAME>. Run-Length Matrices For Texture Analysis. Insight Journal 2008 January - June. <http://www.insight-journal.org/browse/publication/231>`_ """ def __init__(self, inputImage, inputMask, **kwargs): super(RadiomicsGLRLM, self).__init__(inputImage, inputMask, **kwargs) self.weightingNorm = kwargs.get('weightingNorm', None) # manhattan, euclidean, infinity self.P_glrlm = None self.imageArray = self._applyBinning(self.imageArray) def _initCalculation(self, voxelCoordinates=None): self.P_glrlm = self._calculateMatrix(voxelCoordinates) self._calculateCoefficients() self.logger.debug('GLRLM feature class initialized, calculated GLRLM with shape %s', self.P_glrlm.shape) def _calculateMatrix(self, voxelCoordinates=None): self.logger.debug('Calculating GLRLM matrix in C') Ng = self.coefficients['Ng'] Nr = numpy.max(self.imageArray.shape) matrix_args = [ self.imageArray, self.maskArray, Ng, Nr, self.settings.get('force2D', False), self.settings.get('force2Ddimension', 0) ] if self.voxelBased: matrix_args += [self.settings.get('kernelRadius', 1), voxelCoordinates] P_glrlm, angles = cMatrices.calculate_glrlm(*matrix_args) # shape (Nvox, Ng, Nr, Na) self.logger.debug('Process calculated matrix') # Delete rows that specify gray levels not present in the ROI NgVector = range(1, Ng + 1) # All possible gray values GrayLevels = self.coefficients['grayLevels'] # Gray values present in ROI emptyGrayLevels = numpy.array(list(set(NgVector) - set(GrayLevels)), dtype=int) # Gray values NOT present in ROI P_glrlm = numpy.delete(P_glrlm, emptyGrayLevels - 1, 1) # Optionally apply a weighting factor if self.weightingNorm is not None: self.logger.debug('Applying weighting (%s)', self.weightingNorm) pixelSpacing = self.inputImage.GetSpacing()[::-1] weights = numpy.empty(len(angles)) for a_idx, a in enumerate(angles): if self.weightingNorm == 'infinity': weights[a_idx] = max(numpy.abs(a) * pixelSpacing) elif self.weightingNorm == 'euclidean': weights[a_idx] = numpy.sqrt(numpy.sum((numpy.abs(a) * pixelSpacing) ** 2)) elif self.weightingNorm == 'manhattan': weights[a_idx] = numpy.sum(numpy.abs(a) * pixelSpacing) elif self.weightingNorm == 'no_weighting': weights[a_idx] = 1 else: self.logger.warning('weigthing norm "%s" is unknown, weighting factor is set to 1', self.weightingNorm) weights[a_idx] = 1 P_glrlm = numpy.sum(P_glrlm * weights[None, None, None, :], 3, keepdims=True) Nr = numpy.sum(P_glrlm, (1, 2)) # Delete empty angles if no weighting is applied if P_glrlm.shape[3] > 1: emptyAngles = numpy.where(numpy.sum(Nr, 0) == 0) if len(emptyAngles[0]) > 0: # One or more angles are 'empty' self.logger.debug('Deleting %d empty angles:\n%s', len(emptyAngles[0]), angles[emptyAngles]) P_glrlm = numpy.delete(P_glrlm, emptyAngles, 3) Nr = numpy.delete(Nr, emptyAngles, 1) else: self.logger.debug('No empty angles') Nr[Nr == 0] = numpy.nan # set sum to numpy.spacing(1) if sum is 0? self.coefficients['Nr'] = Nr return P_glrlm def _calculateCoefficients(self): self.logger.debug('Calculating GLRLM coefficients') pr = numpy.sum(self.P_glrlm, 1) # shape (Nvox, Nr, Na) pg = numpy.sum(self.P_glrlm, 2) # shape (Nvox, Ng, Na) ivector = self.coefficients['grayLevels'].astype(float) # shape (Ng,) jvector = numpy.arange(1, self.P_glrlm.shape[2] + 1, dtype=numpy.float64) # shape (Nr,) # Delete columns that run lengths not present in the ROI emptyRunLenghts = numpy.where(numpy.sum(pr, (0, 2)) == 0) self.P_glrlm = numpy.delete(self.P_glrlm, emptyRunLenghts, 2) jvector = numpy.delete(jvector, emptyRunLenghts) pr = numpy.delete(pr, emptyRunLenghts, 1) self.coefficients['pr'] = pr self.coefficients['pg'] = pg self.coefficients['ivector'] = ivector self.coefficients['jvector'] = jvector def getShortRunEmphasisFeatureValue(self): r""" **1. Short Run Emphasis (SRE)** .. math:: \textit{SRE} = \frac{\sum^{N_g}_{i=1}\sum^{N_r}_{j=1}{\frac{\textbf{P}(i,j|\theta)}{j^2}}}{N_r(\theta)} SRE is a measure of the distribution of short run lengths, with a greater value indicative of shorter run lengths and more fine textural textures. """ pr = self.coefficients['pr'] jvector = self.coefficients['jvector'] Nr = self.coefficients['Nr'] sre = numpy.sum((pr / (jvector[None, :, None] ** 2)), 1) / Nr return numpy.nanmean(sre, 1) def getLongRunEmphasisFeatureValue(self): r""" **2. Long Run Emphasis (LRE)** .. math:: \textit{LRE} = \frac{\sum^{N_g}_{i=1}\sum^{N_r}_{j=1}{\textbf{P}(i,j|\theta)j^2}}{N_r(\theta)} LRE is a measure of the distribution of long run lengths, with a greater value indicative of longer run lengths and more coarse structural textures. """ pr = self.coefficients['pr'] jvector = self.coefficients['jvector'] Nr = self.coefficients['Nr'] lre = numpy.sum((pr * (jvector[None, :, None] ** 2)), 1) / Nr return numpy.nanmean(lre, 1) def getGrayLevelNonUniformityFeatureValue(self): r""" **3. Gray Level Non-Uniformity (GLN)** .. math:: \textit{GLN} = \frac{\sum^{N_g}_{i=1}\left(\sum^{N_r}_{j=1}{\textbf{P}(i,j|\theta)}\right)^2}{N_r(\theta)} GLN measures the similarity of gray-level intensity values in the image, where a lower GLN value correlates with a greater similarity in intensity values. """ pg = self.coefficients['pg'] Nr = self.coefficients['Nr'] gln = numpy.sum((pg ** 2), 1) / Nr return numpy.nanmean(gln, 1) def getGrayLevelNonUniformityNormalizedFeatureValue(self): r""" **4. Gray Level Non-Uniformity Normalized (GLNN)** .. math:: \textit{GLNN} = \frac{\sum^{N_g}_{i=1}\left(\sum^{N_r}_{j=1}{\textbf{P}(i,j|\theta)}\right)^2}{N_r(\theta)^2} GLNN measures the similarity of gray-level intensity values in the image, where a lower GLNN value correlates with a greater similarity in intensity values. This is the normalized version of the GLN formula. """ pg = self.coefficients['pg'] Nr = self.coefficients['Nr'] glnn = numpy.sum(pg ** 2, 1) / (Nr ** 2) return numpy.nanmean(glnn, 1) def getRunLengthNonUniformityFeatureValue(self): r""" **5. Run Length Non-Uniformity (RLN)** .. math:: \textit{RLN} = \frac{\sum^{N_r}_{j=1}\left(\sum^{N_g}_{i=1}{\textbf{P}(i,j|\theta)}\right)^2}{N_r(\theta)} RLN measures the similarity of run lengths throughout the image, with a lower value indicating more homogeneity among run lengths in the image. """ pr = self.coefficients['pr'] Nr = self.coefficients['Nr'] rln = numpy.sum((pr ** 2), 1) / Nr return numpy.nanmean(rln, 1) def getRunLengthNonUniformityNormalizedFeatureValue(self): r""" **6. Run Length Non-Uniformity Normalized (RLNN)** .. math:: \textit{RLNN} = \frac{\sum^{N_r}_{j=1}\left(\sum^{N_g}_{i=1}{\textbf{P}(i,j|\theta)}\right)^2}{N_r(\theta)^2} RLNN measures the similarity of run lengths throughout the image, with a lower value indicating more homogeneity among run lengths in the image. This is the normalized version of the RLN formula. """ pr = self.coefficients['pr'] Nr = self.coefficients['Nr'] rlnn = numpy.sum((pr ** 2), 1) / Nr ** 2 return numpy.nanmean(rlnn, 1) def getRunPercentageFeatureValue(self): r""" **7. Run Percentage (RP)** .. math:: \textit{RP} = {\frac{N_r(\theta)}{N_p}} RP measures the coarseness of the texture by taking the ratio of number of runs and number of voxels in the ROI. Values are in range :math:`\frac{1}{N_p} \leq RP \leq 1`, with higher values indicating a larger portion of the ROI consists of short runs (indicates a more fine texture). .. note:: Note that when weighting is applied and matrices are merged before calculation, :math:`N_p` is multiplied by :math:`n` number of matrices merged to ensure correct normalization (as each voxel is considered :math:`n` times) """ pr = self.coefficients['pr'] jvector = self.coefficients['jvector'] Nr = self.coefficients['Nr'] Np = numpy.sum(pr * jvector[None, :, None], 1) # shape (Nvox, Na) rp = Nr / Np return numpy.nanmean(rp, 1) def getGrayLevelVarianceFeatureValue(self): r""" **8. Gray Level Variance (GLV)** .. math:: \textit{GLV} = \displaystyle\sum^{N_g}_{i=1}\displaystyle\sum^{N_r}_{j=1}{p(i,j|\theta)(i - \mu)^2} Here, :math:`\mu = \displaystyle\sum^{N_g}_{i=1}\displaystyle\sum^{N_r}_{j=1}{p(i,j|\theta)i}` GLV measures the variance in gray level intensity for the runs. """ ivector = self.coefficients['ivector'] Nr = self.coefficients['Nr'] pg = self.coefficients['pg'] / Nr[:, None, :] # divide by Nr to get the normalized matrix u_i = numpy.sum(pg * ivector[None, :, None], 1, keepdims=True) glv = numpy.sum(pg * (ivector[None, :, None] - u_i) ** 2, 1) return numpy.nanmean(glv, 1) def getRunVarianceFeatureValue(self): r""" **9. Run Variance (RV)** .. math:: \textit{RV} = \displaystyle\sum^{N_g}_{i=1}\displaystyle\sum^{N_r}_{j=1}{p(i,j|\theta)(j - \mu)^2} Here, :math:`\mu = \displaystyle\sum^{N_g}_{i=1}\displaystyle\sum^{N_r}_{j=1}{p(i,j|\theta)j}` RV is a measure of the variance in runs for the run lengths. """ jvector = self.coefficients['jvector'] Nr = self.coefficients['Nr'] pr = self.coefficients['pr'] / Nr[:, None, :] # divide by Nr to get the normalized matrix u_j = numpy.sum(pr * jvector[None, :, None], 1, keepdims=True) rv = numpy.sum(pr * (jvector[None, :, None] - u_j) ** 2, 1) return numpy.nanmean(rv, 1) def getRunEntropyFeatureValue(self): r""" **10. Run Entropy (RE)** .. math:: \textit{RE} = -\displaystyle\sum^{N_g}_{i=1}\displaystyle\sum^{N_r}_{j=1} {p(i,j|\theta)\log_{2}(p(i,j|\theta)+\epsilon)} Here, :math:`\epsilon` is an arbitrarily small positive number (:math:`\approx 2.2\times10^{-16}`). RE measures the uncertainty/randomness in the distribution of run lengths and gray levels. A higher value indicates more heterogeneity in the texture patterns. """ eps = numpy.spacing(1) Nr = self.coefficients['Nr'] p_glrlm = self.P_glrlm / Nr[:, None, None, :] # divide by Nr to get the normalized matrix re = -numpy.sum(p_glrlm * numpy.log2(p_glrlm + eps), (1, 2)) return numpy.nanmean(re, 1) def getLowGrayLevelRunEmphasisFeatureValue(self): r""" **11. Low Gray Level Run Emphasis (LGLRE)** .. math:: \textit{LGLRE} = \frac{\sum^{N_g}_{i=1}\sum^{N_r}_{j=1}{\frac{\textbf{P}(i,j|\theta)}{i^2}}}{N_r(\theta)} LGLRE measures the distribution of low gray-level values, with a higher value indicating a greater concentration of low gray-level values in the image. """ pg = self.coefficients['pg'] ivector = self.coefficients['ivector'] Nr = self.coefficients['Nr'] lglre = numpy.sum((pg / (ivector[None, :, None] ** 2)), 1) / Nr return

numpy.nanmean(lglre, 1)

numpy.nanmean

# -*- coding: utf-8 -*- import unittest import os import numpy as np try: from karta import Point from karta.crs import LonLatWGS84 except ImportError: from narwhal.geo import Point, LonLatWGS84 import narwhal from narwhal import gsw from narwhal.cast import Cast, CTDCast, XBTCast, LADCP from narwhal.cast import CastCollection from narwhal.bathymetry import Bathymetry from narwhal.util import force_monotonic, diff2, uintegrate, diff2_inner from narwhal import util directory = os.path.dirname(__file__) DATADIR = os.path.join(directory, "data") if not os.path.exists(DATADIR): os.mkdir(DATADIR) class CastTests(unittest.TestCase): def setUp(self): p = np.arange(1, 1001, 2) temp = 10. * np.exp(-.008*p) - 15. * np.exp(-0.005*(p+100)) + 2. sal = -14. * np.exp(-.01*p) + 34. self.p = p self.temp = temp self.sal = sal self.cast = CTDCast(p, sal, temp) return def test_numerical_indexing(self): r = self.cast[40] self.assertTrue(r["pressure"] == 81) self.assertTrue(r["salinity"] == 27.771987072878822) self.assertTrue(r["temperature"] == 1.1627808544797258) r = self.cast[100] self.assertTrue(r["pressure"] == 201) self.assertTrue(r["salinity"] == 32.124158554636729) self.assertTrue(r["temperature"] == 0.67261848597249019) r = self.cast[400] self.assertTrue(r["pressure"] == 801) self.assertTrue(r["salinity"] == 33.995350253934227) self.assertTrue(r["temperature"] == 1.8506793256302907) return def test_kw_indexing(self): self.assertTrue(np.all(self.cast["pressure"] == self.p)) self.assertTrue(np.all(self.cast["salinity"] == self.sal)) self.assertTrue(np.all(self.cast["temperature"] == self.temp)) return def test_kw_property_indexing(self): cast = Cast(pressure=self.p, temp=self.temp, sal=self.sal, name="Cruise station 7") self.assertEqual(cast.p["name"], "Cruise station 7") return def test_concatenation(self): p = np.arange(1, 1001, 2) temp = 12. * np.exp(-.007*p) - 14. * np.exp(-0.005*(p+100)) + 1.8 sal = -13. * np.exp(-.01*p) + 34.5 cast2 = Cast(pres=p, temp=temp, sal=sal) cc = self.cast + cast2 self.assertTrue(isinstance(cc, CastCollection)) self.assertEqual(len(cc), 2) return def test_interpolate(self): self.assertEqual(np.round(self.cast.interpolate("temperature", "pressure", 4.0), 8), 2.76745605) self.assertEqual(np.round(self.cast.interpolate("temperature", "salinity", 33.0), 8), 0.77935861) # temp not monotonic, which screws up the simple interpolation scheme #self.assertEqual(np.round(self.cast.interpolate("pres", "temp", 1.5), 8), # 2.7674560521632685) return def test_add_property_using_alias(self): cast = Cast(pres=self.p, temp=self.temp, sal=self.sal) cast.p["comment"] = "performed bottle cast #23" self.assertEqual(cast.properties["comment"][-2:], "23") return def test_read_property_using_alias(self): cast = Cast(pressure=self.p, temp=self.temp, sal=self.sal, time="late") self.assertEqual(cast.p["time"], "late") return def test_add_density(self): p = np.arange(10) t = 20.0 * 0.2 * p s = 30.0 * 0.25 * p x = [-20.0 for _ in p] y = [50.0 for _ in p] sa = gsw.sa_from_sp(s, p, x, y) ct = gsw.ct_from_t(sa, t, p) rho = gsw.rho(sa, ct, p) cast = CTDCast(p, s, t, coordinates=(-20, 50)) cast.add_density() self.assertTrue(np.allclose(rho, cast["density"])) return def test_add_buoyancy_freq_squared(self): # This is a fairly lousy test, merely ensuring that an N^2 field was # calculated, and that it's not wildly different than the direct # calculation. p = np.arange(10) t = 20.0 * 0.2 * p s = 30.0 * 0.25 * p x = [-20.0 for _ in p] y = [50.0 for _ in p] sa = gsw.sa_from_sp(s, p, x, y) ct = gsw.ct_from_t(sa, t, p) rho = np.asarray(gsw.rho(sa, ct, p)) cast = CTDCast(p, s, t, coordinates=(-20, 50), density=rho) cast.add_depth() cast.add_Nsquared(depthkey="depth") # Calculate the buoyancy frequency directly z = cast["depth"].values drhodz = -np.r_[rho[1]-rho[0], rho[2:]-rho[:-2], rho[-1]-rho[-2]] / \ np.r_[z[1]-z[0], z[2:]-z[:-2], z[-1]-z[-2]] N2_direct = -9.81 / rho * drhodz self.assertTrue(np.mean(np.abs(cast["N2"][1:] - N2_direct[1:])) < 0.0004) return def test_LADCP_shear(self): z = np.arange(0, 300) u = z**1.01 - z v = z**1.005 - z u_ans = 1.01 * z**0.01 - 1 v_ans = 1.005 * z**0.005 - 1 lad = narwhal.LADCP(z, u, v) lad.add_shear() self.assertTrue(np.max(abs(lad["dudz"][1:-1] - u_ans[1:-1])) < 0.005) self.assertTrue(np.max(abs(lad["dvdz"][1:-1] - v_ans[1:-1])) < 0.005) return #def test_projectother(self): # pass #def test_calculate_sigma(self): # pass #def test_calculate_theta(self): # pass class CastCollectionTests(unittest.TestCase): def setUp(self): p = np.linspace(1, 999, 500) casts = [] for i in range(10): cast = Cast(pres=p, temp=2*np.ones_like(p), sal=30*np.ones_like(p), station=i, val=abs(i-5), uniq_val=-i**2) casts.append(cast) self.cc = CastCollection(casts) return def test_iteration1(self): for cast in self.cc: self.assertTrue(isinstance(cast, Cast)) return def test_iteration2(self): for i, cast in enumerate(self.cc): pass self.assertEqual(i, 9) return def test_len(self): self.assertEqual(len(self.cc), 10) return def test_slicing(self): subcc = self.cc[2:7] self.assertTrue(isinstance(subcc, CastCollection)) return def test_get_properties(self): self.assertEqual(self.cc["station"], [c.properties["station"] for c in self.cc]) return def test_castwhere(self): cc = self.cc self.assertEqual(cc.castwhere("station", 5), cc[5]) return def test_castswhere(self): cc = self.cc self.assertEqual(cc.castswhere("station", (3,5,6,7)), cc[3]+cc[5:8]) return def test_castswhere_onearg(self): cc = self.cc self.assertEqual(cc.castswhere("station", 5), CastCollection(cc[5])) return def test_castswhere_multiple_results(self): cc = self.cc self.assertEqual(cc.castswhere("val", (1, 2)), cc[3:5] + cc[6:8]) return def test_castswhere_function(self): cc = self.cc casts = cc.castswhere("val", lambda x: x <=3) self.assertEqual(casts, cc[2:-1]) return def test_select(self): cc = self.cc casts = cc.select("uniq_val", (-36, -49, -16)) self.assertEqual(casts, cc[6:8] + cc[4]) return def test_nearest_to(self): casts = [] for i in range(10): casts.append(Cast(pressure=[1, 2, 3], temperature=[5, 6, 7], coordinates=(-30.0 + i, 10.0 - 2*i))) cc = CastCollection(casts) pt = Point((-26.2, 2.1), crs=LonLatWGS84) nearest, dist = cc.nearest_to_point(pt) self.assertEqual(nearest.coordinates.vertex, (-26.0, 2.0)) self.assertAlmostEqual(dist, 24845.9422, places=4) return def test_defray(self): lengths = np.arange(50, 71) casts = [] for n in lengths: p = np.r_[np.arange(0, 250, 5), np.arange(250, 250 + 5*(n-50), 5)] t = np.ones(n) * 10.0 s = np.ones(n) * 34.0 cast = Cast(pres=p, temp=t, sal=s) casts.append(cast) defrayed_casts = CastCollection(casts).defray() for cast in defrayed_casts: self.assertEqual(len(cast), 70) return class MiscTests(unittest.TestCase): def test_force_monotonic(self): s = np.array([1, 3, 5, 6, 7, 9, 13, 14, 15]) sm = force_monotonic(s) self.assertTrue(np.all(sm == s)) s = np.array([1, 3, 5, 4, 7, 9, 13, 11, 15]) sm = force_monotonic(s) self.assertTrue(np.all(sm == np.array([1, 3, 5, 5+1e-16, 7, 9, 13, 13+1e-16, 15]))) return def test_diff2(self): x = np.atleast_2d(np.linspace(-1, 1, 100)) A = x**2 - (x + x.T)**3 ans = 2*x - 3*(x + x.T)**2 # true answer # add holes A[30:40,1] = np.nan A[15,35] = np.nan A[30:50,50:55] = np.nan A[60:65,60] = np.nan A[60:70,-2] = np.nan D = diff2(A, x.ravel()) self.assertTrue(np.max(abs(ans[~np.isnan(D)] - D[~np.isnan(D)])) < 0.15) return def test_diff2_inner(self): x = np.atleast_2d(np.linspace(-1, 1, 100)) A = x**2 - (x + x.T)**3 xinner = np.atleast_2d(0.5 * (x[0,1:] + x[0,:-1])) ans = 2*xinner - 3*(xinner + x.T)**2 # true answer # add holes A[30:40,1] = np.nan A[15,35] = np.nan A[30:50,50:55] = np.nan A[60:65,60] = np.nan A[60:70,-2] = np.nan D = diff2_inner(A, x.ravel()) self.assertTrue(np.max(abs(ans[~np.isnan(D)] - D[~np.isnan(D)])) < 0.0002) return def test_diff2_dinterp(self): x = np.atleast_2d(

np.linspace(-1, 1, 100)

numpy.linspace

# -*- coding: utf-8 -*- """ Created on Fri Oct 5 10:40:35 2018 @author: hamed """ try: import torch from torch.utils import data except: pass import numpy as np from sklearn import datasets #%% class kk_mimic_dataset(data.Dataset): def __init__(self, phase="train", seq_len=10, data_norm=True, test=False): percent = 20 n_valid = percent/20 * 328 ind_valid = np.ones(n_valid) ind_valid = np.concatenate((ind_valid, np.zeros(6564-n_valid))) ind_valid = np.random.permutation(ind_valid) ind_test = 1 - ind_valid self.ind_valid = np.greater(ind_valid, 0) self.ind_test = np.greater(ind_test, 0) super(kk_mimic_dataset, self).__init__() if phase == "train": if test: data_path = "../../mimic-libsvm/" + "PATIENTS_SPLIT_XGB_TRAIN" else: data_path = "../mimic-libsvm/" + "PATIENTS_SPLIT_XGB_TRAIN" data = datasets.load_svmlight_file(data_path) else: if test: data_path = "../../mimic-libsvm/" + "PATIENTS_SPLIT_XGB_VALID" else: data_path = "../mimic-libsvm/" + "PATIENTS_SPLIT_XGB_VALID" data = np.array(datasets.load_svmlight_file(data_path)) if phase == "valid":# # data = [ data[0][:data[1].shape[0]//percent], data[1][:data[1].shape[0]//percent] ] data = [ data[0][self.ind_valid], data[1][self.ind_valid] ] else: # data = [ data[0][data[1].shape[0]//percent:], data[1][data[1].shape[0]//percent:] ] data = [ data[0][self.ind_test], data[1][self.ind_test] ] # # TODO: ONLY for fast debugging ## factor = 10 # data = [ data[0][:data[1].shape[0]//factor], data[1][:data[1].shape[0]//factor] ] #Random selection factor = 20 n_data = data[1].shape[0] ind_ =

np.ones(n_data//factor)

numpy.ones

import isopy import numpy as np import pytest # calculate_mass_fractionation_factor, remove_mass_fractionation, add_mass_fractionation def test_mass_fractionation1(): # Testing with input as isotope array # Using default reference values mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 unfractionated = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed = 46) unfractionated = unfractionated * fraction_ref unfractionated['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated['105pd'] mf_factor = isopy.random(100, (0, 2), seed=47) c_fractionated1 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor, '105pd') c_fractionated2 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor) assert c_fractionated1.keys == unfractionated.keys assert c_fractionated1.size == unfractionated.size assert c_fractionated2.keys == unfractionated.keys assert c_fractionated2.size == unfractionated.size c_unfractionated1 = isopy.tb.remove_mass_fractionation(c_fractionated1, mf_factor, '105pd') c_unfractionated2 = isopy.tb.remove_mass_fractionation(c_fractionated2, mf_factor) assert c_unfractionated1.keys == unfractionated.keys assert c_unfractionated1.size == unfractionated.size assert c_unfractionated2.keys == unfractionated.keys assert c_unfractionated2.size == unfractionated.size c_mf_factor2 = isopy.tb.calculate_mass_fractionation_factor(c_fractionated1, '108pd/105pd') np.testing.assert_allclose(c_mf_factor2, mf_factor) for key in unfractionated.keys: mass_diff = mass_ref.get(key/'105pd') fractionated = unfractionated[key] * (mass_diff ** mf_factor) np.testing.assert_allclose(c_fractionated1[key], fractionated) np.testing.assert_allclose(c_unfractionated1[key], unfractionated[key]) np.testing.assert_allclose(c_unfractionated2[key], unfractionated[key]) #Changing reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 unfractionated = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed=46) unfractionated = unfractionated * fraction_ref unfractionated['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated['105pd'] unfractionated2 = unfractionated.ratio('105pd') mf_factor = isopy.random(100, (0, 2), seed=47) c_fractionated1 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor, '105pd', isotope_masses=mass_ref) c_fractionated2 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor, isotope_masses=mass_ref) assert c_fractionated1.keys == unfractionated.keys assert c_fractionated1.size == unfractionated.size assert c_fractionated2.keys == unfractionated.keys assert c_fractionated2.size == unfractionated.size c_unfractionated1 = isopy.tb.remove_mass_fractionation(c_fractionated1, mf_factor, '105pd', isotope_masses=mass_ref) c_unfractionated2 = isopy.tb.remove_mass_fractionation(c_fractionated2, mf_factor, isotope_masses=mass_ref) assert c_unfractionated1.keys == unfractionated.keys assert c_unfractionated1.size == unfractionated.size assert c_unfractionated2.keys == unfractionated.keys assert c_unfractionated2.size == unfractionated.size c_mf_factor2 = isopy.tb.calculate_mass_fractionation_factor(c_fractionated1, '108pd/105pd', isotope_masses=mass_ref, isotope_fractions=fraction_ref) np.testing.assert_allclose(c_mf_factor2, mf_factor) for key in unfractionated.keys: mass_diff = mass_ref.get(key / '105pd') fractionated = unfractionated[key] * (mass_diff ** mf_factor) np.testing.assert_allclose(c_fractionated1[key], fractionated) np.testing.assert_allclose(c_unfractionated1[key], unfractionated[key]) np.testing.assert_allclose(c_unfractionated2[key], unfractionated[key]) # calculate_mass_fractionation_factor, remove_mass_fractionation, add_mass_fractionation def test_mass_fractionation2(): # Testing with input as ratio array # Using default reference values mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 unfractionated = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed=46) unfractionated = unfractionated * fraction_ref unfractionated['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated['105pd'] unfractionated = unfractionated.ratio('105pd') mf_factor = isopy.random(100, (0, 2), seed=47) c_fractionated2 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor) assert c_fractionated2.keys == unfractionated.keys assert c_fractionated2.size == unfractionated.size c_unfractionated2 = isopy.tb.remove_mass_fractionation(c_fractionated2, mf_factor) assert c_unfractionated2.keys == unfractionated.keys assert c_unfractionated2.size == unfractionated.size c_mf_factor2 = isopy.tb.calculate_mass_fractionation_factor(c_fractionated2, '108pd/105pd') np.testing.assert_allclose(c_mf_factor2, mf_factor) for key in unfractionated.keys: mass_diff = mass_ref.get(key) fractionated = unfractionated[key] * (mass_diff ** mf_factor) np.testing.assert_allclose(c_fractionated2[key], fractionated) np.testing.assert_allclose(c_unfractionated2[key], unfractionated[key]) # Changing reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 unfractionated = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed=46) unfractionated = unfractionated * fraction_ref unfractionated['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated['105pd'] unfractionated = unfractionated.ratio('105pd') mf_factor = isopy.random(100, (0, 2), seed=47) c_fractionated2 = isopy.tb.add_mass_fractionation(unfractionated, mf_factor, isotope_masses=mass_ref) assert c_fractionated2.keys == unfractionated.keys assert c_fractionated2.size == unfractionated.size c_unfractionated2 = isopy.tb.remove_mass_fractionation(c_fractionated2, mf_factor, isotope_masses=mass_ref) assert c_unfractionated2.keys == unfractionated.keys assert c_unfractionated2.size == unfractionated.size c_mf_factor2 = isopy.tb.calculate_mass_fractionation_factor(c_fractionated2, '108pd/105pd', isotope_masses=mass_ref, isotope_fractions=fraction_ref) np.testing.assert_allclose(c_mf_factor2, mf_factor) for key in unfractionated.keys: mass_diff = mass_ref.get(key) fractionated = unfractionated[key] * (mass_diff ** mf_factor) np.testing.assert_allclose(c_fractionated2[key], fractionated) np.testing.assert_allclose(c_unfractionated2[key], unfractionated[key]) class Test_MassIndependentCorrection: def test_one(self): # Default reference values mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 unfractionated1 = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed=46) unfractionated1 = unfractionated1 * fraction_ref unfractionated1['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated1['105pd'] unfractionated2 = unfractionated1.ratio('105pd') n_unfractionated2 = (unfractionated2 / fraction_ref - 1) * 10000 mf_factor = isopy.random(100, (0, 2), seed=47) fractionated1 = isopy.tb.add_mass_fractionation(unfractionated2, mf_factor) fractionated2 = fractionated1.deratio(unfractionated1['105pd']) self.run(fractionated1, unfractionated2, '108pd/105pd') self.run(fractionated2, unfractionated2, '108pd/105pd') self.run(fractionated1, n_unfractionated2, '108pd/105pd', factor=10_000) self.run(fractionated2, n_unfractionated2, '108pd/105pd', factor=10_000) self.run(fractionated1, n_unfractionated2, '108pd/105pd', factor='epsilon') self.run(fractionated2, n_unfractionated2, '108pd/105pd', factor='epsilon') # Different reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 unfractionated1 = isopy.random(100, (1, 0.001), keys=isopy.refval.element.isotopes['pd'], seed=46) unfractionated1 = unfractionated1 * fraction_ref unfractionated1['108pd'] = fraction_ref.get('108pd/105pd') * unfractionated1['105pd'] unfractionated2 = unfractionated1.ratio('105pd') n_unfractionated2 = (unfractionated2 / fraction_ref - 1) * 10000 mf_factor = isopy.random(100, (0, 2), seed=47) fractionated1 = isopy.tb.add_mass_fractionation(unfractionated2, mf_factor, isotope_masses=mass_ref) fractionated2 = fractionated1.deratio(unfractionated1['105pd']) self.run(fractionated1, unfractionated2, '108pd/105pd', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated2, unfractionated2, '108pd/105pd', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated1, n_unfractionated2, '108pd/105pd', factor=10_000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated2, n_unfractionated2, '108pd/105pd', factor=10_000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated1, n_unfractionated2, '108pd/105pd', factor='epsilon', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated2, n_unfractionated2, '108pd/105pd', factor='epsilon', mass_ref=mass_ref, fraction_ref=fraction_ref) def test_two(self): # With interference correctionn # We wont get an exact match here so we have to lower the tolerance. # Default reference values mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 mf_factor = isopy.random(100, (0, 2), seed=47) data = isopy.random(100, (1, 0.1), keys='101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd'.split(), seed=46) data = data * fraction_ref data['108pd'] = fraction_ref.get('108pd/105pd') * data['105pd'] fractionated = data.copy() fractionated = isopy.tb.add_mass_fractionation(fractionated, mf_factor) for key in fractionated.keys.filter(element_symbol='pd'): if (ru:=fraction_ref.get(f'ru{key.mass_number}/ru101', 0)) > 0: ru *= fractionated['101ru'] * (mass_ref.get(f'ru{key.mass_number}/ru101', 0) ** mf_factor) fractionated[key] += ru if (cd:=fraction_ref.get(f'cd{key.mass_number}/cd111', 0)) > 0: cd *= fractionated['111cd'] * (mass_ref.get(f'cd{key.mass_number}/cd111', 0) ** mf_factor) fractionated[key] += cd correct1 = data.copy(element_symbol = 'pd').ratio('105pd') correct2 = (correct1 / fraction_ref - 1) correct3 = (correct1 / fraction_ref - 1) * 10_000 self.run(fractionated, correct1, '108pd/105pd') self.run(fractionated, correct2, '108pd/105pd', factor=1) self.run(fractionated, correct3, '108pd/105pd', factor=10_000) self.run(fractionated, correct3, '108pd/105pd', factor='epsilon') # Different reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 mf_factor = isopy.random(100, (0, 2), seed=47) data = isopy.random(100, (1, 0.1), keys='101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd'.split(), seed=46) data = data * fraction_ref data['108pd'] = fraction_ref.get('108pd/105pd') * data['105pd'] fractionated = data.copy() fractionated = isopy.tb.add_mass_fractionation(fractionated, mf_factor, isotope_masses=mass_ref) for key in fractionated.keys.filter(element_symbol='pd'): if (ru := fraction_ref.get(f'ru{key.mass_number}/ru101', 0)) > 0: ru *= fractionated['101ru'] * ( mass_ref.get(f'ru{key.mass_number}/ru101', 0) ** mf_factor) fractionated[key] += ru if (cd := fraction_ref.get(f'cd{key.mass_number}/cd111', 0)) > 0: cd *= fractionated['111cd'] * ( mass_ref.get(f'cd{key.mass_number}/cd111', 0) ** mf_factor) fractionated[key] += cd correct1 = data.copy(element_symbol='pd').ratio('105pd') correct2 = (correct1 / fraction_ref - 1) correct3 = (correct1 / fraction_ref - 1) * 10_000 self.run(fractionated, correct1, '108pd/105pd', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct2, '108pd/105pd', factor=1, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct3, '108pd/105pd', factor=10_000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct3, '108pd/105pd', factor='epsilon', mass_ref=mass_ref, fraction_ref=fraction_ref) def test_three(self): # Normalisations # Default reference values mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 mf_factor = isopy.random(100, (0, 2), seed=47) data = isopy.random(100, (1, 0.1), keys='102pd 104pd 105pd 106pd 108pd 110pd'.split(), seed=46) data = data * fraction_ref data['108pd'] = fraction_ref.get('108pd/105pd') * data['105pd'] fractionated = data.copy() fractionated = isopy.tb.add_mass_fractionation(fractionated, mf_factor) correct1 = data.copy(element_symbol='pd').ratio('105pd') correct2 = (correct1 / fraction_ref - 1) correct3 = correct2 * 1000 correct4 = correct2 * 10_000 correct5 = correct2 * 1_000_000 self.run(fractionated, correct1, '108pd/105pd') self.run(fractionated, correct2, '108pd/105pd', factor=1) self.run(fractionated, correct3, '108pd/105pd', factor=1000) self.run(fractionated, correct3, '108pd/105pd', factor='ppt') self.run(fractionated, correct3, '108pd/105pd', factor='permil') self.run(fractionated, correct4, '108pd/105pd', factor=10_000) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon') self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000) self.run(fractionated, correct5, '108pd/105pd', factor='mu') self.run(fractionated, correct5, '108pd/105pd', factor='ppm') # Single value std1 = isopy.random(100, (1, 0.1), keys='102pd 104pd 105pd 106pd 108pd 110pd'.split(), seed=48) std1 = std1 * fraction_ref rstd1 = std1.ratio('pd105') correct1 = data.copy(element_symbol='pd').ratio('105pd') correct2 = (correct1 / np.mean(rstd1) - 1) correct3 = correct2 * 1000 correct4 = correct2 * 10_000 correct5 = correct2 * 1_000_000 self.run(fractionated, correct2, '108pd/105pd', norm_val=rstd1) self.run(fractionated, correct2, '108pd/105pd', factor=1, norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor=1000, norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor='permil', norm_val=rstd1) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, norm_val=rstd1) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor='mu', norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', norm_val=rstd1) std1 = np.mean(std1) rstd1 = np.mean(rstd1) self.run(fractionated, correct2, '108pd/105pd', norm_val=rstd1) self.run(fractionated, correct2, '108pd/105pd', factor=1, norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor=1000, norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', norm_val=rstd1) self.run(fractionated, correct3, '108pd/105pd', factor='permil', norm_val=rstd1) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, norm_val=rstd1) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor='mu', norm_val=rstd1) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', norm_val=rstd1) # Multiple std1 = isopy.random(100, (1, 0.1), keys='102pd 104pd 105pd 106pd 108pd 110pd'.split(), seed=48) std1 = std1 * fraction_ref rstd1 = std1.ratio('pd105') std2 = isopy.random(50, (1, 0.1), keys='102pd 104pd 105pd 106pd 108pd 110pd'.split(), seed=49) std2 = std2 * fraction_ref rstd2 = std2.ratio('pd105') correct1 = data.copy(element_symbol='pd').ratio('105pd') correct2 = (correct1 / (np.mean(rstd1)/2 + np.mean(rstd2)/2) - 1) correct3 = correct2 * 1000 correct4 = correct2 * 10_000 correct5 = correct2 * 1_000_000 self.run(fractionated, correct2, '108pd/105pd', norm_val=(rstd1, rstd2)) self.run(fractionated, correct2, '108pd/105pd', factor=1, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor=1000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='permil', norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='mu', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', norm_val=(rstd1, rstd2)) std1 = np.mean(std1) rstd1 = np.mean(rstd1) self.run(fractionated, correct2, '108pd/105pd', norm_val=(rstd1, rstd2)) self.run(fractionated, correct2, '108pd/105pd', factor=1, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor=1000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='permil', norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='mu', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', norm_val=(rstd1, rstd2)) std2 = np.mean(std2) rstd2 = np.mean(rstd2) self.run(fractionated, correct2, '108pd/105pd', norm_val=(rstd1, rstd2)) self.run(fractionated, correct2, '108pd/105pd', factor=1, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor=1000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', norm_val=(rstd1, rstd2)) self.run(fractionated, correct3, '108pd/105pd', factor='permil', norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='mu', norm_val=(rstd1, rstd2)) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', norm_val=(rstd1, rstd2)) # Different reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 mf_factor = isopy.random(100, (0, 2), seed=47) data = isopy.random(100, (1, 0.1), keys='102pd 104pd 105pd 106pd 108pd 110pd'.split(), seed=46) data = data * fraction_ref data['108pd'] = fraction_ref.get('108pd/105pd') * data['105pd'] fractionated = data.copy() fractionated = isopy.tb.add_mass_fractionation(fractionated, mf_factor, isotope_masses=mass_ref) correct1 = data.copy(element_symbol='pd').ratio('105pd') correct2 = (correct1 / fraction_ref - 1) correct3 = correct2 * 1000 correct4 = correct2 * 10_000 correct5 = correct2 * 1_000_000 self.run(fractionated, correct1, '108pd/105pd', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct2, '108pd/105pd', factor=1, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct3, '108pd/105pd', factor=1000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct3, '108pd/105pd', factor='ppt', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct3, '108pd/105pd', factor='permil', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct4, '108pd/105pd', factor=10_000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct4, '108pd/105pd', factor='epsilon', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct5, '108pd/105pd', factor=1_000_000, mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct5, '108pd/105pd', factor='mu', mass_ref=mass_ref, fraction_ref=fraction_ref) self.run(fractionated, correct5, '108pd/105pd', factor='ppm', mass_ref=mass_ref, fraction_ref=fraction_ref) def run(self, data, correct, mb_ratio, factor = None, mass_ref = None, fraction_ref=None, norm_val = None): if type(factor) is str: func = getattr(isopy.tb.internal_normalisation, factor) factor2 = None else: factor2 = factor func = isopy.tb.internal_normalisation kwargs = {} if factor2 is not None: kwargs['extnorm_factor'] = factor2 if mass_ref is not None: kwargs['isotope_masses'] = mass_ref if fraction_ref is not None: kwargs['isotope_fractions'] = fraction_ref if norm_val is not None: kwargs['extnorm_value'] = norm_val corrected = func(data, mb_ratio, **kwargs) assert corrected.keys == correct.keys - mb_ratio assert corrected.size == correct.size assert corrected.ndim == correct.ndim for key in corrected.keys: np.testing.assert_allclose(corrected[key], correct[key]) # mass independent correction if type(factor) is str: func = getattr(isopy.tb.mass_independent_correction, factor) factor2 = None else: factor2 = factor func = isopy.tb.mass_independent_correction kwargs = {} if factor2 is not None: kwargs['normalisation_factor'] = factor2 if mass_ref is not None: kwargs['isotope_masses'] = mass_ref if fraction_ref is not None: kwargs['isotope_fractions'] = fraction_ref if norm_val is not None: kwargs['normalisation_value'] = norm_val corrected = func(data, mb_ratio, **kwargs) assert corrected.keys == correct.keys - mb_ratio assert corrected.size == correct.size assert corrected.ndim == correct.ndim for key in corrected.keys: np.testing.assert_allclose(corrected[key], correct[key]) class Test_IsobaricInterferences: def test_one(self): # No mass fractionation factor # Single interference isotope # Default reference values fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 base_data = isopy.random(100, (1, 0.01), keys='101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd'.split()) base_data = base_data * fraction_ref data = base_data.copy() for key in data.keys.filter(element_symbol='pd'): data[key] += fraction_ref.get(f'ru{key.mass_number}/ru101', 0) * data['101ru'] data[key] += fraction_ref.get(f'cd{key.mass_number}/cd111', 0) * data['111cd'] interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '111cd'] = 0 interferences2 = {'ru': ('104pd',), 'cd': ('106pd', '108pd')} correct2 = base_data.copy() correct2['101ru', '111cd'] = 0 correct2['102pd'] = data['102pd'] correct2['110pd'] = data['110pd'] self.run(data, data, correct1, correct2, interferences1, interferences2, '105pd') # Different reference values fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 base_data = isopy.random(100, (1, 0.01), keys='101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd'.split()) base_data = base_data * fraction_ref data = base_data.copy() for key in data.keys.filter(element_symbol='pd'): data[key] += fraction_ref.get(f'ru{key.mass_number}/ru101', 0) * data['101ru'] data[key] += fraction_ref.get(f'cd{key.mass_number}/cd111', 0) * data['111cd'] interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '111cd'] = 0 interferences2 = {'ru': ('104pd',), 'cd': ('106pd', '108pd')} correct2 = base_data.copy() correct2['101ru', '111cd'] = 0 correct2['102pd'] = data['102pd'] correct2['110pd'] = data['110pd'] self.run(data, data, correct1, correct2, interferences1, interferences2, '105pd', fraction_ref=fraction_ref) def test_two(self): # No mass fractionation factor # Multiple interference isotopes # Default reference values fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 base_data = isopy.random(100, (1, 0.01), keys='99ru 101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd 112cd'.split()) # 112cd > 111cd, 101ru > 99ru base_data = base_data * fraction_ref data1 = base_data.copy() data1['99ru', '111cd'] = -1 # so that we dont accidentally make this the largest isotope for key in data1.keys.filter(key_neq = '<KEY>'.split()): data1[key] += fraction_ref.get(f'ru{key.mass_number}/ru101', 0) * data1['101ru'] data1[key] += fraction_ref.get(f'cd{key.mass_number}/cd112', 0) * data1['112cd'] interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '112cd'] = 0 correct1['99ru', '111cd'] = -1 interferences2 = {'ru99': ('104pd',), 'cd111': ('106pd', '108pd')} data2 = base_data.copy() data2['ru101', 'cd112'] = -1 # so that we dont accidentally make this the largest isotope for key in data2.keys.filter(key_neq='ru99 cd111 102pd 110pd'.split()): data2[key] += fraction_ref.get(f'ru{key.mass_number}/ru99', 0) * data2['99ru'] data2[key] += fraction_ref.get(f'cd{key.mass_number}/cd111', 0) * data2['111cd'] correct2 = base_data.copy() correct2['99ru', '111cd'] = 0 correct2['101ru', '112cd'] = -1 self.run(data1, data2, correct1, correct2, interferences1, interferences2, '105pd') # Different reference values fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 base_data = isopy.random(100, (1, 0.01), keys='99ru 101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd 112cd'.split()) # 112cd > 111cd, 101ru > 99ru base_data = base_data * fraction_ref data1 = base_data.copy() data1['99ru', '111cd'] = -1 # so that we dont accidentally make this the largest isotope for key in data1.keys.filter(key_neq='<KEY>'.split()): data1[key] += fraction_ref.get(f'ru{key.mass_number}/ru101', 0) * data1['101ru'] data1[key] += fraction_ref.get(f'cd{key.mass_number}/cd112', 0) * data1['112cd'] interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '112cd'] = 0 correct1['99ru', '111cd'] = -1 interferences2 = {'ru99': ('104pd',), 'cd111': ('106pd', '108pd')} data2 = base_data.copy() data2['ru101', 'cd112'] = -1 # so that we dont accidentally make this the largest isotope for key in data2.keys.filter(key_neq='<KEY>'.split()): data2[key] += fraction_ref.get(f'ru{key.mass_number}/ru99', 0) * data2['99ru'] data2[key] += fraction_ref.get(f'cd{key.mass_number}/cd111', 0) * data2['111cd'] correct2 = base_data.copy() correct2['99ru', '111cd'] = 0 correct2['101ru', '112cd'] = -1 self.run(data1, data2, correct1, correct2, interferences1, interferences2, '105pd', fraction_ref=fraction_ref) def test_three(self): #Mass fractionation #Single interference isotope mass_ref = isopy.refval.isotope.mass_W17 fraction_ref = isopy.refval.isotope.best_measurement_fraction_M16 base_data = isopy.random(100, (1, 0.01), keys='<KEY>'.split()) mf_factor = isopy.random(100, (0,2)) base_data = base_data * fraction_ref data = base_data.copy() for key in data.keys.filter(element_symbol='pd'): if (ru:=fraction_ref.get(f'ru{key.mass_number}/ru101', 0)) > 0: ru *= data['101ru'] * (mass_ref.get(f'ru{key.mass_number}/ru101', 0) ** mf_factor) data[key] += ru if (cd:=fraction_ref.get(f'cd{key.mass_number}/cd111', 0)) > 0: cd *= data['111cd'] * (mass_ref.get(f'cd{key.mass_number}/cd111', 0) ** mf_factor) data[key] += cd interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '111cd'] = 0 interferences2 = {'ru': ('104pd',), 'cd': ('106pd', '108pd')} correct2 = base_data.copy() correct2['101ru', '111cd'] = 0 correct2['102pd'] = data['102pd'] correct2['110pd'] = data['110pd'] self.run(data, data, correct1, correct2, interferences1, interferences2, '105pd', mf_factor=mf_factor) #M Multiple interference isotopes # Different reference values mass_ref = isopy.refval.isotope.mass_number fraction_ref = isopy.refval.isotope.initial_solar_system_fraction_L09 base_data = isopy.random(100, (1, 0.01), keys='99ru 101ru 102pd 104pd 105pd 106pd 108pd 110pd 111cd 112cd'.split()) # 112cd > 111cd, 101ru > 99ru base_data = base_data * fraction_ref data1 = base_data.copy() data1['99ru', '111cd'] = -1 # so that we dont accidentally make this the largest isotope for key in data1.keys.filter(key_neq='<KEY>'.split()): if (ru:=fraction_ref.get(f'ru{key.mass_number}/ru101', 0)) > 0: ru *= data1['101ru'] * (mass_ref.get(f'ru{key.mass_number}/ru101', 0) ** mf_factor) data1[key] += ru if (cd:=fraction_ref.get(f'cd{key.mass_number}/cd112', 0)) > 0: cd *= data1['cd112'] * (mass_ref.get(f'cd{key.mass_number}/cd112', 0) ** mf_factor) data1[key] += cd interferences1 = {'ru': ('102pd', '104pd'), 'cd': ('106pd', '108pd', '110pd')} correct1 = base_data.copy() correct1['101ru', '112cd'] = 0 correct1['99ru', '111cd'] = -1 interferences2 = {'ru99': ('104pd',), 'cd111': ('106pd', '108pd')} data2 = base_data.copy() data2['ru101', 'cd112'] = -1 # so that we dont accidentally make this the largest isotope for key in data2.keys.filter(key_neq='ru99 cd111 102pd 110pd'.split()): if (ru:=fraction_ref.get(f'ru{key.mass_number}/ru99', 0)) > 0: ru *= data2['ru99'] * (mass_ref.get(f'ru{key.mass_number}/ru99', 0) ** mf_factor) data2[key] += ru if (cd:=fraction_ref.get(f'cd{key.mass_number}/cd111', 0)) > 0: cd *= data2['111cd'] * (mass_ref.get(f'cd{key.mass_number}/cd111', 0) ** mf_factor) data2[key] += cd correct2 = base_data.copy() correct2['99ru', '111cd'] = 0 correct2['101ru', '112cd'] = -1 self.run(data1, data2, correct1, correct2, interferences1, interferences2, '105pd', fraction_ref=fraction_ref, mass_ref=mass_ref, mf_factor=mf_factor) def run(self, data1, data2, correct1, correct2, interferences1, interferences2, denom=None, mf_factor=None, fraction_ref=None, mass_ref=None): interferences = isopy.tb.find_isobaric_interferences('pd', data1) assert len(interferences) == len(interferences) for key in interferences1: assert key in interferences assert interferences[key] == interferences1[key] corrected1 = isopy.tb.remove_isobaric_interferences(data1, interferences, mf_factor=mf_factor, isotope_fractions=fraction_ref, isotope_masses=mass_ref) assert corrected1.keys == correct1.keys assert corrected1.size == correct1.size for key in corrected1.keys: np.testing.assert_allclose(corrected1[key], correct1[key]) corrected2 = isopy.tb.remove_isobaric_interferences(data2, interferences2, mf_factor=mf_factor, isotope_fractions=fraction_ref, isotope_masses=mass_ref) assert corrected2.keys == correct2.keys assert corrected2.size == correct2.size for key in corrected2.keys: np.testing.assert_allclose(corrected2[key], correct2[key]) #Ratio test data if denom is not None: data1 = data1.ratio(denom) data2 = data2.ratio(denom) correct1 = correct1.ratio(denom) correct2 = correct2.ratio(denom) interferences = isopy.tb.find_isobaric_interferences('pd', data1) assert len(interferences) == len(interferences) for key in interferences1: assert key in interferences assert interferences[key] == interferences1[key] corrected1 = isopy.tb.remove_isobaric_interferences(data1, interferences, mf_factor=mf_factor, isotope_fractions=fraction_ref, isotope_masses=mass_ref) assert corrected1.keys == correct1.keys assert corrected1.size == correct1.size for key in corrected1.keys: np.testing.assert_allclose(corrected1[key], correct1[key]) corrected2 = isopy.tb.remove_isobaric_interferences(data2, interferences2, mf_factor=mf_factor, isotope_fractions=fraction_ref, isotope_masses=mass_ref) assert corrected2.keys == correct2.keys assert corrected2.size == correct2.size for key in corrected2.keys: np.testing.assert_allclose(corrected2[key], correct2[key]) def test_find(self): interferences = isopy.tb.find_isobaric_interferences('pd', ('ru', 'cd')) assert len(interferences) == 2 assert 'ru' in interferences assert interferences['ru'] == ('102Pd', '104Pd') assert 'cd' in interferences assert interferences['cd'] == ('106Pd', '108Pd', '110Pd') interferences = isopy.tb.find_isobaric_interferences('pd', ('ru', 'rh', 'ag', 'cd')) assert len(interferences) == 2 assert 'ru' in interferences assert interferences['ru'] == ('102Pd', '104Pd') assert 'cd' in interferences assert interferences['cd'] == ('106Pd', '108Pd', '110Pd') interferences = isopy.tb.find_isobaric_interferences('ce') assert len(interferences) == 4 assert 'xe' in interferences assert interferences['xe'] == ('136Ce',) assert 'ba' in interferences assert interferences['ba'] == ('136Ce', '138Ce') assert 'la' in interferences assert interferences['la'] == ('138Ce', ) assert 'nd' in interferences assert interferences['nd'] == ('142Ce',) interferences = isopy.tb.find_isobaric_interferences('138ce') assert len(interferences) == 2 assert 'ba' in interferences assert interferences['ba'] == ('138Ce',) assert 'la' in interferences assert interferences['la'] == ('138Ce',) interferences = isopy.tb.find_isobaric_interferences('zn', ('ni', 'ge', 'ba++')) assert len(interferences) == 3 assert 'ni' in interferences assert interferences['ni'] == ('64Zn',) assert 'ge' in interferences assert interferences['ge'] == ('70Zn',) assert 'ba++' in interferences assert interferences['ba++'] == ('66Zn', '67Zn', '68Zn') class Test_rDelta(): def test_rDelta1(self): # Data is a single value data = isopy.refval.isotope.fraction.to_array(element_symbol='pd') # Dict reference = isopy.refval.isotope.fraction correct1 = isopy.zeros(None, data.keys) correct2 = isopy.ones(None, data.keys) self.run(data, data, reference, correct1, correct2) # Single array reference = isopy.random(100, keys=data.keys) correct1 = data / np.mean(reference) - 1 correct2 = data / np.mean(reference) self.run(data, data, reference, correct1, correct2) self.run(data, data, np.mean(reference), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data, reference, correct1, correct2, 10_000) self.run(data, data, np.mean(reference), correct1, correct2, 10_000) # Multiple values reference1 = isopy.random(100, keys=data.keys) reference2 = isopy.random(100, keys=data.keys) meanmean = np.mean(reference1)/2 + np.mean(reference2)/2 correct1 = data / meanmean - 1 correct2 = data / meanmean self.run(data, data, (reference1, reference2), correct1, correct2) self.run(data, data, (np.mean(reference1), reference2), correct1, correct2) self.run(data, data, (np.mean(reference1), np.mean(reference2)), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data, (reference1, reference2), correct1, correct2, 10_000) self.run(data, data, (np.mean(reference1), reference2), correct1, correct2, 10_000) self.run(data, data, (np.mean(reference1), np.mean(reference2)), correct1, correct2, 10_000) # Keys that do not match data2 = data.copy() data2['105pd', '106pd'] = np.nan reference1 = isopy.random(100, keys='101ru 102pd 104pd 105pd 108pd 110pd 111cd'.split()) reference2 = isopy.random(100, keys='101ru 102pd 104pd 106pd 108pd 110pd 111cd'.split()) meanmean = np.mean(reference1) / 2 + np.mean(reference2) / 2 correct1 = data / meanmean - 1 correct2 = data / meanmean self.run(data, data2, (reference1, reference2), correct1, correct2) self.run(data, data2, (np.mean(reference1), reference2), correct1, correct2) self.run(data, data2, (np.mean(reference1), np.mean(reference2)), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data2, (reference1, reference2), correct1, correct2, 10_000) self.run(data, data2, (np.mean(reference1), reference2), correct1, correct2, 10_000) self.run(data, data2, (np.mean(reference1), np.mean(reference2)), correct1, correct2, 10_000) def test_rDelta2(self): data = isopy.random(100, keys=isopy.refval.element.isotopes['pd']) data = data * isopy.refval.isotope.fraction # Dict reference = isopy.refval.isotope.fraction correct1 = data / reference - 1 correct2 = data / reference self.run(data, data, reference, correct1, correct2) # Single array reference = isopy.random(100, keys=data.keys) correct1 = data / np.mean(reference) - 1 correct2 = data / np.mean(reference) self.run(data, data, reference, correct1, correct2) self.run(data, data, np.mean(reference), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data, reference, correct1, correct2, 10_000) self.run(data, data, np.mean(reference), correct1, correct2, 10_000) # Multiple values reference1 = isopy.random(100, keys=data.keys) reference2 = isopy.random(100, keys=data.keys) meanmean = np.mean(reference1)/2 + np.mean(reference2)/2 correct1 = data / meanmean - 1 correct2 = data / meanmean self.run(data, data, (reference1, reference2), correct1, correct2) self.run(data, data, (np.mean(reference1), reference2), correct1, correct2) self.run(data, data, (np.mean(reference1), np.mean(reference2)), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data, (reference1, reference2), correct1, correct2, 10_000) self.run(data, data, (np.mean(reference1), reference2), correct1, correct2, 10_000) self.run(data, data, (np.mean(reference1), np.mean(reference2)), correct1, correct2, 10_000) # Keys that do not match data2 = data.copy() data2['105pd', '106pd'] = np.nan reference1 = isopy.random(100, keys='101ru 102pd 104pd 105pd 108pd 110pd 111cd'.split()) reference2 = isopy.random(100, keys='101ru 102pd 104pd 106pd 108pd 110pd 111cd'.split()) meanmean = np.mean(reference1) / 2 + np.mean(reference2) / 2 correct1 = data / meanmean - 1 correct2 = data / meanmean self.run(data, data2, (reference1, reference2), correct1, correct2) self.run(data, data2, (np.mean(reference1), reference2), correct1, correct2) self.run(data, data2, (np.mean(reference1), np.mean(reference2)), correct1, correct2) correct1 = correct1 * 10_000 correct2 = correct2 * 10_000 self.run(data, data2, (reference1, reference2), correct1, correct2, 10_000) self.run(data, data2, (np.mean(reference1), reference2), correct1, correct2, 10_000) self.run(data, data2, (np.mean(reference1), np.mean(reference2)), correct1, correct2, 10_000) def test_presets(self): data = isopy.random(100, keys=isopy.refval.element.isotopes['pd']) data = data * isopy.refval.isotope.fraction reference = isopy.refval.isotope.fraction correct = (data / reference - 1) * 1000 normalised = isopy.tb.rDelta.ppt(data, reference) denormalised = isopy.tb.inverse_rDelta.ppt(normalised, reference) self.compare(correct, normalised) self.compare(data, denormalised) correct = (data / reference - 1) * 1000 normalised = isopy.tb.rDelta.permil(data, reference) denormalised = isopy.tb.inverse_rDelta.permil(normalised, reference) self.compare(correct, normalised) self.compare(data, denormalised) correct = (data / reference - 1) * 10_000 normalised = isopy.tb.rDelta.epsilon(data, reference) denormalised = isopy.tb.inverse_rDelta.epsilon(normalised, reference) self.compare(correct, normalised) self.compare(data, denormalised) correct = (data / reference - 1) * 1_000_000 normalised = isopy.tb.rDelta.mu(data, reference) denormalised = isopy.tb.inverse_rDelta.mu(normalised, reference) self.compare(correct, normalised) self.compare(data, denormalised) correct = (data / reference - 1) * 1_000_000 normalised = isopy.tb.rDelta.ppm(data, reference) denormalised = isopy.tb.inverse_rDelta.ppm(normalised, reference) self.compare(correct, normalised) self.compare(data, denormalised) def run(self, data1, data2, reference_value, correct1, correct2, factor=1): normalised = isopy.tb.rDelta(data1, reference_value, factor=factor) assert normalised.keys == data1.keys assert normalised.size == data1.size assert normalised.ndim == data1.ndim for key in normalised.keys: np.testing.assert_allclose(normalised[key], correct1[key]) denormalised = isopy.tb.inverse_rDelta(normalised, reference_value, factor=factor) assert denormalised.keys == data1.keys assert denormalised.size == data1.size assert denormalised.ndim == data1.ndim for key in denormalised.keys: np.testing.assert_allclose(denormalised[key], data2[key]) normalised = isopy.tb.rDelta(data1, reference_value, factor=factor, deviations=0) assert normalised.keys == data1.keys assert normalised.size == data1.size assert normalised.ndim == data1.ndim for key in normalised.keys: np.testing.assert_allclose(normalised[key], correct2[key]) denormalised = isopy.tb.inverse_rDelta(normalised, reference_value, factor=factor, deviations=0) assert denormalised.keys == data1.keys assert denormalised.size == data1.size assert denormalised.ndim == data1.ndim for key in denormalised.keys: np.testing.assert_allclose(denormalised[key], data2[key]) def compare(self, correct, calculated): assert calculated.keys == correct.keys assert calculated.size == correct.size assert calculated.ndim == correct.ndim for key in calculated.keys: np.testing.assert_allclose(calculated[key], correct[key]) class Test_OutliersLimits: def test_limits(self): data = isopy.random(100, (1,1), keys=isopy.refval.element.isotopes['pd']) median = np.median(data) mean = np.mean(data) mad3 = isopy.mad3(data) sd2 = isopy.sd2(data) upper = isopy.tb.upper_limit(data) assert upper == median + mad3 upper = isopy.tb.upper_limit(data, np.mean, isopy.sd2) assert upper == mean + sd2 upper = isopy.tb.upper_limit.sd2(data) assert upper == mean + sd2 upper = isopy.tb.upper_limit(data, 1, isopy.sd2) assert upper == 1 + sd2 upper = isopy.tb.upper_limit(data, np.mean, 1) assert upper == mean + 1 upper = isopy.tb.upper_limit(data, 1, 1) assert upper == 2 lower = isopy.tb.lower_limit(data) assert lower == median - mad3 lower = isopy.tb.lower_limit.sd2(data) assert lower == mean - sd2 lower = isopy.tb.lower_limit(data, np.mean, isopy.sd2) assert lower == mean - sd2 lower = isopy.tb.lower_limit(data, 1, isopy.sd2) assert lower == 1 - sd2 lower = isopy.tb.lower_limit(data, np.mean, 1) assert lower == mean - 1 lower = isopy.tb.lower_limit(data, 1, 1) assert lower == 0 def test_find_outliers1(self): #axis = 0 data = isopy.random(100, (1, 1), keys=isopy.refval.element.isotopes['pd']) median = np.median(data) mean = np.mean(data) mad3 = isopy.mad3(data) sd = isopy.sd(data) median_outliers = (data > (median + mad3)) + (data < (median - mad3)) mean_outliers = (data > (mean + sd)) + (data < (mean - sd)) mean_outliers1 = (data > (1 + sd)) + (data < (1 - sd)) mean_outliers2 = (data > (mean + 1)) + (data < (mean - 1)) mean_outliers3 = (data > (1 + 1)) + (data < (1 - 1)) outliers = isopy.tb.find_outliers(data) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], median_outliers[key]) outliers = isopy.tb.find_outliers(data, np.mean, isopy.sd) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], mean_outliers[key]) outliers = isopy.tb.find_outliers.sd(data) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], mean_outliers[key]) outliers = isopy.tb.find_outliers(data, 1, isopy.sd) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], mean_outliers1[key]) outliers = isopy.tb.find_outliers(data, np.mean, 1) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], mean_outliers2[key]) outliers = isopy.tb.find_outliers(data, 1, 1) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys: np.testing.assert_allclose(outliers[key], mean_outliers3[key]) # invert median_outliers = np.invert(median_outliers) mean_outliers = np.invert(mean_outliers) mean_outliers1 = np.invert(mean_outliers1) mean_outliers2 = np.invert(mean_outliers2) mean_outliers3 = np.invert(mean_outliers3) outliers = isopy.tb.find_outliers(data, invert=True) assert outliers.keys == data.keys assert outliers.size == data.size for key in outliers.keys:

np.testing.assert_allclose(outliers[key], median_outliers[key])

numpy.testing.assert_allclose

import numpy as np from pype3 import pypeify,pypeify_namespace,p,_,_0,_1,_2,ep,tup,db,a,iff,d from pype3.helpers import * from pype3 import ep # from numba import njit,jit from functools import reduce ''' This is a series of operations for numpy. Will document later. ''' def agg_sum(m): indices=m[:,0].argsort() m[:,0]=m[indices,0] m[:,1:]=m[indices,1:] uniqueKeys=np.unique(m[:,0],return_counts=True) cumSum=np.cumsum(uniqueKeys[1])[:-1] splitValues=np.split(m[:,1:],cumSum) sm=np.array([np.sum(l,axis=0) for l in splitValues]) return sm,uniqueKeys[0],uniqueKeys[1] def build_mat(y,X): m=np.zeros([y.shape[0],X.shape[1]+1]) m[:,0]=y m[:,1:]=X return m # @njit def shuffle(m): np.random.shuffle(m) return m def aggregate_by_first_column(m): indices=m[:,0].argsort() m[:,0]=m[indices,0] m[:,1:]=m[indices,1:] uniqueKeys=np.unique(m[:,0],return_counts=True) cumSum=np.cumsum(uniqueKeys[1])[:-1] splitValues=np.split(m[:,1:],cumSum) return splitValues,uniqueKeys[0],uniqueKeys[1] # @njit def vectors_to_column_matrix(vecs,m): for (i,vec) in enumerate(vecs): m[:vec.shape[0],i]=vec return m # @njit def sizes(vecs,s): for (i,vec) in enumerate(vecs): s[i]=vec.shape[0] return s def np_tile_cols(vec,numCols): return np.tile(vec,(numCols,1)).T def np_tile_rows(vec,numCols): return np.tile(vec,(numCols,1)) def np_zero_array(rows): return np.zeros([rows]) def np_zeros(rows,cols): return np.zeros([rows,cols]) def square_zeros(ln): return np.zeros([ln,ln]) def aggregate_by_key(m,padVal=0,pad=True): ''' This is a helper which takes an array with two columns. It is the numpy equivalent of grouping represented by tup_ls_dct in pype. The first column is the key, and the second column is the value. We perform the following operations on this: 1) Sort the keys of m, getting their indices. 2) Reorder the keys and values of m accordingly. 3) Find the unique keys and their counts, stored in uniqueKeys[1]. 4) The np.split function takes an array, and splits it according to the counts of the unique elements. So, take the first x elements, put it in one part of the list, then take the next y elements, append it to the list, etc. 5) In the resulting list of arrays, we find the maximum length. 6) We pad these arrays with zeros if they're shorter than the maximum length. 7) Then, we convert this into a matrix, whose i-th row represents the i-th key, and whose j-th column represents the j-th value with that key. 8) We return the matrix and the unique keys. We do this rather than json-style grouping for performance reasons, as many people have complained about using pure json-style aggregation. Thanks to: https://stackoverflow.com/questions/38013778/is-there-any-numpy-group-by-function ''' indices=m[:,0].argsort() m[:,0]=m[indices,0] m[:,1]=m[indices,1] uniqueKeys=np.unique(m[:,0],return_counts=True) splitValues=np.split(m[:, 1], np.cumsum(uniqueKeys[1])[:-1]) if pad: maxLen=np.max([a.shape[0] for a in splitValues]) aggregatedValues=[np.lib.pad(a, (0,maxLen-a.shape[0]), 'constant', constant_values=(padVal,padVal))\ for a in splitValues] aggregatedValues=np.array(aggregatedValues) else: aggregatedValues=splitValues return aggregatedValues,uniqueKeys[0],uniqueKeys[1] def sorted_aggregate_by_key(m,padVal=0,pad=True): aggregatedValues,uniqueKeys,uniqueCounts=aggregate_by_key(m,padVal,pad) aggregatedValues.sort(axis=1) return aggregatedValues,uniqueKeys,uniqueCounts def aggregate_jsons_by_key(ls,key): uniqueVals=np.unique([js[key] for js in ls]) indexToKeyMap={k:i for (i,k) in enumerate(uniqueVals)} m=np.array([(indexToKeyMap(js[key]),i) for (i,js) in enumerate(ls)]) aggregatedValues,keys,uniqueKeys=aggregate_by_key(m,False) return {k:[ls[index] for index in l] \ for (k,l) in zip(uniqueVals,aggregatedValues)} def np_int_array(x): return np.array(x,dtype=np.int32) def sum_by_row(x): return np.sum(x,axis=1) def sum_by_column(x): return np.sum(x,axis=0) def vector_copy_matrix(shape,vector): z=

np.zeros(shape)

numpy.zeros

################################################################################# ### ### ### Date created - Monday, Nov 11, 2019 ### ### Author - <NAME> <<EMAIL>, <EMAIL> > ### ### ### ################################################################################# """ * This library is only made to work for binary images. The goal was to detect outer boundary and loops in handwritten word images. Using this library, all edges, outer boundary and loops can be quickly detected in a binary image. * The input is binary image. * The output is a list of loops, edges, outer boundary in the same order as mentioned. Each of the return value is an image with the same size as input image with relevant points marked as foreground. """ import cv2, sys import numpy as np from scipy.ndimage import convolve # Find 8 connected neighbors of a point def GetNeighbors(row, col, x, y) : """ This function gives 8 connected neighbors of a pixel.""" neighbors = [ [x-1,y-1], [x-1,y], [x-1, y+1], [x, y-1], [x, y+1], [x+1, y-1], [x+1, y], [x+1, y+1] ] neighbors = [[p,q] for p,q in neighbors if p>=0 and p<row and q >=0 and q<col ] return neighbors # Find 8 connected neighbors of a point which are foreground pixels def GetForegroundNeighbors(Im, x, y) : """ This function gives 8 connected neighbors of a pixel which are foreground pixels.""" row, col = Im.shape neighbors = GetNeighbors(row, col, x, y) FG = [[p,q] for p,q in neighbors if Im[p][q] == 0 ] return FG # Check if image is valid def CheckImage(Im) : """ This function asserts if the image is valid or not.""" if type(Im) is not np.ndarray : if not Im : print("Error! NoneType object") sys.exit(1) print("Error! Input is not ndarray") sys.exit(1) shape = Im.shape if len(shape) <=1 : print("Error! Input is a 1D array, expected 2D or 3D np.ndarray") sys.exit(1) elif len(shape) == 3 : if shape[0] == 0 : print("Error! Image width is zero") sys.exit(1) if shape[1] == 0 : print("Error! Image height is zero") sys.exit(1) gray = cv2.cvtColor(Im, cv2.COLOR_BGR2GRAY) # Convert Image to Binary (thresh, Im) = cv2.threshold(gray, 128, 255, cv2.THRESH_BINARY | cv2.THRESH_OTSU) elif len(shape) == 2 : if shape[0] == 0 : print("Error! Image width is zero") sys.exit(1) if shape[1] == 0 : print("Error! Image height is zero") sys.exit(1) # If image is not binary if len(np.unique(Im)) > 2 : # Convert Image to Binary (thresh, Im) = cv2.threshold(gray, 128, 255, cv2.THRESH_BINARY | cv2.THRESH_OTSU) return Im # Detect edges in binary images def DetectLoopsEdges(Im) : """ This function detects loops, edges and outer boundary in binary image in order [loops, edges, outer_boundary].""" Im = CheckImage(Im) # Pad image with background pixels from all sides(top, bottom, left and right) Im = 1 - Im/255 Im =

np.pad(Im, ((1, 1), (1, 1)), 'constant')

numpy.pad

# execfile("read.py") import numpy as np import pandas as pd def get_data(limit=None): print("Reading data...") df = pd.read_csv('train.csv') data = df.as_matrix() np.random.shuffle(data) X = data[:, 1:] / 255.0 # data is from 0..255 Y = data[:, 0] if limit is not None: X, Y = X[:limit], Y[:limit] return X, Y def get_xor(): X = np.zeros((200, 2)) X[:50] = np.random.random((50, 2)) / 2 + 0.5 # (0.5-1, 0.5-1) X[50:100] = np.random.random((50, 2)) / 2 # (0-0.5, 0-0.5) X[100:150] = np.random.random((50, 2)) / 2 + np.array([[0, 0.5]]) # (0-0.5, 0.5-1) X[150:] = np.random.random((50, 2)) / 2 + np.array([[0.5, 0]]) # (0.5-1, 0-0.5) Y =

np.array([0]*100 + [1]*100)

numpy.array

""" A pytest module to test Galois field polynomial alternate constructors. """ import numpy as np import pytest import galois FIELDS = [ galois.GF2, # GF(2) galois.GF(31), # GF(p) with np.int dtypes galois.GF(36893488147419103183), # GF(p) with object dtype galois.GF(2**8), # GF(2^m) with np.int dtypes galois.GF(2**100), # GF(2^m) with object dtype galois.GF(7**3), # GF(p^m) with np.int dtypes galois.GF(109987**4), # GF(p^m) with object dtypes ] @pytest.mark.parametrize("field", FIELDS) def test_zero(field): p = galois.Poly.Zero(field) assert isinstance(p, galois.Poly) assert p.field is field assert p.degree == 0 assert np.array_equal(p.nonzero_degrees, []) assert np.array_equal(p.nonzero_coeffs, []) assert np.array_equal(p.degrees, [0]) assert np.array_equal(p.coeffs, [0]) assert p.integer == 0 @pytest.mark.parametrize("field", FIELDS) def test_one(field): p = galois.Poly.One(field) assert isinstance(p, galois.Poly) assert p.field is field assert p.degree == 0 assert np.array_equal(p.nonzero_degrees, [0]) assert np.array_equal(p.nonzero_coeffs, [1]) assert

np.array_equal(p.degrees, [0])

numpy.array_equal

# stdlib imports import re # third party imports import numpy as np import logging from strec.subtype import SubductionSelector def get_weights(origin, config): """Get list of GMPEs and their weights for a given earthquake. Args: origin (Origin object): ShakeMap Origin object, containing earthquake info. config (dict-like): Configuration information regarding earthquake type. Returns: tuple: Tuple with elements that are: - list of strings indicating the GMPEs selected for this earthquake. - ndarray (float) of GMPE weights. - Pandas series containing STREC output. """ tprobs, strec_results = get_probs(origin, config) gmpelist = [] weightlist = [] # remove all probabilities that are == 0 probs = {} for key, value in tprobs.items(): if value > 0.0: probs[key] = value all_keylist = list(probs.keys()) # let's have the code default to use the slab data if config["tectonic_regions"]["subduction"]: use_slab = config["tectonic_regions"]["subduction"]["use_slab"] else: use_slab = True for region, rdict in config["tectonic_regions"].items(): if (region == "subduction") and use_slab: if "crustal" in probs or "subduction_0" in probs: if "crustal" in probs: topkey = "crustal" else: topkey = "subduction_0" gmpelist += rdict["crustal"]["gmpe"] weightlist.append(probs[topkey]) if "interface" in probs or "subduction_1" in probs: if "interface" in probs: midkey = "interface" else: midkey = "subduction_1" gmpelist += rdict["interface"]["gmpe"] weightlist.append(probs[midkey]) if "intraslab" in probs or "subduction_2" in probs: if "intraslab" in probs: botkey = "intraslab" else: botkey = "subduction_2" gmpelist += rdict["intraslab"]["gmpe"] weightlist.append(probs[botkey]) else: pat = re.compile(region + "_") keylist = sorted(list(filter(pat.search, all_keylist))) if len(keylist): for key in keylist: weightlist.append(probs[key]) idx = int(key.split("_")[1]) gmpelist.append(rdict["gmpe"][idx]) weightlist = np.array(weightlist) logging.debug(f"gmpelist: {gmpelist}") logging.debug(f"weightlist: {weightlist}") gmmdict = {"gmpelist": gmpelist, "weightlist": weightlist} # # Here we get the region-specific ipe, gmice, and ccf. If they are # not specified in the config, we use None, and let the value # fall back to whatever is specified in the system config. # if strec_results["TectonicRegion"] == "Active": gmmdict["ipe"] = config["tectonic_regions"]["acr"].get("ipe", None) gmmdict["gmice"] = config["tectonic_regions"]["acr"].get("gmice", None) gmmdict["ccf"] = config["tectonic_regions"]["acr"].get("ccf", None) elif strec_results["TectonicRegion"] == "Stable": gmmdict["ipe"] = config["tectonic_regions"]["scr"].get("ipe", None) gmmdict["gmice"] = config["tectonic_regions"]["scr"].get("gmice", None) gmmdict["ccf"] = config["tectonic_regions"]["scr"].get("ccf", None) elif strec_results["TectonicRegion"] == "Subduction": gmmdict["ipe"] = config["tectonic_regions"]["subduction"].get("ipe", None) gmmdict["gmice"] = config["tectonic_regions"]["subduction"].get("gmice", None) gmmdict["ccf"] = config["tectonic_regions"]["subduction"].get("ccf", None) elif strec_results["TectonicRegion"] == "Volcanic": gmmdict["ipe"] = config["tectonic_regions"]["volcanic"].get("ipe", None) gmmdict["gmice"] = config["tectonic_regions"]["volcanic"].get("gmice", None) gmmdict["ccf"] = config["tectonic_regions"]["volcanic"].get("ccf", None) return gmmdict, strec_results def get_probs(origin, config): """Calculate probabilities for each earthquake type. The results here contain probabilities that can be rolled up in many ways: - The probabilities of acr, scr, volcanic, and subduction should sum to one. - The probabilities of acr_X,scr_X,volcanic_X, crustal, interface and intraslab should sum to 1. - The probabilities of acr_X should sum to acr, and so on. Args: origin (Origin object): ShakeMap Origin object, containing earthquake info. config (dict-like): Configuration information regarding earthquake type. Returns: (dict, dict): Probabilities for each earthquake type, with fields: - acr Probability that the earthquake is in an active region. - acr_X Probability that the earthquake is in a depth layer of ACR, starting from the top. - scr Probability that the earthquake is in a stable region. - scr_X Probability that the earthquake is in a depth layer of SCR, starting from the top. - volcanic Probability that the earthquake is in a volcanic region. - volcanic_X Probability that the earthquake is in a depth layer of Volcanic, starting from the top. - subduction Probability that the earthquake is in a subduction zone. - crustal Probability that the earthquake is in the crust above an interface. - interface Probability that the earthquake is on the interface. - intraslab Probability that the earthquake is in the slab below interface. STREC results """ selector = SubductionSelector() lat, lon, depth, mag = origin.lat, origin.lon, origin.depth, origin.mag if origin.id is not None and not origin.id.startswith(origin.netid): eid = origin.netid + origin.id else: eid = origin.id tensor_params = None if hasattr(origin, "moment"): tensor_params = origin.moment strec_results = selector.getSubductionType( lat, lon, depth, eid, tensor_params=tensor_params ) region_probs = get_region_probs(eid, depth, strec_results, config) in_subduction = strec_results["TectonicRegion"] == "Subduction" above_slab = not

np.isnan(strec_results["SlabModelDepth"])

numpy.isnan

# -*- coding: utf-8 -*- # @Author: <NAME> # @Email: <EMAIL> # @Date: 2016-09-19 22:30:46 # @Last Modified by: <NAME> # @Last Modified time: 2021-05-15 11:04:35 ''' Definition of generic utility functions used in other modules ''' import sys import itertools import csv from functools import wraps import operator import time from inspect import signature import os from shutil import get_terminal_size import lockfile import math import pickle import json from tqdm import tqdm import logging import tkinter as tk from tkinter import filedialog import base64 import datetime import numpy as np from scipy.optimize import brentq from scipy import linalg import colorlog from pushbullet import Pushbullet # Package logger my_log_formatter = colorlog.ColoredFormatter( '%(log_color)s %(asctime)s %(message)s', datefmt='%d/%m/%Y %H:%M:%S:', reset=True, log_colors={ 'DEBUG': 'green', 'INFO': 'white', 'WARNING': 'yellow', 'ERROR': 'red', 'CRITICAL': 'red,bg_white', }, style='%') def setHandler(logger, handler): for h in logger.handlers: logger.removeHandler(h) logger.addHandler(handler) return logger def setLogger(name, formatter): handler = colorlog.StreamHandler() handler.setFormatter(formatter) handler.stream = sys.stdout logger = colorlog.getLogger(name) logger.addHandler(handler) return logger class TqdmHandler(logging.StreamHandler): def __init__(self, formatter): logging.StreamHandler.__init__(self) self.setFormatter(formatter) def emit(self, record): msg = self.format(record) tqdm.write(msg) logger = setLogger('PySONIC', my_log_formatter) LOOKUP_DIR = os.path.abspath(os.path.split(__file__)[0] + "/lookups/") def fillLine(text, char='-', totlength=None): ''' Surround a text with repetitions of a specific character in order to fill a line to a given total length. :param text: text to be surrounded :param char: surrounding character :param totlength: target number of characters in filled text line :return: filled text line ''' if totlength is None: totlength = get_terminal_size().columns - 1 ndashes = totlength - len(text) - 2 if ndashes < 2: return text else: nside = ndashes // 2 nleft, nright = nside, nside if ndashes % 2 == 1: nright += 1 return f'{char * nleft} {text} {char * nright}' # SI units prefixes si_prefixes = { 'y': 1e-24, # yocto 'z': 1e-21, # zepto 'a': 1e-18, # atto 'f': 1e-15, # femto 'p': 1e-12, # pico 'n': 1e-9, # nano 'u': 1e-6, # micro 'm': 1e-3, # mili '': 1e0, # None 'k': 1e3, # kilo 'M': 1e6, # mega 'G': 1e9, # giga 'T': 1e12, # tera 'P': 1e15, # peta 'E': 1e18, # exa 'Z': 1e21, # zetta 'Y': 1e24, # yotta } sorted_si_prefixes = sorted(si_prefixes.items(), key=operator.itemgetter(1)) def getSIpair(x, scale='lin'): ''' Get the correct SI factor and prefix for a floating point number. ''' if isIterable(x): # If iterable, get a representative number of the distribution x = np.asarray(x) x = x.prod()**(1.0 / x.size) if scale == 'log' else np.mean(x) if x == 0: return 1e0, '' else: vals = [tmp[1] for tmp in sorted_si_prefixes] ix = np.searchsorted(vals, np.abs(x)) - 1 if

np.abs(x)

numpy.abs

#!/usr/bin/env python """SPECFIT.PY - Generic stellar abundance determination software """ from __future__ import print_function __authors__ = '<NAME> <<EMAIL>>' __version__ = '20200711' # yyyymmdd import os import shutil import contextlib, io, sys import numpy as np import warnings from astropy.io import fits from astropy.table import Table from dlnpyutils.minpack import curve_fit from dlnpyutils.least_squares import least_squares from scipy.interpolate import interp1d from dlnpyutils import utils as dln, bindata, astro import doppler from doppler.spec1d import Spec1D from doppler import (cannon,utils,reader) import copy import logging import time import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt from matplotlib.legend import Legend import tempfile from . import models from synple import synple # Ignore these warnings, it's a bug warnings.filterwarnings("ignore", message="numpy.dtype size changed") warnings.filterwarnings("ignore", message="numpy.ufunc size changed") cspeed = 2.99792458e5 # speed of light in km/s def synmodel(spec,params,alinefile=None,mlinefile=None,verbose=False,normalize=True): """ Synthetic spectrum model. Parameters ---------- spec : Spec1D object or str The observed Spec1D spectrum to match or the name of a spectrum file. params : dict Dictionary of initial values to use or parameters/elements to hold fixed. normalize : bool, optional Renormalize the model spectrum using the observed spectrum's continuum function. The synthetic spectrum will already have been normalized using the "true" continuum. This step is to simulate any systematic effects of the spectrum normalization algorithm that the observed spectrum undergoes. Default is True. verbose : int, optional Verbosity level (0, 1, or 2). The default is 0 and verbose=2 is for debugging. alinefile : str, optional The atomic linelist to use. Default is None which means the default synple linelist is used. mlinefile : str, optional The molecular linelist to use. Default is None which means the default synple linelist is used. Returns ------- model : Spec1D object The synthetic spectrum. The "true" continuum is in model.cont. Example ------- .. code-block:: python model = synmodel(spec,params) """ # Read in the spectrum if type(spec) is str: filename = spec spec = doppler.read(filename) if spec is None: print('Problem loading '+filename) return params = dict((key.upper(), value) for (key, value) in params.items()) # all CAPS # Initialize the fitter fitparams = ['TEFF'] # "dummy" fitting variable spfitter = SpecFitter(spec,params,fitparams=fitparams,verbose=(verbose>=2), alinefile=alinefile,mlinefile=mlinefile) spfitter.norm = normalize # normalize the synthetic spectrum model = spfitter.model(spec.wave.flatten(),params['TEFF'],retobj=True) model.instrument = 'Model' return model class SpecFitter: def __init__ (self,spec,params,fitparams=None,norm=True,verbose=False, alinefile=None,mlinefile=None): # Parameters self.params = params if fitparams is not None: self.fitparams = fitparams else: self.fitparams = list(params.keys()) # by default fit all parameters self.nsynfev = 0 # number of synthetic spectra made self.njac = 0 # number of times jacobian called # Save spectrum information self.spec = spec.copy() self.flux = spec.flux.flatten() self.err = spec.err.flatten() self.wave = spec.wave.flatten() self.lsf = spec.lsf.copy() self.lsf.wavevac = spec.wavevac # need this later for synspec prep self.wavevac = spec.wavevac self.verbose = verbose self.norm = norm # normalize self.continuum_func = spec.continuum_func self.alinefile = alinefile self.mlinefile = mlinefile # Convert vacuum to air wavelengths # synspec uses air wavelengths if spec.wavevac is True: wave = astro.vactoair(spec.wave.copy().flatten()).reshape(spec.wave.shape) else: wave = spec.wave.copy() if wave.ndim==1: wave = np.atleast_2d(wave).T # Figure out the wavelength parameters npix = spec.npix norder = spec.norder xp = np.arange(npix//20)*20 wr = np.zeros((spec.lsf.norder,2),np.float64) dw = np.zeros(spec.lsf.norder,np.float64) mindw = np.zeros(norder,np.float64) for o in range(spec.norder): dw[o] = np.median(dln.slope(wave[:,o])) wr[o,0] = np.min(wave[:,o]) wr[o,1] = np.max(wave[:,o]) fwhm = spec.lsf.fwhm(wave[xp,o],xtype='Wave',order=o) # FWHM is in units of lsf.xtype, convert to wavelength/angstroms, if necessary if spec.lsf.xtype.lower().find('pix')>-1: fwhm *= np.abs(dw[o]) # need at least ~4 pixels per LSF FWHM across the spectrum # using 3 affects the final profile shape mindw[o] = np.min(fwhm/4) self._dwair = np.min(mindw) # IN AIR WAVELENGTHS!! self._w0air = np.min(wave) self._w1air = np.max(wave) # parameters to save self._all_pars = [] self._all_model = [] self._all_chisq = [] self._jac_array = None @property def params(self): return self._params @params.setter def params(self,params): """ Dictionary, keys must be all CAPS.""" self._params = dict((key.upper(), value) for (key, value) in params.items()) # all CAPS @property def fitparams(self): return self._fitparams @fitparams.setter def fitparams(self,fitparams): """ list, keys must be all CAPS.""" self._fitparams = [v.upper() for v in fitparams] # all CAPS def mkinputs(self,args): """ Make INPUTS dictionary.""" # Create INPUTS with all arguments needed to make the spectrum inputs = self.params.copy() # initialize with initial/fixed values for k in range(len(self.fitparams)): # this overwrites the values for the fitted values inputs[self.fitparams[k]] = args[k] inputs['DW'] = self._dwair # add in wavelength parameters inputs['W0'] = self._w0air inputs['W1'] = self._w1air return inputs def chisq(self,model): return np.sqrt( np.sum( (self.flux-model)**2/self.err**2 )/len(self.flux) ) def model(self, xx, *args, retobj=False): """ Return a model spectrum flux with the given input arguments.""" # The input arguments correspond to FITPARAMS # This corrects for air/vacuum wavelength differences if self.verbose: print(args) # The arguments correspond to the fitting parameters inputs = self.mkinputs(args) if self.verbose: print(inputs) # Create the synthetic spectrum synspec = model_spectrum(inputs,verbose=self.verbose, # always returns air wavelengths alinefile=self.alinefile,mlinefile=self.mlinefile) self.nsynfev += 1 # Convolve with the LSF and do air/vacuum wave conversion pspec = prepare_synthspec(synspec,self.lsf,norm=self.norm, continuum_func=self.continuum_func) # Save models/pars/chisq self._all_pars.append(list(args).copy()) self._all_model.append(pspec.flux.flatten().copy()) self._all_chisq.append(self.chisq(pspec.flux.flatten())) # Return flattened spectrum if retobj: return pspec else: return pspec.flux.flatten() def getstep(self,name,val,relstep=0.02): """ Calculate step for a parameter.""" # It mainly deals with edge cases #if val != 0.0: # step = relstep*val #else: # if name=='RV': # step = 1.0 # elif name=='VROT': # step = 0.5 # elif name=='VMICRO': # step = 0.5 # elif name.endswith('_H'): # step = 0.02 # else: # step = 0.02 if name=='TEFF': step = 5.0 elif name=='RV': step = 0.1 elif name=='VROT': step = 0.5 elif name=='VMICRO': step = 0.5 elif name.endswith('_H'): step = 0.01 else: step = 0.01 return step return step def jac(self,x,*args): """ Compute the Jacobian matrix (an m-by-n matrix, where element (i, j) is the partial derivative of f[i] with respect to x[j]). """ if hasattr(self,'logger') is False: logger = dln.basiclogger() else: logger = self.logger logger.info(args) if self.verbose: logger.info(' ') logger.info('##### Calculating Jacobian Matrix #####') logger.info(' ') # A new synthetic spectrum does not need to be generated RV, vmicro or vsini. # Some time can be saved by not remaking those. # Use a one-sided derivative. # Boundaries lbounds,ubounds = mkbounds(self.fitparams) relstep = 0.02 npix = len(x) npar = len(args) # Get INPUTS dictionary and make keys all CAPS inputs = self.mkinputs(args) inputs = dict((key.upper(), value) for (key, value) in inputs.items()) # Some important parameters w0 = inputs['W0'] w1 = inputs['W1'] dw = inputs['DW'] rv = inputs.get('RV') vrot = inputs.get('VROT') vmicro = inputs.get('VMICRO') # Create synthetic spectrum at current values # set vrot=vmicro=rv=0, will modify later if necessary if self.verbose: logger.info('--- Current values ---') logger.info(args) tinputs = inputs.copy() tinputs['VMICRO'] = 0 tinputs['VROT'] = 0 tinputs['RV'] = 0 origspec = model_spectrum(tinputs,keepextend=True, # always are wavelengths alinefile=self.alinefile,mlinefile=self.mlinefile) self.nsynfev += 1 # Smooth and shift smorigspec = smoothshift_spectrum(origspec,vrot=vrot,vmicro=vmicro,rv=rv) # Trim to final wavelengths smorigspec = trim_spectrum(smorigspec,w0,w1) # Convolve with the LSF and do air/vacuum wave conversion pspec = prepare_synthspec(smorigspec,self.lsf,norm=self.norm, continuum_func=self.continuum_func) # Flatten the spectrum f0 = pspec.flux.flatten() # Save models/pars/chisq self._all_pars.append(list(args).copy()) self._all_model.append(f0.copy()) self._all_chisq.append(self.chisq(f0)) chisq = np.sqrt( np.sum( (self.flux-f0)**2/self.err**2 )/len(self.flux) ) self if self.verbose: logger.info('chisq = '+str(chisq)) # MASK PIXELS!? # Initialize jacobian matrix jac = np.zeros((npix,npar),np.float64) # Loop over parameters for i in range(npar): pars = np.array(copy.deepcopy(args)) step = self.getstep(self.fitparams[i],pars[i],relstep) # Check boundaries, if above upper boundary # go the opposite way if pars[i]>ubounds[i]: step *= -1 pars[i] += step tinputs = self.mkinputs(pars) if self.verbose: logger.info(' ') logger.info('--- '+str(i+1)+' '+self.fitparams[i]+' '+str(pars[i])+' ---') logger.info(pars) # VROT/VMICRO/RV, just shift/smooth original spectrum if self.fitparams[i]=='VROT' or self.fitparams[i]=='VMICRO' or self.fitparams[i]=='RV': tvrot = tinputs.get('VROT') tvmicro = tinputs.get('VMICRO') trv = tinputs.get('RV') #import pdb; pdb.set_trace() # Smooth and shift synspec = smoothshift_spectrum(origspec,vrot=tvrot,vmicro=tvmicro,rv=trv) # Trim to final wavelengths synspec = trim_spectrum(synspec,w0,w1) else: synspec = model_spectrum(tinputs,alinefile=self.alinefile, mlinefile=self.mlinefile) # always returns air wavelengths self.nsynfev += 1 # Convert to vacuum wavelengths if necessary if self.wavevac: synspec.wave = astro.airtovac(synspec.wave) synspec.wavevac = True # Convolve with the LSF and do air/vacuum wave conversion pspec = prepare_synthspec(synspec,self.lsf,norm=self.norm, continuum_func=self.continuum_func) # Flatten the spectrum f1 = pspec.flux.flatten() # Save models/pars/chisq self._all_pars.append(list(pars).copy()) self._all_model.append(f1.copy()) self._all_chisq.append(self.chisq(f1)) if np.sum(~np.isfinite(f1))>0: print('some nans/infs') import pdb; pdb.set_trace() jac[:,i] = (f1-f0)/step if np.sum(~np.isfinite(jac))>0: print('some nans/infs') import pdb; pdb.set_trace() self._jac_array = jac.copy() # keep a copy self.njac += 1 return jac def trim_spectrum(spec,w0,w1): """ Trim a synthetic spectrum to [w0,w1].""" # This assumes that the spectrum has a single order wv1, ind1 = dln.closest(spec.wave,w0) wv2, ind2 = dln.closest(spec.wave,w1) # Nothing to do if ind1==0 and ind2==(spec.npix-1): return spec outspec = spec.copy() outspec.flux = outspec.flux[ind1:ind2+1] outspec.wave = outspec.wave[ind1:ind2+1] if outspec.err is not None: outspec.err = outspec.err[ind1:ind2+1] if outspec.mask is not None: outspec.mask = outspec.mask[ind1:ind2+1] if hasattr(outspec,'cont'): if outspec.cont is not None: outspec.cont = outspec.cont[ind1:ind2+1] outspec.npix = len(outspec.flux) return outspec def getabund(inputs,verbose=False): """ Grab the abundances out of the input file and return array of abundances.""" # Create the input 99-element abundance array codedir = os.path.dirname(os.path.abspath(__file__)) pertab = Table.read(codedir+'/data/periodic_table.txt',format='ascii') feh = inputs.get('FEH') if feh is None: feh = inputs.get('FE_H') if feh is None: raise ValueError('FE_H missing from inputs') # Read model atmosphere modelfile = inputs.get('modelfile') if modelfile is None: raise ValueError('modelfile missing from inputs') atmostype, teff, logg, vmicro2, mabu, nd, atmos = synple.read_model(modelfile,verbose=verbose) mlines = dln.readlines(modelfile) # solar abundances # first two are Teff and logg # last two are Hydrogen and Helium solar_abund = np.array([ 4750., 2.5, -10.99, -10.66, -9.34, -3.61, -4.21, -3.35, -7.48, -4.11, -5.80, -4.44, -5.59, -4.53, -6.63, -4.92, -6.54, -5.64, -7.01, -5.70, -8.89, -7.09, -8.11, -6.40, -6.61, -4.54, -7.05, -5.82, -7.85, -7.48, -9.00, -8.39, -9.74, -8.70, -9.50, -8.79, -9.52, -9.17, -9.83, -9.46, -10.58, -10.16, -20.00, -10.29, -11.13, -10.47, -11.10, -10.33, -11.24, -10.00, -11.03, -9.86, -10.49, -9.80, -10.96, -9.86, -10.94, -10.46, -11.32, -10.62, -20.00, -11.08, -11.52, -10.97, -11.74, -10.94, -11.56, -11.12, -11.94, -11.20, -11.94, -11.19, -12.16, -11.19, -11.78, -10.64, -10.66, -10.42, -11.12, -10.87, -11.14, -10.29, -11.39, -20.00, -20.00, -20.00, -20.00, -20.00, -20.00, -12.02, -20.00, -12.58, -20.00, -20.00, -20.00, -20.00, -20.00, -20.00, -20.00]) # Deal with alpha abundances # only add the individual alpha abundance if it's not already there # sometimes we might fit a single alpha element but want to use # ALPHA_H to set the rest of them if inputs.get('ALPHA_H') is not None: alpha = inputs['ALPHA_H'] elem = ['O','MG','SI','S','CA','TI'] for k in range(len(elem)): if inputs.get(elem[k]+'_H') is None: inputs[elem[k]+'_H'] = alpha # Scale global metallicity abu = solar_abund.copy() abu[2:] += feh # Now offset the elements with [X/Fe], [X/Fe]=[X/H]-[Fe/H] g, = np.where( (np.char.array(list(inputs.keys())).find('_H') != -1) & (np.char.array(list(inputs.keys())) != 'FE_H') ) if len(g)>0: ind1,ind2 = dln.match(np.char.array(list(inputs.keys()))[g],np.char.array(pertab['symbol']).upper()+'_H') for k in range(len(ind1)): key1 = np.char.array(list(inputs.keys()))[g[ind1[k]]] abu[ind2[k]] += float(inputs[key1]) - feh if verbose: print('%s %f' % (key1,float(inputs[key1]))) # convert to linear abu[2:] = 10**abu[2:] # Divide by N(H) g, = np.where(np.char.array(mlines).find('ABUNDANCE SCALE') != -1) nhtot = np.float64(mlines[g[0]].split()[6]) abu[2:] /= nhtot # use model values for H and He abu[0:2] = mabu[0:2] return abu def synple_wrapper(inputs,verbose=False,tmpbase='/tmp',alinefile=None,mlinefile=None): """ This is a wrapper around synple to generate a new synthetic spectrum.""" # Wavelengths are all AIR!! # inputs is a dictionary with all of the inputs # Teff, logg, [Fe/H], some [X/Fe], and the wavelength parameters (w0, w1, dw). # Make temporary directory for synple to work in curdir = os.path.abspath(os.curdir) tdir = os.path.abspath(tempfile.mkdtemp(prefix="syn",dir=tmpbase)) os.chdir(tdir) # Linelists to use linelist = ['gfallx3_bpo.19','kmol3_0.01_30.20'] # default values if alinefile is not None: # atomic linelist input linelist[0] = alinefile if mlinefile is not None: # molecular linelist input linelist[1] = mlinefile if verbose: print('Using linelist: ',linelist) # Make key names all CAPS inputs = dict((key.upper(), value) for (key, value) in inputs.items()) # Make the model atmosphere file teff = inputs['TEFF'] logg = inputs['LOGG'] metal = inputs['FE_H'] tid,modelfile = tempfile.mkstemp(prefix="mod",dir=".") os.close(tid) # close the open file # Limit values # of course the logg/feh ranges vary with Teff mteff = dln.limit(teff,3500.0,60000.0) mlogg = dln.limit(logg,0.0,5.0) mmetal = dln.limit(metal,-2.5,0.5) model, header, tail = models.mkmodel(mteff,mlogg,mmetal,modelfile) inputs['modelfile'] = modelfile if os.path.exists(modelfile) is False or os.stat(modelfile).st_size==0: print('model atmosphere file does NOT exist') import pdb; pdb.set_trace() # Create the synspec synthetic spectrum w0 = inputs['W0'] w1 = inputs['W1'] dw = inputs['DW'] vmicro = inputs.get('VMICRO') vrot = inputs.get('VROT') if vrot is None: vrot = 0.0 # Get the abundances abu = getabund(inputs,verbose=verbose) wave,flux,cont = synple.syn(modelfile,(w0,w1),dw,vmicro=vmicro,vrot=vrot, abu=list(abu),verbose=verbose,linelist=linelist) # Delete temporary files shutil.rmtree(tdir) os.chdir(curdir) return (wave,flux,cont) def smoothshift_spectrum(inpspec,vmicro=None,vrot=None,rv=None): """ This smoothes the spectrum by Vrot+Vmicro and shifts it by RV.""" #vmicro = inputs.get('VMICRO') #vrot = inputs.get('VROT') #rv = inputs.get('RV') # Nothing to do if vmicro is None and vrot is None and rv is None: return inpspec.copy() # Initialize output spectrum spec = inpspec.copy() # Some broadening if vmicro is not None or vrot is not None: flux = utils.broaden(spec.wave,spec.flux,vgauss=vmicro,vsini=vrot) spec.flux = flux ## Vrot/Vsini (km/s) and Vmicro (in km/s) #if vrot is not None or vmicro is not None: # wave, flux = synple.call_rotin(wave, flux, vrot, fwhm, space, steprot, stepfwhm, clean=False, reuseinputfiles=True) # Doppler shift only (in km/s) if rv is not None: if rv != 0.0: shiftwave = spec.wave*(1+rv/cspeed) gd,ngd,bd,nbd = dln.where( (spec.wave >= np.min(shiftwave)) & (spec.wave <= np.max(shiftwave)), comp=True) # Doppler shift and interpolate onto wavelength array if hasattr(spec,'cont'): cont = synple.interp_spl(spec.wave[gd], shiftwave, spec.cont) spec.cont *= 0 spec.cont[gd] = cont # interpolate the continuing to the missing pixels if nbd>0: contmissing = dln.interp(spec.wave[gd],spec.cont[gd],spec.wave[bd],kind='linear',assume_sorted=False) spec.cont[bd] = contmissing flux = synple.interp_spl(spec.wave[gd], shiftwave, spec.flux) spec.flux *= 0 spec.flux[gd] = flux if nbd>0: # Fill in missing values with interpolated values if np.sum(np.isfinite(spec.flux[gd]))>0: coef = dln.poly_fit(spec.wave[gd],spec.flux[gd],2) fluxmissing = dln.poly(spec.wave[bd],coef) spec.flux[bd] = fluxmissing # Mask these pixels if spec.mask is None: spec.mask = np.zeros(len(spec.flux),bool) spec.mask[bd] = True return spec def model_spectrum(inputs,verbose=False,keepextend=False,alinefile=None,mlinefile=None): """ This creates a model spectrum given the inputs: RV, Teff, logg, vmicro, vsini, [Fe/H], [X/Fe], w0, w1, dw. This creates the new synthetic spectrum and then convolves with vmicro, vsini and shifts to velocity RV. The returned spectrum always uses AIR wavelengths!!! Parameters ---------- inputs : dictionary Input parameters, stellar parameters, abundances. keepextend : bool, optional Keep the extensions on the ends. Default is False. alinefile : str, optional Atomic linelist filename. Default is None (use synple's default one). mlinefile : str, optional Molecular linelist filename. Default is None (use synple's default one). verbose : bool, optional Verbose output. Default is False. Returns ------- synspec : Spec1D The synthetic spectrum as Spec1D object. """ # Make key names all CAPS inputs = dict((key.upper(), value) for (key, value) in inputs.items()) # Extend on the ends for RV/convolution purposes w0 = inputs['W0'] w1 = inputs['W1'] dw = inputs['DW'] rv = inputs.get('RV') vrot = inputs.get('VROT') vmicro = inputs.get('VMICRO') inputsext = inputs.copy() if rv is not None or vrot is not None or vmicro is not None: numext = int(np.ceil(w1*(1.0+1500/cspeed)-w1)) inputsext['W0'] = w0-numext*dw inputsext['W1'] = w1+numext*dw if verbose: print('Extending wavelength by '+str(numext)+' pixels on each end') # Create the synthetic spectrum # set vrot=vmicro=0, will convolve later if necessary inputsext['VMICRO'] = 0 inputsext['VROT'] = 0 wave1,flux1,cont1 = synple_wrapper(inputsext,verbose=verbose,alinefile=alinefile, mlinefile=mlinefile) # Get final wavelength array wv1, ind1 = dln.closest(wave1,w0) wv2, ind2 = dln.closest(wave1,w1) synspec = Spec1D(flux1/cont1,err=flux1*0,wave=wave1,lsfpars=np.array(0.0)) synspec.cont = cont1 synspec.wavevac = False # Smooth and shift if rv is not None or vrot is not None or vmicro is not None: synspec = smoothshift_spectrum(synspec,vrot=vrot,vmicro=vmicro,rv=rv) # Trim to final wavelengths if keepextend is False: synspec = trim_spectrum(synspec,w0,w1) return synspec def prepare_synthspec(synspec,lsf,norm=True,continuum_func=None): """ Prepare a synthetic spectrum to be compared to an observed spectrum.""" # Convolve with LSF and do air<->vacuum wavelength conversion # Convert wavelength from air->vacuum or vice versa if synspec.wavevac != lsf.wavevac: # Air -> Vacuum if synspec.wavevac is False: synspec.wave = astro.airtovac(synspec.wave) synspec.wavevac = True # Vacuum -> Air else: synspec.dispersion = astro.vactoair(synspec.wave) synspec.wavevac = False # Initialize the output spectrum if lsf.wave.ndim==2: npix,norder = lsf.wave.shape else: npix = len(lsf.wave) norder = 1 pspec = Spec1D(np.zeros((npix,norder),np.float32),err=np.zeros((npix,norder),np.float32), wave=lsf.wave,lsfpars=lsf.pars,lsftype=lsf.lsftype,lsfxtype=lsf.xtype) pspec.cont = np.zeros((npix,norder),np.float32) if continuum_func is not None: pspec.continuum_func = continuum_func # Loop over orders if lsf.wave.ndim==1: wave = np.atleast_2d(lsf.wave.copy()).T else: wave = lsf.wave.copy() for o in range(lsf.norder): wobs = wave[:,o] dw = np.median(dln.slope(wobs)) wv1,ind1 = dln.closest(synspec.wave,np.min(wobs)-2*np.abs(dw)) wv2,ind2 = dln.closest(synspec.wave,np.max(wobs)+2*np.abs(dw)) modelflux = synspec.flux[ind1:ind2+1] modelwave = synspec.wave[ind1:ind2+1] modelcont = synspec.cont[ind1:ind2+1] # Rebin, if necessary # get LSF FWHM (A) for a handful of positions across the spectrum xp = np.arange(npix//20)*20 fwhm = lsf.fwhm(wobs[xp],xtype='Wave',order=o) # FWHM is in units of lsf.xtype, convert to wavelength/angstroms, if necessary if lsf.xtype.lower().find('pix')>-1: fwhm *= np.abs(dw) # convert FWHM (A) in number of model pixels at those positions dwmod = dln.slope(modelwave) dwmod = np.hstack((dwmod,dwmod[-1])) xpmod = dln.interp(modelwave,np.arange(len(modelwave)),wobs[xp],kind='cubic',assume_sorted=False,extrapolate=True) xpmod = np.round(xpmod).astype(int) fwhmpix = np.abs(fwhm/dwmod[xpmod]) # need at least ~4 pixels per LSF FWHM across the spectrum # using 3 affects the final profile shape nbin = np.round(np.min(fwhmpix)//4).astype(int) if np.min(fwhmpix) < 3.7: warnings.warn('Model has lower resolution than the observed spectrum. Only '+str(np.min(fwhmpix))+' model pixels per resolution element') if np.min(fwhmpix) < 2.8: raise Exception('Model has lower resolution than the observed spectrum. Only '+str(np.min(fwhmpix))+' model pixels per resolution element') if nbin>1: npix2 = np.round(len(synspec.flux) // nbin).astype(int) modelflux = dln.rebin(modelflux[0:npix2*nbin],npix2) modelwave = dln.rebin(modelwave[0:npix2*nbin],npix2) modelcont = dln.rebin(modelcont[0:npix2*nbin],npix2) # Convolve lsf2d = lsf.anyarray(modelwave,xtype='Wave',order=o,original=False) cflux = utils.convolve_sparse(modelflux,lsf2d) # Interpolate onto final wavelength array flux = synple.interp_spl(wobs, modelwave, cflux) cont = synple.interp_spl(wobs, modelwave, modelcont) pspec.flux[:,o] = flux pspec.cont[:,o] = cont pspec.normalized = True # Normalize if norm is True: newcont = pspec.continuum_func(pspec) pspec.flux /= newcont pspec.cont *= newcont return pspec def mkbounds(params,paramlims=None): """ Make lower and upper boundaries for parameters """ params = np.char.array(params).upper() if paramlims is not None: limkeys = np.char.array(list(paramlims.keys())).upper() n = len(params) lbounds = np.zeros(n,np.float64) ubounds = np.zeros(n,np.float64) # Teff g, = np.where(params=='TEFF') if len(g)>0: lbounds[g[0]] = 3500 ubounds[g[0]] = 60000 # logg g, = np.where(params=='LOGG') if len(g)>0: lbounds[g[0]] = 0 ubounds[g[0]] = 5 # fe_h g, = np.where(params=='FE_H') if len(g)>0: lbounds[g[0]] = -3 ubounds[g[0]] = 1 # Vmicro g, = np.where(params=='VMICRO') if len(g)>0: lbounds[g[0]] = 0 ubounds[g[0]] = 5 # Vsini/vrot g, = np.where(params=='VROT') if len(g)>0: lbounds[g[0]] = 0 ubounds[g[0]] = 500 # RV g, = np.where(params=='RV') if len(g)>0: lbounds[g[0]] = -1500 ubounds[g[0]] = 1500 # abundances g, = np.where( (params.find('_H') != -1) & (params != 'FE_H') ) if len(g)>0: lbounds[g] = -3 ubounds[g] = 10 # Use input parameter limits if paramlims is not None: for i,f in enumerate(params): g, = np.where(limkeys==f) if len(g)>0: lbounds[i] = paramlims[limkeys[g[0]]][0] ubounds[i] = paramlims[limkeys[g[0]]][1] bounds = (lbounds,ubounds) return bounds def mkdxlim(fitparams): """ Make array of parameter changes at which curve_fit should finish.""" npar = len(fitparams) dx_lim = np.zeros(npar,float) for k in range(npar): if fitparams[k]=='TEFF': dx_lim[k] = 1.0 elif fitparams[k]=='LOGG': dx_lim[k] = 0.005 elif fitparams[k]=='VMICRO': dx_lim[k] = 0.1 elif fitparams[k]=='VROT': dx_lim[k] = 0.1 elif fitparams[k]=='RV': dx_lim[k] = 0.01 elif fitparams[k].endswith('_H'): dx_lim[k] = 0.005 else: dx_lim[k] = 0.01 return dx_lim def initpars(params,fitparams,bounds=None): """ Make initial set of parameters given PARAMS and FITPARAMS.""" params = dict((key.upper(), value) for (key, value) in params.items()) # all CAPS fitparams = [v.upper() for v in fitparams] # all CAPS npars = len(fitparams) pinit = np.zeros(npars,np.float64) # Loop over parameters for k in range(npars): ind, = np.where(np.char.array(list(params.keys()))==fitparams[k]) # This parameter is in PARAMS if len(ind)>0: pinit[k] = params[fitparams[k]] # Not in PARAMS else: if fitparams[k]=='RV': pinit[k] = 0.0 elif fitparams[k]=='VMICRO': pinit[k] = 2.0 elif fitparams[k]=='VROT': pinit[k] = 0.0 elif fitparams[k]=='TEFF': pinit[k] = 5000.0 elif fitparams[k]=='LOGG': pinit[k] = 3.0 elif fitparams[k].endswith('_H'): # Abundances, use FE_H if possible if 'FE_H' in params.keys(): pinit[k] = params['FE_H'] else: pinit[k] = 0.0 else: pinit[k] = 0.0 # Make sure inital parameters are within the boundary limits if bounds is not None: for k in range(npars): pinit[k] = dln.limit(pinit[k],bounds[0][k],bounds[1][k]) return pinit def specfigure(figfile,spec,fmodel,out,original=None,verbose=True,figsize=10): """ Make diagnostic figure.""" #import matplotlib matplotlib.use('Agg') #import matplotlib.pyplot as plt if os.path.exists(figfile): os.remove(figfile) norder = spec.norder nlegcol = 2 if original is not None: nlegcol=3 # Single-order plot if norder==1: fig,ax = plt.subplots() fig.set_figheight(figsize*0.5) fig.set_figwidth(figsize) if original is not None: plt.plot(original.wave,original.flux,color='green',label='Original',linewidth=1) plt.plot(spec.wave,spec.flux,'b',label='Masked Data',linewidth=0.5) plt.plot(fmodel.wave,fmodel.flux,'r',label='Model',linewidth=0.5,alpha=0.8) leg = ax.legend(loc='upper left', frameon=True, framealpha=0.8, ncol=nlegcol) plt.xlabel('Wavelength (Angstroms)') plt.ylabel('Normalized Flux') xr = dln.minmax(spec.wave) yr = [np.min([spec.flux,fmodel.flux]), np.max([spec.flux,fmodel.flux])] if original is not None: yr = [np.min([original.flux,spec.flux,fmodel.flux]), np.max([spec.flux,fmodel.flux])] yr = [yr[0]-dln.valrange(yr)*0.15,yr[1]+dln.valrange(yr)*0.005] yr = [np.max([yr[0],-0.2]), np.min([yr[1],2.0])] plt.xlim(xr) plt.ylim(yr) snr = np.nanmedian(spec.flux/spec.err) plt.title(spec.filename) #ax.annotate(r'S/N=%5.1f Teff=%5.1f$\pm$%5.1f logg=%5.2f$\pm$%5.2f [Fe/H]=%5.2f$\pm$%5.2f Vrel=%5.2f$\pm$%5.2f chisq=%5.2f' % # (snr, out['TEFF'], out['tefferr'], out['LOGG'], out['loggerr'], out['FE_H'], out['feherr'], out['RV'], out['vrelerr'], out['chisq']), # xy=(np.mean(xr), yr[0]+dln.valrange(yr)*0.05),ha='center') # Multi-order plot else: fig,ax = plt.subplots(norder) fig.set_figheight(figsize) fig.set_figwidth(figsize) for i in range(norder): if original is not None: ax[i].plot(original.wave[:,i],original.flux[:,i],color='green',label='Original',linewidth=1) ax[i].plot(spec.wave[:,i],spec.flux[:,i],'b',label='Masked Data',linewidth=0.5) ax[i].plot(fmodel.wave[:,i],fmodel.flux[:,i],'r',label='Model',linewidth=0.5,alpha=0.8) if i==0: leg = ax[i].legend(loc='upper left', frameon=True, framealpha=0.8, ncol=nlegcol) ax[i].set_xlabel('Wavelength (Angstroms)') ax[i].set_ylabel('Normalized Flux') xr = dln.minmax(spec.wave[:,i]) yr = [np.min([spec.flux[:,i],fmodel.flux[:,i]]), np.max([spec.flux[:,i],fmodel.flux[:,i]])] if original is not None: yr = [np.min([original.flux[:,i],spec.flux[:,i],fmodel.flux[:,i]]), np.max([spec.flux[:,i],fmodel.flux[:,i]])] yr = [yr[0]-dln.valrange(yr)*0.05,yr[1]+dln.valrange(yr)*0.05] if i==0: yr = [yr[0]-dln.valrange(yr)*0.15,yr[1]+dln.valrange(yr)*0.05] yr = [np.max([yr[0],-0.2]), np.min([yr[1],2.0])] ax[i].set_xlim(xr) ax[i].set_ylim(yr) # legend if i==0: snr = np.nanmedian(spec.flux/spec.err) ax[i].set_title(spec.filename) #ax[i].annotate(r'S/N=%5.1f Teff=%5.1f$\pm$%5.1f logg=%5.2f$\pm$%5.2f [Fe/H]=%5.2f$\pm$%5.2f Vrel=%5.2f$\pm$%5.2f chisq=%5.2f' % # (snr,out['teff'],out['tefferr'],out['logg'],out['loggerr'],out['feh'],out['feherr'],out['vrel'],out['vrelerr'],out['chisq']), # xy=(np.mean(xr), yr[0]+dln.valrange(yr)*0.05),ha='center') plt.savefig(figfile,bbox_inches='tight') plt.close(fig) if verbose is True: print('Figure saved to '+figfile) def dopvrot_lsq(spec,models=None,initpar=None,verbose=False,logger=None): """ Least Squares fitting with forward modeling of the spectrum. Parameters ---------- spec : Spec1D object The observed spectrum to match. models : list of Cannon models, optional A list of Cannon models to use. The default is to load all of the Cannon models in the data/ directory and use those. initpar : numpy array, optional Initial estimate for [teff, logg, feh, RV, vsini], optional. verbose : bool, optional Verbose output of the various steps. This is False by default. Returns ------- out : numpy structured array The output structured array of the final derived RVs, stellar parameters and errors. bmodel : Spec1D object The best-fitting Cannon model spectrum (as Spec1D object). Example ------- .. code-block:: python out, bmodel = fit_lsq(spec) """ if logger is None: logger = dln.basiclogger() # Load and prepare the Cannon models #------------------------------------------- if models is None: models = cannon.models.copy() models.prepare(spec) # Get initial estimates if initpar is None: initpar = np.array([6000.0, 2.5, -0.5, 0.0, 0.0]) initpar =

np.array(initpar)

numpy.array

# Licensed under a 3-clause BSD style license - see LICENSE.rst """ Utilities to generate toymodel (fake) reconstruction inputs for testing purposes. Examples: .. code-block:: python >>> from ctapipe.instrument import CameraGeometry >>> geom = CameraGeometry.make_rectangular(20, 20) >>> showermodel = Gaussian(x=0.25 * u.m, y=0.0 * u.m, length=0.1 * u.m, width=0.02 * u.m, psi='40d') >>> image, signal, noise = showermodel.generate_image(geom, intensity=1000) >>> print(image.shape) (400,) """ import numpy as np from ctapipe.utils import linalg from ctapipe.image.hillas import camera_to_shower_coordinates import astropy.units as u from astropy.coordinates import Angle from scipy.stats import multivariate_normal, skewnorm, norm from scipy.ndimage import convolve1d from abc import ABCMeta, abstractmethod __all__ = [ "WaveformModel", "Gaussian", "SkewedGaussian", "ImageModel", "obtain_time_image", ] @u.quantity_input( x=u.m, y=u.m, centroid_x=u.m, centroid_y=u.m, psi=u.deg, time_gradient=u.ns / u.m, time_intercept=u.ns, ) def obtain_time_image(x, y, centroid_x, centroid_y, psi, time_gradient, time_intercept): """Create a pulse time image for a toymodel shower. Assumes the time development occurs only along the longitudinal (major) axis of the shower, and scales linearly with distance along the axis. Parameters ---------- x : u.Quantity[length] X camera coordinate to evaluate the time at. Usually the array of pixel X positions y : u.Quantity[length] Y camera coordinate to evaluate the time at. Usually the array of pixel Y positions centroid_x : u.Quantity[length] X camera coordinate for the centroid of the shower centroid_y : u.Quantity[length] Y camera coordinate for the centroid of the shower psi : convertible to `astropy.coordinates.Angle` rotation angle about the centroid (0=x-axis) time_gradient : u.Quantity[time/length] Rate at which the time changes with distance along the shower axis time_intercept : u.Quantity[time] Pulse time at the shower centroid Returns ------- float or ndarray Pulse time in nanoseconds at (x, y) """ longitudinal, _ = camera_to_shower_coordinates(x, y, centroid_x, centroid_y, psi) longitudinal_m = longitudinal.to_value(u.m) time_gradient_ns_m = time_gradient.to_value(u.ns / u.m) time_intercept_ns = time_intercept.to_value(u.ns) return longitudinal_m * time_gradient_ns_m + time_intercept_ns class WaveformModel: @u.quantity_input(reference_pulse_sample_width=u.ns, sample_width=u.ns) def __init__(self, reference_pulse, reference_pulse_sample_width, sample_width): """Generate a toy model waveform using the reference pulse shape of a camera. Useful for testing image extraction algorithms. Does not include the electronic noise and the Excess Noise Factor of the photosensor, and therefore should not be used to make charge resolution conclusions about a camera. Parameters ---------- reference_pulse_sample_width : u.Quantity[time] Sample width of the reference pulse shape reference_pulse : ndarray Reference pulse shape sample_width : u.Quantity[time] Sample width of the waveform """ self.upsampling = 10 reference_pulse_sample_width = reference_pulse_sample_width.to_value(u.ns) sample_width_ns = sample_width.to_value(u.ns) ref_max_sample = reference_pulse.size * reference_pulse_sample_width reference_pulse_x = np.arange(0, ref_max_sample, reference_pulse_sample_width) self.ref_width_ns = sample_width_ns / self.upsampling self.ref_interp_x = np.arange(0, reference_pulse_x.max(), self.ref_width_ns) self.ref_interp_y = np.interp( self.ref_interp_x, reference_pulse_x, reference_pulse ) self.ref_interp_y /= self.ref_interp_y.sum() * self.ref_width_ns self.origin = self.ref_interp_y.argmax() - self.ref_interp_y.size // 2 def get_waveform(self, charge, time, n_samples): """Obtain the waveform toy model. Parameters ---------- charge : ndarray Amount of charge in each pixel Shape: (n_pixels) time : ndarray The signal time in the waveform in nanoseconds Shape: (n_pixels) n_samples : int Number of samples in the waveform Returns ------- waveform : ndarray Toy model waveform Shape (n_pixels, n_samples) """ n_pixels = charge.size n_upsampled_samples = n_samples * self.upsampling readout = np.zeros((n_pixels, n_upsampled_samples)) sample = (time / self.ref_width_ns).astype(np.int) outofrange = (sample < 0) | (sample >= n_upsampled_samples) sample[outofrange] = 0 charge[outofrange] = 0 readout[np.arange(n_pixels), sample] = charge convolved = convolve1d( readout, self.ref_interp_y, mode="constant", origin=self.origin ) sampled = ( convolved.reshape( (n_pixels, convolved.shape[-1] // self.upsampling, self.upsampling) ).sum(-1) * self.ref_width_ns # Waveform units: p.e. ) return sampled @classmethod def from_camera_readout(cls, readout, gain_channel=0): """Create class from a `ctapipe.instrument.CameraReadout`. Parameters ---------- readout : `ctapipe.instrument.CameraReadout` gain_channel : int The reference pulse gain channel to use Returns ------- WaveformModel """ return cls( readout.reference_pulse_shape[gain_channel], readout.reference_pulse_sample_width, (1 / readout.sampling_rate).to(u.ns), ) class ImageModel(metaclass=ABCMeta): @u.quantity_input(x=u.m, y=u.m) @abstractmethod def pdf(self, x, y): """Probability density function. """ def generate_image(self, camera, intensity=50, nsb_level_pe=20): """Generate a randomized DL1 shower image. For the signal, poisson random numbers are drawn from the expected signal distribution for each pixel. For the background, for each pixel a poisson random number if drawn with mean `nsb_level_pe`. Parameters ---------- camera : `ctapipe.instrument.CameraGeometry` camera geometry object intensity : int Total number of photo electrons to generate nsb_level_pe : type level of NSB/pedestal in photo-electrons Returns ------- image: array with length n_pixels containing the image signal: only the signal part of image noise: only the noise part of image """ expected_signal = self.expected_signal(camera, intensity) signal = np.random.poisson(expected_signal) noise = np.random.poisson(nsb_level_pe, size=signal.shape) image = (signal + noise) - np.mean(noise) return image, signal, noise def expected_signal(self, camera, intensity): """Expected signal in each pixel for the given camera and total intensity. Parameters ---------- camera: `ctapipe.instrument.CameraGeometry` camera geometry object intensity: int Total number of expected photo electrons Returns ------- image: array with length n_pixels containing the image """ pdf = self.pdf(camera.pix_x, camera.pix_y) return pdf * intensity * camera.pix_area.value class Gaussian(ImageModel): @u.quantity_input(x=u.m, y=u.m, length=u.m, width=u.m) def __init__(self, x, y, length, width, psi): """Create 2D Gaussian model for a shower image in a camera. Parameters ---------- centroid : u.Quantity[length, shape=(2, )] position of the centroid of the shower in camera coordinates width: u.Quantity[length] width of shower (minor axis) length: u.Quantity[length] length of shower (major axis) psi : convertable to `astropy.coordinates.Angle` rotation angle about the centroid (0=x-axis) Returns ------- a `scipy.stats` object """ self.x = x self.y = y self.width = width self.length = length self.psi = psi @u.quantity_input(x=u.m, y=u.m) def pdf(self, x, y): """2d probability for photon electrons in the camera plane""" aligned_covariance = np.array( [[self.length.to_value(u.m) ** 2, 0], [0, self.width.to_value(u.m) ** 2]] ) # rotate by psi angle: C' = R C R+ rotation = linalg.rotation_matrix_2d(self.psi) rotated_covariance = rotation @ aligned_covariance @ rotation.T return multivariate_normal( mean=[self.x.to_value(u.m), self.y.to_value(u.m)], cov=rotated_covariance, ).pdf(np.column_stack([x.to_value(u.m), y.to_value(u.m)])) class SkewedGaussian(ImageModel): """A shower image that has a skewness along the major axis. """ @u.quantity_input(x=u.m, y=u.m, length=u.m, width=u.m) def __init__(self, x, y, length, width, psi, skewness): """Create 2D skewed Gaussian model for a shower image in a camera. Skewness is only applied along the main shower axis. See https://en.wikipedia.org/wiki/Skew_normal_distribution and https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skewnorm.html for details. Parameters ---------- centroid : u.Quantity[length, shape=(2, )] position of the centroid of the shower in camera coordinates width: u.Quantity[length] width of shower (minor axis) length: u.Quantity[length] length of shower (major axis) psi : convertable to `astropy.coordinates.Angle` rotation angle about the centroid (0=x-axis) Returns ------- a `scipy.stats` object """ self.x = x self.y = y self.width = width self.length = length self.psi = psi self.skewness = skewness def _moments_to_parameters(self): """Returns loc and scale from mean, std and skewnewss.""" # see https://en.wikipedia.org/wiki/Skew_normal_distribution#Estimation skew23 =

np.abs(self.skewness)

numpy.abs

# Note that we test the main astropy.wcs.WCS class directly rather than testing # the mix-in class on its own (since it's not functional without being used as # a mix-in) import warnings from packaging.version import Version import numpy as np import pytest from numpy.testing import assert_equal, assert_allclose from itertools import product from astropy import units as u from astropy.time import Time from astropy.tests.helper import assert_quantity_allclose from astropy.units import Quantity from astropy.coordinates import ICRS, FK5, Galactic, SkyCoord, SpectralCoord, ITRS, EarthLocation from astropy.io.fits import Header from astropy.io.fits.verify import VerifyWarning from astropy.units.core import UnitsWarning from astropy.utils.data import get_pkg_data_filename from astropy.wcs.wcs import WCS, FITSFixedWarning, Sip, NoConvergence from astropy.wcs.wcsapi.fitswcs import custom_ctype_to_ucd_mapping, VELOCITY_FRAMES from astropy.wcs._wcs import __version__ as wcsver from astropy.utils import iers from astropy.utils.exceptions import AstropyUserWarning ############################################################################### # The following example is the simplest WCS with default values ############################################################################### WCS_EMPTY = WCS(naxis=1) WCS_EMPTY.wcs.crpix = [1] def test_empty(): wcs = WCS_EMPTY # Low-level API assert wcs.pixel_n_dim == 1 assert wcs.world_n_dim == 1 assert wcs.array_shape is None assert wcs.pixel_shape is None assert wcs.world_axis_physical_types == [None] assert wcs.world_axis_units == [''] assert wcs.pixel_axis_names == [''] assert wcs.world_axis_names == [''] assert_equal(wcs.axis_correlation_matrix, True) assert wcs.world_axis_object_components == [('world', 0, 'value')] assert wcs.world_axis_object_classes['world'][0] is Quantity assert wcs.world_axis_object_classes['world'][1] == () assert wcs.world_axis_object_classes['world'][2]['unit'] is u.one assert_allclose(wcs.pixel_to_world_values(29), 29) assert_allclose(wcs.array_index_to_world_values(29), 29) assert np.ndim(wcs.pixel_to_world_values(29)) == 0 assert np.ndim(wcs.array_index_to_world_values(29)) == 0 assert_allclose(wcs.world_to_pixel_values(29), 29) assert_equal(wcs.world_to_array_index_values(29), (29,)) assert np.ndim(wcs.world_to_pixel_values(29)) == 0 assert np.ndim(wcs.world_to_array_index_values(29)) == 0 # High-level API coord = wcs.pixel_to_world(29) assert_quantity_allclose(coord, 29 * u.one) assert np.ndim(coord) == 0 coord = wcs.array_index_to_world(29) assert_quantity_allclose(coord, 29 * u.one) assert np.ndim(coord) == 0 coord = 15 * u.one x = wcs.world_to_pixel(coord) assert_allclose(x, 15.) assert np.ndim(x) == 0 i = wcs.world_to_array_index(coord) assert_equal(i, 15) assert np.ndim(i) == 0 ############################################################################### # The following example is a simple 2D image with celestial coordinates ############################################################################### HEADER_SIMPLE_CELESTIAL = """ WCSAXES = 2 CTYPE1 = RA---TAN CTYPE2 = DEC--TAN CRVAL1 = 10 CRVAL2 = 20 CRPIX1 = 30 CRPIX2 = 40 CDELT1 = -0.1 CDELT2 = 0.1 CROTA2 = 0. CUNIT1 = deg CUNIT2 = deg """ with warnings.catch_warnings(): warnings.simplefilter('ignore', VerifyWarning) WCS_SIMPLE_CELESTIAL = WCS(Header.fromstring( HEADER_SIMPLE_CELESTIAL, sep='\n')) def test_simple_celestial(): wcs = WCS_SIMPLE_CELESTIAL # Low-level API assert wcs.pixel_n_dim == 2 assert wcs.world_n_dim == 2 assert wcs.array_shape is None assert wcs.pixel_shape is None assert wcs.world_axis_physical_types == ['pos.eq.ra', 'pos.eq.dec'] assert wcs.world_axis_units == ['deg', 'deg'] assert wcs.pixel_axis_names == ['', ''] assert wcs.world_axis_names == ['', ''] assert_equal(wcs.axis_correlation_matrix, True) assert wcs.world_axis_object_components == [('celestial', 0, 'spherical.lon.degree'), ('celestial', 1, 'spherical.lat.degree')] assert wcs.world_axis_object_classes['celestial'][0] is SkyCoord assert wcs.world_axis_object_classes['celestial'][1] == () assert isinstance(wcs.world_axis_object_classes['celestial'][2]['frame'], ICRS) assert wcs.world_axis_object_classes['celestial'][2]['unit'] is u.deg assert_allclose(wcs.pixel_to_world_values(29, 39), (10, 20)) assert_allclose(wcs.array_index_to_world_values(39, 29), (10, 20)) assert_allclose(wcs.world_to_pixel_values(10, 20), (29., 39.)) assert_equal(wcs.world_to_array_index_values(10, 20), (39, 29)) # High-level API coord = wcs.pixel_to_world(29, 39) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, ICRS) assert_allclose(coord.ra.deg, 10) assert_allclose(coord.dec.deg, 20) coord = wcs.array_index_to_world(39, 29) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, ICRS) assert_allclose(coord.ra.deg, 10) assert_allclose(coord.dec.deg, 20) coord = SkyCoord(10, 20, unit='deg', frame='icrs') x, y = wcs.world_to_pixel(coord) assert_allclose(x, 29.) assert_allclose(y, 39.) i, j = wcs.world_to_array_index(coord) assert_equal(i, 39) assert_equal(j, 29) # Check that if the coordinates are passed in a different frame things still # work properly coord_galactic = coord.galactic x, y = wcs.world_to_pixel(coord_galactic) assert_allclose(x, 29.) assert_allclose(y, 39.) i, j = wcs.world_to_array_index(coord_galactic) assert_equal(i, 39) assert_equal(j, 29) # Check that we can actually index the array data = np.arange(3600).reshape((60, 60)) coord = SkyCoord(10, 20, unit='deg', frame='icrs') index = wcs.world_to_array_index(coord) assert_equal(data[index], 2369) coord = SkyCoord([10, 12], [20, 22], unit='deg', frame='icrs') index = wcs.world_to_array_index(coord) assert_equal(data[index], [2369, 3550]) ############################################################################### # The following example is a spectral cube with axes in an unusual order ############################################################################### HEADER_SPECTRAL_CUBE = """ WCSAXES = 3 CTYPE1 = GLAT-CAR CTYPE2 = FREQ CTYPE3 = GLON-CAR CNAME1 = Latitude CNAME2 = Frequency CNAME3 = Longitude CRVAL1 = 10 CRVAL2 = 20 CRVAL3 = 25 CRPIX1 = 30 CRPIX2 = 40 CRPIX3 = 45 CDELT1 = -0.1 CDELT2 = 0.5 CDELT3 = 0.1 CUNIT1 = deg CUNIT2 = Hz CUNIT3 = deg """ with warnings.catch_warnings(): warnings.simplefilter('ignore', VerifyWarning) WCS_SPECTRAL_CUBE = WCS(Header.fromstring(HEADER_SPECTRAL_CUBE, sep='\n')) def test_spectral_cube(): # Spectral cube with a weird axis ordering wcs = WCS_SPECTRAL_CUBE # Low-level API assert wcs.pixel_n_dim == 3 assert wcs.world_n_dim == 3 assert wcs.array_shape is None assert wcs.pixel_shape is None assert wcs.world_axis_physical_types == ['pos.galactic.lat', 'em.freq', 'pos.galactic.lon'] assert wcs.world_axis_units == ['deg', 'Hz', 'deg'] assert wcs.pixel_axis_names == ['', '', ''] assert wcs.world_axis_names == ['Latitude', 'Frequency', 'Longitude'] assert_equal(wcs.axis_correlation_matrix, [[True, False, True], [False, True, False], [True, False, True]]) assert len(wcs.world_axis_object_components) == 3 assert wcs.world_axis_object_components[0] == ('celestial', 1, 'spherical.lat.degree') assert wcs.world_axis_object_components[1][:2] == ('spectral', 0) assert wcs.world_axis_object_components[2] == ('celestial', 0, 'spherical.lon.degree') assert wcs.world_axis_object_classes['celestial'][0] is SkyCoord assert wcs.world_axis_object_classes['celestial'][1] == () assert isinstance(wcs.world_axis_object_classes['celestial'][2]['frame'], Galactic) assert wcs.world_axis_object_classes['celestial'][2]['unit'] is u.deg assert wcs.world_axis_object_classes['spectral'][0] is Quantity assert wcs.world_axis_object_classes['spectral'][1] == () assert wcs.world_axis_object_classes['spectral'][2] == {} assert_allclose(wcs.pixel_to_world_values(29, 39, 44), (10, 20, 25)) assert_allclose(wcs.array_index_to_world_values(44, 39, 29), (10, 20, 25)) assert_allclose(wcs.world_to_pixel_values(10, 20, 25), (29., 39., 44.)) assert_equal(wcs.world_to_array_index_values(10, 20, 25), (44, 39, 29)) # High-level API coord, spec = wcs.pixel_to_world(29, 39, 44) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, Galactic) assert_allclose(coord.l.deg, 25) assert_allclose(coord.b.deg, 10) assert isinstance(spec, SpectralCoord) assert_allclose(spec.to_value(u.Hz), 20) coord, spec = wcs.array_index_to_world(44, 39, 29) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, Galactic) assert_allclose(coord.l.deg, 25) assert_allclose(coord.b.deg, 10) assert isinstance(spec, SpectralCoord) assert_allclose(spec.to_value(u.Hz), 20) coord = SkyCoord(25, 10, unit='deg', frame='galactic') spec = 20 * u.Hz with pytest.warns(AstropyUserWarning, match='No observer defined on WCS'): x, y, z = wcs.world_to_pixel(coord, spec) assert_allclose(x, 29.) assert_allclose(y, 39.) assert_allclose(z, 44.) # Order of world coordinates shouldn't matter with pytest.warns(AstropyUserWarning, match='No observer defined on WCS'): x, y, z = wcs.world_to_pixel(spec, coord) assert_allclose(x, 29.) assert_allclose(y, 39.) assert_allclose(z, 44.) with pytest.warns(AstropyUserWarning, match='No observer defined on WCS'): i, j, k = wcs.world_to_array_index(coord, spec) assert_equal(i, 44) assert_equal(j, 39) assert_equal(k, 29) # Order of world coordinates shouldn't matter with pytest.warns(AstropyUserWarning, match='No observer defined on WCS'): i, j, k = wcs.world_to_array_index(spec, coord) assert_equal(i, 44) assert_equal(j, 39) assert_equal(k, 29) HEADER_SPECTRAL_CUBE_NONALIGNED = HEADER_SPECTRAL_CUBE.strip() + '\n' + """ PC2_3 = -0.5 PC3_2 = +0.5 """ with warnings.catch_warnings(): warnings.simplefilter('ignore', VerifyWarning) WCS_SPECTRAL_CUBE_NONALIGNED = WCS(Header.fromstring( HEADER_SPECTRAL_CUBE_NONALIGNED, sep='\n')) def test_spectral_cube_nonaligned(): # Make sure that correlation matrix gets adjusted if there are non-identity # CD matrix terms. wcs = WCS_SPECTRAL_CUBE_NONALIGNED assert wcs.world_axis_physical_types == ['pos.galactic.lat', 'em.freq', 'pos.galactic.lon'] assert wcs.world_axis_units == ['deg', 'Hz', 'deg'] assert wcs.pixel_axis_names == ['', '', ''] assert wcs.world_axis_names == ['Latitude', 'Frequency', 'Longitude'] assert_equal(wcs.axis_correlation_matrix, [[True, True, True], [False, True, True], [True, True, True]]) # NOTE: we check world_axis_object_components and world_axis_object_classes # again here because in the past this failed when non-aligned axes were # present, so this serves as a regression test. assert len(wcs.world_axis_object_components) == 3 assert wcs.world_axis_object_components[0] == ('celestial', 1, 'spherical.lat.degree') assert wcs.world_axis_object_components[1][:2] == ('spectral', 0) assert wcs.world_axis_object_components[2] == ('celestial', 0, 'spherical.lon.degree') assert wcs.world_axis_object_classes['celestial'][0] is SkyCoord assert wcs.world_axis_object_classes['celestial'][1] == () assert isinstance(wcs.world_axis_object_classes['celestial'][2]['frame'], Galactic) assert wcs.world_axis_object_classes['celestial'][2]['unit'] is u.deg assert wcs.world_axis_object_classes['spectral'][0] is Quantity assert wcs.world_axis_object_classes['spectral'][1] == () assert wcs.world_axis_object_classes['spectral'][2] == {} ############################################################################### # The following example is from Rots et al (2015), Table 5. It represents a # cube with two spatial dimensions and one time dimension ############################################################################### HEADER_TIME_CUBE = """ SIMPLE = T / Fits standard BITPIX = -32 / Bits per pixel NAXIS = 3 / Number of axes NAXIS1 = 2048 / Axis length NAXIS2 = 2048 / Axis length NAXIS3 = 11 / Axis length DATE = '2008-10-28T14:39:06' / Date FITS file was generated OBJECT = '2008 TC3' / Name of the object observed EXPTIME = 1.0011 / Integration time MJD-OBS = 54746.02749237 / Obs start DATE-OBS= '2008-10-07T00:39:35.3342' / Observing date TELESCOP= 'VISTA' / ESO Telescope Name INSTRUME= 'VIRCAM' / Instrument used. TIMESYS = 'UTC' / From Observatory Time System TREFPOS = 'TOPOCENT' / Topocentric MJDREF = 54746.0 / Time reference point in MJD RADESYS = 'ICRS' / Not equinoctal CTYPE2 = 'RA---ZPN' / Zenithal Polynomial Projection CRVAL2 = 2.01824372640628 / RA at ref pixel CUNIT2 = 'deg' / Angles are degrees always CRPIX2 = 2956.6 / Pixel coordinate at ref point CTYPE1 = 'DEC--ZPN' / Zenithal Polynomial Projection CRVAL1 = 14.8289418840003 / Dec at ref pixel CUNIT1 = 'deg' / Angles are degrees always CRPIX1 = -448.2 / Pixel coordinate at ref point CTYPE3 = 'UTC' / linear time (UTC) CRVAL3 = 2375.341 / Relative time of first frame CUNIT3 = 's' / Time unit CRPIX3 = 1.0 / Pixel coordinate at ref point CTYPE3A = 'TT' / alternative linear time (TT) CRVAL3A = 2440.525 / Relative time of first frame CUNIT3A = 's' / Time unit CRPIX3A = 1.0 / Pixel coordinate at ref point OBSGEO-B= -24.6157 / [deg] Tel geodetic latitute (=North)+ OBSGEO-L= -70.3976 / [deg] Tel geodetic longitude (=East)+ OBSGEO-H= 2530.0000 / [m] Tel height above reference ellipsoid CRDER3 = 0.0819 / random error in timings from fit CSYER3 = 0.0100 / absolute time error PC1_1 = 0.999999971570892 / WCS transform matrix element PC1_2 = 0.000238449608932 / WCS transform matrix element PC2_1 = -0.000621542859395 / WCS transform matrix element PC2_2 = 0.999999806842218 / WCS transform matrix element CDELT1 = -9.48575432499806E-5 / Axis scale at reference point CDELT2 = 9.48683176211164E-5 / Axis scale at reference point CDELT3 = 13.3629 / Axis scale at reference point PV1_1 = 1. / ZPN linear term PV1_3 = 42. / ZPN cubic term """ with warnings.catch_warnings(): warnings.simplefilter('ignore', (VerifyWarning, FITSFixedWarning)) WCS_TIME_CUBE = WCS(Header.fromstring(HEADER_TIME_CUBE, sep='\n')) def test_time_cube(): # Spectral cube with a weird axis ordering wcs = WCS_TIME_CUBE assert wcs.pixel_n_dim == 3 assert wcs.world_n_dim == 3 assert wcs.array_shape == (11, 2048, 2048) assert wcs.pixel_shape == (2048, 2048, 11) assert wcs.world_axis_physical_types == ['pos.eq.dec', 'pos.eq.ra', 'time'] assert wcs.world_axis_units == ['deg', 'deg', 's'] assert wcs.pixel_axis_names == ['', '', ''] assert wcs.world_axis_names == ['', '', ''] assert_equal(wcs.axis_correlation_matrix, [[True, True, False], [True, True, False], [False, False, True]]) components = wcs.world_axis_object_components assert components[0] == ('celestial', 1, 'spherical.lat.degree') assert components[1] == ('celestial', 0, 'spherical.lon.degree') assert components[2][:2] == ('time', 0) assert callable(components[2][2]) assert wcs.world_axis_object_classes['celestial'][0] is SkyCoord assert wcs.world_axis_object_classes['celestial'][1] == () assert isinstance(wcs.world_axis_object_classes['celestial'][2]['frame'], ICRS) assert wcs.world_axis_object_classes['celestial'][2]['unit'] is u.deg assert wcs.world_axis_object_classes['time'][0] is Time assert wcs.world_axis_object_classes['time'][1] == () assert wcs.world_axis_object_classes['time'][2] == {} assert callable(wcs.world_axis_object_classes['time'][3]) assert_allclose(wcs.pixel_to_world_values(-449.2, 2955.6, 0), (14.8289418840003, 2.01824372640628, 2375.341)) assert_allclose(wcs.array_index_to_world_values(0, 2955.6, -449.2), (14.8289418840003, 2.01824372640628, 2375.341)) assert_allclose(wcs.world_to_pixel_values(14.8289418840003, 2.01824372640628, 2375.341), (-449.2, 2955.6, 0)) assert_equal(wcs.world_to_array_index_values(14.8289418840003, 2.01824372640628, 2375.341), (0, 2956, -449)) # High-level API coord, time = wcs.pixel_to_world(29, 39, 44) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, ICRS) assert_allclose(coord.ra.deg, 1.7323356692202325) assert_allclose(coord.dec.deg, 14.783516054817797) assert isinstance(time, Time) assert_allclose(time.mjd, 54746.03429755324) coord, time = wcs.array_index_to_world(44, 39, 29) assert isinstance(coord, SkyCoord) assert isinstance(coord.frame, ICRS) assert_allclose(coord.ra.deg, 1.7323356692202325)

assert_allclose(coord.dec.deg, 14.783516054817797)

numpy.testing.assert_allclose

""" Data preparation file """ import numpy as np import pandas as pd def clean_string(string): return ''.join(e for e in string if e.isalnum()) def reverse_dict(d): new_d = {} for k,i in d.items(): new_d[i] = k return new_d def mapping(files): """ Creates a unique index for ever entity and relation. """ E = set() R = set() for filename in files: with open(filename,'r') as f: for line in f: s,p,o = line.split() E.add(s) E.add(o) R.add(p) E_mapping = {e:i for i,e in enumerate(E)} R_mapping = {e:i for i,e in enumerate(R)} return E_mapping, R_mapping def prep_data(filename): """ Prep data without labels """ sub = [] obj = [] pred = [] with open(filename, 'r') as f: for l in f: s,p,o = l.split() sub.append(s.strip()) obj.append(o.strip()) pred.append(p.strip()) return sub, obj, pred def class_distribution(filename, R_mapping): """ Return the a priori probability for each class. """ _, _, pred = prep_data(filename) labels = np.asarray([R_mapping[i] for i in pred]) unique, counts =

np.unique(labels, return_counts=True)

numpy.unique

#!/opt/anaconda/bin/python # -*- coding: utf-8 -*- # Unfortunately the `which` way of calling python can't accept command-line arguments. """ Created on Mon Nov 03 16:13:48 2014 @author: <NAME> @email: <EMAIL> OR <EMAIL> A selection of alignment routines designed for registering and summing stacks of images or diffraction patterns in the field of electron microscopy. """ from __future__ import division, print_function, absolute_import, unicode_literals import numpy as np if np.version.version.split('.')[1] == 7: print( "WARNING: NUMPY VERSION 1.7 DETECTED, ZORRO IS DESIGNED FOR >1.10" ) print( "CHECK YOUR ENVIRONMENT VARIABLES TO SEE IF EMAN2 HAS HIJACKED YOUR PYTHON DISTRIBUTION" ) import numexprz as nz # Now see which numexpr we have, by the dtype of float (whether it casts or not) try: # Now see which numexpr we have, by the dtype of float (whether it casts or not) tdata = np.complex64( 1.0 + 2.0j ) fftw_dtype = nz.evaluate( 'tdata + tdata' ).dtype float_dtype = nz.evaluate( 'real(tdata+tdata)' ).dtype except: fftw_dtype = 'complex128' float_dtype = 'float64' import scipy.optimize import scipy.ndimage import scipy.stats import time try: import ConfigParser as configparser except: import configparser # Python 3 # Here we have to play some games depending on where the file was called from # with the use of absolute_import # print( "__name__ of zorro: " + str(__name__) ) try: import zorro_util as util import zorro_plotting as plot except ImportError: from . import zorro_util as util from . import zorro_plotting as plot import mrcz import os, os.path, tempfile, sys import subprocess # Should we disable Multiprocessing on Windows due to general bugginess in the module? import multiprocessing as mp try: import pyfftw except: print( "Zorro did not find pyFFTW package: get it at https://pypi.python.org/pypi/pyFFTW" ) try: import tables except: print( "Zorro did not find pyTables installation for HDF5 file support" ) import matplotlib.pyplot as plt # Numpy.pad is bad at dealing with interpreted strings if sys.version_info >= (3,0): symmetricPad = u'symmetric' constantPad = u'constant' else: symmetricPad = b'symmetric' constantPad = b'constant' #### OBJECT-ORIENTED INTERFACE #### class ImageRegistrator(object): # Should be able to handle differences in translation, rotation, and scaling # between images def __init__( self ): # Declare class members self.verbose = 0 self.umask = 2 # Meta-information for processing, not saved in configuration files. self.METApriority = 0.0 self.METAstatus = u'new' self.METAmtime = 0.0 self.METAsize = 0 self.xcorrMode = 'zorro' # 'zorro', 'unblur v1.02', 'motioncorr v2.1' # FFTW_PATIENT is bugged for powers of 2, so use FFTW_MEASURE as default self.fftw_effort = u"FFTW_MEASURE" # TODO: change this to drop into cachePath self.n_threads = nz.nthreads # Number of cores to limit FFTW to, if None uses all cores self.cachePath = tempfile.gettempdir() # CALIBRATIONS self.pixelsize = None # Typically we use nanometers, the same units as Digital Micrograph self.voltage = 300.0 # Accelerating voltage, kV self.C3 = 2.7 # Spherical aberration of objective, mm self.gain = None self.detectorPixelSize = None # Physical dimensions of detector pixel (5 um for K2) # Timings self.bench = {} # Dict holds various benchmark times for the code self.saveC = False # Save the cross-correlation within +/- maxShift # INFORMATION REDUCTION # The SNR at high spatial frequencies tends to be lower due to how information transfer works, so # removing/filtering those frequencies can improve stability of the registration. YMMV, IMHO, etc. self.Brad = 512 # Gaussian low-pass applied to data before registration, units are radius in Fourier space, or equivalent point-spread function in real-space self.Bmode = u'opti' # can be a real-space Gaussian convolution, 'conv' or Fourier filter, 'fourier', or 'opti' for automatic Brad # For Bmode = 'fourier', a range of available filters can be used: gaussian, gauss_trunc, butterworth.order (order is an int), hann, hamming self.BfiltType = u'gaussian' self.fouCrop = [3072,3072] # Size of FFT in frequency-space to crop to (e.g. [2048,2048]) self.reloadData = True # Data self.images = None self.imageSum = None self.filtSum = None # Dose-filtered, Wiener-filtered, etc. representations go here self.gainRef = None # For application of gain reference in Zorro rather than Digital Micrograph/TIA/etc. self.gainInfo = { "Horizontal": True, "Vertical": True, "Diagonal":False, "GammaParams": [ 0.12035633, -1.04171635, -0.03363192, 1.03902726], } # One of None, 'dose', 'dose,background', 'dosenorm', 'gaussLP', 'gaussLP,background' # also 'hot' can be in the comma-seperated list for pre-filtering of hot pixels self.filterMode = None # Dose filt param = [dosePerFrame, critDoseA, critDoseB, critDoseC, cutoffOrder, missingStartFrame] self.doseFiltParam = [None, 0.24499, -1.6649, 2.8141, 32, 0] # for 'hot' in filterMode self.hotpixInfo = { u"logisticK":6.0, u"relax":0.925, u"maxSigma":8.0, u"psf": u"K2", u"guessHotpix":0, u"guessDeadpix":0, u"decorrOutliers":False, u"cutoffLower":-4.0, u"cutoffUpper":3.25, u"neighborPix":0 } self.FFTSum = None # If you want to use one mask, it should have dims [1,N_Y,N_X]. This is # to ensure Cythonized code can interact safely with Numpy self.incohFouMag = None # Incoherent Fourier magnitude, for CTF determination, resolution checks self.masks = None self.maskSum = None self.C = None # Results self.translations = None self.transEven = None # For even-odd tiled FRC, the half-stack translations self.transOdd = None # For even-odd tiled FRC, the half-stack translations self.velocities = None # pixel velocity, in pix/frame, to find frames that suffer from excessive drift self.rotations = None # rotations, for polar-transformed data self.scales = None # scaling, for polar-transformed data self.errorDictList = [] # A list of dictionaries of errors and such from different runs on the same data. self.trackCorrStats = False self.corrStats = None self.doLazyFRC = True self.doEvenOddFRC = False self.FRC = None # A Fourier ring correlation # Filtering # TODO: add more fine control over filtering options # CTF currently supports CTFFIND4.1 or GCTF self.CTFProgram = None # None, "ctffind4.1", or "gctf", 'ctffind4.1,sum' works on (aligned) sum, same for 'gctf,sum' self.CTFInfo = { u'DefocusU':None, u'DefocusV': None, u'DefocusAngle':None, u'CtfFigureOfMerit':None, u'FinalResolution': None, u'AmplitudeContrast':0.07, u'AdditionalPhaseShift':None, } self.CTFDiag = None # Diagnostic image from CTFFIND4.1 or GCTF # DEPRICATED ctf stuff #self.doCTF = False #self.CTF4Results = None # Micrograph number, DF1, DF2, Azimuth, Additional Phase shift, CC, and max spacing fit-to #self.CTF4Diag = None # Registration parameters self.shapePadded = [4096,4096] self.shapeOriginal = None self.shapeBinned = None self.subPixReg = 16 # fraction of a pixel to REGISTER image shift to # Subpixel alignment method: None (shifts still registered subpixally), lanczos, or fourier # lanczos is cheaper computationally and has fewer edge artifacts self.shiftMethod = u'lanczos' self.maxShift = 100 # Generally should be 1/2 distance to next lattice spacing # Pre-shift every image by that of the previous frame, useful for high-resolution where one can jump a lattice # i.e. should be used with small values for maxShift self.preShift = False # Solver weighting can be raw max correlation coeffs (None), normalized to [0,1] by the # min and max correlations ('norm'), or 'logistic' function weighted which # requires corrThres to be set. self.peakLocMode = u'interpolated' # interpolated (oversampled), or a RMS-best fit like fitlaplacian self.weightMode = u'autologistic' # autologistic, normalized, unweighted, logistic, or corr self.peaksigThres = 6.0 self.logisticK = 5.0 self.logisticNu = 0.15 self.originMode = u'centroid' # 'centroid' or None self.suppressOrigin = True # Delete the XC pixel at (0,0). Only necessary if gain reference is bad, but defaults to on. # Triangle-matrix indexing parameters self.triMode = u'diag' # Can be: tri, diag, auto, first self.startFrame = 0 self.endFrame = 0 self.diagStart = 0 # XC to neighbour frame on 0, next-nearest neighbour on +1, etc. self.diagWidth = 5 self.autoMax = 10 self.corrThres = None # Use with 'auto' mode to stop doing cross-correlations if the values drop below the threshold self.velocityThres = None # Pixel velocity threshold (pix/frame), above which to throw-out frames with too much motion blur. #### INPUT/OUTPUT #### self.files = { u"config":None, u"stack":None, u"mask":None, u"sum":None, u"align":None, u"figurePath":None, u"xc":None, u"moveRawPath":None, u"original":None, u"gainRef":None, u"stdout": None, u"automatch":None, u"rejected":None, u"compressor": None, u"clevel": 1 } #self.savePDF = False self.savePNG = True self.saveMovie = True self.doCompression = False self.compress_ext = ".bz2" #### PLOTTING #### self.plotDict = { u"imageSum":True, u"imageFirst":False, u"FFTSum":True, u"polarFFTSum":True, u"filtSum":True, u'stats': False, u"corrTriMat":False, u"peaksigTriMat": True, u"translations":True, u"pixRegError":True, u"CTFDiag":True, u"logisticWeights": True, u"FRC": True, u'Transparent': True, u'plot_dpi':144, u'image_dpi':250, u'image_cmap':u'gray', u'graph_cmap':u'gnuplot', u'fontsize':12, u'fontstyle': u'serif', u'colorbar': True, u'backend': u'Qt4Agg', u'multiprocess':True, u'show':False } pass def initDefaultFiles( self, stackName ): self.files[u'stack'] = stackName self.files[u'config'] = stackName + u".zor" stackPath, stackFront = os.path.split( stackName ) stackFront = os.path.splitext( stackFront )[0] if not 'compressor' in self.files or not bool(self.files['compressor']): mrcExt = ".mrc" mrcsExt = ".mrcs" else: mrcExt = ".mrcz" mrcsExt = ".mrcsz" self.files[u'align'] = os.path.relpath( os.path.join( u"./align", "%s_zorro_movie%s" %(stackFront, mrcsExt) ), start=stackPath ) self.files[u'sum'] = os.path.relpath( stackPath, os.path.join( u"./sum", "%s_zorro%s" %(stackFront, mrcExt) ), start=stackPath ) self.files[u'figurePath'] = os.path.relpath( os.path.join(stackPath, u"./figs"), start=stackPath ) def xcorr2_mc2_1( self, gpu_id = 0, loadResult=True, clean=True ): """ This makes an external operating system call to the Cheng's lab GPU-based B-factor multireference executable. It and CUDA libraries must be on the system path and libary path respectively. NOTE: Spyder looks loads PATH and LD_LIBRARY_PATH from .profile, not .bashrc """ dosef_cmd = util.which("dosefgpu_driftcorr") if dosef_cmd is None: print( "Error: dosefgpu_driftcorr not found in system path." ) return #tempFileHash = str(uuid.uuid4() ) # Key let's us multiprocess safely stackBase = os.path.basename( os.path.splitext( self.files['stack'] )[0] ) if self.cachePath is None: self.cachePath = "." InName = os.path.join( self.cachePath, stackBase + u"_mcIn.mrc" ) # Unfortunately these files may as well be in the working directory. OutAvName = os.path.join( self.cachePath, stackBase + u"_mcOutAv.mrc" ) OutStackName = os.path.join( self.cachePath, stackBase + u"_mcOut.mrc" ) logName = os.path.join( self.cachePath, stackBase + u"_mc.zor" ) mrcz.writeMRC( self.images, InName ) # Force binning to 1, as performance with binning is poor binning = 1 if self.Brad is not None: # Li masking is in MkPosList() in cufunc.cu (line 413) # Their r2 is normalized and mine isn't # Li has mask = exp( -0.5 * bfactor * r_norm**2 ) # r_norm**2 = x*x/Nx*Nx + y*y/Ny*Ny = r**2 / (Nx**2 + Ny**2) # For non-square arrays they have a non-square (but constant frequency) filter # RAM has mask = exp( -(r/brad)**2 ) # We can only get Bfactor approximately then but it's close enough for 3710x3838 bfac = 2.0 * (self.images.shape[1]**2 + self.images.shape[2]**2) / (self.Brad**2) print( "Using B-factor of " + str(bfac) + " for dosefgpu_driftcorr" ) else: bfac = 1000 # dosef default 'safe' bfactor for mediocre gain reference # Consider: Dosef suffers at the ends of the sequence, so make the middle frame zero drift? # align_to = np.floor( self.images.shape[0]/2 ) # This seems to cause more problems then it's worth. align_to = 0 if self.diagWidth != None: fod = self.diagWidth else: fod = 0 # Dosef can limit search to a certain box size if self.maxShift == None: maxshift = 96 else: maxshift = self.maxShift * 2 if self.startFrame == None: self.startFrame = 0 if self.endFrame == None: self.endFrame = 0 motion_flags = ( " " + InName + " -gpu " + str(gpu_id) + " -nss " + str(self.startFrame) + " -nes " + str(self.endFrame) + " -fod " + str(fod) + " -bin " + str(binning) + " -bft " + str(bfac) + " -atm -" + str(align_to) + " -pbx " + str(maxshift) + " -ssc 1 -fct " + OutStackName + " -fcs " + OutAvName + " -flg " + logName ) sub = subprocess.Popen( dosef_cmd + motion_flags, shell=True ) sub.wait() self.loadMCLog( logName ) time.sleep(0.5) if bool(clean): try: os.remove(InName) except: pass try: os.remove(OutStackName) except: pass try: os.remove(OutAvName) except: pass try: os.remove(logName) except: pass def loadMCLog( self, logName ): """ Load and part a MotionCorr log from disk using regular expressions. """ import re # Parse to get the translations fhMC = open( logName ) MClog = fhMC.readlines() fhMC.close() # Number of footer lines changes with the options you use. # I would rather find Sum Frame #000 for linenumber, line in enumerate(MClog): try: test = re.findall( "Sum Frame #000", line) if bool(test): frameCount = np.int( re.findall( "\d\d\d", line )[1] ) + 1 break except: pass MClog_crop = MClog[linenumber+1:linenumber+frameCount+1] MCdrifts = np.zeros( [frameCount,2] ) for J in np.arange(0,frameCount): MCdrifts[J,:] = re.findall( r"([+-]?\d+.\d+)", MClog_crop[J] )[1:] # Zorro saves translations, motioncorr saves shifts. self.translations = -np.fliplr( MCdrifts ) if self.originMode == u'centroid': centroid = np.mean( self.translations, axis=0 ) self.translations -= centroid def xcorr2_unblur1_02( self, dosePerFrame = None, minShift = 2.0, terminationThres = 0.1, maxIteration=10, verbose=False, loadResult=True, clean=True ): """ Calls UnBlur by <NAME> Rohou using the Zorro interface. """ self.bench['unblur0'] = time.time() unblur_exename = "unblur_openmp_7_17_15.exe" if util.which( unblur_exename ) is None: print( "UnBlur not found in system path" ) return print( "Calling UnBlur for " + self.files['stack'] ) print( " written by <NAME> and <NAME>: http://grigoriefflab.janelia.org/unblur" ) print( " http://grigoriefflab.janelia.org/node/4900" ) import os try: os.umask( self.umask ) # Why is Python not using default umask from OS? except: pass if self.cachePath is None: self.cachePath = "." # Force trailing slashes onto cachePatch stackBase = os.path.basename( os.path.splitext( self.files[u'stack'] )[0] ) frcOutName = os.path.join( self.cachePath, stackBase + u"_unblur_frc.txt" ) shiftsOutName = os.path.join( self.cachePath, stackBase + u"_unblur_shifts.txt" ) outputAvName = os.path.join( self.cachePath, stackBase + u"_unblur.mrc" ) outputStackName = os.path.join( self.cachePath, stackBase + u"_unblur_movie.mrc" ) ps = self.pixelsize * 10.0 if 'dose' in self.filterMode: doDoseFilter = True if dosePerFrame == None: # We have to guesstimate the dose per frame in e/A^2 if it's not provided dosePerFrame = np.mean( self.images ) / (ps*ps) preExposure = 0.0 if 'dosenorm' in self.filterMode: restoreNoise=True else: restoreNoise=False else: doDoseFilter = False if self.Brad is not None: # Li masking is in MkPosList() in cufunc.cu (line 413) # Their r2 is normalized and mine isn't # Li has mask = exp( -0.5 * bfactor * r_norm**2 ) # r_norm**2 = x*x/Nx*Nx + y*y/Ny*Ny = r**2 / (Nx**2 + Ny**2) # For non-square arrays they have a non-square (but constant frequency) filter # RAM has mask = exp( -(r/brad)**2 ) # We can only get Bfactor approximately then but it's close enough for 3710x3838 bfac = 2.0 * (self.images.shape[1]**2 + self.images.shape[2]**2) / (self.Brad**2) print( "Using B-factor of " + str(bfac) + " for UnBlur" ) else: bfac = 1500 # dosef default 'safe' bfactor for mediocre gain reference outerShift = self.maxShift * ps # RAM: I see no reason to let people change the Fourier cross masking vertFouMaskHW = 1 horzFouMaskHW = 1 try: mrcName = os.path.join( self.cachePath, stackBase + "_unblurIN.mrc" ) mrcz.writeMRC( self.images, mrcName ) except: print( "Error in exporting MRC file to UnBlur" ) return # Are there flags for unblur? Check the source code. flags = "" # Not using any flags unblurexec = ( unblur_exename + " " + flags + " << STOP_PARSING \n" + mrcName ) unblurexec = (unblurexec + "\n" + str(self.images.shape[0]) + "\n" + outputAvName + "\n" + shiftsOutName + "\n" + str(ps) + "\n" + str(doDoseFilter) ) if bool(doDoseFilter): unblurexec += "\n" + str(dosePerFrame) + "\n" + str(self.voltage) + "\n" + str(preExposure) unblurexec += ("\n yes \n" + outputStackName + "\n yes \n" + frcOutName + "\n" + str(minShift) + "\n" + str(outerShift) + "\n" + str(bfac) + "\n" + str( np.int(vertFouMaskHW) ) + "\n" + str( np.int(horzFouMaskHW) ) + "\n" + str(terminationThres) + "\n" + str(maxIteration) ) if bool(doDoseFilter): unblurexec += "\n" + str(restoreNoise) unblurexec += "\n" + str(verbose) unblurexec = unblurexec + "\nSTOP_PARSING" print( unblurexec ) sub = subprocess.Popen( unblurexec, shell=True ) sub.wait() try: # Their FRC is significantly different from mine. self.FRC = np.loadtxt(frcOutName, comments='#', skiprows=0 ) self.translations = np.loadtxt( shiftsOutName, comments='#', skiprows=0 ).transpose() # UnBlur uses Fortran ordering, so we need to swap y and x for Zorro C-ordering self.translations = np.fliplr( self.translations ) # UnBlur returns drift in Angstroms self.translations /= ps # UnBlur registers to middle frame self.translations -= self.translations[0,:] if bool( loadResult ): print( "Loading UnBlur aligned frames into ImageRegistrator.images" ) if 'dose' in self.filterMode: # TODO: WHow to get both filtered images and unfiltered? self.imageSum = mrcz.readMRC( outputAvName )[0] else: self.imageSum = mrcz.readMRC( outputAvName )[0] # TODO: We have a bit of an issue, this UnBlur movie is dose filtered... self.images = mrcz.readMRC( outputStackName )[0] except IOError: print( "UnBlur likely core-dumped, try different input parameters?" ) finally: time.sleep(0.5) # DEBUG: try and see if temporary files are deleteable now. frcOutName = os.path.join( self.cachePath, stackBase + "_unblur_frc.txt" ) shiftsOutName = os.path.join( self.cachePath, stackBase + "_unblur_shifts.txt" ) outputAvName = os.path.join( self.cachePath, stackBase + "_unblur.mrc" ) outputStackName = os.path.join( self.cachePath, stackBase + "_unblur_movie.mrc" ) pass if self.originMode == 'centroid': centroid = np.mean( self.translations, axis=0 ) self.translations -= centroid time.sleep(0.5) if bool(clean): try: os.remove( mrcName ) except: print( "Could not remove Unblur MRC input file" ) try: os.remove( frcOutName ) except: print( "Could not remove Unblur FRC file" ) try: os.remove( shiftsOutName ) except: print( "Could not remove Unblur Shifts file" ) try: os.remove( outputAvName ) except: print( "Could not remove Unblur MRC average" ) try: os.remove( outputStackName ) except: print( "Could not remove Unblur MRC stack" ) self.bench['unblur1'] = time.time() def __init_xcorrnm2( self, triIndices=None ): """ """ self.bench['xcorr0'] = time.time() shapeImage = np.array( [self.images.shape[1], self.images.shape[2]] ) self.__N = np.asarray( self.images.shape )[0] if self.preShift: print( "Warning: Preshift will break if there are skipped frames in a triIndices row." ) # Test to see if triIndices is a np.array or use self.triMode if hasattr( triIndices, "__array__" ): # np.array # Ensure triIndices is a square array of the right size if triIndices.shape[0] != self.__N or triIndices.shape[1] != self.__N: raise IndexError("triIndices is wrong size, should be of length: " + str(self.__N) ) elif triIndices is None: [xmesh, ymesh] = np.meshgrid( np.arange(0,self.__N), np.arange(0,self.__N) ) trimesh = xmesh - ymesh # Build the triMat if it wasn't passed in as an array if( self.triMode == 'first' ): print( "Correlating in template mode to first image" ) triIndices = np.ones( [1,self.__N], dtype='bool' ) triIndices[0,0] = False # Don't autocorrelate the first frame. elif( self.triMode == u'diag' ): if (self.diagWidth is None) or (self.diagWidth < 0): # For negative numbers, align the entire triangular matrix self.diagWidth = self.__N triIndices = (trimesh <= self.diagWidth + self.diagStart ) * (trimesh > self.diagStart ) print( "Correlating in diagonal mode with width " + str(self.diagWidth) ) elif( self.triMode == u'autocorr' ): triIndices = (trimesh == 0) elif( self.triMode == u'refine' ): triIndices = trimesh == 0 else: # 'tri' or 'auto' ; default is an upper triangular matrix triIndices = trimesh >= 1 pass else: raise TypeError( "Error: triIndices not recognized as valid: " + str(triIndices) ) if self.masks is None or self.masks == []: print( "Warning: No mask not recommened with MNXC-style correlation" ) self.masks = np.ones( [1,shapeImage[0],shapeImage[1]], dtype = self.images.dtype ) if( self.masks.ndim == 2 ): self.masks = np.reshape( self.masks.astype(self.images.dtype), [1,shapeImage[0],shapeImage[1]] ) # Pre-loop allocation self.__shiftsTriMat = np.zeros( [self.__N,self.__N,2], dtype=float_dtype ) # Triagonal matrix of shifts in [I,J,(y,x)] self.__corrTriMat = np.zeros( [self.__N,self.__N], dtype=float_dtype ) # Triagonal matrix of maximum correlation coefficient in [I,J] self.__peaksigTriMat = np.zeros( [self.__N,self.__N], dtype=float_dtype ) # Triagonal matrix of correlation peak contrast level self.__originTriMat= np.zeros( [self.__N,self.__N], dtype=float_dtype ) # Triagonal matrix of origin correlation coefficient in [I,J] # Make pyFFTW objects if not bool( np.any( self.fouCrop ) ): self.__tempFullframe = np.empty( shapeImage, dtype=fftw_dtype ) self.__FFT2, self.__IFFT2 = util.pyFFTWPlanner( self.__tempFullframe, wisdomFile=os.path.join( self.cachePath, "fftw_wisdom.pkl" ), effort = self.fftw_effort, n_threads=self.n_threads ) self.__shapeCropped = shapeImage self.__tempComplex = np.empty( self.__shapeCropped, dtype=fftw_dtype ) else: self.__tempFullframe = np.empty( shapeImage, dtype=fftw_dtype ) self.__FFT2, _ = util.pyFFTWPlanner( self.__tempFullframe, wisdomFile=os.path.join( self.cachePath, "fftw_wisdom.pkl" ) , effort = self.fftw_effort, n_threads=self.n_threads, doReverse=False ) # Force fouCrop to multiple of 2 self.__shapeCropped = 2 * np.floor( np.array( self.fouCrop ) / 2.0 ).astype('int') self.__tempComplex = np.empty( self.__shapeCropped, dtype=fftw_dtype ) _, self.__IFFT2 = util.pyFFTWPlanner( self.__tempComplex, wisdomFile=os.path.join( self.cachePath, "fftw_wisdom.pkl" ) , effort = self.fftw_effort, n_threads=self.n_threads, doForward=False ) self.__shapeCropped2 = (np.array( self.__shapeCropped) / 2.0).astype('int') self.__templateImageFFT = np.empty( self.__shapeCropped, dtype=fftw_dtype ) self.__templateSquaredFFT = np.empty( self.__shapeCropped, dtype=fftw_dtype ) self.__templateMaskFFT = np.empty( self.__shapeCropped, dtype=fftw_dtype ) self.__tempComplex2 = np.empty( self.__shapeCropped, dtype=fftw_dtype ) # Subpixel initialization # Ideally subPix should be a power of 2 (i.e. 2,4,8,16,32) self.__subR = 8 # Sampling range around peak of +/- subR if self.subPixReg is None: self.subPixReg = 1; if self.subPixReg > 1.0: # hannfilt = np.fft.fftshift( ram.apodization( name='hann', size=[subR*2,subR*2], radius=[subR,subR] ) ).astype( fftw_dtype ) # Need a forward transform that is [subR*2,subR*2] self.__Csub = np.empty( [self.__subR*2,self.__subR*2], dtype=fftw_dtype ) self.__CsubFFT = np.empty( [self.__subR*2,self.__subR*2], dtype=fftw_dtype ) self.__subFFT2, _ = util.pyFFTWPlanner( self.__Csub, fouMage=self.__CsubFFT, wisdomFile=os.path.join( self.cachePath, "fftw_wisdom.pkl" ) , effort = self.fftw_effort, n_threads=self.n_threads, doReverse = False ) # and reverse transform that is [subR*2*subPix, subR*2*subPix] self.__CpadFFT = np.empty( [self.__subR*2*self.subPixReg,self.__subR*2*self.subPixReg], dtype=fftw_dtype ) self.__Csub_over = np.empty( [self.__subR*2*self.subPixReg,self.__subR*2*self.subPixReg], dtype=fftw_dtype ) _, self.__subIFFT2 = util.pyFFTWPlanner( self.__CpadFFT, fouMage=self.__Csub_over, wisdomFile=os.path.join( self.cachePath, "fftw_wisdom.pkl" ) , effort = self.fftw_effort, n_threads=self.n_threads, doForward = False ) self.__maskProduct = np.zeros( self.__shapeCropped, dtype=float_dtype ) self.__normConst2 = np.float32( 1.0 / ( np.float64(self.__shapeCropped[0])*np.float64(self.__shapeCropped[1]))**2.0 ) self.bench['xcorr1'] = time.time() return triIndices def xcorrnm2_speckle( self, triIndices=None ): """ <NAME> <EMAIL> October 1, 2016 With data recorded automatically from SerialEM, we no long have access to the gain reference normalization step provided by Gatan. With the K2 detector, gain normalization is no longer a simple multiplication. Therefore we see additional, multiplicative (or speckle) noise in the images compared to those recorded by Gatan Microscopy Suite. Here we want to use a different approach from the Padfield algorithm, which is useful for suppressing additive noise, and In general Poisson noise should be speckle noise, especially at the dose rates commonly seen in cryo-EM. """ triIndices = self.__init_xcorrnm2( triIndices = triIndices) # Pre-compute forward FFTs (template will just be copied conjugate Fourier spectra) self.__imageFFT = np.empty( [self.__N, self.shapePadded[0], self.shapePadded[1]], dtype=fftw_dtype ) self.__autocorrHalfs = np.empty( [self.__N, self.__shapeCropped[0], self.__shapeCropped[1]], dtype=float_dtype ) currIndex = 0 self.__originC = []; self.C = [] print( "Pre-computing forward Fourier transforms and autocorrelations" ) # For even-odd and noise estimates, we often skip many rows # precompIndices = np.unique( np.vstack( [np.argwhere( np.sum( triIndices, axis=1 ) > 0 ), np.argwhere( np.sum( triIndices, axis=0 ) > 0 ) ] ) ) precompIndices = np.unique( np.vstack( [np.argwhere( np.sum( triIndices, axis=1 ) >= 0 ), np.argwhere( np.sum( triIndices, axis=0 ) >= 0 ) ] ) ) for I in precompIndices: if self.verbose >= 2: print( "Precomputing forward FFT frame: " + str(I) ) # Apply masks to images if self.masks.shape[0] == 1: masks_block = self.masks[0,:,:] images_block = self.images[I,:,:] else: masks_block = self.masks[I,:,:] images_block = self.images[I,:,:] self.__tempComplex = nz.evaluate( "masks_block * images_block" ).astype( fftw_dtype ) self.__FFT2.update_arrays( self.__tempComplex, self.__imageFFT[I,:,:]); self.__FFT2.execute() print( "TODO: FOURIER CROPPING" ) # Compute autocorrelation imageFFT = self.__imageFFT[I,:,:] # Not sure if numexpr is useful for such a simple operation? self.__tempComplex = nz.evaluate( "imageFFT * conj(imageFFT)" ) self.__IFFT2.update_arrays( self.__tempComplex, self.__tempComplex2 ) tempComplex2 = self.__tempComplex2 nz.evaluate( "0.5*abs(tempComplex2)", out=self.__autocorrHalfs[I,:,:] ) self.bench['xcorr2'] = time.time() ########### COMPUTE PHASE CORRELATIONS ############# print( "Starting correlation calculations, mode: " + self.triMode ) if self.triMode == u'refine': # Find FFT sum (it must be reduced by the current frame later) # FIXME: Is there some reason this might not be linear after FFT? # FIXME: is it the complex conjugate operation below??? self.__sumFFT = np.sum( self.__baseImageFFT, axis = 0 ) self.__sumSquaredFFT = np.sum( self.__baseSquaredFFT, axis = 0 ) print( "In refine" ) for I in np.arange(self.images.shape[0] - 1): # In refine mode we have to build the template on the fly from imageSum - currentImage self.__templateImageFFT = np.conj( self.__sumFFT - self.__baseImageFFT[I,:,:] ) / self.images.shape[0] self.__templateSquaredFFT = np.conj( self.__sumSquaredFFT - self.__baseSquaredFFT[I,:,:] ) / self.images.shape[0] tempComplex2 = None self.mnxc2_SPECKLE( I, I, self.__shapeCropped, refine=True ) #### Find maximum positions #### self.locatePeak( I, I ) if self.verbose: print( "Refine # " + str(I) + " shift: [%.2f"%self.__shiftsTriMat[I,I,0] + ", %.2f"%self.__shiftsTriMat[I,I,1] + "], cc: %.6f"%self.__corrTriMat[I,I] + ", peak sig: %.3f"%self.__peaksigTriMat[I,I] ) else: # For even-odd and noise estimates, we often skip many rows rowIndices = np.unique( np.argwhere( np.sum( triIndices, axis=1 ) > 0 ) ) #print( "rowIndices: " + str(rowIndices) ) for I in rowIndices: # I is the index of the template image tempComplex = self.__baseImageFFT[I,:,:] self.__templateImageFFT = nz.evaluate( "conj(tempComplex)") # Now we can start looping through base images columnIndices = np.unique( np.argwhere( triIndices[I,:] ) ) #print( "columnIndices: " + str(columnIndices) ) for J in columnIndices: ####### MNXC2 revisement with private variable to make the code more manageable. self.mnxc2_speckle( I, J, self.__shapeCropped ) #### Find maximum positions #### self.locatePeak( I, J ) if self.verbose: print( "# " + str(I) + "->" + str(J) + " shift: [%.2f"%self.__shiftsTriMat[I,J,0] + ", %.2f"%self.__shiftsTriMat[I,J,1] + "], cc: %.6f"%self.__corrTriMat[I,J] + ", peak sig: %.3f"%self.__peaksigTriMat[I,J] ) # Correlation stats is for establishing correlation scores for fixed-pattern noise. if bool( self.trackCorrStats ): self.calcCorrStats( currIndex, triIndices ) # triMode 'auto' diagonal mode if self.triMode == u'auto' and (self.__peaksigTriMat[I,J] <= self.peaksigThres or J-I >= self.autoMax): if self.verbose: print( "triMode 'auto' stopping at frame: " + str(J) ) break currIndex += 1 pass # C max position location if bool( np.any( self.fouCrop ) ): self.__shiftsTriMat[:,:,0] *= self.shapePadded[0] / self.__shapeCropped[0] self.__shiftsTriMat[:,:,1] *= self.shapePadded[1] / self.__shapeCropped[1] self.bench['xcorr3'] = time.time() # Pointer reference house-keeping del images_block, masks_block, imageFFT, tempComplex2 def xcorrnm2_tri( self, triIndices=None ): """ <NAME> <EMAIL> April 16, 2015 triIndices is the index locations to correlate to. If None, self.triMode is used to build one. Normally you should use self.triMode for the first iteration, and pass in a triIndice from the errorDict if you want to repeat. returns : [shiftsTriMat, corrTriMat, peaksTriMat] This is an evolution of the Padfield cross-correlation algorithm to take advantage of the Cheng multi-reference approach for cross-correlation alignment of movies. Padfield, "Masked object registration in the Fourier domain," IEEE Transactions on Image Processing 21(5) (2012): 3706-2718. <NAME> al. Nature Methods, 10 (2013): 584-590. It cross-correlates every frame to every other frame to build a triangular matrix of shifts and then does a functional minimization over the set of equations. This means the computational cost grows with a power law with the number of frames but it is more noise resistant. triIndices can be an arbitrary boolean N x N matrix of frames to correlate Alternatively it can be a string which will generate an appropriate matrix: 'tri' (default) correlates all frames to eachother 'first' is correlate to the first frame as a template 'diag' correlates to the next frame (i.e. a diagonal ) 'auto' is like diag but automatically determines when to stop based on corrcoeffThes diagWidth is for 'diag' and the number of frames to correlate each frame to, default is None, which does the entire triangular matrix diagWidth = 1 correlates to each preceding frame NOTE: only calculates FFTs up to Nyquist/2. """ triIndices = self.__init_xcorrnm2( triIndices = triIndices) if self.masks.shape[0] == 1 : # tempComplex = self.masks[0,:,:].astype( fftw_dtype ) self.__baseMaskFFT = np.empty( self.__shapeCropped, dtype=fftw_dtype ) self.__FFT2.update_arrays( self.masks[0,:,:].squeeze().astype( fftw_dtype ), self.__tempFullframe ); self.__FFT2.execute() # FFTCrop sC2 = self.__shapeCropped2 self.__baseMaskFFT[0:sC2[0],0:sC2[1]] = self.__tempFullframe[0:sC2[0],0:sC2[1]] self.__baseMaskFFT[0:sC2[0],-sC2[1]:] = self.__tempFullframe[0:sC2[0],-sC2[1]:] self.__baseMaskFFT[-sC2[0]:,0:sC2[1]] = self.__tempFullframe[-sC2[0]:,0:sC2[1]] self.__baseMaskFFT[-sC2[0]:,-sC2[1]:] = self.__tempFullframe[-sC2[0]:,-sC2[1]:] self.__templateMaskFFT = np.conj( self.__baseMaskFFT ) # maskProduct term is M1^* .* M2 templateMaskFFT = self.__templateMaskFFT; baseMaskFFT = self.__baseMaskFFT # Pointer assignment self.__tempComplex2 = nz.evaluate( "templateMaskFFT * baseMaskFFT" ) self.__IFFT2.update_arrays( self.__tempComplex2, self.__tempComplex ); self.__IFFT2.execute() tempComplex = self.__tempComplex normConst2 = self.__normConst2 self.__maskProduct = nz.evaluate( "normConst2*real(tempComplex)" ) else: # Pre-allocate only self.__baseMaskFFT = np.zeros( [self.__N, self.__shapeCropped[0], self.__shapeCropped[1]], dtype=fftw_dtype ) if bool( self.maxShift ) or self.Bmode is u'fourier': if self.maxShift is None or self.preShift is True: [xmesh,ymesh] = np.meshgrid( np.arange(-self.__shapeCropped2[0], self.__shapeCropped2[0]), np.arange(-self.__shapeCropped2[1], self.__shapeCropped2[1]) ) else: [xmesh,ymesh] = np.meshgrid( np.arange(-self.maxShift, self.maxShift), np.arange(-self.maxShift, self.maxShift) ) rmesh2 = nz.evaluate( "xmesh*xmesh + ymesh*ymesh" ) # rmesh2 = xmesh*xmesh + ymesh*ymesh if bool( self.maxShift ): self.__mask_maxShift = ( rmesh2 < self.maxShift**2.0 ) if self.Bmode is u'fourier': self.__Bfilter = np.fft.fftshift( util.apodization( name=self.BfiltType, size=self.__shapeCropped, radius=[self.Brad,self.Brad] ) ) self.bench['xcorr1'] = time.time() # Pre-compute forward FFTs (template will just be copied conjugate Fourier spectra) self.__imageFFT = np.empty( [self.__N, self.shapePadded[0], self.shapePadded[1]], dtype=fftw_dtype ) self.__baseImageFFT = np.empty( [self.__N, self.__shapeCropped[0], self.__shapeCropped[1]], dtype=fftw_dtype ) self.__baseSquaredFFT =

np.empty( [self.__N, self.__shapeCropped[0], self.__shapeCropped[1]], dtype=fftw_dtype )

numpy.empty

import xarray as xr import numpy as np import dask.bag as db import dask.array as da from time import time from scipy.interpolate import LinearNDInterpolator from ..core import Instrument, Model from .attenuation import calc_radar_atm_attenuation from .psd import calc_mu_lambda from ..core.instrument import ureg, quantity def calc_total_reflectivity(model, detect_mask=False): """ This method calculates the total (convective + stratiform) reflectivity (Ze). Parameters ---------- model: :func:`emc2.core.Model` class The model to calculate the parameters for. detect_mask: bool True - generating a mask determining signal below noise floor. Returns ------- model: :func:`emc2.core.Model` The xarray Dataset containing the calculated radar moments. """ Ze_tot = np.where(np.isfinite(model.ds["sub_col_Ze_tot_strat"].values), 10 ** (model.ds["sub_col_Ze_tot_strat"].values / 10.), 0) if model.process_conv: Ze_tot = np.where(np.isfinite(model.ds["sub_col_Ze_tot_conv"].values), Ze_tot + 10 ** (model.ds["sub_col_Ze_tot_conv"].values / 10.), Ze_tot) model.ds['sub_col_Ze_tot'] = xr.DataArray(10 * np.log10(Ze_tot), dims=model.ds["sub_col_Ze_tot_strat"].dims) model.ds['sub_col_Ze_tot'].values = np.where(np.isinf(model.ds['sub_col_Ze_tot'].values), np.nan, model.ds['sub_col_Ze_tot'].values) model.ds['sub_col_Ze_tot'].attrs["long_name"] = \ "Total (convective + stratiform) equivalent radar reflectivity factor" model.ds['sub_col_Ze_tot'].attrs["units"] = "dBZ" if model.process_conv: model.ds['sub_col_Ze_att_tot'] = 10 * np.log10(Ze_tot * model.ds['hyd_ext_conv'].fillna(1) * model.ds[ 'hyd_ext_strat'].fillna(1) * model.ds['atm_ext'].fillna(1)) else: model.ds['sub_col_Ze_att_tot'] = 10 * np.log10(Ze_tot * model.ds['hyd_ext_strat'].fillna(1) * model.ds['atm_ext'].fillna(1)) model.ds['sub_col_Ze_att_tot'].values = np.where(np.isinf(model.ds['sub_col_Ze_att_tot'].values), np.nan, model.ds['sub_col_Ze_att_tot'].values) model.ds['sub_col_Ze_att_tot'].attrs["long_name"] = \ "Total (convective + stratiform) attenuated (hydrometeor + gaseous) equivalent radar reflectivity factor" model.ds['sub_col_Ze_att_tot'].attrs["units"] = "dBZ" model.ds["sub_col_Ze_tot"] = model.ds["sub_col_Ze_tot"].where(np.isfinite(model.ds["sub_col_Ze_tot"])) model.ds["sub_col_Ze_att_tot"] = model.ds["sub_col_Ze_att_tot"].where( np.isfinite(model.ds["sub_col_Ze_att_tot"])) model.ds["detect_mask"] = model.ds["Ze_min"] >= model.ds["sub_col_Ze_att_tot"] model.ds["detect_mask"].attrs["long_name"] = "Radar detectability mask" model.ds["detect_mask"].attrs["units"] = ("1 = radar signal below noise floor, 0 = signal detected") return model def accumulate_attenuation(model, is_conv, z_values, hyd_ext, atm_ext, OD_from_sfc=True, use_empiric_calc=False, **kwargs): """ Accumulates atmospheric and condensate radar attenuation (linear units) from TOA or the surface. Output fields are condensate and atmospheric transmittance. Parameters ---------- model: Model The model to generate the parameters for. is_conv: bool True if the cell is convective z_values: ndarray model output height array in m. hyd_ext: ndarray fwd calculated extinction due to condensate per layer (empirical - dB km^-1, m^-1 otherwise). atm_ext: ndarray atmospheric attenuation per layer (dB/km). OD_from_sfc: bool If True, then calculate optical depth from the surface. use_empirical_calc: bool When True using empirical relations from literature for the fwd calculations (the cloud fraction still follows the scheme logic set by use_rad_logic). Returns ------- model: :func:`emc2.core.Model` The model with the added simulated lidar parameters. """ if is_conv: cloud_str = "conv" else: cloud_str = "strat" if not use_empiric_calc: hyd_ext = hyd_ext * 1e3 if OD_from_sfc: OD_str = "model layer base" else: OD_str = "model layer top" n_subcolumns = model.num_subcolumns Dims = model.ds["%s_q_subcolumns_cl" % cloud_str].shape if OD_from_sfc: dz = np.diff(z_values / 1e3, axis=1, prepend=0.) hyd_ext = np.cumsum( np.tile(dz, (n_subcolumns, 1, 1)) * np.concatenate((np.zeros(Dims[:2] + (1,)), hyd_ext[:, :, :-1]), axis=2), axis=2) atm_ext = np.cumsum(dz * np.concatenate((np.zeros((Dims[1],) + (1,)), atm_ext[:, :-1]), axis=1), axis=1) else: dz = np.diff(z_values / 1e3, axis=1, append=0.) hyd_ext = np.flip( np.cumsum(np.flip(np.tile(dz, (n_subcolumns, 1, 1)) * np.concatenate((hyd_ext[:, :, 1:], np.zeros(Dims[:2] + (1,))), axis=2), axis=2), axis=2), axis=2) atm_ext = np.flip( np.cumsum(np.flip(dz * np.concatenate((atm_ext[:, 1:], np.zeros((Dims[1],) + (1,))), axis=1), axis=1), axis=1), axis=1) if use_empiric_calc: model.ds['hyd_ext_%s' % cloud_str] = xr.DataArray(10 ** (-2 * hyd_ext / 10.), dims=model.ds["%s_q_subcolumns_cl" % cloud_str].dims) else: model.ds['hyd_ext_%s' % cloud_str] = \ xr.DataArray(np.exp(-2 * hyd_ext), dims=model.ds["sub_col_Ze_tot_%s" % cloud_str].dims) model.ds['atm_ext'] = xr.DataArray(10 ** (-2 * atm_ext / 10), dims=model.ds[model.T_field].dims) model.ds['hyd_ext_%s' % cloud_str].attrs["long_name"] = \ "Two-way %s hydrometeor transmittance at %s" % (cloud_str, OD_str) model.ds['hyd_ext_%s' % cloud_str].attrs["units"] = "1" model.ds['atm_ext'].attrs["long_name"] = \ "Two-way atmospheric transmittance due to H2O and O2 at %s" % OD_str model.ds['atm_ext'].attrs["units"] = "1" return model def calc_radar_empirical(instrument, model, is_conv, p_values, t_values, z_values, atm_ext, OD_from_sfc=True, use_empiric_calc=False, hyd_types=None, **kwargs): """ Calculates the radar stratiform or convective reflectivity and attenuation in a sub-columns using empirical formulation from literature. Parameters ---------- instrument: :func:`emc2.core.Instrument` class The instrument to calculate the reflectivity parameters for. model: :func:`emc2.core.Model` class The model to calculate the parameters for. is_conv: bool True if the cell is convective p_values: ndarray model output pressure array in Pa. t_values: ndarray model output temperature array in C. z_values: ndarray model output height array in m. atm_ext: ndarray atmospheric attenuation per layer (dB/km). OD_from_sfc: bool If True, then calculate optical depth from the surface. hyd_types: list or None list of hydrometeor names to include in calcuation. using default Model subclass types if None. Additonal keyword arguments are passed into :py:func:`emc2.simulator.lidar_moments.accumulate_attenuation`. Returns ------- model: :func:`emc2.core.Model` The model with the added simulated lidar parameters. """ hyd_types = model.set_hyd_types(hyd_types) if is_conv: cloud_str = "conv" else: cloud_str = "strat" if not instrument.instrument_class.lower() == "radar": raise ValueError("Reflectivity can only be derived from a radar!") Dims = model.ds["%s_q_subcolumns_cl" % cloud_str].shape model.ds["sub_col_Ze_tot_%s" % cloud_str] = xr.DataArray( np.zeros(Dims), dims=model.ds["%s_q_subcolumns_cl" % cloud_str].dims) for hyd_type in hyd_types: q_field = "%s_q_subcolumns_%s" % (cloud_str, hyd_type) WC_tot = np.zeros(Dims) WC = model.ds["%s_q_subcolumns_%s" % (cloud_str, hyd_type)] * p_values / \ (instrument.R_d * (t_values + 273.15)) * 1e3 # Fox and Illingworth (1997) if hyd_type.lower() == "cl": Ze_emp = 0.031 * WC ** 1.56 WC_tot += WC # Hagen and Yuter (2003) elif hyd_type.lower() == "pl": Ze_emp = ((WC * 1e3) / 3.4) ** 1.75 WC_tot += WC else: # Hogan et al. (2006) if 2e9 <= instrument.freq < 4e9: Ze_emp = 10 ** (((np.log10(WC) + 0.0197 * t_values + 1.7) / 0.060) / 10.) elif 27e9 <= instrument.freq < 40e9: Ze_emp = 10 ** (((np.log10(WC) + 0.0186 * t_values + 1.63) / (0.000242 * t_values + 0.0699)) / 10.) elif 75e9 <= instrument.freq < 110e9: Ze_emp = 10 ** (((np.log10(WC) + 0.00706 * t_values + 0.992) / (0.000580 * t_values + 0.0923)) / 10.) else: Ze_emp = 10 ** (((np.log10(WC) + 0.0186 * t_values + 1.63) / (0.000242 * t_values + 0.0699)) / 10.) var_name = "sub_col_Ze_%s_%s" % (hyd_type, cloud_str) model.ds[var_name] = xr.DataArray( Ze_emp.values, dims=model.ds[q_field].dims) model.ds["sub_col_Ze_tot_%s" % cloud_str] += Ze_emp.fillna(0) kappa_f = 6 * np.pi / (instrument.wavelength * model.Rho_hyd["cl"].magnitude) * \ ((instrument.eps_liq - 1) / (instrument.eps_liq + 2)).imag * 4.34e6 # dB m^3 g^-1 km^-1 model = accumulate_attenuation(model, is_conv, z_values, WC_tot * kappa_f, atm_ext, OD_from_sfc=OD_from_sfc, use_empiric_calc=True, **kwargs) return model def calc_radar_bulk(instrument, model, is_conv, p_values, z_values, atm_ext, OD_from_sfc=True, hyd_types=None, mie_for_ice=False, **kwargs): """ Calculates the radar stratiform or convective reflectivity and attenuation in a sub-columns using bulk scattering LUTs assuming geometric scatterers (radiation scheme logic). Effective radii for each hydrometeor class must be provided (in model.ds). Parameters ---------- instrument: Instrument The instrument to simulate. The instrument must be a lidar. model: Model The model to generate the parameters for. is_conv: bool True if the cell is convective p_values: ndarray model output pressure array in Pa. z_values: ndarray model output height array in m. atm_ext: ndarray atmospheric attenuation per layer (dB/km). OD_from_sfc: bool If True, then calculate optical depth from the surface. hyd_types: list or None list of hydrometeor names to include in calcuation. using default Model subclass types if None. mie_for_ice: bool If True, using bulk mie caculation LUTs. Otherwise, currently using the bulk C6 scattering LUTs for 8-column severly roughned aggregate. Additonal keyword arguments are passed into :py:func:`emc2.simulator.lidar_moments.accumulate_attenuation`. Returns ------- model: :func:`emc2.core.Model` The model with the added simulated lidar parameters. """ hyd_types = model.set_hyd_types(hyd_types) n_subcolumns = model.num_subcolumns if is_conv: cloud_str = "conv" re_fields = model.conv_re_fields else: cloud_str = "strat" re_fields = model.strat_re_fields if model.model_name in ["E3SM", "CESM2"]: bulk_ice_lut = "CESM_ice" bulk_mie_ice_lut = "mie_ice_CESM_PSD" bulk_liq_lut = "CESM_liq" else: bulk_ice_lut = "E3_ice" bulk_mie_ice_lut = "mie_ice_E3_PSD" bulk_liq_lut = "E3_liq" Dims = model.ds["%s_q_subcolumns_cl" % cloud_str].shape model.ds["sub_col_Ze_tot_%s" % cloud_str] = xr.DataArray( np.zeros(Dims), dims=model.ds["%s_q_subcolumns_cl" % cloud_str].dims) hyd_ext = np.zeros(Dims) rhoa_dz = np.tile( np.abs(np.diff(p_values, axis=1, append=0.)) / instrument.g, (n_subcolumns, 1, 1)) dz = np.tile( np.diff(z_values, axis=1, append=0.), (n_subcolumns, 1, 1)) for hyd_type in hyd_types: if hyd_type[-1] == 'l': rho_b = model.Rho_hyd[hyd_type] # bulk water re_array = np.tile(model.ds[re_fields[hyd_type]].values, (n_subcolumns, 1, 1)) if model.lambda_field is not None: # assuming my and lambda can be provided only for liq hydrometeors if not model.lambda_field[hyd_type] is None: lambda_array = model.ds[model.lambda_field[hyd_type]].values mu_array = model.ds[model.mu_field[hyd_type]].values else: rho_b = instrument.rho_i # bulk ice fi_factor = model.fluffy[hyd_type].magnitude * model.Rho_hyd[hyd_type] / rho_b + \ (1 - model.fluffy[hyd_type].magnitude) * (model.Rho_hyd[hyd_type] / rho_b) ** (1 / 3) re_array = np.tile(model.ds[re_fields[hyd_type]].values * fi_factor, (n_subcolumns, 1, 1)) tau_hyd = np.where(model.ds["%s_q_subcolumns_%s" % (cloud_str, hyd_type)] > 0, 3 * model.ds["%s_q_subcolumns_%s" % (cloud_str, hyd_type)] * rhoa_dz / (2 * rho_b * re_array * 1e-6), 0) A_hyd = tau_hyd / (2 * dz) # model assumes geometric scatterers if np.isin(hyd_type, ["ci", "pi"]): if mie_for_ice: r_eff_bulk = instrument.bulk_table[bulk_mie_ice_lut]["r_e"].values.copy() Qback_bulk = instrument.bulk_table[bulk_mie_ice_lut]["Q_back"].values Qext_bulk = instrument.bulk_table[bulk_mie_ice_lut]["Q_ext"].values else: r_eff_bulk = instrument.bulk_table[bulk_ice_lut]["r_e"].values.copy() Qback_bulk = instrument.bulk_table[bulk_ice_lut]["Q_back"].values Qext_bulk = instrument.bulk_table[bulk_ice_lut]["Q_ext"].values else: if model.model_name in ["E3SM", "CESM2"]: mu_b = np.tile(instrument.bulk_table[bulk_liq_lut]["mu"].values, (instrument.bulk_table[bulk_liq_lut]["lambdas"].size)).flatten() lambda_b = instrument.bulk_table[bulk_liq_lut]["lambda"].values.flatten() else: r_eff_bulk = instrument.bulk_table[bulk_liq_lut]["r_e"].values Qback_bulk = instrument.bulk_table[bulk_liq_lut]["Q_back"].values Qext_bulk = instrument.bulk_table[bulk_liq_lut]["Q_ext"].values if np.logical_and(np.isin(hyd_type, ["cl", "pl"]), model.model_name in ["E3SM", "CESM2"]): print("2-D interpolation of bulk liq radar backscattering using mu-lambda values") rel_locs = model.ds[model.q_names_stratiform[hyd_type]].values > 0. interpolator = LinearNDInterpolator(

np.stack((mu_b, lambda_b), axis=1)

numpy.stack

#!/usr/bin/env python # coding: utf-8 import h5py import numpy as np from functools import reduce from tqdm import tqdm import disk.funcs as dfn class binary_mbh(object): def __init__(self, filename): self.filename = filename with h5py.File(self.filename, 'r') as f: self.SubhaloMassInHalfRadType = np.array(f['meta/SubhaloMassInHalfRadType']) self.SubhaloSFRinHalfRad = np.array(f['meta/SubhaloSFRinHalfRad']) self.snapshot = np.array(f['meta/snapshot']) self.subhalo_id = np.array(f['meta/subhalo_id']) self.masses = np.array(f['evolution/masses']) #g self.mdot = np.array(f['evolution/mdot_eff']) #g/s self.sep = np.array(f['evolution/sep']) #cm self.dadt = np.array(f['evolution/dadt']) #cm/s self.dadt_df = np.array(f['evolution/dadt_df']) #cm/s self.dadt_gw = np.array(f['evolution/dadt_gw']) #cm/s self.dadt_lc = np.array(f['evolution/dadt_lc']) #cm/s self.dadt_vd = np.array(f['evolution/dadt_vd']) #cm/s self.scales = np.array(f['evolution/scales']) #NA self.times = np.array(f['evolution/times']) #s self.eccen = np.array(f['evolution/eccen']) #NA self.z = (1./self.scales)-1 #NA self.m1 = self.masses[:,0] self.m2 = self.masses[:,1] self.mtot = self.m1+self.m2 self.q = self.m2/self.m1 def find_Rlc(self): R_lc = np.zeros((self.sep.shape[0],3)) for i in range(len(self.sep)): try: idx = reduce(np.intersect1d,(np.where(np.abs(self.dadt_lc[i])>np.abs(self.dadt_df[i]))[0], np.where(np.abs(self.dadt_lc[i])>np.abs(self.dadt_vd[i]))[0], np.where(np.abs(self.dadt_lc[i])>np.abs(self.dadt_gw[i]))[0]))[0] R_lc[i]=[i,idx,self.sep[i][idx]] except: R_lc[i]=[i,np.nan,np.nan] return R_lc def find_Rvd(self): R_vd = np.zeros((self.sep.shape[0],3)) for i in range(len(self.sep)): try: idx = reduce(np.intersect1d,(np.where(np.abs(self.dadt_vd[i])>np.abs(self.dadt_df[i]))[0], np.where(np.abs(self.dadt_vd[i])>np.abs(self.dadt_lc[i]))[0], np.where(

np.abs(self.dadt_vd[i])

numpy.abs

import argparse import os import numpy as np import matplotlib.pyplot as plt from scipy.misc import imread from scipy.misc import imsave def blend(x, y, overlay): blended = x * (1 - overlay) + y * overlay blended = np.clip(blended, 0.0, 1.0) blended = np.where(y != 0, blended, x) return blended def is_mask(img): i = 0 for row in img: for col in row: for px in col: if px != 0.0 and px != 1.0: i = i + 1 f = np.vectorize(lambda x: x == 0.0 or x == 1.0) non_zero = np.count_nonzero(f(img)) / 3 total = np.shape(img)[0] *

np.shape(img)

numpy.shape

import os import pickle import warnings import platform import tempfile import numpy as np from pytransform3d.rotations import ( q_id, active_matrix_from_intrinsic_euler_xyz, random_quaternion) from pytransform3d.transformations import ( random_transform, invert_transform, concat, transform_from_pq, transform_from) from pytransform3d.transform_manager import TransformManager from pytransform3d import transform_manager from numpy.testing import assert_array_almost_equal from nose.tools import (assert_raises_regexp, assert_equal, assert_true, assert_false) from nose import SkipTest def test_request_added_transform(): """Request an added transform from the transform manager.""" random_state = np.random.RandomState(0) A2B = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) A2B_2 = tm.get_transform("A", "B") assert_array_almost_equal(A2B, A2B_2) def test_request_inverse_transform(): """Request an inverse transform from the transform manager.""" random_state = np.random.RandomState(0) A2B = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) A2B_2 = tm.get_transform("A", "B") assert_array_almost_equal(A2B, A2B_2) B2A = tm.get_transform("B", "A") B2A_2 = invert_transform(A2B) assert_array_almost_equal(B2A, B2A_2) def test_has_frame(): """Check if frames have been registered with transform.""" tm = TransformManager() tm.add_transform("A", "B", np.eye(4)) assert_true(tm.has_frame("A")) assert_true(tm.has_frame("B")) assert_false(tm.has_frame("C")) def test_transform_not_added(): """Test request for transforms that have not been added.""" random_state = np.random.RandomState(0) A2B = random_transform(random_state) C2D = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) tm.add_transform("C", "D", C2D) assert_raises_regexp(KeyError, "Unknown frame", tm.get_transform, "A", "G") assert_raises_regexp(KeyError, "Unknown frame", tm.get_transform, "G", "D") assert_raises_regexp(KeyError, "Cannot compute path", tm.get_transform, "A", "D") def test_request_concatenated_transform(): """Request a concatenated transform from the transform manager.""" random_state = np.random.RandomState(0) A2B = random_transform(random_state) B2C = random_transform(random_state) F2A = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) tm.add_transform("B", "C", B2C) tm.add_transform("D", "E", np.eye(4)) tm.add_transform("F", "A", F2A) A2C = tm.get_transform("A", "C") assert_array_almost_equal(A2C, concat(A2B, B2C)) C2A = tm.get_transform("C", "A") assert_array_almost_equal(C2A, concat(invert_transform(B2C), invert_transform(A2B))) F2B = tm.get_transform("F", "B") assert_array_almost_equal(F2B, concat(F2A, A2B)) def test_update_transform(): """Update an existing transform.""" random_state = np.random.RandomState(0) A2B1 = random_transform(random_state) A2B2 = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B1) tm.add_transform("A", "B", A2B2) A2B = tm.get_transform("A", "B") # Hack: test depends on internal member assert_array_almost_equal(A2B, A2B2) assert_equal(len(tm.i), 1) assert_equal(len(tm.j), 1) def test_pickle(): """Test if a transform manager can be pickled.""" random_state = np.random.RandomState(1) A2B = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) _, filename = tempfile.mkstemp(".pickle") try: pickle.dump(tm, open(filename, "wb")) tm2 = pickle.load(open(filename, "rb")) finally: if os.path.exists(filename): try: os.remove(filename) except WindowsError: pass # workaround for permission problem on Windows A2B2 = tm2.get_transform("A", "B") assert_array_almost_equal(A2B, A2B2) def test_whitelist(): """Test correct handling of whitelists for plotting.""" random_state = np.random.RandomState(2) A2B = random_transform(random_state) tm = TransformManager() tm.add_transform("A", "B", A2B) nodes = tm._whitelisted_nodes(None) assert_equal({"A", "B"}, nodes) nodes = tm._whitelisted_nodes(["A"]) assert_equal({"A"}, nodes) assert_raises_regexp(KeyError, "unknown nodes", tm._whitelisted_nodes, "C") def test_check_consistency(): """Test correct detection of inconsistent graphs.""" random_state = np.random.RandomState(2) tm = TransformManager() A2B = random_transform(random_state) tm.add_transform("A", "B", A2B) B2A = random_transform(random_state) tm.add_transform("B", "A", B2A) assert_false(tm.check_consistency()) tm = TransformManager() A2B = random_transform(random_state) tm.add_transform("A", "B", A2B) assert_true(tm.check_consistency()) C2D = random_transform(random_state) tm.add_transform("C", "D", C2D) assert_true(tm.check_consistency()) B2C = random_transform(random_state) tm.add_transform("B", "C", B2C) assert_true(tm.check_consistency()) A2D_over_path = tm.get_transform("A", "D") A2D = random_transform(random_state) tm.add_transform("A", "D", A2D) assert_false(tm.check_consistency()) tm.add_transform("A", "D", A2D_over_path) assert_true(tm.check_consistency()) def test_connected_components(): """Test computation of connected components in the graph.""" tm = TransformManager() tm.add_transform("A", "B", np.eye(4)) assert_equal(tm.connected_components(), 1) tm.add_transform("D", "E", np.eye(4)) assert_equal(tm.connected_components(), 2) tm.add_transform("B", "C",

np.eye(4)

numpy.eye

import random from typing import List, Dict, Tuple import math import numpy as np from synthetic_data.observation import Observation import os import pickle import time from llr.llr import * # Created by <NAME> 29 November 2017 class Simulator: def __init__(self, n_users: int, user_features: List[int], n_items: int, item_features: int, bias: int, users_distribution: str = "zipf", items_distribution: str = "zipf", read_cache_dir: str = None, save_cache_dir: str = None, timestamp: bool=True, tout: bool=True) -> None: """Produce a list of observations --users who "buy" items. e.g. ``` s = Simulator(n_users=101, user_features=0, n_items=1500, item_features=10, bias=1.0) s.run() ``` :param int n_users: Number of users :param List[int] user_features: [feature1_n_values, feature2... ] :param int n_items: Number of items :param List[int] item_features: as for users :param int bias: how similarity influences. If 0, at all. If 1, p(item after an item sim=-1)=0 :param int timestamp: unix-like timestamp (in seconds) :return List[Tuple3]: list of observations (user_id, item_id, timestamp) """ self.user_buying_dict = {} # {user: [(item, timestamp), (), ...], ...} self.observations_list = [] self._user_features = user_features self._item_features = item_features self.n_users = n_users self.n_items = n_items self._reset_cooccurrences_matrices() self._reset_sequentials_matrices() self.tout = tout assert read_cache_dir is None or save_cache_dir is None, \ "saving and reading the cache at the same time does not make sense" self.read_cache_dir = read_cache_dir self.save_cache_dir = save_cache_dir if bias >= 0: self.bias =

np.float32(bias)

numpy.float32

import argparse import dill import jax import numpy as np import pomdp pomdp.horizon = 25 parser = argparse.ArgumentParser() parser.add_argument('--silent', action='store_true') parser.add_argument('--bias', action='store_true') args = parser.parse_args() with open('data/data{}-meta.obj'.format('-bias' if args.bias else ''), 'rb') as f: data_meta = dill.load(f) S = data_meta['S'] A = data_meta['A'] Z = data_meta['Z'] envr_b0 = data_meta['envr_b0'] envr_O = data_meta['envr_O'] plcy_b0 = data_meta['plcy_b0'] plcy_T = data_meta['plcy_T'] plcy_O = data_meta['plcy_O'] plcy_mu = data_meta['plcy_mu'] def log_pi_il(mu, eta, b): res = -eta * np.sum((mu - b[None,...])**2, axis=-1) return res - np.log(np.sum(np.exp(res))) def log_pi_irl(alp, bet, b): res = np.zeros(A) for a in range(A): if alp[a].size == 0: res[a] = -1e6 else: res[a] = bet * np.amax(alp[a] @ b) return res - np.log(np.sum(np.exp(res))) algs = list() with open('res/res{}-interpole.obj'.format('-bias' if args.bias else ''), 'rb') as f: res = dill.load(f) algs.append(dict()) algs[-1]['name'] = 'interpole' algs[-1]['log_pi'] = log_pi_il algs[-1]['b0'] = res['b0'] algs[-1]['O'] = res['O'] algs[-1]['tht'] = res['mu'] with open('res/res{}-offpoirl.obj'.format('-bias' if args.bias else ''), 'rb') as f: res = dill.load(f) res = res['out'][500::10] algs.append(dict()) algs[-1]['name'] = 'offpoirl' algs[-1]['log_pi'] = log_pi_irl algs[-1]['b0'] = np.zeros(S) algs[-1]['O'] = np.zeros((A,S,Z)) algs[-1]['R'] = np.zeros((S,A)) for b0, _, O, R in res: algs[-1]['b0'] += b0 algs[-1]['O'] += O algs[-1]['R'] += R algs[-1]['b0'] /= len(res) algs[-1]['O'] /= len(res) algs[-1]['R'] /= len(res) algs[-1]['tht'] = pomdp.solve(S, A, Z, algs[-1]['b0'], plcy_T, algs[-1]['O'], algs[-1]['R']) with open('res/res{}-poirl.obj'.format('-bias' if args.bias else ''), 'rb') as f: res = dill.load(f) res = res['out'][500::10] algs.append(dict()) algs[-1]['name'] = 'poirl' algs[-1]['log_pi'] = log_pi_irl algs[-1]['b0'] = np.zeros(S) algs[-1]['O'] = np.zeros((A,S,Z)) algs[-1]['R'] = np.zeros((S,A)) for b0, _, O, R in res: algs[-1]['b0'] += b0 algs[-1]['O'] += O algs[-1]['R'] += R algs[-1]['b0'] /= len(res) algs[-1]['O'] /= len(res) algs[-1]['R'] /= len(res) algs[-1]['tht'] = pomdp.solve(S, A, Z, algs[-1]['b0'], plcy_T, algs[-1]['O'], algs[-1]['R']) with open('res/res{}-pombil.obj'.format('-bias' if args.bias else ''), 'rb') as f: res = dill.load(f) algs.append(dict()) algs[-1]['name'] = 'pombil' algs[-1]['log_pi'] = log_pi_il algs[-1]['b0'] = res['b0'] algs[-1]['O'] = res['O'] algs[-1]['tht'] = res['mu'] with open('res/res{}-rbc.obj'.format('-bias' if args.bias else ''), 'rb') as f: alg_rbc = dill.load(f) for alg in algs: alg['e1'] = list() alg['e2'] = list() alg['e3'] = list() e1_rbc = list() e2_rbc = list() for i in range(500): if not args.silent: if i % 100 == 0: print('i = {}'.format(i)) s = np.random.choice(range(S), p=envr_b0) b = plcy_b0 tau = None for alg in algs: alg['b'] = alg['b0'] alg['tau'] = None h_rbc = np.zeros(alg_rbc['H']) c_rbc = np.zeros(alg_rbc['H']) tau_rbc = None t = 0 while True: t += 1 pi = np.exp(log_pi_il(plcy_mu, 10, b)) for alg in algs: alg['pi'] = np.exp(alg['log_pi'](alg['tht'], 10, alg['b'])) if t > 1: pi_rbc = np.array(jax.nn.softmax(alg_rbc['W_y'] @ l_rbc + alg_rbc['b_y'])) if tau is None: for alg in algs: alg['e2'].append(np.sum(pi * np.log(pi / alg['pi']))) alg['e3'].append(np.sum(b * np.log(b / alg['b']))) if t > 1: e2_rbc.append(np.sum(pi * np.log(pi / pi_rbc))) a = np.random.choice(range(A), p=pi) for alg in algs: alg['a'] = np.random.choice(range(A), p=alg['pi']) if t > 1: a_rbc = np.random.choice(range(A), p=pi_rbc) z = np.random.choice(range(Z), p=envr_O[2,s,:]) b = plcy_O[2,:,z] * b b /= b.sum() for alg in algs: alg['b'] = alg['O'][2,:,z] * alg['b'] alg['b'] /= alg['b'].sum() x = np.concatenate((np.array([0, 0, 1]), jax.nn.one_hot(z, Z))) f = jax.nn.sigmoid(alg_rbc['W_f'] @ x + alg_rbc['U_f'] @ h_rbc + alg_rbc['b_f']) i = jax.nn.sigmoid(alg_rbc['W_i'] @ x + alg_rbc['U_i'] @ h_rbc + alg_rbc['b_i']) o = jax.nn.sigmoid(alg_rbc['W_o'] @ x + alg_rbc['U_o'] @ h_rbc + alg_rbc['b_o']) c_rbc = f * c_rbc + i * np.tanh(alg_rbc['W_c'] @ x + alg_rbc['U_c'] @ h_rbc + alg_rbc['b_c']) h_rbc = o * np.tanh(c_rbc) l_rbc = np.tanh(alg_rbc['W_l'] @ h_rbc + alg_rbc['b_l']) if tau is None and a != 2: tau = t for alg in algs: if alg['tau'] is None and alg['a'] != 2: alg['tau'] = t if t > 1: if tau_rbc is None and a_rbc != 2: tau_rbc = t brk = tau is not None for alg in algs: brk = brk and alg['tau'] is not None brk = brk and tau_rbc is not None if brk: break for alg in algs: alg['e1'].append(np.abs(alg['tau'] - tau)) e1_rbc.append(

np.abs(tau_rbc - tau)

numpy.abs

import pytest import numpy as np import sys if (sys.version_info > (3, 0)): from io import StringIO else: from StringIO import StringIO from keras_contrib import callbacks from keras.models import Sequential, Model from keras.layers import Input, Dense, Conv2D, Flatten, Activation from keras import backend as K n_out = 11 # with 1 neuron dead, 1/11 is just below the threshold of 10% with verbose = False def check_print(do_train, expected_warnings, nr_dead=None, perc_dead=None): """ Receive stdout to check if correct warning message is delivered :param nr_dead: int :param perc_dead: float, 10% should be written as 0.1 """ saved_stdout = sys.stdout out = StringIO() out.flush() sys.stdout = out # overwrite current stdout do_train() stdoutput = out.getvalue().strip() # get prints, can be something like: "Layer dense (#0) has 2 dead neurons (20.00%)!" str_to_count = "dead neurons" count = stdoutput.count(str_to_count) sys.stdout = saved_stdout # restore stdout out.close() assert expected_warnings == count if expected_warnings and (nr_dead is not None): str_to_check = 'has {} dead'.format(nr_dead) assert str_to_check in stdoutput, '"{}" not in "{}"'.format(str_to_check, stdoutput) if expected_warnings and (perc_dead is not None): str_to_check = 'neurons ({:.2%})!'.format(perc_dead) assert str_to_check in stdoutput, '"{}" not in "{}"'.format(str_to_check, stdoutput) def test_DeadDeadReluDetector(): n_samples = 9 input_shape = (n_samples, 3, 4) # 4 input features shape_out = (n_samples, 3, n_out) # 11 output features shape_weights = (4, n_out) # ignore batch size input_shape_dense = tuple(input_shape[1:]) def do_test(weights, expected_warnings, verbose, nr_dead=None, perc_dead=None): def do_train(): dataset = np.ones(input_shape) # data to be fed as training model = Sequential() model.add(Dense(n_out, activation='relu', input_shape=input_shape_dense, use_bias=False, weights=[weights], name='dense')) model.compile(optimizer='sgd', loss='categorical_crossentropy') model.fit( dataset, np.ones(shape_out), batch_size=1, epochs=1, callbacks=[callbacks.DeadReluDetector(dataset, verbose=verbose)], verbose=False ) check_print(do_train, expected_warnings, nr_dead, perc_dead) weights_1_dead = np.ones(shape_weights) # weights that correspond to NN with 1/11 neurons dead weights_2_dead = np.ones(shape_weights) # weights that correspond to NN with 2/11 neurons dead weights_all_dead = np.zeros(shape_weights) # weights that correspond to all neurons dead weights_1_dead[:, 0] = 0 weights_2_dead[:, 0:2] = 0 do_test(weights_1_dead, verbose=True, expected_warnings=1, nr_dead=1, perc_dead=1. / n_out) do_test(weights_1_dead, verbose=False, expected_warnings=0) do_test(weights_2_dead, verbose=True, expected_warnings=1, nr_dead=2, perc_dead=2. / n_out) # do_test(weights_all_dead, verbose=True, expected_warnings=1, nr_dead=n_out, perc_dead=1.) def test_DeadDeadReluDetector_bias(): n_samples = 9 input_shape = (n_samples, 4) # 4 input features shape_weights = (4, n_out) shape_bias = (n_out, ) shape_out = (n_samples, n_out) # 11 output features # ignore batch size input_shape_dense = tuple(input_shape[1:]) def do_test(weights, bias, expected_warnings, verbose, nr_dead=None, perc_dead=None): def do_train(): dataset = np.ones(input_shape) # data to be fed as training model = Sequential() model.add(Dense(n_out, activation='relu', input_shape=input_shape_dense, use_bias=True, weights=[weights, bias], name='dense')) model.compile(optimizer='sgd', loss='categorical_crossentropy') model.fit( dataset, np.ones(shape_out), batch_size=1, epochs=1, callbacks=[callbacks.DeadReluDetector(dataset, verbose=verbose)], verbose=False ) check_print(do_train, expected_warnings, nr_dead, perc_dead) weights_1_dead = np.ones(shape_weights) # weights that correspond to NN with 1/11 neurons dead weights_2_dead = np.ones(shape_weights) # weights that correspond to NN with 2/11 neurons dead weights_all_dead = np.zeros(shape_weights) # weights that correspond to all neurons dead weights_1_dead[:, 0] = 0 weights_2_dead[:, 0:2] = 0 bias =

np.zeros(shape_bias)

numpy.zeros

from __future__ import absolute_import, division, print_function import six import logging import os import json import numpy as np import torch from madminer.utils.ml import ratio_losses, flow_losses from madminer.utils.ml.models.maf import ConditionalMaskedAutoregressiveFlow from madminer.utils.ml.models.maf_mog import ConditionalMixtureMaskedAutoregressiveFlow from madminer.utils.ml.models.ratio import ParameterizedRatioEstimator, DoublyParameterizedRatioEstimator from madminer.utils.ml.models.score import LocalScoreEstimator from madminer.utils.ml.flow_trainer import train_flow_model, evaluate_flow_model from madminer.utils.ml.ratio_trainer import train_ratio_model, evaluate_ratio_model from madminer.utils.ml.score_trainer import train_local_score_model, evaluate_local_score_model from madminer.utils.various import create_missing_folders, load_and_check, shuffle logger = logging.getLogger(__name__) class MLForge: """ Estimating likelihood ratios and scores with machine learning. Each instance of this class represents one neural estimator. The most important functions are: * `MLForge.train()` to train an estimator. The keyword `method` determines the inference technique and whether a class instance represents a single-parameterized likelihood ratio estimator, a doubly-parameterized likelihood ratio estimator, or a local score estimator. * `MLForge.evaluate()` to evaluate the estimator. * `MLForge.save()` to save the trained model to files. * `MLForge.load()` to load the trained model from files. Please see the tutorial for a detailed walk-through. """ def __init__(self): self.method_type = None self.model = None self.method = None self.nde_type = None self.n_observables = None self.n_parameters = None self.n_hidden = None self.activation = None self.maf_n_mades = None self.maf_batch_norm = None self.maf_batch_norm_alpha = None self.features = None self.x_scaling_means = None self.x_scaling_stds = None def train( self, method, x_filename, y_filename=None, theta0_filename=None, theta1_filename=None, r_xz_filename=None, t_xz0_filename=None, t_xz1_filename=None, features=None, nde_type="mafmog", n_hidden=(100, 100), activation="tanh", maf_n_mades=3, maf_batch_norm=False, maf_batch_norm_alpha=0.1, maf_mog_n_components=10, alpha=1.0, trainer="amsgrad", n_epochs=50, batch_size=128, initial_lr=0.001, final_lr=0.0001, nesterov_momentum=None, validation_split=None, early_stopping=True, scale_inputs=True, shuffle_labels=False, grad_x_regularization=None, limit_samplesize=None, return_first_loss=False, verbose=False, ): """ Trains a neural network to estimate either the likelihood ratio or, if method is 'sally' or 'sallino', the score. The keyword method determines the structure of the estimator that an instance of this class represents: * For 'alice', 'alices', 'carl', 'nde', 'rascal', 'rolr', and 'scandal', the neural network models the likelihood ratio as a function of the observables `x` and the numerator hypothesis `theta0`, while the denominator hypothesis is kept at a fixed reference value ("single-parameterized likelihood ratio estimator"). In addition to the likelihood ratio, the estimator allows to estimate the score at `theta0`. * For 'alice2', 'alices2', 'carl2', 'rascal2', and 'rolr2', the neural network models the likelihood ratio as a function of the observables `x`, the numerator hypothesis `theta0`, and the denominator hypothesis `theta1` ("doubly parameterized likelihood ratio estimator"). The score at `theta0` and `theta1` can also be evaluated. * For 'sally' and 'sallino', the neural networks models the score evaluated at some reference hypothesis ("local score regression"). The likelihood ratio cannot be estimated directly from the neural network, but can be estimated in a second step through density estimation in the estimated score space. Parameters ---------- method : str The inference method used. Allows values are 'alice', 'alices', 'carl', 'nde', 'rascal', 'rolr', and 'scandal' for a single-parameterized likelihood ratio estimator; 'alice2', 'alices2', 'carl2', 'rascal2', and 'rolr2' for a doubly-parameterized likelihood ratio estimator; and 'sally' and 'sallino' for local score regression. x_filename : str Path to an unweighted sample of observations, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for all inference methods. y_filename : str or None, optional Path to an unweighted sample of class labels, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'alice', 'alice2', 'alices', 'alices2', 'carl', 'carl2', 'rascal', 'rascal2', 'rolr', and 'rolr2' methods. Default value: None. theta0_filename : str or None, optional Path to an unweighted sample of numerator parameters, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'alice', 'alice2', 'alices', 'alices2', 'carl', 'carl2', 'nde', 'rascal', 'rascal2', 'rolr', 'rolr2', and 'scandal' methods. Default value: None. theta1_filename : str or None, optional Path to an unweighted sample of denominator parameters, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'alice2', 'alices2', 'carl2', 'rascal2', and 'rolr2' methods. Default value: None. r_xz_filename : str or None, optional Path to an unweighted sample of joint likelihood ratios, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'alice', 'alice2', 'alices', 'alices2', 'rascal', 'rascal2', 'rolr', and 'rolr2' methods. Default value: None. t_xz0_filename : str or None, optional Path to an unweighted sample of joint scores at theta0, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'alices', 'alices2', 'rascal', 'rascal2', 'sallino', 'sally', and 'scandal' methods. Default value: None. t_xz1_filename : str or None, optional Path to an unweighted sample of joint scores at theta1, as saved by the `madminer.sampling.SampleAugmenter` functions. Required for the 'rascal2' and 'alices2' methods. Default value: None. features : list of int or None, optional Indices of observables (features) that are used as input to the neural networks. If None, all observables are used. Default value: None. nde_type : {'maf', 'mafmog'}, optional If the method is 'nde' or 'scandal', nde_type determines the architecture used in the neural density estimator. Currently supported are 'maf' for a Masked Autoregressive Flow with a Gaussian base density, or 'mafmog' for a Masked Autoregressive Flow with a mixture of Gaussian base densities. Default value: 'mafmog'. n_hidden : tuple of int, optional Units in each hidden layer in the neural networks. If method is 'nde' or 'scandal', this refers to the setup of each individual MADE layer. Default value: (100, 100). activation : {'tanh', 'sigmoid', 'relu'}, optional Activation function. Default value: 'tanh'. maf_n_mades : int, optional If method is 'nde' or 'scandal', this sets the number of MADE layers. Default value: 3. maf_batch_norm : bool, optional If method is 'nde' or 'scandal', switches batch normalization layers after each MADE layer on or off. Default: False. maf_batch_norm_alpha : float, optional If method is 'nde' or 'scandal' and maf_batch_norm is True, this sets the alpha parameter in the calculation of the running average of the mean and variance. Default value: 0.1. maf_mog_n_components : int, optional If method is 'nde' or 'scandal' and nde_type is 'mafmog', this sets the number of Gaussian base components. Default value: 10. alpha : float, optional Hyperparameter weighting the score error in the loss function of the 'alices', 'alices2', 'rascal', 'rascal2', and 'scandal' methods. Default value: 1. trainer : {"adam", "amsgrad", "sgd"}, optional Optimization algorithm. Default value: "amsgrad". n_epochs : int, optional Number of epochs. Default value: 50. batch_size : int, optional Batch size. Default value: 128. initial_lr : float, optional Learning rate during the first epoch, after which it exponentially decays to final_lr. Default value: 0.001. final_lr : float, optional Learning rate during the last epoch. Default value: 0.0001. nesterov_momentum : float or None, optional If trainer is "sgd", sets the Nesterov momentum. Default value: None. validation_split : float or None, optional Fraction of samples used for validation and early stopping (if early_stopping is True). If None, the entire sample is used for training and early stopping is deactivated. Default value: None. early_stopping : bool, optional Activates early stopping based on the validation loss (only if validation_split is not None). Default value: True. scale_inputs : bool, optional Scale the observables to zero mean and unit variance. Default value: True. shuffle_labels : bool, optional If True, the labels (`y`, `r_xz`, `t_xz`) are shuffled, while the observations (`x`) remain in their normal order. This serves as a closure test, in particular as cross-check against overfitting: an estimator trained with shuffle_labels=True should predict to likelihood ratios around 1 and scores around 0. grad_x_regularization : float or None, optional If not None, a term of the form `grad_x_regularization * |grad_x f(x)|^2` is added to the loss, where `f(x)` is the neural network output (the estimated log likelihood ratio or score). Default value: None. limit_samplesize : int or None, optional If not None, only this number of samples (events) is used to train the estimator. Default value: None. return_first_loss : bool, optional If True, the training routine only proceeds until the loss is calculated for the first time, at which point the loss tensor is returned. This can be useful for debugging or visualization purposes (but of course not for training a model). verbose : bool, optional If True, prints loss updates after every epoch. Returns ------- None """ logger.info("Starting training") logger.info(" Method: %s", method) logger.info(" Training data: x at %s", x_filename) if theta0_filename is not None: logger.info(" theta0 at %s", theta0_filename) if theta1_filename is not None: logger.info(" theta1 at %s", theta1_filename) if y_filename is not None: logger.info(" y at %s", y_filename) if r_xz_filename is not None: logger.info(" r_xz at %s", r_xz_filename) if t_xz0_filename is not None: logger.info(" t_xz (theta0) at %s", t_xz0_filename) if t_xz1_filename is not None: logger.info(" t_xz (theta1) at %s", t_xz1_filename) if features is None: logger.info(" Features: all") else: logger.info(" Features: %s", features) logger.info(" Method: %s", method) if method in ["nde", "scandal"]: logger.info(" Neural density est.: %s", nde_type) if method not in ["nde", "scandal"]: logger.info(" Hidden layers: %s", n_hidden) if method in ["nde", "scandal"]: logger.info(" MAF, number MADEs: %s", maf_n_mades) logger.info(" MAF, batch norm: %s", maf_batch_norm) logger.info(" MAF, BN alpha: %s", maf_batch_norm_alpha) logger.info(" MAF MoG, components: %s", maf_mog_n_components) logger.info(" Activation function: %s", activation) if method in ["cascal", "cascal2", "rascal", "rascal2", "scandal", "alices"]: logger.info(" alpha: %s", alpha) logger.info(" Batch size: %s", batch_size) logger.info(" Trainer: %s", trainer) logger.info(" Epochs: %s", n_epochs) logger.info(" Learning rate: %s initially, decaying to %s", initial_lr, final_lr) if trainer == "sgd": logger.info(" Nesterov momentum: %s", nesterov_momentum) logger.info(" Validation split: %s", validation_split) logger.info(" Early stopping: %s", early_stopping) logger.info(" Scale inputs: %s", scale_inputs) logger.info(" Shuffle labels %s", shuffle_labels) if grad_x_regularization is None: logger.info(" Regularization: None") else: logger.info(" Regularization: %s * |grad_x f(x)|^2", grad_x_regularization) if limit_samplesize is None: logger.info(" Samples: all") else: logger.info(" Samples: %s", limit_samplesize) # Load training data logger.info("Loading training data") theta0 = load_and_check(theta0_filename) theta1 = load_and_check(theta1_filename) x = load_and_check(x_filename) y = load_and_check(y_filename) r_xz = load_and_check(r_xz_filename) t_xz0 = load_and_check(t_xz0_filename) t_xz1 = load_and_check(t_xz1_filename) if y is not None: y = y.reshape((-1, 1)) # Check necessary information is theere assert x is not None if method in [ "carl", "carl2", "nde", "scandal", "rolr", "alice", "rascal", "alices", "rolr2", "alice2", "rascal2", "alices2", ]: assert theta0 is not None if method in ["rolr", "alice", "rascal", "alices", "rolr2", "alice2", "rascal2", "alices2"]: assert r_xz is not None if method in ["carl", "carl2", "rolr", "alice", "rascal", "alices", "rolr2", "alice2", "rascal2", "alices2"]: assert y is not None if method in ["scandal", "rascal", "alices", "rascal2", "alices2", "sally", "sallino"]: assert t_xz0 is not None if method in ["carl2", "rolr2", "alice2", "rascal2", "alices2"]: assert theta1 is not None if method in ["rascal2", "alices2"]: assert t_xz1 is not None if method in ["nde", "scandal"]: assert nde_type in ["maf", "mafmog"] calculate_model_score = method in ["rascal", "cascal", "alices", "scandal", "rascal2", "cascal2", "alices2"] # Infer dimensions of problem n_samples = x.shape[0] n_observables = x.shape[1] if theta0 is not None: n_parameters = theta0.shape[1] else: n_parameters = t_xz0.shape[1] logger.info("Found %s samples with %s parameters and %s observables", n_samples, n_parameters, n_observables) # Limit sample size if limit_samplesize is not None and limit_samplesize < n_samples: logger.info("Only using %s of %s training samples", limit_samplesize, n_samples) x = x[:limit_samplesize] if theta0 is not None: theta0 = theta0[:limit_samplesize] if theta1 is not None: theta1 = theta1[:limit_samplesize] if y is not None: y = y[:limit_samplesize] if r_xz is not None: r_xz = r_xz[:limit_samplesize] if t_xz0 is not None: t_xz0 = t_xz0[:limit_samplesize] if t_xz1 is not None: t_xz1 = t_xz1[:limit_samplesize] # Scale features if scale_inputs: logger.info("Rescaling inputs") self.x_scaling_means = np.mean(x, axis=0) self.x_scaling_stds = np.maximum(np.std(x, axis=0), 1.0e-6) x[:] -= self.x_scaling_means x[:] /= self.x_scaling_stds else: self.x_scaling_means = np.zeros(n_parameters) self.x_scaling_stds = np.ones(n_parameters) logger.debug("Observable ranges:") for i in range(n_observables): logger.debug( " x_%s: mean %s, std %s, range %s ... %s", i + 1, np.mean(x[:, i]), np.std(x[:, i]), np.min(x[:, i]),

np.max(x[:, i])

numpy.max

import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt import matplotlib.colors as colors import astropy.units as u from astropy.cosmology import z_at_value from astropy.cosmology import WMAP9 as cosmo def Plot_SNR( var_x, sample_x, var_y, sample_y, SNRMatrix, fig=None, ax=None, display=True, return_plt=False, dl_axis=False, lb_axis=False, smooth_contours=True, cfill=True, display_cbar=True, x_axis_label=True, y_axis_label=True, x_axis_line=None, y_axis_line=None, logLevels_min=-1.0, logLevels_max=0.0, hspace=0.15, wspace=0.1, contour_kwargs={}, contourf_kwargs={}, xticklabels_kwargs={}, xlabels_kwargs={}, xline_kwargs={}, yticklabels_kwargs={}, ylabels_kwargs={}, yline_kwargs={}, ): """Plots the SNR contours from calcSNR Parameters ---------- var_x: str x-axis variable sample_x: array samples at which ``SNRMatrix`` was calculated corresponding to the x-axis variable var_y: str y-axis variable sample_y: array samples at which ``SNRMatrix`` was calculated corresponding to the y-axis variable SNRMatrix: array-like the matrix at which the SNR was calculated corresponding to the particular x and y-axis variable choices fig: object, optional matplotlib figure object on which to collate the individual plots ax: object, optional matplotlib axes object on which to plot the individual plot display: bool, optional Option to turn off display if saving multiple plots to a file return_plt: bool, optional Option to return ``fig`` and ``ax`` dl_axis: bool, optional Option to turn on the right hand side labels of luminosity distance lb_axis: bool, optional Option to turn on the right hand side labels of lookback time smooth_contours: bool, optional Option to have contours appear smooth instead of tiered (depending on sample size the edges appear boxey). cfill: bool, optional Option to use filled contours or not, default is ``True`` display_cbar: bool, optional Option to display the colorbar on the axes object x_axis_label: bool, optional Option to display the x axis label y_axis_label: bool, optional Option to display the y axis label x_axis_line: int,float, optional Option to display a line on the x axis if not None y_axis_line: int,float, optional Option to display a line on the y axis if not None logLevels_min: float, optional Sets the minimum log level of the colorbar, default is -1.0 which set the minimum to the log minimum of the given ``SNRMatrix`` logLevels_max: float, optional Sets the maximum log level of the colorbar, default is 0.0, which sets the maximum to the log maximum value of the given ``SNRMatrix`` hspace: float, optional Sets the vertical space between axes objects, default is 0.15 wspace: float, optional Sets the horizontal space between axes objects, default is 0.1 contour_kwargs: dict, optional Sets additional kwargs taken by contour in matplotlib contourf_kwargs: dict, optional Sets additional kwargs taken by contourf in matplotlib xticklabels_kwargs: dict, optional Sets additional kwargs taken by xticklabel in matplotlib xlabels_kwargs=: dict, optional Sets additional kwargs taken by xlabel in matplotlib xline_kwargs: dict, optional Sets additional kwargs taken by ax.axvline in matplotlib yticklabels_kwargs: dict, optional Sets additional kwargs taken by yticklabel in matplotlib ylabels_kwargs: dict, optional Sets additional kwargs taken by ylabel in matplotlib yline_kwargs: dict, optional Sets additional kwargs taken by ax.axhline in matplotlib """ if fig is not None: if ax is not None: pass else: fig, ax = plt.subplots() else: fig, ax = plt.subplots() if "colors" not in contour_kwargs.keys() and "cmap" not in contour_kwargs.keys(): contour_kwargs["colors"] = "k" if "linewidths" not in contour_kwargs.keys(): contour_kwargs["linewidths"] = 2.0 if "cmap" not in contourf_kwargs.keys(): contourf_kwargs["cmap"] = "viridis" logSNR = np.log10(SNRMatrix) if logLevels_min == -1.0: logLevels_min = np.log10(np.array([1.0])) if logLevels_max == 0.0: logLevels_max = np.ceil(np.amax(logSNR)) if logLevels_max < logLevels_min: raise ValueError("All SNRs are lower than 5.") logLevels_add = np.log10(np.array([3.0, 10.0, 31.0])) print_logLevels = np.concatenate( (logLevels_min, logLevels_add, np.arange(2.0, logLevels_max + 1.0)) ) logLevels = print_logLevels ylabel_min = min(sample_y) ylabel_max = max(sample_y) xlabel_min = min(sample_x) xlabel_max = max(sample_x) # Set whether log or linearly spaced axes if xlabel_max < 0.0 or xlabel_min < 0.0 or var_x in ["n_p", "T_obs"]: xaxis_type = "lin" step_size = int(xlabel_max - xlabel_min + 1) x_labels = np.linspace(xlabel_min, xlabel_max, step_size) else: x_log_range = np.log10(xlabel_max) - np.log10(xlabel_min) if x_log_range >= 2.0: xaxis_type = "log" step_size = int(np.log10(xlabel_max) - np.log10(xlabel_min) + 1) x_labels = np.logspace( np.log10(xlabel_min), np.log10(xlabel_max), step_size ) else: xaxis_type = "lin" x_scale = 10 ** round(np.log10(xlabel_min)) x_labels = ( np.arange( round(xlabel_min / x_scale), round(xlabel_max / x_scale) + 1, 1 ) * x_scale ) if x_labels[0] < xlabel_min: x_labels[0] = xlabel_min if x_labels[-1] > xlabel_max: x_labels[-1] = xlabel_max if ylabel_max < 0.0 or ylabel_min < 0.0 or var_y in ["n_p", "T_obs"]: yaxis_type = "lin" step_size = int(ylabel_max - ylabel_min + 1) y_labels = np.linspace(ylabel_min, ylabel_max, step_size) else: y_log_range = np.log10(ylabel_max) - np.log10(ylabel_min) if y_log_range >= 2.0: yaxis_type = "log" step_size = int(np.log10(ylabel_max) - np.log10(ylabel_min) + 1) y_labels = np.logspace( np.log10(ylabel_min), np.log10(ylabel_max), step_size ) else: yaxis_type = "lin" y_scale = 10 ** round(np.log10(ylabel_min)) y_labels = ( np.arange( round(ylabel_min / y_scale), round(ylabel_max / y_scale) + 1, 1 ) * y_scale ) if y_labels[0] < ylabel_min: y_labels[0] = ylabel_min if y_labels[-1] > ylabel_max: y_labels[-1] = ylabel_max # Set axis scales based on what data sampling we used if yaxis_type == "lin" and xaxis_type == "log": if not cfill: CS1 = ax.contour( np.log10(sample_x), sample_y, logSNR, print_logLevels, **contour_kwargs ) else: if smooth_contours: cmap = mpl.cm.get_cmap(name=contourf_kwargs["cmap"]) cmap.set_under(color="white") CS1 = ax.imshow( logSNR, extent=[ np.log10(xlabel_min), np.log10(xlabel_max), ylabel_min, ylabel_max, ], vmin=logLevels_min, vmax=logLevels_max, origin="lower", aspect="auto", cmap=cmap, ) else: CS1 = ax.contourf( np.log10(sample_x), sample_y, logSNR, logLevels, **contourf_kwargs ) ax.contour( np.log10(sample_x), sample_y, logSNR, print_logLevels, **contour_kwargs ) ax.set_xlim(np.log10(xlabel_min), np.log10(xlabel_max)) ax.set_ylim(ylabel_min, ylabel_max) elif yaxis_type == "log" and xaxis_type == "lin": if not cfill: CS1 = ax.contour( sample_x, np.log10(sample_y), logSNR, print_logLevels, **contour_kwargs ) else: if smooth_contours: cmap = mpl.cm.get_cmap(name=contourf_kwargs["cmap"]) cmap.set_under(color="white") CS1 = ax.imshow( logSNR, extent=[ xlabel_min, xlabel_max, np.log10(ylabel_min), np.log10(ylabel_max), ], vmin=logLevels_min, vmax=logLevels_max, origin="lower", aspect="auto", cmap=cmap, ) else: CS1 = ax.contourf( sample_x, np.log10(sample_y), logSNR, logLevels, **contourf_kwargs ) ax.contour( sample_x, np.log10(sample_y), logSNR, print_logLevels, **contour_kwargs ) ax.set_xlim(xlabel_min, xlabel_max) ax.set_ylim(np.log10(ylabel_min), np.log10(ylabel_max)) elif yaxis_type == "lin" and xaxis_type == "lin": if not cfill: CS1 = ax.contour( sample_x, sample_y, logSNR, print_logLevels, **contour_kwargs ) else: if smooth_contours: cmap = mpl.cm.get_cmap(name=contourf_kwargs["cmap"]) cmap.set_under(color="white") CS1 = ax.imshow( logSNR, extent=[xlabel_min, xlabel_max, ylabel_min, ylabel_max], vmin=logLevels_min, vmax=logLevels_max, origin="lower", aspect="auto", cmap=cmap, ) else: CS1 = ax.contourf( sample_x, sample_y, logSNR, logLevels, **contourf_kwargs ) ax.contour(sample_x, sample_y, logSNR, print_logLevels, **contour_kwargs) ax.set_xlim(xlabel_min, xlabel_max) ax.set_ylim(ylabel_min, ylabel_max) else: if not cfill: CS1 = ax.contour( np.log10(sample_x), np.log10(sample_y), logSNR, print_logLevels, **contour_kwargs ) else: if smooth_contours: cmap = mpl.cm.get_cmap(name=contourf_kwargs["cmap"]) cmap.set_under(color="white") CS1 = ax.imshow( logSNR, extent=[

np.log10(xlabel_min)

numpy.log10

# This file is part of QuTiP: Quantum Toolbox in Python. # # Copyright (c) 2011 and later, <NAME> and <NAME>. # All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions are # met: # # 1. Redistributions of source code must retain the above copyright notice, # this list of conditions and the following disclaimer. # # 2. Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in the # documentation and/or other materials provided with the distribution. # # 3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names # of its contributors may be used to endorse or promote products derived # from this software without specific prior written permission. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS # "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT # LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A # PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT # HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, # SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT # LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, # DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY # THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT # (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE # OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ############################################################################### import numpy as np from numpy.testing import run_module_suite, assert_equal, assert_almost_equal import scipy.sparse as sp from qutip.random_objects import (rand_dm, rand_herm, rand_ket) from qutip.states import coherent from qutip.sparse import (sp_bandwidth, sp_permute, sp_reverse_permute, sp_profile, sp_one_norm, sp_inf_norm) from qutip.cy.spmath import zcsr_kron def _permutateIndexes(array, row_perm, col_perm): return array[np.ix_(row_perm, col_perm)] def _dense_profile(B): row_pro = 0 for i in range(B.shape[0]): j = np.where(B[i, :] != 0)[0] if np.any(j): if j[-1] > i: row_pro += (j[-1]-i) col_pro = 0 for j in range(B.shape[0]): i = np.where(B[:, j] != 0)[0] if np.any(i): if i[-1] > j: col_pro += i[-1]-j ans = (row_pro+col_pro, col_pro, row_pro) return ans def test_sparse_symmetric_permute(): "Sparse: Symmetric Permute" # CSR version A = rand_dm(25, 0.5) perm = np.random.permutation(25) x = sp_permute(A.data, perm, perm).toarray() z = _permutateIndexes(A.full(), perm, perm) assert_equal((x - z).all(), 0) # CSC version B = A.data.tocsc() y = sp_permute(B, perm, perm).toarray() assert_equal((y - z).all(), 0) def test_sparse_nonsymmetric_permute(): "Sparse: Nonsymmetric Permute" # CSR version A = rand_dm(25, 0.5) rperm = np.random.permutation(25) cperm = np.random.permutation(25) x = sp_permute(A.data, rperm, cperm).toarray() z = _permutateIndexes(A.full(), rperm, cperm) assert_equal((x - z).all(), 0) # CSC version B = A.data.tocsc() y = sp_permute(B, rperm, cperm).toarray() assert_equal((y - z).all(), 0) def test_sparse_symmetric_reverse_permute(): "Sparse: Symmetric Reverse Permute" # CSR version A = rand_dm(25, 0.5) perm = np.random.permutation(25) x = sp_permute(A.data, perm, perm) B = sp_reverse_permute(x, perm, perm) assert_equal((A.full() - B.toarray()).all(), 0) # CSC version B = A.data.tocsc() perm = np.random.permutation(25) x = sp_permute(B, perm, perm) B = sp_reverse_permute(x, perm, perm) assert_equal((A.full() - B.toarray()).all(), 0) def test_sparse_nonsymmetric_reverse_permute(): "Sparse: Nonsymmetric Reverse Permute" # CSR square array check A = rand_dm(25, 0.5) rperm = np.random.permutation(25) cperm = np.random.permutation(25) x = sp_permute(A.data, rperm, cperm) B = sp_reverse_permute(x, rperm, cperm) assert_equal((A.full() - B.toarray()).all(), 0) # CSC square array check A = rand_dm(25, 0.5) rperm = np.random.permutation(25) cperm = np.random.permutation(25) B = A.data.tocsc() x = sp_permute(B, rperm, cperm) B = sp_reverse_permute(x, rperm, cperm) assert_equal((A.full() - B.toarray()).all(), 0) # CSR column vector check A = coherent(25, 1) rperm = np.random.permutation(25) x = sp_permute(A.data, rperm, []) B = sp_reverse_permute(x, rperm, []) assert_equal((A.full() - B.toarray()).all(), 0) # CSC column vector check A = coherent(25, 1) rperm = np.random.permutation(25) B = A.data.tocsc() x = sp_permute(B, rperm, []) B = sp_reverse_permute(x, rperm, []) assert_equal((A.full() - B.toarray()).all(), 0) # CSR row vector check A = coherent(25, 1).dag() cperm =

np.random.permutation(25)

numpy.random.permutation

#!/usr/bin/env python """ A TensorFlow-based 2D Cardiac Electrophysiology Modeler Copyright 2017-2018 <NAME> (<EMAIL>) Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. """ import tensorflow as tf import numpy as np from screen import Screen from ionic import IonicModel from functools import partial class Courtemanche(IonicModel): """ The modified Courtemanche atrial model """ def __init__(self, props): super().__init__(props) self.min_v = -100.0 # mV self.max_v = 50.0 # mV self.depol = -81.0 # mV self.chronic = True self.fast_states = ['V', '_Na_i_', '_m_', '_h_'] def init_state_variable(self, state, name, value): if name in state: print('Warning! The state variable arlready exists') state[name] = np.full([self.height, self.width], value, dtype=np.float32) def define(self, s1=True, state=None): """ Defines the tensorflow model It sets ode_op, s2_op and V used by other methods """ super().define() if state is None: state = {} self.init_state_variable(state, 'V', -81.18) self.init_state_variable(state, '_Na_i_', 1.117e+01) # self.init_state_variable(state, '_Na_i_', 1.3e+01) self.init_state_variable(state, '_m_', 2.98e-3) self.init_state_variable(state, '_h_', 9.649e-1) self.init_state_variable(state, '_j_', 9.775e-1) self.init_state_variable(state, '_K_i_', 1.39e+02) self.init_state_variable(state, '_oa_', 3.043e-2) self.init_state_variable(state, '_oi_', 9.992e-1) self.init_state_variable(state, '_ua_', 4.966e-3) self.init_state_variable(state, '_ui_', 9.986e-1) self.init_state_variable(state, '_xr_', 3.296e-5) self.init_state_variable(state, '_xs_', 1.869e-2) self.init_state_variable(state, '_Ca_i_', 1.013e-4) self.init_state_variable(state, '_d_', 1.367e-4) self.init_state_variable(state, '_f_', 9.996e-1) self.init_state_variable(state, '_f_Ca_', 7.755e-1) self.init_state_variable(state, '_Ca_rel_', 1.488) self.init_state_variable(state, '_u_', 0.0) self.init_state_variable(state, '_v_', 1.0) self.init_state_variable(state, '_w_', 0.9992) self.init_state_variable(state, '_Ca_up_', 1.488) if self.ultra_slow: self.init_state_variable(state, '_us_', 0.72) # steady-state at 500 ms # S1 stimulation: vertical along the left side if s1: state['V'][:,:25] = 20.0 # define the graph... with tf.device('/device:GPU:0'): # Create variables for simulation state State = {} for s in state: State[s] = tf.Variable(state[s]) State1, inter = self.solve(State) self.dt_per_step = 1 fasts = [] slows = [] # for s in State: # if s in self.fast_states: # fasts.append(tf.assign(State[s], State1[s])) # else: # slows.append(tf.assign(State[s], State1[s])) for s in State: fasts.append(tf.assign(State[s], State1[s])) self._ode_op = tf.group(*fasts) self._ops['slow'] = tf.group(*slows) self._V = State['V'] # V is needed by self.image() self._State = State self._Inter = inter Trend = tf.Variable(np.zeros([2], dtype=np.float32)) self._ops['trend'] = tf.group( tf.assign(Trend[0], self._V[self.width//2,self.height//8]) # tf.assign(Trend[1], State['_us_'][self.width//2,self.height//8]) ) self._Trend = Trend def euler(self, g, Rate, dt): return g + Rate * dt def δt(self, name): return self.dt # if name in self.fast_states: # return self.dt # else: # return self.dt * 10 def solve(self, State): """ Explicit Euler ODE solver """ V0 = State['V'] V = self.enforce_boundary(V0) R = 8.3143 # (joule/mole_kelvin). T = 310; # (kelvin). F = 96.4867 # (coulomb/millimole). Cm = 100 # Cm is Cm in membrane (picoF). g_Na = 7.8 # fast_sodium_current (nanoS/picoF). Na_o = 140 # (millimolar). K_o = 5.4 # (millimolar). g_to = 0.1652 # transient_outward_K_current (nanoS/picoF). g_Ks = 0.12941176 # slow_delayed_rectifier_K_current (nanoS/picoF). g_Ca_L = 0.12375 # L_type_Ca_channel (nanoS/picoF). Km_Na_i = 10 # sodium_potassium_pump (millimolar). Km_K_o = 1.5 # sodium_potassium_pump (millimolar). i_NaK_max = 0.59933874 # sodium_potassium_pump (picoA/picoF). i_CaP_max = 0.275 # sarcolemmal_calcium_pump_current (picoA/picoF). g_B_Na = 0.0006744375 # background_currents (nanoS/picoF). g_B_Ca = 0.001131 # background_currents (nanoS/picoF). g_B_K = 0 # background_currents (nanoS/picoF). Ca_o = 1.8 # (millimolar). K_rel = 30 # Ca_release_current_from_JSR (per_millisecond). tau_tr = 180 # transfer_current_from_NSR_to_JSR (millisecond). I_up_max = 0.005 # Ca_uptake_current_by_the_NSR (millimolar/millisecond). K_up = 0.00092 # Ca_uptake_current_by_the_NSR (millimolar). Ca_up_max = 15 # Ca_leak_current_by_the_NSR (millimolar). CMDN_max = 0.05 # CMDN_max is CMDN_max in Ca_buffers (millimolar). TRPN_max = 0.07 # TRPN_max is TRPN_max in Ca_buffers (millimolar). CSQN_max = 10 # CSQN_max is CSQN_max in Ca_buffers (millimolar). Km_CMDN = 0.00238 # Km_CMDN is Km_CMDN in Ca_buffers (millimolar). Km_TRPN = 0.0005 # Km_TRPN is Km_TRPN in Ca_buffers (millimolar). Km_CSQN = 0.8 # Km_CSQN is Km_CSQN in Ca_buffers (millimolar). V_cell = 20100 # intracellular_ion_concentrations (micrometre_3). V_i = V_cell * 0.68 # intracellular_ion_concentrations (micrometre_3). tau_f_Ca = 2.0 # L_type_Ca_channel_f_Ca_gate (millisecond). tau_u = 8.0 # Ca_release_current_from_JSR_u_gate (millisecond). V_rel = 0.0048 * V_cell # intracellular_ion_concentrations (micrometre_3). V_up = 0.0552 * V_cell # intracellular_ion_concentrations (micrometre_3). State1 = {} if self.chronic: chronic = 1.0 else: chronic = 0.0 with self.jit_scope(): inter = self.calc_inter(V, tf) State1['_d_'] = self.rush_larsen(State['_d_'], inter['d_infinity'], inter['tau_d'], self.δt('_d_')) State1['_f_'] = self.rush_larsen(State['_f_'], inter['f_infinity'], inter['tau_f'], self.δt('_f_')) State1['_w_'] = self.rush_larsen(State['_w_'], inter['w_infinity'], inter['tau_w'], self.δt('_d_')) State1['_m_'] = self.rush_larsen(State['_m_'], inter['m_inf'], inter['tau_m'], self.δt('_m_')) State1['_h_'] = self.rush_larsen(State['_h_'], inter['h_inf'], inter['tau_h'], self.δt('_h_')) State1['_j_'] = self.rush_larsen(State['_j_'], inter['j_inf'], inter['tau_j'], self.δt('_j_')) State1['_oa_'] = self.rush_larsen(State['_oa_'], inter['oa_infinity'], inter['tau_oa'], self.δt('_oa_')) State1['_oi_'] = self.rush_larsen(State['_oi_'], inter['oi_infinity'], inter['tau_oi'], self.δt('_oi_')) State1['_ua_'] = self.rush_larsen(State['_ua_'], inter['ua_infinity'], inter['tau_ua'], self.δt('_ua_')) State1['_ui_'] = self.rush_larsen(State['_ui_'], inter['ui_infinity'], inter['tau_ui'], self.δt('_ui_')) State1['_xr_'] = self.rush_larsen(State['_xr_'], inter['xr_infinity'], inter['tau_xr'], self.δt('_xr_')) State1['_xs_'] = self.rush_larsen(State['_xs_'], inter['xs_infinity'], inter['tau_xs'], self.δt('_xs_')) if self.ultra_slow: State1['_us_'] = self.rush_larsen(State['_us_'], inter['us_infinity'], inter['tau_us'], self.δt('_us_')) f_Ca_infinity = tf.reciprocal(1.0 + State['_Ca_i_'] / 0.00035) State1['_f_Ca_'] = self.rush_larsen(State['_f_Ca_'], f_Ca_infinity, tau_f_Ca, self.δt('_f_Ca_')) E_K = ((R * T) / F) * tf.log(K_o / State['_K_i_']) i_K1 = inter['i_K1a'] * (V - E_K) i_to = (1.0-0.5*chronic) * Cm * g_to * tf.pow(State['_oa_'], 3) * State['_oi_'] * (V - E_K) i_Kur = (1.0-0.5*chronic) * Cm * inter['g_Kur'] * tf.pow(State['_ua_'], 3) * State['_ui_'] * (V - E_K) i_Kr = inter['i_Kra'] * State['_xr_'] * (V - E_K) i_Ks = Cm * g_Ks * tf.square(State['_xs_']) * (V - E_K) i_NaK = ((Cm * i_NaK_max * inter['f_NaK']) / (1.0 + tf.sqrt(tf.pow(Km_Na_i / State['_Na_i_'], 3.0)))) * (K_o / (K_o + Km_K_o)) i_B_K = Cm * g_B_K * (V - E_K) State1['_K_i_'] = self.euler( State['_K_i_'], (2.0 * i_NaK - (i_K1 + i_to + i_Kur + i_Kr + i_Ks + i_B_K)) / (V_i * F), self.δt('_K_i_') ) E_Na = ((R * T) / F) * tf.log(Na_o / State['_Na_i_']) i_Na = Cm * g_Na * tf.pow(State['_m_'], 3) * State['_h_'] * State['_j_'] * (V - E_Na) if self.ultra_slow: i_Na *= State['_us_'] i_NaCa = inter['i_NaCaa'] * tf.pow(State['_Na_i_'], 3) - inter['i_NaCab'] * State['_Ca_i_'] i_B_Na = Cm * g_B_Na * (V - E_Na) State1['_Na_i_'] = self.euler( State['_Na_i_'], (-3.0 * i_NaK - (3.0 * i_NaCa + i_B_Na + i_Na)) / (V_i * F), self.δt('_Na_i_') ) i_st = 0.0 i_Ca_L = (1.0-0.7*chronic) * Cm * g_Ca_L * State['_d_'] * State['_f_'] * State['_f_Ca_'] * (V - 65.0) i_CaP = (Cm * i_CaP_max * State['_Ca_i_']) / (0.0005 + State['_Ca_i_']) E_Ca = ((R * T) / (2.0 * F)) * tf.log(Ca_o / State['_Ca_i_']) i_B_Ca = Cm * g_B_Ca * (V - E_Ca) DV = self.euler( V, -(i_Na + i_K1 + i_to + i_Kur + i_Kr + i_Ks + i_B_Na + i_B_Ca + i_NaK + i_CaP + i_NaCa + i_Ca_L + i_st) / Cm, self.δt('V') ) State1['V'] = DV + self.diff * self.δt('V') * self.laplace(V) i_rel = K_rel * tf.square(State['_u_']) * State['_v_'] * State['_w_'] * (State['_Ca_rel_'] - State['_Ca_i_']) i_tr = (State['_Ca_up_'] - State['_Ca_rel_']) / tau_tr State1['_Ca_rel_'] = self.euler( State['_Ca_rel_'], (i_tr - i_rel) * tf.reciprocal(1.0 + (CSQN_max * Km_CSQN) / tf.square(State['_Ca_rel_'] + Km_CSQN)), self.δt('_Ca_rel_') ) Fn = 1000.0 * (1.0e-15 * V_rel * i_rel - (1.0e-15 / (2.0 * F)) * (0.5 * i_Ca_L - 0.2 * i_NaCa)) u_infinity = tf.reciprocal(1.0 + tf.exp(-(Fn - 3.4175e-13) / 1.367e-15)) State1['_u_'] = self.rush_larsen(State['_u_'], u_infinity, tau_u, self.δt('_u_')) tau_v = 1.91 + 2.09 * u_infinity v_infinity = 1.0 - tf.reciprocal(1.0 + tf.exp(-(Fn - 6.835e-14) / 1.367e-15)) State1['_v_'] = self.rush_larsen(State['_v_'], v_infinity, tau_v, self.δt('_v_')) i_up = I_up_max / (1.0 + K_up / State['_Ca_i_']) i_up_leak = (I_up_max * State['_Ca_up_']) / Ca_up_max State1['_Ca_up_'] = self.euler( State['_Ca_up_'], i_up - (i_up_leak + (i_tr * V_rel) / V_up), self.δt('_Ca_up_') ) B1 = (2.0 * i_NaCa - (i_CaP + i_Ca_L + i_B_Ca)) / (2.0 * V_i * F) + (V_up * (i_up_leak - i_up) + i_rel * V_rel) / V_i B2 = 1.0 + (TRPN_max * Km_TRPN) / tf.square(State['_Ca_i_'] + Km_TRPN) + (CMDN_max * Km_CMDN) / tf.square(State['_Ca_i_'] + Km_CMDN) State1['_Ca_i_'] = self.euler( State['_Ca_i_'], B1 / B2, self.δt('_Ca_i_') ) for s in State: if not s in State1: print('Warning! Missing New State: %s' % s) return State1, inter def calc_inter(self, V, mod=np): R = 8.3143 # R in membrane (joule/mole_kelvin). T = 310 # T in (kelvin). F = 96.4867 # F in membrane (coulomb/millimole). Cm = 100 # Cm in membrane (picoF). Na_o = 140 # Na_o (millimolar). g_K1 = 0.09 # g_K1 (nanoS/picoF). K_Q10 = 3 # transient_outward_K_current (dimensionless). g_Kr = 0.029411765 # rapid_delayed_rectifier_K_current (nanoS/picoF). Ca_o = 1.8 # (millimolar). I_NaCa_max = 1600 # Na_Ca_exchanger_current(picoA/picoF). K_mNa = 87.5 # Na_Ca_exchanger_current (millimolar). K_mCa = 1.38 # Na_Ca_exchanger_current (millimolar). K_sat = 0.1 # Na_Ca_exchanger_current (dimensionless). gamma_ = 0.35 # Na_Ca_exchanger_current (dimensionless). sigma = 1.0 # sodium_potassium_pump (dimensionless). def where(cond, x, y): ret = mod.where(cond, x, y) if type(ret) is np.ndarray and ret.shape == (): ret = float(ret) return ret inter = {} ϵ = V * 1e-20 inter['d_infinity'] = mod.reciprocal(1.0 + mod.exp((V + 10.0) / -8.0)) # note: V + 10 is changed to V + 10.0001 to suppress a warning passing V = -10 inter['tau_d'] = where( mod.abs(V + 10.0001) < 1.0e-10, 4.579 / (1.0 + mod.exp((V + 10.0) / -6.24)), (1.0 - mod.exp((V + 10.0001) / -6.24)) / (0.0350000 * (V + 10.0001) * (1.0 + mod.exp((V + 10.0001) / -6.24))) ) inter['f_infinity'] = mod.exp(-(V + 28.0) / 6.9) / (1.0 + mod.exp(-(V + 28.0) / 6.9)) inter['tau_f'] = 9.0 * mod.reciprocal(0.0197000 * mod.exp(-mod.square(0.0337) * mod.square(V + 10.0)) + 0.02) inter['tau_w'] = where( mod.abs(V - 7.9) < 1.0e-10, ϵ + ((6.0 * 0.2) / 1.3), (6.0 * (1.0 - mod.exp(-(V - 7.9) / 5.0))) / ((1.0 + 0.3 * mod.exp(-(V - 7.9) / 5.0)) * 1.0 * (V - 7.9)) ) inter['w_infinity'] = 1.0 - mod.reciprocal(1.0 + mod.exp(-(V - 40.0) / 17.0)) alpha_m = where( mod.abs(V - -47.13) < 0.001, ϵ + 3.2, (0.32 * (V + 47.13)) / (1.0 - mod.exp(-0.1 * (V + 47.13))) ) beta_m = 0.08 * mod.exp(-V / 11.0) inter['m_inf'] = alpha_m / (alpha_m + beta_m) inter['tau_m'] = mod.reciprocal(alpha_m + beta_m) alpha_h = where( V < -40.0, 0.135 * mod.exp((V + 80.0) / -6.8), ϵ ) beta_h = where( V < -40.0, 3.56 * mod.exp(0.079 * V) + 310000. * mod.exp(0.35 * V), mod.reciprocal(0.13 * (1.0 + mod.exp((V + 10.66) / -11.1))) ) inter['h_inf'] = alpha_h / (alpha_h + beta_h) inter['tau_h'] = mod.reciprocal(alpha_h + beta_h) alpha_j = where( V < -40.0, ((-127140. * mod.exp(0.2444 * V) - 3.474e-05 * mod.exp(-0.04391 * V)) * (V + 37.78)) / (1.0 + mod.exp(0.311 * (V + 79.23))), ϵ ) beta_j = where( V < -40.0, (0.1212 * mod.exp(-0.01052 * V)) / (1.0 + mod.exp(-0.1378 * (V + 40.14))), (0.3 * mod.exp(-2.535e-07 * V)) / (1.0 + mod.exp(-0.1 * (V + 32.0))) ) inter['j_inf'] = alpha_j / (alpha_j + beta_j) inter['tau_j'] = mod.reciprocal(alpha_j + beta_j) alpha_oa = 0.65 * mod.reciprocal(mod.exp((V - -10.0) / -8.5) + mod.exp(((V - -10.0) - 40.0) / -59.0)) beta_oa = 0.65 * mod.reciprocal(2.5 + mod.exp(((V - -10.0) + 72.0) / 17.0)) inter['tau_oa'] = mod.reciprocal(alpha_oa + beta_oa) / K_Q10 inter['oa_infinity'] = mod.reciprocal(1.0 + mod.exp(((V - -10.0) + 10.47) / -17.54)) alpha_oi = mod.reciprocal(18.53 + 1.0 * mod.exp(((V - -10.0) + 103.7) / 10.95)) beta_oi = mod.reciprocal(35.56 + 1.0 * mod.exp(((V - -10.0) - 8.74) / -7.44)) inter['tau_oi'] = mod.reciprocal(alpha_oi + beta_oi) / K_Q10 inter['oi_infinity'] = mod.reciprocal(1.0 + mod.exp(((V - -10.0) + 33.1) / 5.3)) alpha_ua = 0.65 * mod.reciprocal(mod.exp((V - -10.0) / -8.5) + mod.exp(((V - -10.0) - 40.0) / -59.0)) beta_ua = 0.65 * mod.reciprocal(2.5 + mod.exp(((V - -10.0) + 72.0) / 17.0)) inter['tau_ua'] = mod.reciprocal(alpha_ua + beta_ua) / K_Q10 inter['ua_infinity'] = mod.reciprocal(1.0 + mod.exp(((V - -10.0) + 20.3) / -9.6)) alpha_ui = mod.reciprocal(21.0 + 1.0 * mod.exp(((V - -10.0) - 195.000) / -28.0)) beta_ui = mod.reciprocal(mod.exp(((V - -10.0) - 168.0) / -16.0)) inter['tau_ui'] = mod.reciprocal(alpha_ui + beta_ui) / K_Q10 inter['ui_infinity'] = mod.reciprocal(1.0 + mod.exp(((V - -10.0) - 109.45) / 27.48)) alpha_xr = where( mod.abs(V + 14.1) < 1.0e-10, ϵ + 0.0015, (0.0003 * (V + 14.1)) / (1.0 - mod.exp((V + 14.1) / -5.0)) ) beta_xr = where( mod.abs(V - 3.3328) < 1.0e-10, ϵ + 0.000378361, (7.3898e-05 * (V - 3.3328)) / (mod.exp((V - 3.3328) / 5.1237) - 1.0) ) inter['tau_xr'] = mod.reciprocal(alpha_xr + beta_xr); inter['xr_infinity'] = mod.reciprocal(1.0 + mod.exp((V + 14.1) / -6.5)) alpha_xs = where( mod.abs(V - 19.9) < 1.0e-10, ϵ + 0.00068, (4.0e-05 * (V - 19.9)) / (1.0 - mod.exp((V - 19.9) / -17.0)) ) beta_xs = where( mod.abs(V - 19.9) < 1.0e-10, ϵ + 0.000315, (3.5e-05 * (V - 19.9)) / (mod.exp((V - 19.9) / 9.0) - 1.0) ) inter['tau_xs'] = 0.5 * mod.reciprocal(alpha_xs + beta_xs) inter['xs_infinity'] = mod.sqrt(mod.reciprocal(1.0 + mod.exp((V - 19.9) / -12.7))) inter['g_Kur'] = 0.005 + 0.05 / (1.0 + mod.exp((V - 15.0) / -13.0)) inter['f_NaK'] = mod.reciprocal(1.0 + 0.1245 * mod.exp((-0.1 * F * V) / (R * T)) + 0.0365 * sigma * mod.exp((-F * V) / (R * T))) i_NaCad = (K_mNa*K_mNa*K_mNa + Na_o*Na_o*Na_o) * (K_mCa + Ca_o) * (1.0 + K_sat * mod.exp(((gamma_ - 1.0) * V * F) / (R * T))) inter['i_NaCaa'] = (Cm * I_NaCa_max * (mod.exp((gamma_ * F * V) / (R * T)) * Ca_o)) / i_NaCad inter['i_NaCab'] = (Cm * I_NaCa_max * (mod.exp(((gamma_ - 1.0) * F * V) / (R * T)) * (Na_o*Na_o*Na_o))) / i_NaCad inter['i_K1a'] = (Cm * g_K1) / (1.0 + mod.exp(0.07 * (V + 80.0))) # * (V - E_K) inter['i_Kra'] = (Cm * g_Kr) / (1.0 + mod.exp((V + 15.0) / 22.4)) # * state[_xr_] * (V - E_K) V_us = -83.0 K_us = 23.0 alpha_us = 3e-5 * (0.5 * (1 - mod.tanh((V - V_us) / K_us))) beta_us = 1e-5 * (0.5 * (1 + mod.tanh((V - (V_us + 30)) / K_us))) inter['us_infinity'] = alpha_us / (alpha_us + beta_us) inter['tau_us'] = mod.reciprocal(alpha_us + beta_us) return inter def pot(self): return self._V def image(self): """ Returns a [height x width] float ndarray in the range 0 to 1 that encodes V in grayscale """ v = self._V.eval() return (v - self.min_v) / (self.max_v - self.min_v) def cl_observer(m, cyclelengths, i0, i, cl): na = m._State['_Na_i_'].eval() mean_na =

np.average(na, weights=m.phase)

numpy.average

from datetime import datetime from dateutil.tz import tzlocal, tzutc import pandas as pd import numpy as np from hdmf.backends.hdf5 import HDF5IO from hdmf.common import DynamicTable from pynwb import NWBFile, TimeSeries, NWBHDF5IO, get_manager from pynwb.file import Subject from pynwb.epoch import TimeIntervals from pynwb.ecephys import ElectricalSeries from pynwb.testing import NWBH5IOMixin, TestCase, remove_test_file class TestNWBFileHDF5IO(TestCase): """ Test reading/writing an NWBFile using HDF5IO """ def setUp(self): """ Set up an NWBFile object with an acquisition TimeSeries, analysis TimeSeries, and a processing module """ self.start_time = datetime(1970, 1, 1, 12, tzinfo=tzutc()) self.ref_time = datetime(1979, 1, 1, 0, tzinfo=tzutc()) self.create_date = datetime(2017, 4, 15, 12, tzinfo=tzlocal()) self.manager = get_manager() self.filename = 'test_nwbfileio.h5' self.nwbfile = NWBFile(session_description='a test NWB File', identifier='TEST123', session_start_time=self.start_time, timestamps_reference_time=self.ref_time, file_create_date=self.create_date, experimenter='test experimenter', stimulus_notes='test stimulus notes', data_collection='test data collection notes', experiment_description='test experiment description', institution='nomad', lab='nolab', notes='nonotes', pharmacology='nopharmacology', protocol='noprotocol', related_publications='nopubs', session_id='007', slices='noslices', source_script='nosources', surgery='nosurgery', virus='novirus', source_script_file_name='nofilename') self.ts = TimeSeries(name='test_timeseries', data=list(range(100, 200, 10)), unit='SIunit', timestamps=np.arange(10.), resolution=0.1) self.nwbfile.add_acquisition(self.ts) self.ts2 = TimeSeries(name='test_timeseries2', data=list(range(200, 300, 10)), unit='SIunit', timestamps=np.arange(10.), resolution=0.1) self.nwbfile.add_analysis(self.ts2) self.mod = self.nwbfile.create_processing_module('test_module', 'a test module') self.ts3 = TimeSeries(name='test_timeseries2', data=list(range(100, 200, 10)), unit='SIunit', timestamps=np.arange(10.), resolution=0.1) self.mod.add(self.ts3) def tearDown(self): """ Delete the created test file """ remove_test_file(self.filename) def test_children(self): """ Test that the TimeSeries and processing module are children of their respective parents """ self.assertIn(self.ts, self.nwbfile.children) self.assertIn(self.ts2, self.nwbfile.children) self.assertIn(self.mod, self.nwbfile.children) self.assertIn(self.ts3, self.mod.children) def test_write(self): """ Test writing the NWBFile using HDF5IO """ hdf5io = HDF5IO(self.filename, manager=self.manager, mode='a') hdf5io.write(self.nwbfile) hdf5io.close() # TODO add some asserts def test_read(self): """ Test reading the NWBFile using HDF5IO """ hdf5io = HDF5IO(self.filename, manager=self.manager, mode='w') hdf5io.write(self.nwbfile) hdf5io.close() hdf5io = HDF5IO(self.filename, manager=self.manager, mode='r') container = hdf5io.read() self.assertIsInstance(container, NWBFile) self.assertEqual(len(container.acquisition), 1) self.assertEqual(len(container.analysis), 1) for v in container.acquisition.values(): self.assertIsInstance(v, TimeSeries) self.assertContainerEqual(container, self.nwbfile) hdf5io.close() class TestNWBFileIO(NWBH5IOMixin, TestCase): """ Test writing an NWBFile to disk and reading back the file """ # this uses methods tearDown, test_roundtrip, and validate from NWBH5IOMixin. the rest are overridden def setUp(self): super().setUp() self.start_time = datetime(1970, 1, 1, 12, tzinfo=tzutc()) self.ref_time = datetime(1979, 1, 1, 0, tzinfo=tzutc()) self.create_dates = [datetime(2017, 5, 1, 12, tzinfo=tzlocal()), datetime(2017, 5, 2, 13, 0, 0, 1, tzinfo=tzutc()), datetime(2017, 5, 2, 14, tzinfo=tzutc())] def setUpContainer(self): """ Return a placeholder NWBFile """ return NWBFile('placeholder', 'placeholder', datetime(1970, 1, 1, 12, tzinfo=tzutc())) def build_nwbfile(self): """ Create an NWB file """ self.container = NWBFile(session_description='a test session description for a test NWBFile', identifier='FILE123', session_start_time=self.start_time, file_create_date=self.create_dates, timestamps_reference_time=self.ref_time, experimenter='A test experimenter', lab='a test lab', institution='a test institution', experiment_description='a test experiment description', session_id='test1', notes='my notes', pharmacology='drugs', protocol='protocol', related_publications='my pubs', slices='my slices', surgery='surgery', virus='a virus', source_script='noscript', source_script_file_name='nofilename', stimulus_notes='test stimulus notes', data_collection='test data collection notes', keywords=('these', 'are', 'keywords')) def roundtripContainer(self, cache_spec=False): """ Build and write an NWBFile to disk, read the file, and return the NWBFile """ self.build_nwbfile() self.writer = NWBHDF5IO(self.filename, mode='w') self.writer.write(self.container, cache_spec=cache_spec) self.writer.close() self.reader = NWBHDF5IO(self.filename, mode='r') self.read_nwbfile = self.reader.read() return self.read_nwbfile def addContainer(self, nwbfile): """ No-op. roundtripContainer is overridden and no longer uses addContainer """ pass def getContainer(self, nwbfile): """ Get the NWBFile object from the given NWBFile """ return nwbfile class TestExperimentersConstructorRoundtrip(TestNWBFileIO): """ Test that a list of multiple experimenters in a constructor is written to and read from file """ def build_nwbfile(self): description = 'test nwbfile experimenter' identifier = 'TEST_experimenter' self.nwbfile = NWBFile(session_description=description, identifier=identifier, session_start_time=self.start_time, experimenter=('experimenter1', 'experimenter2')) class TestExperimentersSetterRoundtrip(TestNWBFileIO): """ Test that a list of multiple experimenters in a setter is written to and read from file """ def build_nwbfile(self): description = 'test nwbfile experimenter' identifier = 'TEST_experimenter' self.nwbfile = NWBFile(session_description=description, identifier=identifier, session_start_time=self.start_time) self.nwbfile.experimenter = ('experimenter1', 'experimenter2') class TestPublicationsConstructorRoundtrip(TestNWBFileIO): """ Test that a list of multiple publications in a constructor is written to and read from file """ def build_nwbfile(self): description = 'test nwbfile publications' identifier = 'TEST_publications' self.nwbfile = NWBFile(session_description=description, identifier=identifier, session_start_time=self.start_time, related_publications=('pub1', 'pub2')) class TestPublicationsSetterRoundtrip(TestNWBFileIO): """ Test that a list of multiple publications in a setter is written to and read from file """ def build_nwbfile(self): description = 'test nwbfile publications' identifier = 'TEST_publications' self.nwbfile = NWBFile(session_description=description, identifier=identifier, session_start_time=self.start_time) self.nwbfile.related_publications = ('pub1', 'pub2') class TestSubjectIO(NWBH5IOMixin, TestCase): def setUpContainer(self): """ Return the test Subject """ return Subject(age='P90D', description='An unfortunate rat', genotype='WT', sex='M', species='Rattus norvegicus', subject_id='RAT123', weight='2 kg', date_of_birth=datetime(1970, 1, 1, 12, tzinfo=tzutc()), strain='my_strain') def addContainer(self, nwbfile): """ Add the test Subject to the given NWBFile """ nwbfile.subject = self.container def getContainer(self, nwbfile): """ Return the test Subject from the given NWBFile """ return nwbfile.subject class TestEmptySubjectIO(TestSubjectIO): def setUpContainer(self): return Subject() class TestEpochsIO(NWBH5IOMixin, TestCase): def setUpContainer(self): """ Return placeholder epochs object. Tested epochs are added directly to the NWBFile in addContainer """ return TimeIntervals('epochs') def addContainer(self, nwbfile): """ Add the test epochs to the given NWBFile """ nwbfile.add_epoch_column( name='temperature', description='average temperture (c) during epoch' ) nwbfile.add_epoch( start_time=5.3, stop_time=6.1, timeseries=[], tags='ambient', temperature=26.4, ) # reset the thing self.container = nwbfile.epochs def getContainer(self, nwbfile): """ Return the test epochs from the given NWBFile """ return nwbfile.epochs class TestEpochsIODf(TestEpochsIO): def addContainer(self, nwbfile): """ Add the test epochs with TimeSeries objects to the given NWBFile """ tsa, tsb = [ TimeSeries(name='a', data=np.arange(11), unit='flubs', timestamps=np.linspace(0, 1, 11)), TimeSeries(name='b', data=np.arange(13), unit='flubs', timestamps=

np.linspace(0.1, 5, 13)

numpy.linspace

from Bio import pairwise2 from Bio.SubsMat.MatrixInfo import blosum62 import numpy as np import scipy import pandas as pd import regex as re import pickle def sub_pivot_df(pps, sdf, group=True): """function takes a long form datatable of extracts and peaks (input sdf), filters for peptide plasmids of interest (input pps) and outputs a datatable with one row per extract, with columns for 'unmod' and 'mod' (or any other peak type) with the respective peak area. group option specifies if replicates should be grouped (by peptide sequence), with""" #filter for a sub-dataframe that includes just the peptide plasmids of interest sub_df = sdf[sdf['pep_plasmid'].isin(pps)] #Grab the set of sequences of interest (set to make non-redundant) sequences = set(sub_df['sequence']) #grab just the modification information (%mod fractions) for each extract stats_df = sub_df.pivot_table(index='extract', columns='peak_type', values='mod_area', fill_value=0).reset_index() #metadata for all of the extracts meta_df = sub_df.groupby('extract', group_keys=False).first().reset_index().sort_values('extract') #merge metadata with stats data based on extract extract_df = meta_df.merge(stats_df, on='extract', how='inner') #if include_other: # sub_data['mod'] = sub_data['mod'] + sub_data['other'] if group: extract_df['replicate'] = 1 return extract_df.groupby( ['sequence', 'mod_plasmid', 'modification description'], group_keys=False).agg( {'media':'first','ms':'first', 'pep_plasmid':'first', 'replicate':'sum', 'total_area':'mean', 'mod':'mean','unmod':'mean', 'extract':'first'}).reset_index().sort_values('mod', ascending=False) else: return extract_df def seq_alignment(wt_sequence, sdf, score='ddg', penalties=(-15, -2)): """Function takes a wild-type sequence and a dataframe of extracts of sequence variants to align to. Returns four lists, each list having one element per row of the input dataframe: seq_alignments - a list of tuples. Each tuple is the variant sequence, it's alignment to the wild-type sequence, and it's modification score (the type of score specified in 'score' input). labels_sparse - the variant sequence aligned to the wild-type sequence, positions that match wild-type are blank (space), positions that are mutated are the mutant amino acid (or '-' for gap). Note that for the wild-type sequence, the full sequence is here, no spaces, as a reference. labels - the variant sequence, unchanged/unaligned. labels_aligned - the variant sequence, aligned (with gaps) """ seq_alignments = [] labels = [wt_sequence] labels_sparse = [wt_sequence] labels_aligned = [wt_sequence] for ind, row in enumerate(sdf.iterrows()): #get rid of the index row = row[1] seq = row['sequence'] mod_efficiency = row[score] #align the sequences, this will be a list of alignments, we just take the first one, since they are all # functionally equivalent for our purposes alignments = pairwise2.align.globalds(wt_sequence, seq.split("*")[0], blosum62, penalties[0], penalties[1])[0] #skip the wt sequence for the labels/order, so we added it at the beginning if alignments[1] == wt_sequence: seq_alignments.append((seq, alignments[1], mod_efficiency)) else: seq_alignments.append((seq, alignments[1], mod_efficiency)) labels_sparse.append("".join([i if i != w else " " for i, w in zip(alignments[1], wt_sequence)])) labels.append(seq) labels_aligned.append(alignments[1]) return seq_alignments, labels_sparse, labels, labels_aligned def aln2binary_df(wt_sequence, seq_alignments, invert=False): """function takes a wild-type sequence, and a list of sequence alignments from the seq_alignment function (list should be a list of tuples, one tuple per variant: (variant sequence, it's alignment to the wild-type sequence, and it's modification score) Returns a new dataframe that is one row per variant, and one column per amino acid position. At each position, the number 1 means that the variant sequence matches wild-type, 0 means the variant sequence does not match wild-type If invert, then the 1/0 assignment is switched. DOES NOT WORK IF THERE ARE GAPS (or rather, it just assumes that a gap is not a match, it is not recorded specially) """ #Making a new dataframe (seq_df) that has a column for each amino acid indexes = [i for i in range(len(wt_sequence))] #temporary list, 1 element for each variant new_form = [] mod_scores = [] for variant_seq, aligned_seq, mod_eff in seq_alignments: binary_seq = [] for s,w in zip(aligned_seq, wt_sequence): if s == w: binary_seq.append(0 if invert else 1) else: binary_seq.append(1 if invert else 0) new_form.append(binary_seq) mod_scores.append(mod_eff) binary_df = pd.DataFrame(new_form, columns = indexes) #convert modification scores into a numpy array and then into delta delta G for each variant mod_scores =

np.array(mod_scores)

numpy.array

""" qgs tensor module ================= This module computes and holds the tensor representing the tendencies of the model's equations. Notes ----- These are computed using the analytical expressions from: * <NAME>., <NAME>. and <NAME>.: *The Modular Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0*, Geosci. Model Dev., **9**, 2793-2808, `doi:10.5194/gmd-9-2793-2016 <http://dx.doi.org/10.5194/gmd-9-2793-2016>`_, 2016. * <NAME>., & <NAME>. (1987). *Theories of multiple equilibria and weather regimes—A critical reexamination. Part II: Baroclinic two-layer models*. Journal of the atmospheric sciences, **44** (21), 3282-3303. `link <https://journals.ametsoc.org/doi/abs/10.1175/1520-0469(1987)044%3C3282%3ATOMEAW%3E2.0.CO%3B2>`_ """ import numpy as np import sparse as sp class QgsTensor(object): """qgs tendencies tensor class. Parameters ---------- atmospheric_innner_product: AtmosphericInnerProducts or None The inner products of the atmospheric basis functions on which the model's PDE atmospheric equations are projected. If None, disable the atmospheric tendencies. oceanic_innner_product: OceanicInnerProducts or None The inner products of the atmospheric basis functions on which the model's PDE oceanic equations are projected. If None, disable the oceanic tendencies. Attributes ---------- atmospheric_innner_product: AtmosphericInnerProducts or None The inner products of the atmospheric basis functions on which the model's PDE equations are projected. If None, the atmospheric tendencies are disabled. oceanic_innner_product: OceanicInnerProducts or None The inner products of the atmospheric basis functions on which the model's PDE equations are projected. If None, the oceanic tendencies are disabled. params: QgParams The models parameters. tensor: sparse.COO(float) The tensor :math:`\mathcal{T}_{i,j,k}` :math:`i`-th components. jacobian_tensor: sparse.COO(float) The jacobian tensor :math:`\mathcal{T}_{i,j,k} + \mathcal{T}_{i,k,j}` :math:`i`-th components. """ def __init__(self, atmospheric_inner_products=None, oceanic_inner_products=None): self.atmospheric_inner_products = atmospheric_inner_products self.oceanic_inner_products = oceanic_inner_products if self.atmospheric_inner_products is not None: self.params = self.atmospheric_inner_products.params if self.oceanic_inner_products is not None: self.params = self.oceanic_inner_products.params self.tensor = None self.jacobian_tensor = None self.compute_tensor() def _psi_a(self, i): """Transform the :math:`\psi_{\mathrm a}` :math:`i`-th coefficient into the effective model's variable. Parameters ---------- i: int The :math:`i`-th coefficients of :math:`\psi_{\mathrm a}` Returns ------- int The effective model's variable. """ return i def _theta_a(self, i): """Transform the :math:`\\theta_{\mathrm a}` :math:`i`-th coefficient into the effective model's variable. Parameters ---------- i: int The :math:`i`-th coefficients of :math:`\\theta_{\mathrm a}` Returns ------- int The effective model's variable. """ return i + self.params.nmod[0] def _psi_o(self, i): """Transform the :math:`\psi_{\mathrm o}` :math:`i`-th coefficient into the effective model's variable. Parameters ---------- i: int The :math:`i`-th coefficients of :math:`\psi_{\mathrm o}` Returns ------- int The effective model's variable. """ return i + 2 * self.params.nmod[0] def _deltaT_o(self, i): """Transform the :math:`\delta T_{\mathrm o}` :math:`i`-th coefficient into the effective model's variable. Parameters ---------- i: int The :math:`i`-th coefficients of :math:`\delta T_{\mathrm o}` Returns ------- int The effective model's variable. """ return i + 2 * self.params.nmod[0] + self.params.nmod[1] def _deltaT_g(self, i): """Transform the :math:`\delta T_{\mathrm o}` :math:`i`-th coefficient into the effective model's variable. Parameters ---------- i: int The :math:`i`-th coefficients of :math:`\delta T_{\mathrm o}` Returns ------- int The effective model's variable. """ return i + 2 * self.params.nmod[0] def compute_tensor(self): """Routine to compute the tensor.""" aips = self.atmospheric_inner_products oips = self.oceanic_inner_products par = self.params atp = par.atemperature_params ap = par.atmospheric_params op = par.oceanic_params scp = par.scale_params gp = par.ground_params namod = par.nmod[0] ngomod = par.nmod[1] ndim = par.ndim if par.gotemperature_params is not None: ocean = par.gotemperature_params._name == "Oceanic Temperature" ground_temp = par.gotemperature_params._name == "Ground Temperature" else: ocean = False ground_temp = False # 0-th tensor component is an empty matrix tensor = sp.zeros((ndim+1, ndim + 1, ndim + 1), dtype=np.float64, format='dok') jacobian_tensor = sp.zeros((ndim+1, ndim + 1, ndim + 1), dtype=np.float64, format='dok') ## Problem with matmul with object and DOK archi : Temporary fix until a better solution is found hk = np.array(gp.hk, dtype=np.float) g = aips.g.to_coo() ################# # psi_a part for i in range(1, namod + 1): t = np.zeros((ndim + 1, ndim + 1), dtype=np.float64) for j in range(1, namod + 1): t[self._psi_a(j), 0] = -((aips.c[(i - 1), (j - 1)] * scp.beta) / aips.a[(i - 1), (i - 1)]) \ - (ap.kd * _kronecker_delta((i - 1), (j - 1))) / 2 t[self._theta_a(j), 0] = (ap.kd * _kronecker_delta((i - 1), (j - 1))) / 2 if gp.hk is not None: oro = (g[(i - 1), (j - 1), :] @ hk) / (2 * aips.a[(i - 1), (i - 1)]) t[self._psi_a(j), 0] -= oro t[self._theta_a(j), 0] += oro for k in range(1, namod + 1): t[self._psi_a(j), self._psi_a(k)] = - aips.b[(i - 1), (j - 1), (k - 1)] \ / aips.a[(i - 1), (i - 1)] t[self._theta_a(j), self._theta_a(k)] = - aips.b[(i - 1), (j - 1), (k - 1)] \ / aips.a[(i - 1), (i - 1)] if ocean: for j in range(1, ngomod + 1): t[self._psi_o(j), 0] = ap.kd * aips.d[(i - 1), (j - 1)] / \ (2 * aips.a[(i - 1), (i - 1)]) t = self.simplify_matrix(t) tensor[self._psi_a(i)] = t jacobian_tensor[self._psi_a(i)] = t + t.T # theta_a part for i in range(1, namod + 1): t = np.zeros((ndim + 1, ndim + 1), dtype=np.float64) if par.Cpa is not None: t[0, 0] = par.Cpa[i - 1] / (1 - aips.a[0, 0] * ap.sig0) if atp.hd is not None and atp.thetas is not None: t[0, 0] += atp.hd * atp.thetas[(i - 1)] / (1. - ap.sig0 * aips.a[(i - 1), (i - 1)]) for j in range(1, namod + 1): t[self._psi_a(j), 0] = (aips.a[(i - 1), (j - 1)] * ap.kd * ap.sig0) \ / (-2 + 2 * aips.a[(i - 1), (i - 1)] * ap.sig0) if par.LSBpa is not None and par.Lpa is not None: heat = 2. * (par.LSBpa + atp.sc * par.Lpa) * _kronecker_delta((i - 1), (j - 1)) else: heat = 0 t[self._theta_a(j), 0] = (-((ap.sig0 * (2. * aips.c[(i - 1), (j - 1)] * scp.beta + aips.a[(i - 1), (j - 1)] * (ap.kd + 4. * ap.kdp)))) + heat) / (-2. + 2. * aips.a[(i - 1), (i - 1)] * ap.sig0) if atp.hd is not None: t[self._theta_a(j), 0] += (atp.hd * _kronecker_delta((i - 1), (j - 1))) / (ap.sig0 * aips.a[(i - 1), (i - 1)] - 1.) if gp.hk is not None: oro = (ap.sig0 * g[(i - 1), (j - 1), :] @ hk) / (2 * aips.a[(i - 1), (i - 1)] * ap.sig0 - 2.) t[self._theta_a(j), 0] -= oro t[self._psi_a(j), 0] += oro for k in range(1, namod + 1): t[self._psi_a(j), self._theta_a(k)] = (aips.g[(i - 1), (j - 1), (k - 1)] - aips.b[(i - 1), (j - 1), (k - 1)] * ap.sig0) / \ (-1 + aips.a[(i - 1), (i - 1)] * ap.sig0) t[self._theta_a(j), self._psi_a(k)] = (aips.b[(i - 1), (j - 1), (k - 1)] * ap.sig0) \ / (1 - aips.a[(i - 1), (i - 1)] * ap.sig0) if ocean: for j in range(1, ngomod + 1): t[self._psi_o(j), 0] = ap.kd * (aips.d[(i - 1), (j - 1)] * ap.sig0) \ / (2 - 2 * aips.a[(i - 1), (i - 1)] * ap.sig0) if par.LSBpgo is not None and par.Lpa is not None: t[self._deltaT_o(j), 0] = aips.s[(i - 1), (j - 1)] * (2 * par.LSBpgo + par.Lpa) \ / (2 - 2 * aips.a[(i - 1), (i - 1)] * ap.sig0) if ground_temp and i <= ngomod: t[self._deltaT_g(i), 0] = (2 * par.LSBpgo + par.Lpa) / (2 - 2 * aips.a[(i - 1), (i - 1)] * ap.sig0) t = self.simplify_matrix(t) tensor[self._theta_a(i)] = t jacobian_tensor[self._theta_a(i)] = t + t.T if ocean: # psi_o part for i in range(1, ngomod + 1): t =

np.zeros((ndim + 1, ndim + 1), dtype=np.float64)

numpy.zeros

''' Author: <NAME>, <NAME> Acknowledgment: Derived some functions from <NAME>'s work Description: This script is used to train the dual neural network for tool substitution with material properties. ''' import os, sys import numpy as np import cPickle as pickle import csv import keras from keras.models import Sequential, Model from keras.layers import Dense, Input, Lambda, Dropout, merge, MaxPooling1D, Flatten, Conv1D import keras.backend as K from keras import optimizers from keras import regularizers from keras.utils import plot_model from keras.utils.np_utils import to_categorical from sklearn.preprocessing import Normalizer, StandardScaler from sklearn.model_selection import train_test_split from sklearn.metrics import classification_report, confusion_matrix from sklearn.utils import shuffle from sklearn.externals import joblib from sklearn.metrics import accuracy_score import random def sigmoid(z): return 1/(1+np.exp(-z)) def features_scio(csv_file): # Take csv file and retrieve scio_processed_data corresponding to input features = {} obj_materials = {} wavelengthCount = 331 with open(csv_file) as f: reader = csv.reader(f) for idx, row in enumerate(reader): if idx == 10: wavelengths = [float(r.strip().split('_')[-1].split()[0]) + 740.0 for r in row[10:wavelengthCount+10]] try: int(row[0]) # To skip first few rows until first integer encountered if '.ply' not in row[3]: obj_name = row[3] + '.ply' else: obj_name = row[3] features_list = [float(elt) for elt in row[10:wavelengthCount+10]] features_list = firstDeriv(features_list, wavelengths) features[obj_name] = features_list material_name = row[4] obj_materials[obj_name] = row[4] except: pass return features, obj_materials def loadScioDataset(pklFile, csvFile, materialNames=[], objectNames=[]): saveFilename = pklFile + '.pkl' if os.path.isfile(saveFilename): with open(saveFilename, 'rb') as f: X, y_materials, y_objects, wavelengths = pickle.load(f) else: X = [] y_materials = [] y_objects = [] filename = csvFile + '.csv' print(filename) wavelengthCount = 331 with open(filename, 'rb') as f: reader = csv.reader(f) for i, row in enumerate(reader): if i < 10 or i == 11: continue if i == 10: # Header row wavelengths = [float(r.strip().split('_')[-1].split()[0]) + 740.0 for r in row[10:wavelengthCount+10]] continue obj = row[3].strip() material = row[4].strip() if material not in materialNames: continue index = materialNames.index(material) if objectNames is not None and obj not in objectNames[index]: continue values = [float(v) for v in row[10:wavelengthCount+10]] X.append(values) y_materials.append(index) y_objects.append(obj) with open(saveFilename, 'wb') as f: pickle.dump([X, y_materials, y_objects, wavelengths], f, protocol=pickle.HIGHEST_PROTOCOL) return X, y_materials, y_objects, wavelengths def firstDeriv(x, wavelengths): # First derivative of measurements with respect to wavelength x = np.copy(x) for i, xx in enumerate(x): dx = np.zeros(xx.shape, np.float) dx[0:-1] =

np.diff(xx)

numpy.diff

# from __future__ import print_function, absolute_import, division import multiprocessing import re import shutil import types from pathlib import Path import allesfitter import numpy as np import yaml from argparse import ArgumentParser from sherlockpipe.star.HabitabilityCalculator import HabitabilityCalculator import pandas as pd import os from os import path resources_dir = path.join(path.dirname(__file__)) class Fitter: def __init__(self, object_dir, only_initial, mcmc = False, detrend = False): self.args = types.SimpleNamespace() self.args.noshow = True self.args.north = False self.args.o = True self.args.auto = True self.args.save = True self.args.nickname = "" # TODO do we set the sherlock id? self.args.FFI = False # TODO get this from input self.args.targetlist = "best_signal_latte_input.csv" self.args.new_path = "" # TODO check what to do with this self.object_dir = os.getcwd() if object_dir is None else object_dir self.latte_dir = str(Path.home()) + "/.sherlockpipe/latte/" if not os.path.exists(self.latte_dir): os.mkdir(self.latte_dir) self.data_dir = self.object_dir self.only_initial = only_initial self.mcmc = mcmc self.detrend = detrend def fit(self, candidate_df, star_df, cpus, allesfit_dir): candidate_row = candidate_df.iloc[0] sherlock_star_file = self.object_dir + "/params_star.csv" star_file = allesfit_dir + "/params_star.csv" params_file = allesfit_dir + "/params.csv" settings_file = allesfit_dir + "/settings.csv" if candidate_row["number"] is None or

np.isnan(candidate_row["number"])

numpy.isnan

import sys import numpy as np import pandas as pd import openmdao.api as om from wisdem.commonse import gravity eps = 1e-3 # Convenience functions for computing McDonald's C and F parameters def chsMshc(x): return np.cosh(x) * np.sin(x) - np.sinh(x) * np.cos(x) def chsPshc(x): return np.cosh(x) * np.sin(x) + np.sinh(x) * np.cos(x) def carterFactor(airGap, slotOpening, slotPitch): """Return Carter factor (based on Langsdorff's empirical expression) See page 3-13 Boldea Induction machines Chapter 3 """ gma = (2 * slotOpening / airGap) ** 2 / (5 + 2 * slotOpening / airGap) return slotPitch / (slotPitch - airGap * gma * 0.5) # --------------- def carterFactorMcDonald(airGap, h_m, slotOpening, slotPitch): """Return Carter factor using Carter's equation (based on Schwartz-Christoffel's conformal mapping on simplified slot geometry) This code is based on Eq. B.3-5 in Appendix B of McDonald's thesis. It is used by PMSG_arms and PMSG_disc. h_m : magnet height (m) b_so : stator slot opening (m) tau_s : Stator slot pitch (m) """ mu_r = 1.06 # relative permeability (probably for neodymium magnets, often given as 1.05 - GNS) g_1 = airGap + h_m / mu_r # g b_over_a = slotOpening / (2 * g_1) gamma = 4 / np.pi * (b_over_a * np.arctan(b_over_a) - np.log(np.sqrt(1 + b_over_a ** 2))) return slotPitch / (slotPitch - gamma * g_1) # --------------- def carterFactorEmpirical(airGap, slotOpening, slotPitch): """Return Carter factor using Langsdorff's empirical expression""" sigma = (slotOpening / airGap) / (5 + slotOpening / airGap) return slotPitch / (slotPitch - sigma * slotOpening) # --------------- def carterFactorSalientPole(airGap, slotWidth, slotPitch): """Return Carter factor for salient pole rotor Where does this equation come from? It's different from other approximations above. Original code: tau_s = np.pi * dia / S # slot pitch b_s = tau_s * b_s_tau_s # slot width b_t = tau_s - b_s # tooth width K_C1 = (tau_s + 10 * g_a) / (tau_s - b_s + 10 * g_a) # salient pole rotor slotPitch - slotWidth == toothWidth """ return (slotPitch + 10 * airGap) / (slotPitch - slotWidth + 10 * airGap) # salient pole rotor # --------------------------------- def array_seq(q1, b, c, Total_number): Seq = np.array([1, 0, 0, 1, 0]) diff = Total_number * 5 / 6 G = np.prod(Seq.shape) return Seq, diff, G # --------------------------------- def winding_factor(Sin, b, c, p, m): S = int(Sin) # Step 1 Writing q1 as a fraction q1 = b / c # Step 2: Writing a binary sequence of b-c zeros and b ones Total_number = int(S / b) L = array_seq(q1, b, c, Total_number) # STep 3 : Repeat binary sequence Q_s/b times New_seq = np.tile(L[0], Total_number) Actual_seq1 = pd.DataFrame(New_seq[:, None].T) Winding_sequence = ["A", "C1", "B", "A1", "C", "B1"] New_seq2 = np.tile(Winding_sequence, int(L[1])) Actual_seq2 = pd.DataFrame(New_seq2[:, None].T) Seq_f = pd.concat([Actual_seq1, Actual_seq2], ignore_index=True) Seq_f.reset_index(drop=True) Slots = S R = S if S % 2 == 0 else S + 1 Windings_arrange = (pd.DataFrame(index=Seq_f.index, columns=Seq_f.columns[1:R])).fillna(0) counter = 1 # Step #4 Arranging winding in Slots for i in range(0, len(New_seq)): if Seq_f.loc[0, i] == 1: Windings_arrange.loc[0, counter] = Seq_f.loc[1, i] counter = counter + 1 Windings_arrange.loc[1, 1] = "C1" for k in range(1, R): if Windings_arrange.loc[0, k] == "A": Windings_arrange.loc[1, k + 1] = "A1" elif Windings_arrange.loc[0, k] == "B": Windings_arrange.loc[1, k + 1] = "B1" elif Windings_arrange.loc[0, k] == "C": Windings_arrange.loc[1, k + 1] = "C1" elif Windings_arrange.loc[0, k] == "A1": Windings_arrange.loc[1, k + 1] = "A" elif Windings_arrange.loc[0, k] == "B1": Windings_arrange.loc[1, k + 1] = "B" elif Windings_arrange.loc[0, k] == "C1": Windings_arrange.loc[1, k + 1] = "C" Phase_A = np.zeros((1000, 1), dtype=float) counter_A = 0 # Windings_arrange.to_excel('test.xlsx') # Winding vector, W_A for Phase A for l in range(1, R): if Windings_arrange.loc[0, l] == "A" and Windings_arrange.loc[1, l] == "A": Phase_A[counter_A, 0] = l Phase_A[counter_A + 1, 0] = l counter_A = counter_A + 2 elif Windings_arrange.loc[0, l] == "A1" and Windings_arrange.loc[1, l] == "A1": Phase_A[counter_A, 0] = -1 * l Phase_A[counter_A + 1, 0] = -1 * l counter_A = counter_A + 2 elif Windings_arrange.loc[0, l] == "A" or Windings_arrange.loc[1, l] == "A": Phase_A[counter_A, 0] = l counter_A = counter_A + 1 elif Windings_arrange.loc[0, l] == "A1" or Windings_arrange.loc[1, l] == "A1": Phase_A[counter_A, 0] = -1 * l counter_A = counter_A + 1 W_A = (np.trim_zeros(Phase_A)).T # Calculate winding factor K_w = 0 for r in range(0, int(2 * (S) / 3)): Gamma = 2 * np.pi * p * np.abs(W_A[0, r]) / S K_w += np.sign(W_A[0, r]) * (np.exp(Gamma * 1j)) K_w = np.abs(K_w) / (2 * S / 3) CPMR = np.lcm(S, int(2 * p)) N_cog_s = CPMR / S N_cog_p = CPMR / p N_cog_t = CPMR * 0.5 / p A = np.lcm(S, int(2 * p)) b_p_tau_p = 2 * 1 * p / S - 0 b_t_tau_s = (2) * S * 0.5 / p - 2 return K_w # --------------------------------- def shell_constant(R, t, l, x, E, v): Lambda = (3 * (1 - v ** 2) / (R ** 2 * t ** 2)) ** 0.25 D = E * t ** 3 / (12 * (1 - v ** 2)) C_14 = (np.sinh(Lambda * l)) ** 2 + (np.sin(Lambda * l)) ** 2 C_11 = (np.sinh(Lambda * l)) ** 2 - (np.sin(Lambda * l)) ** 2 F_2 = np.cosh(Lambda * x) * np.sin(Lambda * x) + np.sinh(Lambda * x) * np.cos(Lambda * x) C_13 = np.cosh(Lambda * l) * np.sinh(Lambda * l) - np.cos(Lambda * l) * np.sin(Lambda * l) F_1 = np.cosh(Lambda * x) * np.cos(Lambda * x) F_4 = np.cosh(Lambda * x) * np.sin(Lambda * x) - np.sinh(Lambda * x) * np.cos(Lambda * x) return D, Lambda, C_14, C_11, F_2, C_13, F_1, F_4 # --------------------------------- def plate_constant(a, b, E, v, r_o, t): D = E * t ** 3 / (12 * (1 - v ** 2)) C_2 = 0.25 * (1 - (b / a) ** 2 * (1 + 2 * np.log(a / b))) C_3 = 0.25 * (b / a) * (((b / a) ** 2 + 1) * np.log(a / b) + (b / a) ** 2 - 1) C_5 = 0.5 * (1 - (b / a) ** 2) C_6 = 0.25 * (b / a) * ((b / a) ** 2 - 1 + 2 * np.log(a / b)) C_8 = 0.5 * (1 + v + (1 - v) * (b / a) ** 2) C_9 = (b / a) * (0.5 * (1 + v) * np.log(a / b) + 0.25 * (1 - v) * (1 - (b / a) ** 2)) L_11 = (1 / 64) * ( 1 + 4 * (r_o / a) ** 2 - 5 * (r_o / a) ** 4 - 4 * (r_o / a) ** 2 * (2 + (r_o / a) ** 2) * np.log(a / r_o) ) L_17 = 0.25 * (1 - 0.25 * (1 - v) * ((1 - (r_o / a) ** 4) - (r_o / a) ** 2 * (1 + (1 + v) * np.log(a / r_o)))) return D, C_2, C_3, C_5, C_6, C_8, C_9, L_11, L_17 # --------------------------------- debug = False # --------------------------------- class GeneratorBase(om.ExplicitComponent): """ Base class for generators Parameters ---------- B_r : float, [T] Remnant flux density E : float, [Pa] youngs modulus G : float, [Pa] Shear modulus P_Fe0e : float, [W/kg] specific eddy losses @ 1.5T, 50Hz P_Fe0h : float, [W/kg] specific hysteresis losses W / kg @ 1.5 T @50 Hz S_N : float Slip alpha_p : float b_r_tau_r : float Rotor Slot width / Slot pitch ratio b_ro : float, [m] Rotor slot opening width b_s_tau_s : float Stator Slot width/Slot pitch ratio b_so : float, [m] Stator slot opening width cofi : float power factor freq : float, [Hz] grid frequency h_i : float, [m] coil insulation thickness h_sy0 : float h_w : float, [m] Slot wedge height k_fes : float Stator iron fill factor per Grauers k_fillr : float Rotor slot fill factor k_fills : float Stator Slot fill factor k_s : float magnetic saturation factor for iron m : int Number of phases mu_0 : float, [m*kg/s**2/A**2] permeability of free space mu_r : float, [m*kg/s**2/A**2] relative permeability (neodymium) p : float number of pole pairs (taken as int within code) phi : numpy array[90], [rad] tilt angle (during transportation) q1 : int Stator slots per pole per phase q2 : int Rotor slots per pole per phase ratio_mw2pp : float ratio of magnet width to pole pitch(bm / self.tau_p) resist_Cu : float, [ohm/m] Copper resistivity sigma : float, [Pa] assumed max shear stress v : float poisson ratio y_tau_p : float Stator coil span to pole pitch y_tau_pr : float Rotor coil span to pole pitch I_0 : float, [A] no-load excitation current T_rated : float, [N*m] Rated torque d_r : float, [m] arm depth d_r h_m : float, [m] magnet height h_0 : float, [m] Slot height h_s : float, [m] Yoke height h_s len_s : float, [m] Stator core length machine_rating : float, [W] Machine rating shaft_rpm : numpy array[n_pc], [rpm] rated speed of input shaft (lss for direct, hss for geared) n_r : float number of arms n rad_ag : float, [m] airgap radius t_wr : float, [m] arm depth thickness n_s : float number of stator arms n_s b_st : float, [m] arm width b_st d_s : float, [m] arm depth d_s t_ws : float, [m] arm depth thickness D_shaft : float, [m] Shaft diameter rho_Copper : float, [kg*m**-3] Copper density rho_Fe : float, [kg*m**-3] Magnetic Steel density rho_Fes : float, [kg*m**-3] Structural Steel density rho_PM : float, [kg*m**-3] Magnet density Returns ------- B_rymax : float, [T] Peak Rotor yoke flux density B_trmax : float, [T] maximum tooth flux density in rotor B_tsmax : float, [T] maximum tooth flux density in stator B_g : float, [T] Peak air gap flux density B_g B_g1 : float, [T] air gap flux density fundamental B_pm1 : float Fundamental component of peak air gap flux density N_s : float Number of turns in the stator winding b_s : float, [m] slot width b_t : float, [m] tooth width A_Curcalc : float, [mm**2] Conductor cross-section mm^2 A_Cuscalc : float, [mm**2] Stator Conductor cross-section mm^2 b_m : float magnet width mass_PM : float, [kg] Magnet mass Copper : float, [kg] Copper Mass Iron : float, [kg] Electrical Steel Mass Structural_mass : float, [kg] Structural Mass generator_mass : float, [kg] Actual mass f : float Generator output frequency I_s : float, [A] Generator output phase current R_s : float, [ohm] Stator resistance L_s : float Stator synchronising inductance J_s : float, [A*m**-2] Stator winding current density A_1 : float Specific current loading K_rad : float Stack length ratio Losses : numpy array[n_pc], [W] Total loss generator_efficiency : numpy array[n_pc] Generator electromagnetic efficiency values (<1) u_ar : float, [m] Rotor radial deflection u_as : float, [m] Stator radial deflection u_allow_r : float, [m] Allowable radial rotor u_allow_s : float, [m] Allowable radial stator y_ar : float, [m] Rotor axial deflection y_as : float, [m] Stator axial deflection y_allow_r : float, [m] Allowable axial y_allow_s : float, [m] Allowable axial z_ar : float, [m] Rotor circumferential deflection z_as : float, [m] Stator circumferential deflection z_allow_r : float, [m] Allowable circum rotor z_allow_s : float, [m] Allowable circum stator b_allow_r : float, [m] Allowable arm dimensions b_allow_s : float, [m] Allowable arm TC1 : float, [m**3] Torque constraint TC2r : float, [m**3] Torque constraint-rotor TC2s : float, [m**3] Torque constraint-stator R_out : float, [m] Outer radius S : float Stator slots Slot_aspect_ratio : float Slot aspect ratio Slot_aspect_ratio1 : float Stator slot aspect ratio Slot_aspect_ratio2 : float Rotor slot aspect ratio D_ratio : float Stator diameter ratio J_r : float Rotor winding Current density L_sm : float mutual inductance Q_r : float Rotor slots R_R : float Rotor resistance b_r : float rotor slot width b_tr : float rotor tooth width b_trmin : float minimum tooth width """ def initialize(self): self.options.declare("n_pc", default=20) def setup(self): n_pc = self.options["n_pc"] # Constants and parameters self.add_input("B_r", val=1.2, units="T") self.add_input("E", val=0.0, units="Pa") self.add_input("G", val=0.0, units="Pa") self.add_input("P_Fe0e", val=1.0, units="W/kg") self.add_input("P_Fe0h", val=4.0, units="W/kg") self.add_input("S_N", val=-0.002) self.add_input("alpha_p", val=0.5 * np.pi * 0.7) self.add_input("b_r_tau_r", val=0.45) self.add_input("b_ro", val=0.004, units="m") self.add_input("b_s_tau_s", val=0.45) self.add_input("b_so", val=0.004, units="m") self.add_input("cofi", val=0.85) self.add_input("freq", val=60, units="Hz") self.add_input("h_i", val=0.001, units="m") self.add_input("h_sy0", val=0.0) self.add_input("h_w", val=0.005, units="m") self.add_input("k_fes", val=0.9) self.add_input("k_fillr", val=0.7) self.add_input("k_fills", val=0.65) self.add_input("k_s", val=0.2) self.add_discrete_input("m", val=3) self.add_input("mu_0", val=np.pi * 4e-7, units="m*kg/s**2/A**2") self.add_input("mu_r", val=1.06, units="m*kg/s**2/A**2") self.add_input("p", val=3.0) self.add_input("phi", val=np.deg2rad(90), units="rad") self.add_discrete_input("q1", val=6) self.add_discrete_input("q2", val=4) self.add_input("ratio_mw2pp", val=0.7) self.add_input("resist_Cu", val=1.8e-8 * 1.4, units="ohm/m") self.add_input("sigma", val=40e3, units="Pa") self.add_input("v", val=0.3) self.add_input("y_tau_p", val=1.0) self.add_input("y_tau_pr", val=10.0 / 12) # General inputs # self.add_input('r_s', val=0.0, units='m', desc='airgap radius r_s') self.add_input("I_0", val=0.0, units="A") self.add_input("rated_torque", val=0.0, units="N*m") self.add_input("d_r", val=0.0, units="m") self.add_input("h_m", val=0.0, units="m") self.add_input("h_0", val=0.0, units="m") self.add_input("h_s", val=0.0, units="m") self.add_input("len_s", val=0.0, units="m") self.add_input("machine_rating", val=0.0, units="W") self.add_input("shaft_rpm", val=np.zeros(n_pc), units="rpm") self.add_input("n_r", val=0.0) self.add_input("rad_ag", val=0.0, units="m") self.add_input("t_wr", val=0.0, units="m") # Structural design variables self.add_input("n_s", val=0.0) self.add_input("b_st", val=0.0, units="m") self.add_input("d_s", val=0.0, units="m") self.add_input("t_ws", val=0.0, units="m") self.add_input("D_shaft", val=0.0, units="m") # Material properties self.add_input("rho_Copper", val=8900.0, units="kg*m**-3") self.add_input("rho_Fe", val=7700.0, units="kg*m**-3") self.add_input("rho_Fes", val=7850.0, units="kg*m**-3") self.add_input("rho_PM", val=7450.0, units="kg*m**-3") # Magnetic loading self.add_output("B_rymax", val=0.0, units="T") self.add_output("B_trmax", val=0.0, units="T") self.add_output("B_tsmax", val=0.0, units="T") self.add_output("B_g", val=0.0, units="T") self.add_output("B_g1", val=0.0, units="T") self.add_output("B_pm1", val=0.0) # Stator design self.add_output("N_s", val=0.0) self.add_output("b_s", val=0.0, units="m") self.add_output("b_t", val=0.0, units="m") self.add_output("A_Curcalc", val=0.0, units="mm**2") self.add_output("A_Cuscalc", val=0.0, units="mm**2") # Rotor magnet dimension self.add_output("b_m", val=0.0) # Mass Outputs self.add_output("mass_PM", val=0.0, units="kg") self.add_output("Copper", val=0.0, units="kg") self.add_output("Iron", val=0.0, units="kg") self.add_output("Structural_mass", val=0.0, units="kg") self.add_output("generator_mass", val=0.0, units="kg") # Electrical performance self.add_output("f", val=np.zeros(n_pc)) self.add_output("I_s", val=np.zeros(n_pc), units="A") self.add_output("R_s", val=np.zeros(n_pc), units="ohm") self.add_output("L_s", val=0.0) self.add_output("J_s", val=np.zeros(n_pc), units="A*m**-2") self.add_output("A_1", val=np.zeros(n_pc)) # Objective functions self.add_output("K_rad", val=0.0) self.add_output("Losses", val=np.zeros(n_pc), units="W") self.add_output("eandm_efficiency", val=np.zeros(n_pc)) # Structural performance self.add_output("u_ar", val=0.0, units="m") self.add_output("u_as", val=0.0, units="m") self.add_output("u_allow_r", val=0.0, units="m") self.add_output("u_allow_s", val=0.0, units="m") self.add_output("y_ar", val=0.0, units="m") self.add_output("y_as", val=0.0, units="m") self.add_output("y_allow_r", val=0.0, units="m") self.add_output("y_allow_s", val=0.0, units="m") self.add_output("z_ar", val=0.0, units="m") self.add_output("z_as", val=0.0, units="m") self.add_output("z_allow_r", val=0.0, units="m") self.add_output("z_allow_s", val=0.0, units="m") self.add_output("b_allow_r", val=0.0, units="m") self.add_output("b_allow_s", val=0.0, units="m") self.add_output("TC1", val=0.0, units="m**3") self.add_output("TC2r", val=0.0, units="m**3") self.add_output("TC2s", val=0.0, units="m**3") # Other parameters self.add_output("R_out", val=0.0, units="m") self.add_output("S", val=0.0) self.add_output("Slot_aspect_ratio", val=0.0) self.add_output("Slot_aspect_ratio1", val=0.0) self.add_output("Slot_aspect_ratio2", val=0.0) self.add_output("D_ratio", val=0.0) self.add_output("J_r", val=np.zeros(n_pc)) self.add_output("L_sm", val=0.0) self.add_output("Q_r", val=0.0) self.add_output("R_R", val=0.0) self.add_output("b_r", val=0.0) self.add_output("b_tr", val=0.0) self.add_output("b_trmin", val=0.0) # ---------------------------------------------------------------------------------------- class PMSG_Outer(GeneratorBase): """ Estimates overall electromagnetic dimensions and Efficiency of PMSG -arms generator. Parameters ---------- P_mech : float, [W] Shaft mechanical power N_c : float Number of turns per coil b : float Slot pole combination c : float Slot pole combination E_p : float, [V] Stator phase voltage h_yr : float, [m] rotor yoke height h_ys : float, [m] Yoke height h_sr : float, [m] Structural Mass h_ss : float, [m] Stator yoke height t_r : float, [m] Rotor disc thickness t_s : float, [m] Stator disc thickness y_sh : float, [m] Shaft deflection theta_sh : float, [rad] slope of shaft D_nose : float, [m] Nose outer diameter y_bd : float, [m] Deflection of the bedplate theta_bd : float, [rad] Slope at the bedplate u_allow_pcent : float Radial deflection as a percentage of air gap diameter y_allow_pcent : float Radial deflection as a percentage of air gap diameter z_allow_deg : float, [deg] Allowable torsional twist B_tmax : float, [T] Peak Teeth flux density Returns ------- B_smax : float, [T] Peak Stator flux density B_symax : float, [T] Peak Stator flux density tau_p : float, [m] Pole pitch q : float, [N/m**2] Normal stress len_ag : float, [m] Air gap length h_t : float, [m] tooth height tau_s : float, [m] Slot pitch J_actual : float, [A/m**2] Current density T_e : float, [N*m] Electromagnetic torque twist_r : float, [deg] torsional twist twist_s : float, [deg] Stator torsional twist Structural_mass_rotor : float, [kg] Rotor mass (kg) Structural_mass_stator : float, [kg] Stator mass (kg) Mass_tooth_stator : float, [kg] Teeth and copper mass Mass_yoke_rotor : float, [kg] Rotor yoke mass Mass_yoke_stator : float, [kg] Stator yoke mass rotor_mass : float, [kg] Total rotor mass stator_mass : float, [kg] Total stator mass """ def initialize(self): super(PMSG_Outer, self).initialize() def setup(self): super(PMSG_Outer, self).setup() n_pc = self.options["n_pc"] # PMSG_structrual inputs self.add_input("P_mech", units="W") self.add_input("N_c", 0.0) self.add_input("b", 0.0) self.add_input("c", 0.0) self.add_input("E_p", 0.0, units="V") self.add_input("h_yr", val=0.0, units="m") self.add_input("h_ys", val=0.0, units="m") self.add_input("h_sr", 0.0, units="m") self.add_input("h_ss", 0.0, units="m") self.add_input("t_r", 0.0, units="m") self.add_input("t_s", 0.0, units="m") self.add_input("y_sh", units="m") self.add_input("theta_sh", 0.0, units="rad") self.add_input("D_nose", 0.0, units="m") self.add_input("y_bd", units="m") self.add_input("theta_bd", 0.0, units="rad") self.add_input("u_allow_pcent", 0.0) self.add_input("y_allow_pcent", 0.0) self.add_input("z_allow_deg", 0.0, units="deg") # Magnetic loading self.add_input("B_tmax", 0.0, units="T") self.add_output("B_smax", val=0.0, units="T") self.add_output("B_symax", val=0.0, units="T") self.add_output("tau_p", 0.0, units="m") self.add_output("q", 0.0, units="N/m**2") self.add_output("len_ag", 0.0, units="m") # Stator design self.add_output("h_t", 0.0, units="m") self.add_output("tau_s", 0.0, units="m") # Electrical performance self.add_output("J_actual", val=np.zeros(n_pc), units="A/m**2") self.add_output("T_e", 0.0, units="N*m") # Material properties self.add_output("twist_r", 0.0, units="deg") self.add_output("twist_s", 0.0, units="deg") # Mass Outputs self.add_output("Structural_mass_rotor", 0.0, units="kg") self.add_output("Structural_mass_stator", 0.0, units="kg") self.add_output("Mass_tooth_stator", 0.0, units="kg") self.add_output("Mass_yoke_rotor", 0.0, units="kg") self.add_output("Mass_yoke_stator", 0.0, units="kg") self.add_output("rotor_mass", 0.0, units="kg") self.add_output("stator_mass", 0.0, units="kg") def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs rad_ag = float(inputs["rad_ag"]) len_s = float(inputs["len_s"]) p = float(inputs["p"]) b = float(inputs["b"]) c = float(inputs["c"]) h_m = float(inputs["h_m"]) h_ys = float(inputs["h_ys"]) h_yr = float(inputs["h_yr"]) h_s = float(inputs["h_s"]) h_ss = float(inputs["h_ss"]) h_0 = float(inputs["h_0"]) B_tmax = float(inputs["B_tmax"]) E_p = float(inputs["E_p"]) P_mech = float(inputs["P_mech"]) P_av_v = float(inputs["machine_rating"]) h_sr = float(inputs["h_sr"]) t_r = float(inputs["t_r"]) t_s = float(inputs["t_s"]) R_sh = 0.5 * float(inputs["D_shaft"]) R_no = 0.5 * float(inputs["D_nose"]) y_sh = float(inputs["y_sh"]) y_bd = float(inputs["y_bd"]) rho_Fes = float(inputs["rho_Fes"]) rho_Fe = float(inputs["rho_Fe"]) sigma = float(inputs["sigma"]) shaft_rpm = inputs["shaft_rpm"] # Grab constant values B_r = float(inputs["B_r"]) E = float(inputs["E"]) G = float(inputs["G"]) P_Fe0e = float(inputs["P_Fe0e"]) P_Fe0h = float(inputs["P_Fe0h"]) cofi = float(inputs["cofi"]) h_w = float(inputs["h_w"]) k_fes = float(inputs["k_fes"]) k_fills = float(inputs["k_fills"]) m = int(discrete_inputs["m"]) mu_0 = float(inputs["mu_0"]) mu_r = float(inputs["mu_r"]) p = float(inputs["p"]) phi = float(inputs["phi"]) ratio_mw2pp = float(inputs["ratio_mw2pp"]) resist_Cu = float(inputs["resist_Cu"]) v = float(inputs["v"]) """ #Assign values to universal constants B_r = 1.279 # Tesla remnant flux density E = 2e11 # N/m^2 young's modulus ratio = 0.8 # ratio of magnet width to pole pitch(bm/self.tau_p) mu_0 = np.pi*4e-7 # permeability of free space mu_r = 1.06 # relative permeability cofi = 0.85 # power factor #Assign values to design constants h_0 = 0.005 # Slot opening height h_w = 0.004 # Slot wedge height m = 3 # no of phases #b_s_tau_s = 0.45 # slot width to slot pitch ratio k_fills = 0.65 # Slot fill factor P_Fe0h = 4 # specific hysteresis losses W/kg @ 1.5 T P_Fe0e = 1 # specific hysteresis losses W/kg @ 1.5 T k_fes = 0.8 # Iron fill factor #Assign values to universal constants phi = 90*2*np.pi/360 # tilt angle (rotor tilt -90 degrees during transportation) v = 0.3 # Poisson's ratio G = 79.3e9 """ ######################## Electromagnetic design ################################### K_rad = len_s / (2 * rad_ag) # Aspect ratio # Calculating air gap length dia = 2 * rad_ag # air gap diameter len_ag = 0.001 * dia # air gap length r_s = rad_ag - len_ag # Stator outer radius b_so = 2 * len_ag # Slot opening tau_p = np.pi * dia / (2 * p) # pole pitch # Calculating winding factor Slot_pole = b / c S = Slot_pole * 2 * p * m testval = S / (m * np.gcd(int(S), int(p))) if float(np.round(testval, 3)).is_integer(): k_w = winding_factor(int(S), b, c, int(p), m) b_m = ratio_mw2pp * tau_p # magnet width alpha_p = np.pi / 2 * ratio_mw2pp tau_s = np.pi * (dia - 2 * len_ag) / S # Calculating Carter factor for statorand effective air gap length gamma = ( 4 / np.pi * ( b_so / 2 / (len_ag + h_m / mu_r) * np.arctan(b_so / 2 / (len_ag + h_m / mu_r)) - np.log(np.sqrt(1 + (b_so / 2 / (len_ag + h_m / mu_r)) ** 2)) ) ) k_C = tau_s / (tau_s - gamma * (len_ag + h_m / mu_r)) # carter coefficient g_eff = k_C * (len_ag + h_m / mu_r) # angular frequency in radians om_m = 2 * np.pi * shaft_rpm / 60 om_e = p * om_m freq = om_e / 2 / np.pi # outout frequency # Calculating magnetic loading B_pm1 = B_r * h_m / mu_r / (g_eff) B_g = B_r * h_m / (mu_r * g_eff) * (4 / np.pi) * np.sin(alpha_p) B_symax = B_pm1 * b_m / (2 * h_ys) * k_fes B_rymax = B_pm1 * b_m * k_fes / (2 * h_yr) b_t = B_pm1 * tau_s / B_tmax N_c = 2 # Number of turns per coil q = (B_g) ** 2 / 2 / mu_0 # Stator winding length ,cross-section and resistance l_Cus = 2 * (len_s + np.pi / 4 * (tau_s + b_t)) # length of a turn # Calculating no-load voltage induced in the stator N_s = np.rint(E_p / (np.sqrt(2) * len_s * r_s * k_w * om_m * B_g)) # Z = P_av_v / (m*E_p) # Calculating leakage inductance in stator V_1 = E_p / 1.1 I_n = P_av_v / 3 / cofi / V_1 J_s = 6.0 A_Cuscalc = I_n / J_s A_slot = 2 * N_c * A_Cuscalc * (10 ** -6) / k_fills tau_s_new = np.pi * (dia - 2 * len_ag - 2 * h_w - 2 * h_0) / S b_s2 = tau_s_new - b_t # Slot top width b_s1 = np.sqrt(b_s2 ** 2 - 4 * np.pi * A_slot / S) b_s = (b_s1 + b_s2) * 0.5 N_coil = 2 * S P_s = mu_0 * (h_s / 3 / b_s + h_w * 2 / (b_s2 + b_so) + h_0 / b_so) # Slot permeance function L_ssigmas = S / 3 * 4 * N_c ** 2 * len_s * P_s # slot leakage inductance L_ssigmaew = ( N_coil * N_c ** 2 * mu_0 * tau_s * np.log((0.25 * np.pi * tau_s ** 2) / (0.5 * h_s * b_s)) ) # end winding leakage inductance L_aa = 2 * np.pi / 3 * (N_c ** 2 * mu_0 * len_s * r_s / g_eff) L_m = L_aa L_ssigma = L_ssigmas + L_ssigmaew L_s = L_m + L_ssigma G_leak = np.abs((1.1 * E_p) ** 4 - (1 / 9) * (P_av_v * om_e * L_s) ** 2) # Calculating stator current and electrical loading I_s = np.sqrt(2 * (np.abs((E_p * 1.1) ** 2 - G_leak ** 0.5)) / (om_e * L_s) ** 2) A_1 = 6 * I_s * N_s / np.pi / dia J_actual = I_s / (A_Cuscalc * 2 ** 0.5) L_Cus = N_s * l_Cus R_s = inputs["resist_Cu"] * (N_s) * l_Cus / (A_Cuscalc * (10 ** -6)) B_smax = np.sqrt(2) * I_s * mu_0 / g_eff # Calculating Electromagnetically active mass wedge_area = (b_s * 0.5 - b_so * 0.5) * (2 * h_0 + h_w) V_Cus = m * L_Cus * (A_Cuscalc * (10 ** -6)) # copper volume h_t = h_s + h_w + h_0 V_Fest = len_s * S * (b_t * (h_s + h_w + h_0) + wedge_area) # volume of iron in stator tooth V_Fesy = ( len_s * np.pi * ((rad_ag - len_ag - h_s - h_w - h_0) ** 2 - (rad_ag - len_ag - h_s - h_w - h_0 - h_ys) ** 2) ) # volume of iron in stator yoke V_Fery = len_s * np.pi * ((rad_ag + h_m + h_yr) ** 2 - (rad_ag + h_m) ** 2) Copper = V_Cus[-1] * inputs["rho_Copper"] M_Fest = V_Fest * rho_Fe # Mass of stator tooth M_Fesy = V_Fesy * rho_Fe # Mass of stator yoke M_Fery = V_Fery * rho_Fe # Mass of rotor yoke Iron = M_Fest + M_Fesy + M_Fery mass_PM = 2 * np.pi * (rad_ag + h_m) * len_s * h_m * ratio_mw2pp * inputs["rho_PM"] # Calculating Losses ##1. Copper Losses K_R = 1.0 # Skin effect correction co-efficient P_Cu = m * (I_s / 2 ** 0.5) ** 2 * R_s * K_R # Iron Losses ( from Hysteresis and eddy currents) P_Hyys = ( M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in stator yoke P_Ftys = ( M_Fesy * ((B_symax / 1.5) ** 2) * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator yoke P_Fesynom = P_Hyys + P_Ftys P_Hyd = ( M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in stator teeth P_Ftd = ( M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator teeth P_Festnom = P_Hyd + P_Ftd # Iron Losses ( from Hysteresis and eddy currents) P_Hyyr = ( M_Fery * (B_rymax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in stator yoke P_Ftyr = ( M_Fery * ((B_rymax / 1.5) ** 2) * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator yoke P_Ferynom = P_Hyyr + P_Ftyr # additional stray losses due to leakage flux P_ad = 0.2 * (P_Hyys + P_Ftys + P_Hyd + P_Ftd + P_Hyyr + P_Ftyr) pFtm = 300 # specific magnet loss P_Ftm = pFtm * 2 * p * b_m * len_s Losses = P_Cu + P_Festnom + P_Fesynom + P_ad + P_Ftm + P_Ferynom gen_eff = (P_mech - Losses) / (P_mech) I_snom = gen_eff * (P_mech / m / E_p / cofi) # rated current I_qnom = gen_eff * P_mech / (m * E_p) X_snom = om_e * (L_m + L_ssigma) T_e = np.pi * rad_ag ** 2 * len_s * 2 * sigma Stator = M_Fesy + M_Fest + Copper # modified mass_stru_steel Rotor = M_Fery + mass_PM # modified (N_r*(R_1-self.R_sh)*a_r*self.rho_Fes)) Mass_tooth_stator = M_Fest + Copper Mass_yoke_rotor = M_Fery Mass_yoke_stator = M_Fesy R_out = (dia + 2 * h_m + 2 * h_yr + 2 * inputs["h_sr"]) * 0.5 Losses = Losses generator_efficiency = gen_eff else: # Bad design for k in outputs.keys(): outputs[k] = 1e30 return ######################## Rotor inactive (structural) design ################################### # Radial deformation of rotor R = rad_ag + h_m L_r = len_s + t_r + 0.125 constants_x_0 = shell_constant(R, t_r, L_r, 0, E, v) constants_x_L = shell_constant(R, t_r, L_r, L_r, E, v) f_d_denom1 = R / (E * ((R) ** 2 - (R_sh) ** 2)) * ((1 - v) * R ** 2 + (1 + v) * (R_sh) ** 2) f_d_denom2 = ( t_r / (2 * constants_x_0[0] * (constants_x_0[1]) ** 3) * ( constants_x_0[2] / (2 * constants_x_0[3]) * constants_x_0[4] - constants_x_0[5] / constants_x_0[3] * constants_x_0[6] - 0.5 * constants_x_0[7] ) ) f = q * (R) ** 2 * t_r / (E * (h_yr + h_sr) * (f_d_denom1 + f_d_denom2)) u_d = ( f / (constants_x_L[0] * (constants_x_L[1]) ** 3) * ( ( constants_x_L[2] / (2 * constants_x_L[3]) * constants_x_L[4] - constants_x_L[5] / constants_x_L[3] * constants_x_L[6] - 0.5 * constants_x_L[7] ) ) + y_sh ) u_ar = (q * (R) ** 2) / (E * (h_yr + h_sr)) - u_d u_ar = np.abs(u_ar + y_sh) u_allow_r = 2 * rad_ag / 1000 * inputs["u_allow_pcent"] / 100 # axial deformation of rotor W_back_iron = plate_constant(R + h_sr + h_yr, R_sh, E, v, 0.5 * h_yr + R, t_r) W_ssteel = plate_constant(R + h_sr + h_yr, R_sh, E, v, h_yr + R + h_sr * 0.5, t_r) W_mag = plate_constant(R + h_sr + h_yr, R_sh, E, v, h_yr + R - 0.5 * h_m, t_r) W_ir = rho_Fe * gravity * np.sin(phi) * (L_r - t_r) * h_yr y_ai1r = ( -W_ir * (0.5 * h_yr + R) ** 4 / (R_sh * W_back_iron[0]) * (W_back_iron[1] * W_back_iron[4] / W_back_iron[3] - W_back_iron[2]) ) W_sr = rho_Fes * gravity * np.sin(phi) * (L_r - t_r) * h_sr y_ai2r = ( -W_sr * (h_sr * 0.5 + h_yr + R) ** 4 / (R_sh * W_ssteel[0]) * (W_ssteel[1] * W_ssteel[4] / W_ssteel[3] - W_ssteel[2]) ) W_m = np.sin(phi) * mass_PM / (2 * np.pi * (R - h_m * 0.5)) y_ai3r = -W_m * (R - h_m) ** 4 / (R_sh * W_mag[0]) * (W_mag[1] * W_mag[4] / W_mag[3] - W_mag[2]) w_disc_r = rho_Fes * gravity * np.sin(phi) * t_r a_ii = R + h_sr + h_yr r_oii = R_sh M_rb = ( -w_disc_r * a_ii ** 2 / W_ssteel[5] * (W_ssteel[6] * 0.5 / (a_ii * R_sh) * (a_ii ** 2 - r_oii ** 2) - W_ssteel[8]) ) Q_b = w_disc_r * 0.5 / R_sh * (a_ii ** 2 - r_oii ** 2) y_aiir = ( M_rb * a_ii ** 2 / W_ssteel[0] * W_ssteel[1] + Q_b * a_ii ** 3 / W_ssteel[0] * W_ssteel[2] - w_disc_r * a_ii ** 4 / W_ssteel[0] * W_ssteel[7] ) I = np.pi * 0.25 * (R ** 4 - (R_sh) ** 4) F_ecc = q * 2 * np.pi * K_rad * rad_ag ** 3 M_ar = F_ecc * L_r * 0.5 y_ar = ( np.abs(y_ai1r + y_ai2r + y_ai3r) + y_aiir + (R + h_yr + h_sr) * inputs["theta_sh"] + M_ar * L_r ** 2 * 0 / (2 * E * I) ) y_allow_r = L_r / 100 * inputs["y_allow_pcent"] # Torsional deformation of rotor J_dr = 0.5 * np.pi * ((R + h_yr + h_sr) ** 4 - R_sh ** 4) J_cylr = 0.5 * np.pi * ((R + h_yr + h_sr) ** 4 - R ** 4) twist_r = 180 / np.pi * inputs["rated_torque"] / G * (t_r / J_dr + (L_r - t_r) / J_cylr) Structural_mass_rotor = ( rho_Fes * np.pi * (((R + h_yr + h_sr) ** 2 - (R_sh) ** 2) * t_r + ((R + h_yr + h_sr) ** 2 - (R + h_yr) ** 2) * len_s) ) TC1 = inputs["rated_torque"] / (2 * np.pi * sigma) TC2r = (R + (h_yr + h_sr)) ** 2 * L_r ######################## Stator inactive (structural) design ################################### # Radial deformation of Stator L_stator = len_s + t_s + 0.1 R_stator = rad_ag - len_ag - h_t - h_ys - h_ss constants_x_0 = shell_constant(R_stator, t_s, L_stator, 0, E, v) constants_x_L = shell_constant(R_stator, t_s, L_stator, L_stator, E, v) f_d_denom1 = ( R_stator / (E * ((R_stator) ** 2 - (R_no) ** 2)) * ((1 - v) * R_stator ** 2 + (1 + v) * (R_no) ** 2) ) f_d_denom2 = ( t_s / (2 * constants_x_0[0] * (constants_x_0[1]) ** 3) * ( constants_x_0[2] / (2 * constants_x_0[3]) * constants_x_0[4] - constants_x_0[5] / constants_x_0[3] * constants_x_0[6] - 0.5 * constants_x_0[7] ) ) f = q * (R_stator) ** 2 * t_s / (E * (h_ys + h_ss) * (f_d_denom1 + f_d_denom2)) # TODO: Adds y_bd twice? u_as = ( (q * (R_stator) ** 2) / (E * (h_ys + h_ss)) - f * 0 / (constants_x_L[0] * (constants_x_L[1]) ** 3) * ( ( constants_x_L[2] / (2 * constants_x_L[3]) * constants_x_L[4] - constants_x_L[5] / constants_x_L[3] * constants_x_L[6] - 1 / 2 * constants_x_L[7] ) ) + y_bd ) u_as = np.abs(u_as + y_bd) u_allow_s = 2 * rad_ag / 1000 * inputs["u_allow_pcent"] / 100 # axial deformation of stator W_back_iron = plate_constant(R_stator + h_ss + h_ys + h_t, R_no, E, v, 0.5 * h_ys + h_ss + R_stator, t_s) W_ssteel = plate_constant(R_stator + h_ss + h_ys + h_t, R_no, E, v, R_stator + h_ss * 0.5, t_s) W_active = plate_constant(R_stator + h_ss + h_ys + h_t, R_no, E, v, R_stator + h_ss + h_ys + h_t * 0.5, t_s) W_is = rho_Fe * gravity * np.sin(phi) * (L_stator - t_s) * h_ys y_ai1s = ( -W_is * (0.5 * h_ys + R_stator) ** 4 / (R_no * W_back_iron[0]) * (W_back_iron[1] * W_back_iron[4] / W_back_iron[3] - W_back_iron[2]) ) W_ss = rho_Fes * gravity * np.sin(phi) * (L_stator - t_s) * h_ss y_ai2s = ( -W_ss * (h_ss * 0.5 + h_ys + R_stator) ** 4 / (R_no * W_ssteel[0]) * (W_ssteel[1] * W_ssteel[4] / W_ssteel[3] - W_ssteel[2]) ) W_cu = np.sin(phi) * Mass_tooth_stator / (2 * np.pi * (R_stator + h_ss + h_ys + h_t * 0.5)) y_ai3s = ( -W_cu * (R_stator + h_ss + h_ys + h_t * 0.5) ** 4 / (R_no * W_active[0]) * (W_active[1] * W_active[4] / W_active[3] - W_active[2]) ) w_disc_s = rho_Fes * gravity * np.sin(phi) * t_s a_ii = R_stator + h_ss + h_ys + h_t r_oii = R_no M_rb = ( -w_disc_s * a_ii ** 2 / W_ssteel[5] * (W_ssteel[6] * 0.5 / (a_ii * R_no) * (a_ii ** 2 - r_oii ** 2) - W_ssteel[8]) ) Q_b = w_disc_s * 0.5 / R_no * (a_ii ** 2 - r_oii ** 2) y_aiis = ( M_rb * a_ii ** 2 / W_ssteel[0] * W_ssteel[1] + Q_b * a_ii ** 3 / W_ssteel[0] * W_ssteel[2] - w_disc_s * a_ii ** 4 / W_ssteel[0] * W_ssteel[7] ) I = np.pi * 0.25 * (R_stator ** 4 - (R_no) ** 4) F_ecc = q * 2 * np.pi * K_rad * rad_ag ** 2 M_as = F_ecc * L_stator * 0.5 y_as = np.abs( y_ai1s + y_ai2s + y_ai3s + y_aiis + (R_stator + h_ys + h_ss + h_t) * inputs["theta_bd"] ) + M_as * L_stator ** 2 * 0 / (2 * E * I) y_allow_s = L_stator * inputs["y_allow_pcent"] / 100 # Torsional deformation of stator J_ds = 0.5 * np.pi * ((R_stator + h_ys + h_ss + h_t) ** 4 - R_no ** 4) J_cyls = 0.5 * np.pi * ((R_stator + h_ys + h_ss + h_t) ** 4 - R_stator ** 4) twist_s = 180.0 / np.pi * inputs["rated_torque"] / G * (t_s / J_ds + (L_stator - t_s) / J_cyls) Structural_mass_stator = rho_Fes * ( np.pi * ((R_stator + h_ys + h_ss + h_t) ** 2 - (R_no) ** 2) * t_s + np.pi * ((R_stator + h_ss) ** 2 - R_stator ** 2) * len_s ) TC2s = (R_stator + h_ys + h_ss + h_t) ** 2 * L_stator ######################## Outputs ################################### outputs["K_rad"] = K_rad outputs["len_ag"] = len_ag outputs["tau_p"] = tau_p outputs["S"] = S outputs["tau_s"] = tau_s outputs["b_m"] = b_m outputs["f"] = freq outputs["B_pm1"] = B_pm1 outputs["B_g"] = B_g outputs["B_symax"] = B_symax outputs["B_rymax"] = B_rymax outputs["b_t"] = b_t outputs["q"] = q outputs["N_s"] = N_s[-1] outputs["A_Cuscalc"] = A_Cuscalc outputs["b_s"] = b_s outputs["L_s"] = L_s outputs["J_s"] = J_s outputs["Slot_aspect_ratio"] = h_s / b_s outputs["I_s"] = I_s outputs["A_1"] = A_1 outputs["J_actual"] = J_actual outputs["R_s"] = R_s outputs["B_smax"] = B_smax[-1] outputs["h_t"] = h_t outputs["Copper"] = Copper outputs["Iron"] = Iron outputs["mass_PM"] = mass_PM outputs["T_e"] = T_e outputs["Mass_tooth_stator"] = Mass_tooth_stator outputs["Mass_yoke_rotor"] = Mass_yoke_rotor outputs["Mass_yoke_stator"] = Mass_yoke_stator outputs["R_out"] = R_out outputs["Losses"] = Losses outputs["eandm_efficiency"] = np.maximum(eps, gen_eff) outputs["u_ar"] = u_ar outputs["u_allow_r"] = u_allow_r outputs["y_ar"] = y_ar outputs["y_allow_r"] = y_allow_r outputs["twist_r"] = twist_r outputs["Structural_mass_rotor"] = Structural_mass_rotor outputs["TC1"] = TC1 outputs["TC2r"] = TC2r outputs["u_as"] = u_as outputs["u_allow_s"] = u_allow_s outputs["y_as"] = y_as outputs["y_allow_s"] = y_allow_s outputs["twist_s"] = twist_s outputs["Structural_mass_stator"] = Structural_mass_stator outputs["TC2s"] = TC2s outputs["Structural_mass"] = outputs["Structural_mass_rotor"] + outputs["Structural_mass_stator"] outputs["stator_mass"] = Stator + outputs["Structural_mass_stator"] outputs["rotor_mass"] = Rotor + outputs["Structural_mass_rotor"] outputs["generator_mass"] = Stator + Rotor + outputs["Structural_mass"] # ---------------------------------------------------------------------------------------- class PMSG_Disc(GeneratorBase): """ Estimates overall mass dimensions and Efficiency of PMSG-disc rotor generator. Parameters ---------- tau_p : float, [m] Pole pitch self.tau_p t_d : float, [m] disc thickness h_yr : float, [m] rotor yoke height h_ys : float, [m] Yoke height Returns ------- B_tmax : float, [T] Peak Teeth flux density B_smax : float, [T] Peak Stator Yoke flux density B_ymax B_symax : float, [T] Peak Stator Yoke flux density B_ymax E_p : float Stator phase voltage """ def initialize(self): super(PMSG_Disc, self).initialize() def setup(self): super(PMSG_Disc, self).setup() self.add_input("tau_p", val=0.0, units="m") self.add_input("t_d", val=0.0, units="m") self.add_input("h_yr", val=0.0, units="m") self.add_input("h_ys", val=0.0, units="m") self.add_output("B_tmax", val=0.0, units="T") self.add_output("B_smax", val=0.0, units="T") self.add_output("B_symax", val=0.0, units="T") self.add_output("E_p", val=np.zeros(self.options["n_pc"])) def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs rad_ag = inputs["rad_ag"] len_s = inputs["len_s"] h_s = inputs["h_s"] tau_p = inputs["tau_p"] h_m = inputs["h_m"] h_ys = inputs["h_ys"] h_yr = inputs["h_yr"] machine_rating = inputs["machine_rating"] shaft_rpm = inputs["shaft_rpm"] Torque = inputs["rated_torque"] b_st = inputs["b_st"] d_s = inputs["d_s"] t_ws = inputs["t_ws"] n_s = inputs["n_s"] t_d = inputs["t_d"] R_sh = 0.5 * inputs["D_shaft"] rho_Fe = inputs["rho_Fe"] rho_Copper = inputs["rho_Copper"] rho_Fes = inputs["rho_Fes"] rho_PM = inputs["rho_PM"] # Grab constant values B_r = inputs["B_r"] E = inputs["E"] P_Fe0e = inputs["P_Fe0e"] P_Fe0h = inputs["P_Fe0h"] S_N = inputs["S_N"] alpha_p = inputs["alpha_p"] b_r_tau_r = inputs["b_r_tau_r"] b_ro = inputs["b_ro"] b_s_tau_s = inputs["b_s_tau_s"] b_so = inputs["b_so"] cofi = inputs["cofi"] freq = inputs["freq"] h_i = inputs["h_i"] h_sy0 = inputs["h_sy0"] h_w = inputs["h_w"] k_fes = inputs["k_fes"] k_fillr = inputs["k_fillr"] k_fills = inputs["k_fills"] k_s = inputs["k_s"] m = discrete_inputs["m"] mu_0 = inputs["mu_0"] mu_r = inputs["mu_r"] p = inputs["p"] phi = inputs["phi"] q1 = discrete_inputs["q1"] ratio_mw2pp = inputs["ratio_mw2pp"] resist_Cu = inputs["resist_Cu"] sigma = inputs["sigma"] v = inputs["v"] y_tau_p = inputs["y_tau_p"] y_tau_pr = inputs["y_tau_pr"] """ # Assign values to universal constants B_r = 1.2 # remnant flux density (Tesla = kg / (s^2 A)) E = 2e11 # N / m^2 young's modulus sigma = 40000.0 # shear stress assumed ratio_mw2pp = 0.7 # ratio of magnet width to pole pitch(bm / self.tau_p) mu_0 = np.pi * 4e-7 # permeability of free space in m * kg / (s**2 * A**2) mu_r = 1.06 # relative permeability (probably for neodymium magnets, often given as 1.05 - GNS) phi = np.deg2rad(90) # tilt angle (rotor tilt -90 degrees during transportation) cofi = 0.85 # power factor # Assign values to design constants h_w = 0.005 # wedge height y_tau_p = 1.0 # coil span to pole pitch m = 3 # no of phases q1 = 1 # no of slots per pole per phase b_s_tau_s = 0.45 # slot width / slot pitch ratio k_fills = 0.65 # Slot fill factor P_Fe0h = 4.0 # specific hysteresis losses W / kg @ 1.5 T P_Fe0e = 1.0 # specific hysteresis losses W / kg @ 1.5 T resist_Cu = 1.8e-8 * 1.4 # resistivity of copper b_so = 0.004 # stator slot opening k_fes = 0.9 # useful iron stack length #T = Torque v = 0.3 # poisson's ratio """ # back iron thickness for rotor and stator t_s = h_ys t = h_yr # Aspect ratio K_rad = len_s / (2 * rad_ag) # aspect ratio ###################################################### Electromagnetic design############################################# dia_ag = 2 * rad_ag # air gap diameter len_ag = 0.001 * dia_ag # air gap length b_m = ratio_mw2pp * tau_p # magnet width l_u = k_fes * len_s # useful iron stack length l_e = len_s + 2 * 0.001 * rad_ag # equivalent core length r_r = rad_ag - len_ag # rotor radius p = np.round(np.pi * rad_ag / tau_p) # pole pairs Eq.(11) f = p * shaft_rpm / 60.0 # rpm to frequency (Hz) S = 2 * p * q1 * m # Stator slots Eq.(12) N_conductors = S * 2 N_s = N_conductors / 2 / m # Stator turns per phase tau_s = np.pi * dia_ag / S # slot pitch Eq.(13) b_s = b_s_tau_s * tau_s # slot width b_t = tau_s - b_s # tooth width Eq.(14) Slot_aspect_ratio = h_s / b_s alpha_p = np.pi / 2 * 0.7 # Calculating Carter factor for stator and effective air gap length gamma = ( 4 / np.pi * ( b_so / 2 / (len_ag + h_m / mu_r) * np.arctan(b_so / 2 / (len_ag + h_m / mu_r)) - np.log(np.sqrt(1 + (b_so / 2 / (len_ag + h_m / mu_r)) ** 2)) ) ) k_C = tau_s / (tau_s - gamma * (len_ag + h_m / mu_r)) # carter coefficient g_eff = k_C * (len_ag + h_m / mu_r) # angular frequency in radians / sec om_m = 2 * np.pi * (shaft_rpm / 60.0) # rpm to rad/s om_e = p * om_m / 2 # Calculating magnetic loading B_pm1 = B_r * h_m / mu_r / g_eff B_g = B_r * h_m / mu_r / g_eff * (4.0 / np.pi) * np.sin(alpha_p) B_symax = B_g * b_m * l_e / (2 * h_ys * l_u) B_rymax = B_g * b_m * l_e / (2 * h_yr * len_s) B_tmax = B_g * tau_s / b_t k_wd = np.sin(np.pi / 6) / q1 / np.sin(np.pi / 6 / q1) # winding factor L_t = len_s + 2 * tau_p # Stator winding length, cross-section and resistance l_Cus = 2 * N_s * (2 * tau_p + L_t) A_s = b_s * (h_s - h_w) * q1 * p # m^2 A_scalc = b_s * 1e3 * (h_s - h_w) * 1e3 * q1 * p # mm^2 A_Cus = A_s * k_fills / N_s A_Cuscalc = A_scalc * k_fills / N_s R_s = l_Cus * resist_Cu / A_Cus # Calculating leakage inductance in stator L_m = 2 * mu_0 * N_s ** 2 / p * m * k_wd ** 2 * tau_p * L_t / np.pi ** 2 / g_eff L_ssigmas = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * ((h_s - h_w) / (3 * b_s) + h_w / b_so) ) # slot leakage inductance L_ssigmaew = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * 0.34 * len_ag * (l_e - 0.64 * tau_p * y_tau_p) / len_s ) # end winding leakage inductance L_ssigmag = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * (5 * (len_ag * k_C / b_so) / (5 + 4 * (len_ag * k_C / b_so))) ) # tooth tip leakage inductance L_ssigma = L_ssigmas + L_ssigmaew + L_ssigmag L_s = L_m + L_ssigma # Calculating no-load voltage induced in the stator and stator current E_p = np.sqrt(2) * N_s * L_t * rad_ag * k_wd * om_m * B_g Z = machine_rating / (m * E_p) G = np.maximum(0.0, E_p ** 2 - (om_e * L_s * Z) ** 2) # Calculating stator current and electrical loading I_s = np.sqrt(Z ** 2 + (((E_p - G ** 0.5) / (om_e * L_s) ** 2) ** 2)) B_smax = np.sqrt(2) * I_s * mu_0 / g_eff J_s = I_s / A_Cuscalc A_1 = 6 * N_s * I_s / (np.pi * dia_ag) I_snom = machine_rating / (m * E_p * cofi) # rated current I_qnom = machine_rating / (m * E_p) X_snom = om_e * (L_m + L_ssigma) # Calculating electromagnetically active mass V_Cus = m * l_Cus * A_Cus # copper volume V_Fest = L_t * 2 * p * q1 * m * b_t * h_s # volume of iron in stator tooth V_Fesy = L_t * np.pi * ((rad_ag + h_s + h_ys) ** 2 - (rad_ag + h_s) ** 2) # volume of iron in stator yoke V_Fery = L_t * np.pi * ((r_r - h_m) ** 2 - (r_r - h_m - h_yr) ** 2) # volume of iron in rotor yoke Copper = V_Cus * rho_Copper M_Fest = V_Fest * rho_Fe # mass of stator tooth M_Fesy = V_Fesy * rho_Fe # mass of stator yoke M_Fery = V_Fery * rho_Fe # mass of rotor yoke Iron = M_Fest + M_Fesy + M_Fery # Calculating losses # 1.Copper losses K_R = 1.2 # Skin effect correction co - efficient P_Cu = m * I_snom ** 2 * R_s * K_R # Iron Losses ( from Hysteresis and eddy currents) P_Hyys = M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator yoke P_Ftys = ( M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator yoke P_Fesynom = P_Hyys + P_Ftys P_Hyd = M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator teeth P_Ftd = ( M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator teeth P_Festnom = P_Hyd + P_Ftd P_ad = 0.2 * (P_Hyys + P_Ftys + P_Hyd + P_Ftd) # additional stray losses due to leakage flux pFtm = 300 # specific magnet loss P_Ftm = pFtm * 2 * p * b_m * len_s # magnet losses Losses = P_Cu + P_Festnom + P_Fesynom + P_ad + P_Ftm gen_eff = machine_rating / (machine_rating + Losses) ################################################## Structural Design ############################################################ ## Structural deflection calculations # rotor structure R = rad_ag - len_ag - h_m - 0.5 * t # mean radius of the rotor rim # l = L_t using L_t everywhere now b = R_sh # Shaft radius (not used) R_b = R - 0.5 * t # Inner radius of the rotor R_a = R + 0.5 * h_yr # Outer radius of rotor yoke a = R - 0.5 * t # same as R_b a_1 = R_b # same as R_b, a c = R / 500 u_allow_r = c / 20 # allowable radial deflection y_allow = 2 * L_t / 100 # allowable axial deflection R_1 = R - 0.5 * t # inner radius of rotor cylinder # same as R_b, a, a_1 (not used) K = 4 * (np.sin(ratio_mw2pp * np.pi / 2)) / np.pi # (not used) q3 = B_g ** 2 / (2 * mu_0) # normal component of Maxwell's stress mass_PM = 2 * np.pi * (R + 0.5 * t) * L_t * h_m * ratio_mw2pp * rho_PM # magnet mass mass_st_lam = rho_Fe * 2 * np.pi * R * L_t * h_yr # mass of rotor yoke steel # Calculation of radial deflection of rotor # cylindrical shell function and circular plate parameters for disc rotor based on Table 11.2 Roark's formulas # lamb, C* and F* parameters are from Appendix A of McDonald lamb = (3 * (1 - v ** 2) / R_a ** 2 / h_yr ** 2) ** 0.25 # m^-1 x1 = lamb * L_t # no units # ---------------- C_2 = chsPshc(x1) C_4 = chsMshc(x1) C_13 = chsMshc(x1) # (not used) C_a2 = chsPshc(x1 * 0.5) F_2_x0 = chsPshc(lamb * 0) F_2_ls2 = chsPshc(x1 / 2) F_a4_x0 = chsMshc(lamb * (0)) Fa4arg = np.pi / 180 * lamb * (0.5 * len_s - a) F_a4_ls2 = chsMshc(Fa4arg) # print('pmsg_disc: F_a4_ls2, Fa4arg, lamb, len_s, a ', F_a4_ls2, Fa4arg, lamb, len_s, a) # if np.isnan(F_a4_ls2): # sys.stderr.write('*** pmsg_discSE error: F_a4_ls2 is nan\n') # C_2 = np.cosh(x1) * np.sin(x1) + np.sinh(x1) * np.cos(x1) C_3 = np.sinh(x1) * np.sin(x1) # C_4 = np.cosh(x1) * np.sin(x1) - np.sinh(x1) * np.cos(x1) C_11 = (np.sinh(x1)) ** 2 - (np.sin(x1)) ** 2 # C_13 = np.cosh(x1) * np.sinh(x1) - np.cos(x1) * np.sin(x1) # (not used) C_14 = np.sinh(x1) ** 2 + np.sin(x1) ** 2 # (not used) C_a1 = np.cosh(x1 * 0.5) * np.cos(x1 * 0.5) # C_a2 = np.cosh(x1 * 0.5) * np.sin(x1 * 0.5) + np.sinh(x1 * 0.5) * np.cos(x1 * 0.5) F_1_x0 = np.cosh(lamb * 0) * np.cos(lamb * 0) F_1_ls2 = np.cosh(lamb * 0.5 * len_s) * np.cos(lamb * 0.5 * len_s) # F_2_x0 = np.cosh(lamb * 0) * np.sin(lamb * 0) + np.sinh(lamb * 0) * np.cos(lamb * 0) # F_2_ls2 = np.cosh(x1 / 2) * np.sin(x1 / 2) + np.sinh(x1 / 2) * np.cos(x1 / 2) if len_s < 2 * a: a = len_s / 2 else: a = len_s * 0.5 - 1 # F_a4_x0 = np.cosh(lamb * (0)) * np.sin(lamb * (0)) \ # - np.sinh(lamb * (0)) * np.cos(lamb * (0)) # F_a4_ls2 = np.cosh(np.pi / 180 * lamb * (0.5 * len_s - a)) * np.sin(np.pi / 180 * lamb * (0.5 * len_s - a)) \ # - np.sinh(np.pi / 180 * lamb * (0.5 * len_s - a)) * np.cos(np.pi / 180 * lamb * (0.5 * len_s - a)) """ Where did the np.pi/180 factor (conversion to radians) come from? lamb is m^-1 0.5*len_s - a is m """ # ---------------- D_r = E * h_yr ** 3 / (12 * (1 - v ** 2)) D_ax = E * t_d ** 3 / (12 * (1 - v ** 2)) # Radial deflection analytical model from McDonald's thesis defined in parts Part_1 = R_b * ((1 - v) * R_b ** 2 + (1 + v) * R_sh ** 2) / (R_b ** 2 - R_sh ** 2) / E Part_2 = (C_2 * C_a2 - 2 * C_3 * C_a1) / 2 / C_11 Part_3 = (C_3 * C_a2 - C_4 * C_a1) / C_11 Part_4 = 0.25 / D_r / lamb ** 3 Part_5 = q3 * R_b ** 2 / (E * (R_a - R_b)) f_d = Part_5 / (Part_1 - t_d * (Part_4 * Part_2 * F_2_ls2 - Part_3 * 2 * Part_4 * F_1_ls2 - Part_4 * F_a4_ls2)) fr = f_d * t_d u_ar = abs( Part_5 + fr / (2 * D_r * lamb ** 3) * ( (-F_1_x0 / C_11) * (C_3 * C_a2 - C_4 * C_a1) + (F_2_x0 / 2 / C_11) * (C_2 * C_a2 - 2 * C_3 * C_a1) - F_a4_x0 / 2 ) ) # Calculation of Axial deflection of rotor W = ( 0.5 * gravity * np.sin(phi) * ((L_t - t_d) * h_yr * rho_Fes) ) # uniform annular line load acting on rotor cylinder assumed as an annular plate w = rho_Fes * gravity * np.sin(phi) * t_d # disc assumed as plate with a uniformly distributed pressure between a_i = R_sh # Flat circular plate constants according to Roark's table 11.2 C_2p = 0.25 * (1 - (((R_sh / R) ** 2) * (1 + (2 * np.log(R / R_sh))))) C_3p = (R_sh / 4 / R) * ((1 + (R_sh / R) ** 2) * np.log(R / R_sh) + (R_sh / R) ** 2 - 1) C_6 = (R_sh / 4 / R_a) * ((R_sh / R_a) ** 2 - 1 + 2 * np.log(R_a / R_sh)) C_5 = 0.5 * (1 - (R_sh / R) ** 2) C_8 = 0.5 * (1 + v + (1 - v) * ((R_sh / R) ** 2)) C_9 = (R_sh / R) * (0.5 * (1 + v) * np.log(R / R_sh) + (1 - v) / 4 * (1 - (R_sh / R) ** 2)) # Flat circular plate loading constants L_11 = ( 1 + 4 * (R_sh / a_1) ** 2 - 5 * (R_sh / a_1) ** 4 - 4 * ((R_sh / a_1) ** 2) * np.log(a_1 / R_sh) * (2 + (R_sh / a_1) ** 2) ) / 64 L_14 = (1 - (R_sh / R_b) ** 4 - 4 * (R_sh / R_b) ** 2 * np.log(R_b / R_sh)) / 16 y_ai = ( -W * (a_1 ** 3) * (C_2p * (C_6 * a_1 / R_sh - C_6) / C_5 - a_1 * C_3p / R_sh + C_3p) / D_ax ) # Axial deflection of plate due to deflection of an annular plate with a uniform annular line load # Axial Deflection due to uniformaly distributed pressure load M_rb = -w * R ** 2 * (C_6 * (R ** 2 - R_sh ** 2) * 0.5 / R / R_sh - L_14) / C_5 Q_b = w * 0.5 * (R ** 2 - R_sh ** 2) / R_sh y_aii = M_rb * R_a ** 2 * C_2p / D_ax + Q_b * R_a ** 3 * C_3p / D_ax - w * R_a ** 4 * L_11 / D_ax y_ar = abs(y_ai + y_aii) z_allow_r = np.deg2rad(0.05 * R) # allowable torsional deflection of rotor # stator structure deflection calculation R_out = R / 0.995 + h_s + h_ys a_s = (b_st * d_s) - ((b_st - 2 * t_ws) * (d_s - 2 * t_ws)) # cross-sectional area of stator armms A_st = L_t * t_s # cross-sectional area of rotor cylinder N_st = np.round(n_s) theta_s = np.pi * 1 / N_st # half angle between spokes I_st = L_t * t_s ** 3 / 12 # second moment of area of stator cylinder I_arm_axi_s = ( (b_st * d_s ** 3) - ((b_st - 2 * t_ws) * (d_s - 2 * t_ws) ** 3) ) / 12 # second moment of area of stator arm I_arm_tor_s = ( (d_s * b_st ** 3) - ((d_s - 2 * t_ws) * (b_st - 2 * t_ws) ** 3) ) / 12 # second moment of area of rotot arm w.r.t torsion R_st = rad_ag + h_s + h_ys * 0.5 k_2 = np.sqrt(I_st / A_st) # radius of gyration b_allow_s = 2 * np.pi * R_sh / N_st m2 = (k_2 / R_st) ** 2 c1 = R_st / 500 R_1s = R_st - t_s * 0.5 d_se = dia_ag + 2 * (h_ys + h_s + h_w) # stator outer diameter # Calculation of radial deflection of stator Numers = R_st ** 3 * ( (0.25 * (np.sin(theta_s) - (theta_s * np.cos(theta_s))) / (np.sin(theta_s)) ** 2) - (0.5 / np.sin(theta_s)) + (0.5 / theta_s) ) Povs = ((theta_s / (np.sin(theta_s)) ** 2) + 1 / np.tan(theta_s)) * ( (0.25 * R_st / A_st) + (0.25 * R_st ** 3 / I_st) ) Qovs = R_st ** 3 / (2 * I_st * theta_s * (m2 + 1)) Lovs = (R_1s - R_sh) * 0.5 / a_s Denoms = I_st * (Povs - Qovs + Lovs) u_as = (q3 * R_st ** 2 / E / t_s) * (1 + Numers / Denoms) # Calculation of axial deflection of stator mass_st_lam_s = M_Fest + np.pi * L_t * rho_Fe * ((R_st + 0.5 * h_ys) ** 2 - (R_st - 0.5 * h_ys) ** 2) W_is = ( 0.5 * gravity * np.sin(phi) * (rho_Fes * L_t * d_s ** 2) ) # length of stator arm beam at which self-weight acts W_iis = ( gravity * np.sin(phi) * (mass_st_lam_s + V_Cus * rho_Copper) / 2 / N_st ) # weight of stator cylinder and teeth w_s = rho_Fes * gravity * np.sin(phi) * a_s * N_st # uniformly distributed load of the arms l_is = R_st - R_sh # distance at which the weight of the stator cylinder acts l_iis = l_is # distance at which the weight of the stator cylinder acts l_iiis = l_is # distance at which the weight of the stator cylinder acts u_allow_s = c1 / 20 X_comp1 = ( W_is * l_is ** 3 / 12 / E / I_arm_axi_s ) # deflection component due to stator arm beam at which self-weight acts X_comp2 = W_iis * l_iis ** 4 / 24 / E / I_arm_axi_s # deflection component due to 1/nth of stator cylinder X_comp3 = w_s * l_iiis ** 4 / 24 / E / I_arm_axi_s # deflection component due to weight of arms y_as = X_comp1 + X_comp2 + X_comp3 # axial deflection # Stator circumferential deflection z_allow_s = np.deg2rad(0.05 * R_st) # allowable torsional deflection z_as = ( 2 * np.pi * (R_st + 0.5 * t_s) * L_t / (2 * N_st) * sigma * (l_is + 0.5 * t_s) ** 3 / (3 * E * I_arm_tor_s) ) mass_stru_steel = 2 * (N_st * (R_1s - R_sh) * a_s * rho_Fes) TC1 = Torque * 1.0 / (2 * np.pi * sigma) # Torque / shear stress TC2r = R ** 2 * L_t # Evaluating Torque constraint for rotor TC2s = R_st ** 2 * L_t # Evaluating Torque constraint for stator Structural_mass = mass_stru_steel + (np.pi * (R ** 2 - R_sh ** 2) * t_d * rho_Fes) Mass = Structural_mass + Iron + Copper + mass_PM outputs["B_tmax"] = B_tmax outputs["B_rymax"] = B_rymax outputs["B_symax"] = B_symax outputs["B_smax"] = B_smax[-1] outputs["B_pm1"] = B_pm1 outputs["B_g"] = B_g outputs["N_s"] = N_s outputs["b_s"] = b_s outputs["b_t"] = b_t outputs["A_Cuscalc"] = A_Cuscalc outputs["b_m"] = b_m outputs["E_p"] = E_p outputs["f"] = f outputs["I_s"] = I_s outputs["R_s"] = R_s outputs["L_s"] = L_s outputs["A_1"] = A_1 outputs["J_s"] = J_s outputs["Losses"] = Losses outputs["K_rad"] = K_rad outputs["eandm_efficiency"] = np.maximum(eps, gen_eff) outputs["S"] = S outputs["Slot_aspect_ratio"] = Slot_aspect_ratio outputs["Copper"] = Copper outputs["Iron"] = Iron outputs["u_ar"] = u_ar outputs["y_ar"] = y_ar outputs["u_as"] = u_as outputs["y_as"] = y_as outputs["z_as"] = z_as outputs["u_allow_r"] = u_allow_r outputs["u_allow_s"] = u_allow_s outputs["y_allow_r"] = outputs["y_allow_s"] = y_allow outputs["z_allow_s"] = z_allow_s outputs["z_allow_r"] = z_allow_r outputs["b_allow_s"] = b_allow_s outputs["TC1"] = TC1 outputs["TC2r"] = TC2r outputs["TC2s"] = TC2s outputs["R_out"] = R_out outputs["Structural_mass"] = Structural_mass outputs["generator_mass"] = Mass outputs["mass_PM"] = mass_PM # ---------------------------------------------------------------------------------------- class PMSG_Arms(GeneratorBase): """ Estimates overall mass dimensions and Efficiency of PMSG-disc rotor generator. Parameters ---------- b_arm : float, [m] arm width tau_p : float, [m] Pole pitch self.tau_p h_yr : float, [m] rotor yoke height h_ys : float, [m] Yoke height Returns ------- B_tmax : float, [T] Peak Teeth flux density B_smax : float, [T] Peak Stator Yoke flux density B_ymax B_symax : float, [T] Peak Stator Yoke flux density B_ymax E_p : float Stator phase voltage """ def initialize(self): super(PMSG_Arms, self).initialize() def setup(self): super(PMSG_Arms, self).setup() self.add_input("b_arm", val=0.0, units="m") self.add_input("tau_p", val=0.0, units="m") self.add_input("h_yr", val=0.0, units="m") self.add_input("h_ys", val=0.0, units="m") self.add_output("B_tmax", val=0.0, units="T") self.add_output("B_smax", val=0.0, units="T") self.add_output("B_symax", val=0.0, units="T") self.add_output("E_p", val=np.zeros(self.options["n_pc"])) def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs # r_s = inputs['r_s'] rad_ag = inputs["rad_ag"] len_s = inputs["len_s"] h_s = inputs["h_s"] tau_p = inputs["tau_p"] h_m = inputs["h_m"] h_ys = inputs["h_ys"] h_yr = inputs["h_yr"] machine_rating = inputs["machine_rating"] shaft_rpm = inputs["shaft_rpm"] Torque = inputs["rated_torque"] b_st = inputs["b_st"] d_s = inputs["d_s"] t_ws = inputs["t_ws"] n_r = inputs["n_r"] n_s = inputs["n_s"] b_r = inputs["b_arm"] d_r = inputs["d_r"] t_wr = inputs["t_wr"] R_sh = 0.5 * inputs["D_shaft"] rho_Fe = inputs["rho_Fe"] rho_Copper = inputs["rho_Copper"] rho_Fes = inputs["rho_Fes"] rho_PM = inputs["rho_PM"] # Grab constant values B_r = inputs["B_r"] E = inputs["E"] P_Fe0e = inputs["P_Fe0e"] P_Fe0h = inputs["P_Fe0h"] S_N = inputs["S_N"] alpha_p = inputs["alpha_p"] b_r_tau_r = inputs["b_r_tau_r"] b_ro = inputs["b_ro"] b_s_tau_s = inputs["b_s_tau_s"] b_so = inputs["b_so"] cofi = inputs["cofi"] freq = inputs["freq"] h_i = inputs["h_i"] h_sy0 = inputs["h_sy0"] h_w = inputs["h_w"] k_fes = inputs["k_fes"] k_fillr = inputs["k_fillr"] k_fills = inputs["k_fills"] k_s = inputs["k_s"] m = discrete_inputs["m"] mu_0 = inputs["mu_0"] mu_r = inputs["mu_r"] p = inputs["p"] phi = inputs["phi"] q1 = discrete_inputs["q1"] ratio_mw2pp = inputs["ratio_mw2pp"] resist_Cu = inputs["resist_Cu"] sigma = inputs["sigma"] v = inputs["v"] y_tau_p = inputs["y_tau_p"] y_tau_pr = inputs["y_tau_pr"] """ # Assign values to universal constants B_r = 1.2 # Tesla remnant flux density E = 2e11 # N / m^2 young's modulus sigma = 40e3 # shear stress assumed (yield strength of ?? steel, in psi - GNS) ratio_mw2pp = 0.7 # ratio of magnet width to pole pitch(bm / tau_p) mu_0 = np.pi * 4e-7 # permeability of free space in m * kg / (s**2 * A**2) mu_r = 1.06 # relative permeability (probably for neodymium magnets, often given as 1.05 - GNS) phi = np.deg2rad(90) # tilt angle (rotor tilt -90 degrees during transportation) cofi = 0.85 # power factor # Assign values to design constants h_w = 0.005 # Slot wedge height h_i = 0.001 # coil insulation thickness y_tau_p = 1 # Coil span to pole pitch m = 3 # no of phases q1 = 1 # no of slots per pole per phase b_s_tau_s = 0.45 # slot width to slot pitch ratio k_fills = 0.65 # Slot fill factor P_Fe0h = 4 # specific hysteresis losses W / kg @ 1.5 T P_Fe0e = 1 # specific eddy losses W / kg @ 1.5 T resist_Cu = 1.8e-8 * 1.4 # Copper resisitivty k_fes = 0.9 # Stator iron fill factor per Grauers b_so = 0.004 # Slot opening alpha_p = np.pi / 2 * 0.7 """ # back iron thickness for rotor and stator t_s = h_ys t = h_yr ###################################################### Electromagnetic design############################################# K_rad = len_s / (2 * rad_ag) # Aspect ratio # T = Torque # rated torque l_u = k_fes * len_s # useful iron stack length We = tau_p l_b = 2 * tau_p # end winding length l_e = len_s + 2 * 0.001 * rad_ag # equivalent core length b_m = 0.7 * tau_p # magnet width # Calculating air gap length dia_ag = 2 * rad_ag # air gap diameter len_ag = 0.001 * dia_ag # air gap length r_m = rad_ag + h_ys + h_s # magnet radius r_r = rad_ag - len_ag # rotor radius p = np.round(np.pi * dia_ag / (2 * tau_p)) # pole pairs f = shaft_rpm * p / 60.0 # outout frequency rpm to Hz S = 2 * p * q1 * m # Stator slots N_conductors = S * 2 N_s = N_conductors / (2 * m) # Stator turns per phase tau_s = np.pi * dia_ag / S # Stator slot pitch b_s = b_s_tau_s * tau_s # slot width b_t = tau_s - b_s # tooth width Slot_aspect_ratio = h_s / b_s # Calculating Carter factor for stator and effective air gap length ahm = len_ag + h_m / mu_r ba = b_so / (2 * ahm) gamma = 4 / np.pi * (ba * np.arctan(ba) - np.log(np.sqrt(1 + ba ** 2))) k_C = tau_s / (tau_s - gamma * ahm) # carter coefficient g_eff = k_C * ahm # angular frequency in radians om_m = 2 * np.pi * shaft_rpm / 60.0 # rpm to radians per second om_e = p * om_m / 2 # electrical output frequency (Hz) # Calculating magnetic loading B_pm1 = B_r * h_m / mu_r / g_eff B_g = B_r * h_m / mu_r / g_eff * (4 / np.pi) * np.sin(alpha_p) B_symax = B_g * b_m * l_e / (2 * h_ys * l_u) B_rymax = B_g * b_m * l_e / (2 * h_yr * len_s) B_tmax = B_g * tau_s / b_t # Calculating winding factor k_wd = np.sin(np.pi / 6) / q1 / np.sin(np.pi / 6 / q1) L_t = len_s + 2 * tau_p # overall stator len w/end windings - should be tau_s??? # l = L_t # length - now using L_t everywhere # Stator winding length, cross-section and resistance l_Cus = 2 * N_s * (2 * tau_p + L_t) A_s = b_s * (h_s - h_w) * q1 * p A_scalc = b_s * 1000 * (h_s - h_w) * 1000 * q1 * p A_Cus = A_s * k_fills / N_s A_Cuscalc = A_scalc * k_fills / N_s R_s = l_Cus * resist_Cu / A_Cus # Calculating leakage inductance in stator L_m = 2 * mu_0 * N_s ** 2 / p * m * k_wd ** 2 * tau_p * L_t / np.pi ** 2 / g_eff L_ssigmas = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * ((h_s - h_w) / (3 * b_s) + h_w / b_so) ) # slot leakage inductance L_ssigmaew = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * 0.34 * len_ag * (l_e - 0.64 * tau_p * y_tau_p) / len_s ) # end winding leakage inductance L_ssigmag = ( 2 * mu_0 * N_s ** 2 / p / q1 * len_s * (5 * (len_ag * k_C / b_so) / (5 + 4 * (len_ag * k_C / b_so))) ) # tooth tip leakage inductance L_ssigma = L_ssigmas + L_ssigmaew + L_ssigmag L_s = L_m + L_ssigma # Calculating no-load voltage induced in the stator E_p = 2 * N_s * L_t * rad_ag * k_wd * om_m * B_g / np.sqrt(2) Z = machine_rating / (m * E_p) G = np.maximum(0.0, E_p ** 2 - (om_e * L_s * Z) ** 2) # Calculating stator current and electrical loading is2 = Z ** 2 + (((E_p - G ** 0.5) / (om_e * L_s) ** 2) ** 2) I_s = np.sqrt(Z ** 2 + (((E_p - G ** 0.5) / (om_e * L_s) ** 2) ** 2)) J_s = I_s / A_Cuscalc A_1 = 6 * N_s * I_s / (np.pi * dia_ag) I_snom = machine_rating / (m * E_p * cofi) # rated current I_qnom = machine_rating / (m * E_p) X_snom = om_e * (L_m + L_ssigma) B_smax = np.sqrt(2) * I_s * mu_0 / g_eff # Calculating Electromagnetically active mass V_Cus = m * l_Cus * A_Cus # copper volume V_Fest = L_t * 2 * p * q1 * m * b_t * h_s # volume of iron in stator tooth V_Fesy = L_t * np.pi * ((rad_ag + h_s + h_ys) ** 2 - (rad_ag + h_s) ** 2) # volume of iron in stator yoke V_Fery = L_t * np.pi * ((r_r - h_m) ** 2 - (r_r - h_m - h_yr) ** 2) Copper = V_Cus * rho_Copper M_Fest = V_Fest * rho_Fe # Mass of stator tooth M_Fesy = V_Fesy * rho_Fe # Mass of stator yoke M_Fery = V_Fery * rho_Fe # Mass of rotor yoke Iron = M_Fest + M_Fesy + M_Fery # Calculating Losses ##1. Copper Losses K_R = 1.2 # Skin effect correction co-efficient P_Cu = m * I_snom ** 2 * R_s * K_R # Iron Losses ( from Hysteresis and eddy currents) P_Hyys = M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator yoke P_Ftys = ( M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator yoke P_Fesynom = P_Hyys + P_Ftys P_Hyd = M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator teeth P_Ftd = ( M_Fest * (B_tmax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator teeth P_Festnom = P_Hyd + P_Ftd # additional stray losses due to leakage flux P_ad = 0.2 * (P_Hyys + P_Ftys + P_Hyd + P_Ftd) pFtm = 300 # specific magnet loss P_Ftm = pFtm * 2 * p * b_m * len_s Losses = P_Cu + P_Festnom + P_Fesynom + P_ad + P_Ftm gen_eff = machine_rating / (machine_rating + Losses) #################################################### Structural Design ############################################################ ## Deflection Calculations ## # rotor structure calculations a_r = (b_r * d_r) - ((b_r - 2 * t_wr) * (d_r - 2 * t_wr)) # cross-sectional area of rotor arms A_r = L_t * t # cross-sectional area of rotor cylinder N_r = np.round(n_r) # rotor arms theta_r = np.pi * 1 / N_r # half angle between spokes I_r = L_t * t ** 3 / 12 # second moment of area of rotor cylinder I_arm_axi_r = ( (b_r * d_r ** 3) - ((b_r - 2 * t_wr) * (d_r - 2 * t_wr) ** 3) ) / 12 # second moment of area of rotor arm I_arm_tor_r = ( (d_r * b_r ** 3) - ((d_r - 2 * t_wr) * (b_r - 2 * t_wr) ** 3) ) / 12 # second moment of area of rotot arm w.r.t torsion R = rad_ag - len_ag - h_m - 0.5 * t # Rotor mean radius c = R / 500 u_allow_r = c / 20 # allowable radial deflection R_1 = R - t * 0.5 # inner radius of rotor cylinder k_1 = np.sqrt(I_r / A_r) # radius of gyration m1 = (k_1 / R) ** 2 l_ir = R # length of rotor arm beam at which rotor cylinder acts l_iir = R_1 b_allow_r = 2 * np.pi * R_sh / N_r # allowable circumferential arm dimension for rotor q3 = B_g ** 2 / 2 / mu_0 # normal component of Maxwell stress mass_PM = 2 * np.pi * (R + 0.5 * t) * L_t * h_m * ratio_mw2pp * rho_PM # magnet mass # Calculating radial deflection of the rotor Numer = R ** 3 * ( (0.25 * (np.sin(theta_r) - (theta_r * np.cos(theta_r))) / (np.sin(theta_r)) ** 2) - (0.5 / np.sin(theta_r)) + (0.5 / theta_r) ) Pov = ((theta_r / (np.sin(theta_r)) ** 2) + 1 / np.tan(theta_r)) * ((0.25 * R / A_r) + (0.25 * R ** 3 / I_r)) Qov = R ** 3 / (2 * I_r * theta_r * (m1 + 1)) Lov = (R_1 - R_sh) / a_r Denom = I_r * (Pov - Qov + Lov) # radial deflection % rotor u_ar = (q3 * R ** 2 / E / t) * (1 + Numer / Denom) # Calculating axial deflection of the rotor under its own weight w_r = rho_Fes * gravity * np.sin(phi) * a_r * N_r # uniformly distributed load of the weight of the rotor arm mass_st_lam = rho_Fe * 2 * np.pi * R * L_t * h_yr # mass of rotor yoke steel W = gravity * np.sin(phi) * (mass_st_lam / N_r + mass_PM / N_r) # weight of 1/nth of rotor cylinder y_a1 = W * l_ir ** 3 / 12 / E / I_arm_axi_r # deflection from weight component of back iron y_a2 = w_r * l_iir ** 4 / 24 / E / I_arm_axi_r # deflection from weight component of the arms y_ar = y_a1 + y_a2 # axial deflection y_allow = 2 * L_t / 100 # allowable axial deflection # Calculating # circumferential deflection of the rotor z_allow_r = np.deg2rad(0.05 * R) # allowable torsional deflection z_ar = ( (2 * np.pi * (R - 0.5 * t) * L_t / N_r) * sigma * (l_ir - 0.5 * t) ** 3 / 3 / E / I_arm_tor_r ) # circumferential deflection val_str_rotor = mass_PM + (mass_st_lam + (N_r * (R_1 - R_sh) * a_r * rho_Fes)) # rotor mass # stator structure deflection calculation a_s = (b_st * d_s) - ((b_st - 2 * t_ws) * (d_s - 2 * t_ws)) # cross-sectional area of stator armms A_st = L_t * t_s # cross-sectional area of stator cylinder N_st = np.round(n_s) # stator arms theta_s = np.pi * 1 / N_st # half angle between spokes I_st = L_t * t_s ** 3 / 12 # second moment of area of stator cylinder k_2 = np.sqrt(I_st / A_st) # radius of gyration I_arm_axi_s = ( (b_st * d_s ** 3) - ((b_st - 2 * t_ws) * (d_s - 2 * t_ws) ** 3) ) / 12 # second moment of area of stator arm I_arm_tor_s = ( (d_s * b_st ** 3) - ((d_s - 2 * t_ws) * (b_st - 2 * t_ws) ** 3) ) / 12 # second moment of area of rotot arm w.r.t torsion R_st = rad_ag + h_s + h_ys * 0.5 # stator cylinder mean radius R_1s = R_st - t_s * 0.5 # inner radius of stator cylinder, m m2 = (k_2 / R_st) ** 2 d_se = dia_ag + 2 * (h_ys + h_s + h_w) # stator outer diameter # allowable radial deflection of stator c1 = R_st / 500 u_allow_s = c1 / 20 R_out = R / 0.995 + h_s + h_ys l_is = R_st - R_sh # distance at which the weight of the stator cylinder acts l_iis = l_is # distance at which the weight of the stator cylinder acts l_iiis = l_is # distance at which the weight of the stator cylinder acts mass_st_lam_s = M_Fest + np.pi * L_t * rho_Fe * ((R_st + 0.5 * h_ys) ** 2 - (R_st - 0.5 * h_ys) ** 2) W_is = ( 0.5 * gravity * np.sin(phi) * (rho_Fes * L_t * d_s ** 2) ) # length of stator arm beam at which self-weight acts W_iis = ( gravity * np.sin(phi) * (mass_st_lam_s + V_Cus * rho_Copper) / 2 / N_st ) # weight of stator cylinder and teeth w_s = rho_Fes * gravity * np.sin(phi) * a_s * N_st # uniformly distributed load of the arms mass_stru_steel = 2 * (N_st * (R_1s - R_sh) * a_s * rho_Fes) # Structural mass of stator arms # Calculating radial deflection of the stator Numers = R_st ** 3 * ( (0.25 * (np.sin(theta_s) - (theta_s * np.cos(theta_s))) / (np.sin(theta_s)) ** 2) - (0.5 / np.sin(theta_s)) + (0.5 / theta_s) ) Povs = ((theta_s / (np.sin(theta_s)) ** 2) + 1 / np.tan(theta_s)) * ( (0.25 * R_st / A_st) + (0.25 * R_st ** 3 / I_st) ) Qovs = R_st ** 3 / (2 * I_st * theta_s * (m2 + 1)) Lovs = (R_1s - R_sh) * 0.5 / a_s Denoms = I_st * (Povs - Qovs + Lovs) u_as = (q3 * R_st ** 2 / E / t_s) * (1 + Numers / Denoms) # Calculating axial deflection of the stator X_comp1 = ( W_is * l_is ** 3 / 12 / E / I_arm_axi_s ) # deflection component due to stator arm beam at which self-weight acts X_comp2 = W_iis * l_iis ** 4 / 24 / E / I_arm_axi_s # deflection component due to 1 / nth of stator cylinder X_comp3 = w_s * l_iiis ** 4 / 24 / E / I_arm_axi_s # deflection component due to weight of arms y_as = X_comp1 + X_comp2 + X_comp3 # axial deflection # Calculating circumferential deflection of the stator z_as = 2 * np.pi * (R_st + 0.5 * t_s) * L_t / (2 * N_st) * sigma * (l_is + 0.5 * t_s) ** 3 / 3 / E / I_arm_tor_s z_allow_s = np.deg2rad(0.05 * R_st) # allowable torsional deflection b_allow_s = 2 * np.pi * R_sh / N_st # allowable circumferential arm dimension val_str_stator = mass_stru_steel + mass_st_lam_s val_str_mass = val_str_rotor + val_str_stator TC1 = Torque / (2 * np.pi * sigma) # Desired shear stress TC2r = R ** 2 * L_t # Evaluating Torque constraint for rotor TC2s = R_st ** 2 * L_t # Evaluating Torque constraint for stator Structural_mass = mass_stru_steel + (N_r * (R_1 - R_sh) * a_r * rho_Fes) Stator = mass_st_lam_s + mass_stru_steel + Copper Rotor = ((2 * np.pi * t * L_t * R * rho_Fe) + (N_r * (R_1 - R_sh) * a_r * rho_Fes)) + mass_PM Mass = Stator + Rotor outputs["B_tmax"] = B_tmax outputs["B_rymax"] = B_rymax outputs["B_symax"] = B_symax outputs["B_smax"] = B_smax[-1] outputs["B_pm1"] = B_pm1 outputs["B_g"] = B_g outputs["N_s"] = N_s outputs["b_s"] = b_s outputs["b_t"] = b_t outputs["A_Cuscalc"] = A_Cuscalc outputs["b_m"] = b_m outputs["E_p"] = E_p outputs["f"] = f outputs["I_s"] = I_s outputs["R_s"] = R_s outputs["L_s"] = L_s outputs["A_1"] = A_1 outputs["J_s"] = J_s outputs["Losses"] = Losses outputs["K_rad"] = K_rad outputs["eandm_efficiency"] = np.maximum(eps, gen_eff) outputs["S"] = S outputs["Slot_aspect_ratio"] = Slot_aspect_ratio outputs["Copper"] = Copper outputs["Iron"] = Iron outputs["u_ar"] = u_ar outputs["y_ar"] = y_ar outputs["z_ar"] = z_ar outputs["u_as"] = u_as outputs["y_as"] = y_as outputs["z_as"] = z_as outputs["u_allow_r"] = u_allow_r outputs["u_allow_s"] = u_allow_s outputs["y_allow_r"] = outputs["y_allow_s"] = y_allow outputs["z_allow_s"] = z_allow_s outputs["z_allow_r"] = z_allow_r outputs["b_allow_s"] = b_allow_s outputs["b_allow_r"] = b_allow_r outputs["TC1"] = TC1 outputs["TC2r"] = TC2r outputs["TC2s"] = TC2s outputs["R_out"] = R_out outputs["Structural_mass"] = Structural_mass outputs["generator_mass"] = Mass outputs["mass_PM"] = mass_PM # ---------------------------------------------------------------------------------------- class DFIG(GeneratorBase): """ Estimates overall mass, dimensions and Efficiency of DFIG generator. Parameters ---------- S_Nmax : float Max rated Slip B_symax : float, [T] Peak Stator Yoke flux density B_ymax Returns ------- N_r : float Rotor turns L_r : float Rotor inductance h_yr : float rotor yoke height h_ys : float Stator Yoke height tau_p : float Pole pitch Current_ratio : float Rotor current ratio E_p : float Stator phase voltage """ def initialize(self): super(DFIG, self).initialize() def setup(self): super(DFIG, self).setup() n_pc = self.options["n_pc"] self.add_input("S_Nmax", val=0.0) self.add_input("B_symax", val=0.0, units="T") self.add_output("N_r", val=0.0) self.add_output("L_r", val=0.0) self.add_output("h_yr", val=0.0) self.add_output("h_ys", val=0.0) self.add_output("tau_p", val=0.0) self.add_output("Current_ratio", val=np.zeros(n_pc)) self.add_output("E_p", val=np.zeros(n_pc)) def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs rad_ag = inputs["rad_ag"] len_s = inputs["len_s"] h_s = inputs["h_s"] h_0 = inputs["h_0"] I_0 = inputs["I_0"] machine_rating = inputs["machine_rating"] shaft_rpm = inputs["shaft_rpm"] rho_Fe = inputs["rho_Fe"] rho_Copper = inputs["rho_Copper"] B_symax = inputs["B_symax"] S_Nmax = inputs["S_Nmax"] # Grab constant values B_r = inputs["B_r"] E = inputs["E"] P_Fe0e = inputs["P_Fe0e"] P_Fe0h = inputs["P_Fe0h"] S_N = inputs["S_N"] alpha_p = inputs["alpha_p"] b_r_tau_r = inputs["b_r_tau_r"] b_ro = inputs["b_ro"] b_s_tau_s = inputs["b_s_tau_s"] b_so = inputs["b_so"] cofi = inputs["cofi"] freq = inputs["freq"] h_i = inputs["h_i"] h_sy0 = inputs["h_sy0"] h_w = inputs["h_w"] k_fes = inputs["k_fes"] k_fillr = inputs["k_fillr"] k_s = inputs["k_s"] m = discrete_inputs["m"] mu_0 = inputs["mu_0"] mu_r = inputs["mu_r"] p = inputs["p"] phi = inputs["phi"] q1 = discrete_inputs["q1"] q2 = q1 - 1 # Rotor slots per pole per phase ratio_mw2pp = inputs["ratio_mw2pp"] resist_Cu = inputs["resist_Cu"] sigma = inputs["sigma"] v = inputs["v"] y_tau_p = inputs["y_tau_p"] y_tau_pr = inputs["y_tau_pr"] """ #Assign values to universal constants sigma = 21.5e3 # shear stress in psi (what material? Al, brass, Cu?) ~148e6 Pa mu_0 = np.pi * 4e-7 # permeability of free space in m * kg / (s**2 * A**2) cofi = 0.9 # power factor h_w = 0.005 # wedge height m = 3 # Number of phases resist_Cu = 1.8e-8 * 1.4 # copper resisitivity h_sy0 = 0 #Assign values to design constants b_so = 0.004 # Stator slot opening width b_ro = 0.004 # Rotor slot opening width q1 = 5 # Stator slots per pole per phase b_s_tau_s = 0.45 # Stator slot-width / slot-pitch ratio b_r_tau_r = 0.45 # Rotor slot-width / slot-pitch ratio y_tau_p = 12. / 15 # Stator coil span to pole pitch y_tau_pr = 10. / 12 # Rotor coil span to pole pitch p = 3 # pole pairs freq = 60 # grid frequency in Hz k_fillr = 0.55 # Rotor Slot fill factor P_Fe0h = 4 # specific hysteresis losses W / kg @ 1.5 T P_Fe0e = 1 # specific eddy losses W / kg @ 1.5 T """ K_rs = 1 / (-1 * S_Nmax) # Winding turns ratio between rotor and Stator I_SN = machine_rating / (np.sqrt(3) * 3000) # Rated current I_SN_r = I_SN / K_rs # Stator rated current reduced to rotor # Calculating winding factor for stator and rotor k_y1 = np.sin(np.pi / 2 * y_tau_p) # winding chording factor k_q1 = np.sin(np.pi / 6) / (q1 * np.sin(np.pi / (6 * q1))) # winding zone factor k_y2 = np.sin(np.pi / 2 * y_tau_pr) # winding chording factor k_q2 = np.sin(np.pi / 6) / (q2 * np.sin(np.pi / (6 * q2))) # winding zone factor k_wd1 = k_y1 * k_q1 # Stator winding factor k_wd2 = k_q2 * k_y2 # Rotor winding factor ag_dia = 2 * rad_ag # air gap diameter ag_len = (0.1 + 0.012 * machine_rating ** (1.0 / 3)) * 0.001 # air gap length in m K_rad = len_s / ag_dia # Aspect ratio rad_r = rad_ag - ag_len # rotor radius (was r_r) tau_p = np.pi * ag_dia / (2 * p) # pole pitch S = 2 * p * q1 * m # Stator slots N_slots_pp = S / (m * p * 2) # Number of stator slots per pole per phase n = S / 2 * p / q1 # no of slots per pole per phase tau_s = tau_p / (m * q1) # Stator slot pitch b_s = b_s_tau_s * tau_s # Stator slot width b_t = tau_s - b_s # Stator tooth width Q_r = 2 * p * m * q2 # Rotor slots tau_r = np.pi * (ag_dia - 2 * ag_len) / Q_r # Rotor slot pitch b_r = b_r_tau_r * tau_r # Rotor slot width b_tr = tau_r - b_r # Rotor tooth width # Calculating equivalent slot openings mu_rs = 0.005 mu_rr = 0.005 W_s = (b_s / mu_rs) * 1e-3 # Stator, in m W_r = (b_r / mu_rr) * 1e-3 # Rotor, in m Slot_aspect_ratio1 = h_s / b_s Slot_aspect_ratio2 = h_0 / b_r # Calculating Carter factor for stator,rotor and effective air gap length gamma_s = (2 * W_s / ag_len) ** 2 / (5 + 2 * W_s / ag_len) K_Cs = tau_s / (tau_s - ag_len * gamma_s * 0.5) # page 3 - 13 gamma_r = (2 * W_r / ag_len) ** 2 / (5 + 2 * W_r / ag_len) K_Cr = tau_r / (tau_r - ag_len * gamma_r * 0.5) # page 3 - 13 K_C = K_Cs * K_Cr g_eff = K_C * ag_len om_m = 2 * np.pi * shaft_rpm / 60 # mechanical frequency om_e = p * om_m # electrical frequency f = shaft_rpm * p / 60 # generator output freq K_s = 0.3 # saturation factor for Iron n_c1 = 2 # number of conductors per coil a1 = 2 # number of parallel paths N_s = np.round(2 * p * N_slots_pp * n_c1 / a1) # Stator winding turns per phase N_r = np.round(N_s * k_wd1 * K_rs / k_wd2) # Rotor winding turns per phase n_c2 = N_r / (Q_r / m) # rotor turns per coil # Calculating peak flux densities and back iron thickness B_g1 = mu_0 * 3 * N_r * I_0 * np.sqrt(2) * k_y2 * k_q2 / (np.pi * p * g_eff * (1 + K_s)) B_g = B_g1 * K_C h_ys = B_g * tau_p / (B_symax * np.pi) B_rymax = B_symax h_yr = h_ys B_tsmax = B_g * tau_s / b_t d_se = ag_dia + 2 * (h_ys + h_s + h_w) # stator outer diameter D_ratio = d_se / ag_dia # Diameter ratio # Stator slot fill factor if ag_dia > 2: k_fills = 0.65 else: k_fills = 0.4 # Stator winding calculation # End connection length for stator winding coils l_fs = 2 * (0.015 + y_tau_p * tau_p / (2 * np.cos(np.deg2rad(40)))) + np.pi * h_s # added radians() 2019 09 11 l_Cus = 2 * N_s * (l_fs + len_s) / a1 # Length of Stator winding # Conductor cross-section A_s = b_s * (h_s - h_w) A_scalc = b_s * 1000 * (h_s - h_w) * 1000 A_Cus = A_s * q1 * p * k_fills / N_s A_Cuscalc = A_scalc * q1 * p * k_fills / N_s # Stator winding resistance R_s = l_Cus * resist_Cu / A_Cus tau_r_min = np.pi * (ag_dia - 2 * (ag_len + h_0)) / Q_r # Peak magnetic loading on the rotor tooth b_trmin = tau_r_min - b_r_tau_r * tau_r_min B_trmax = B_g * tau_r / b_trmin # Calculating leakage inductance in stator K_01 = 1 - 0.033 * (W_s ** 2 / ag_len / tau_s) sigma_ds = 0.0042 L_ssigmas = (2 * mu_0 * len_s * n_c1 ** 2 * S / m / a1 ** 2) * ( (h_s - h_w) / (3 * b_s) + h_w / b_so ) # slot leakage inductance L_ssigmaew = ( (2 * mu_0 * len_s * n_c1 ** 2 * S / m / a1 ** 2) * 0.34 * q1 * (l_fs - 0.64 * tau_p * y_tau_p) / len_s ) # end winding leakage inductance L_ssigmag = (2 * mu_0 * len_s * n_c1 ** 2 * S / m / a1 ** 2) * ( 0.9 * tau_s * q1 * k_wd1 * K_01 * sigma_ds / g_eff ) # tooth tip leakage inductance L_ssigma = L_ssigmas + L_ssigmaew + L_ssigmag # stator leakage inductance L_sm = 6 * mu_0 * len_s * tau_p * (k_wd1 * N_s) ** 2 / (np.pi ** 2 * (p) * g_eff * (1 + K_s)) L_s = L_ssigmas + L_ssigmaew + L_ssigmag # stator inductance # Calculating leakage inductance in rotor K_02 = 1 - 0.033 * (W_r ** 2 / ag_len / tau_r) sigma_dr = 0.0062 l_fr = (0.015 + y_tau_pr * tau_r / 2 / np.cos(np.deg2rad(40))) + np.pi * h_0 # Rotor end connection length L_rsl = (mu_0 * len_s * (2 * n_c2) ** 2 * Q_r / m) * ( (h_0 - h_w) / (3 * b_r) + h_w / b_ro ) # slot leakage inductance L_rel = ( (mu_0 * len_s * (2 * n_c2) ** 2 * Q_r / m) * 0.34 * q2 * (l_fr - 0.64 * tau_r * y_tau_pr) / len_s ) # end winding leakage inductance L_rtl = (mu_0 * len_s * (2 * n_c2) ** 2 * Q_r / m) * ( 0.9 * tau_s * q2 * k_wd2 * K_02 * sigma_dr / g_eff ) # tooth tip leakage inductance L_r = (L_rsl + L_rtl + L_rel) / K_rs ** 2 # rotor leakage inductance sigma1 = 1 - (L_sm ** 2 / L_s / L_r) # Rotor Field winding # conductor cross-section diff = h_0 - h_w A_Cur = k_fillr * p * q2 * b_r * diff / N_r A_Curcalc = A_Cur * 1e6 L_cur = 2 * N_r * (l_fr + len_s) # rotor winding length Resist_r = resist_Cu * L_cur / A_Cur # Rotor resistance R_R = Resist_r / K_rs ** 2 # Equivalent rotor resistance reduced to stator om_s = shaft_rpm * 2 * np.pi / 60 # synchronous speed in rad / s P_e = machine_rating / (1 - S_Nmax) # Air gap power # Calculating No-load voltage E_p = om_s * N_s * k_wd1 * rad_ag * len_s * B_g1 * np.sqrt(2) I_r = P_e / m / E_p # rotor active current I_sm = E_p / (2 * np.pi * freq * (L_s + L_sm)) # stator reactive current I_s = np.sqrt(I_r ** 2 + I_sm ** 2) # Stator current I_srated = machine_rating / 3 / K_rs / E_p # Rated current # Calculating winding current densities and specific current loading J_s = I_s / A_Cuscalc J_r = I_r / A_Curcalc A_1 = 2 * m * N_s * I_s / (np.pi * 2 * rad_ag) Current_ratio = I_0 / I_srated # Ratio of magnetization current to rated current # Calculating masses of the electromagnetically active materials V_Cuss = m * l_Cus * A_Cus V_Cusr = m * L_cur * A_Cur V_Fest = len_s * np.pi * ((rad_ag + h_s) ** 2 - rad_ag ** 2) - (2 * m * q1 * p * b_s * h_s * len_s) V_Fesy = len_s * np.pi * ((rad_ag + h_s + h_ys) ** 2 - (rad_ag + h_s) ** 2) V_Fert = len_s * np.pi * (rad_r ** 2 - (rad_r - h_0) ** 2) - 2 * m * q2 * p * b_r * h_0 * len_s V_Fery = len_s * np.pi * ((rad_r - h_0) ** 2 - (rad_r - h_0 - h_yr) ** 2) Copper = (V_Cuss + V_Cusr) * rho_Copper M_Fest = V_Fest * rho_Fe M_Fesy = V_Fesy * rho_Fe M_Fert = V_Fert * rho_Fe M_Fery = V_Fery * rho_Fe Iron = M_Fest + M_Fesy + M_Fert + M_Fery M_gen = (Copper) + (Iron) # K_gen = Cu * C_Cu + (Iron) * C_Fe #%M_pm * K_pm L_tot = len_s Structural_mass = 0.0002 * M_gen ** 2 + 0.6457 * M_gen + 645.24 Mass = M_gen + Structural_mass # Calculating Losses and efficiency # 1. Copper losses K_R = 1.2 # skin effect correction coefficient P_Cuss = m * I_s ** 2 * R_s * K_R # Copper loss - stator P_Cusr = m * I_r ** 2 * R_R # Copper loss - rotor P_Cusnom = P_Cuss + P_Cusr # Copper loss - total # Iron Losses ( from Hysteresis and eddy currents) P_Hyys = M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator yoke P_Ftys = M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) # Eddy losses in stator yoke P_Hyd = M_Fest * (B_tsmax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator teeth P_Ftd = M_Fest * (B_tsmax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) # Eddy losses in stator teeth P_Hyyr = ( M_Fery * (B_rymax / 1.5) ** 2 * (P_Fe0h * abs(S_Nmax) * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in rotor yoke P_Ftyr = ( M_Fery * (B_rymax / 1.5) ** 2 * (P_Fe0e * (abs(S_Nmax) * om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in rotor yoke P_Hydr = ( M_Fert * (B_trmax / 1.5) ** 2 * (P_Fe0h * abs(S_Nmax) * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in rotor teeth P_Ftdr = ( M_Fert * (B_trmax / 1.5) ** 2 * (P_Fe0e * (abs(S_Nmax) * om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in rotor teeth P_add = 0.5 * machine_rating / 100 # additional losses P_Fesnom = P_Hyys + P_Ftys + P_Hyd + P_Ftd + P_Hyyr + P_Ftyr + P_Hydr + P_Ftdr # Total iron loss delta_v = 1 # allowable brush voltage drop p_b = 3 * delta_v * I_r # Brush loss Losses = P_Cusnom + P_Fesnom + p_b + P_add gen_eff = (P_e - Losses) / P_e # Calculating stator winding current density J_s = I_s / A_Cuscalc # Calculating electromagnetic torque T_e = p * (machine_rating * 1.01) / (2 * np.pi * freq * (1 - S_Nmax)) # Calculating for tangential stress constraints TC1 = T_e / (2 * np.pi * sigma) TC2r = rad_ag ** 2 * len_s r_out = d_se * 0.5 outputs["R_out"] = r_out outputs["B_g"] = B_g outputs["B_g1"] = B_g1 outputs["B_rymax"] = B_rymax outputs["B_tsmax"] = B_tsmax outputs["B_trmax"] = B_trmax outputs["N_s"] = N_s outputs["S"] = S outputs["h_ys"] = h_ys outputs["b_s"] = b_s outputs["b_t"] = b_t outputs["D_ratio"] = D_ratio outputs["A_Cuscalc"] = A_Cuscalc outputs["Slot_aspect_ratio1"] = Slot_aspect_ratio1 outputs["h_yr"] = h_yr outputs["tau_p"] = tau_p outputs["Q_r"] = Q_r outputs["N_r"] = N_r outputs["b_r"] = b_r outputs["b_trmin"] = b_trmin outputs["b_tr"] = b_tr outputs["A_Curcalc"] = A_Curcalc outputs["Slot_aspect_ratio2"] = Slot_aspect_ratio2 outputs["E_p"] = E_p outputs["f"] = f outputs["I_s"] = I_s outputs["A_1"] = A_1 outputs["J_s"] = J_s outputs["J_r"] = J_r outputs["R_s"] = R_s outputs["R_R"] = R_R outputs["L_r"] = L_r outputs["L_s"] = L_s outputs["L_sm"] = L_sm outputs["generator_mass"] = Mass outputs["K_rad"] = K_rad outputs["Losses"] = Losses outputs["eandm_efficiency"] = np.maximum(eps, gen_eff) outputs["Copper"] = Copper outputs["Iron"] = Iron outputs["Structural_mass"] = Structural_mass outputs["TC1"] = TC1 outputs["TC2r"] = TC2r outputs["Current_ratio"] = Current_ratio # ---------------------------------------------------------------------------------------- class SCIG(GeneratorBase): """ Estimates overall mass dimensions and Efficiency of Squirrel cage Induction generator. Parameters ---------- B_symax : float, [T] Peak Stator Yoke flux density B_ymax Returns ------- h_yr : float rotor yoke height h_ys : float Stator Yoke height tau_p : float Pole pitch D_ratio_UL : float Dia ratio upper limit D_ratio_LL : float Dia ratio Lower limit K_rad_UL : float Aspect ratio upper limit K_rad_LL : float Aspect ratio Lower limit rad_r : float rotor radius A_bar : float Rotor Conductor cross-section mm^2 E_p : float Stator phase voltage """ def initialize(self): super(SCIG, self).initialize() def setup(self): super(SCIG, self).setup() self.add_input("B_symax", val=0.0, units="T") self.add_output("h_yr", val=0.0) self.add_output("h_ys", val=0.0) self.add_output("tau_p", val=0.0) self.add_output("D_ratio_UL", val=0.0) self.add_output("D_ratio_LL", val=0.0) self.add_output("K_rad_UL", val=0.0) self.add_output("K_rad_LL", val=0.0) self.add_output("rad_r", val=0.0) self.add_output("A_bar", val=0.0) self.add_output("E_p", val=np.zeros(self.options["n_pc"])) def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs rad_ag = inputs["rad_ag"] len_s = inputs["len_s"] h_s = inputs["h_s"] h_0 = inputs["h_0"] machine_rating = inputs["machine_rating"] shaft_rpm = inputs["shaft_rpm"] I_0 = inputs["I_0"] rho_Fe = inputs["rho_Fe"] rho_Copper = inputs["rho_Copper"] B_symax = inputs["B_symax"] # Grab constant values B_r = inputs["B_r"] E = inputs["E"] P_Fe0e = inputs["P_Fe0e"] P_Fe0h = inputs["P_Fe0h"] S_N = inputs["S_N"] alpha_p = inputs["alpha_p"] b_r_tau_r = inputs["b_r_tau_r"] b_ro = inputs["b_ro"] b_s_tau_s = inputs["b_s_tau_s"] b_so = inputs["b_so"] cofi = inputs["cofi"] freq = inputs["freq"] h_i = inputs["h_i"] h_sy0 = inputs["h_sy0"] h_w = inputs["h_w"] k_fes = inputs["k_fes"] k_fillr = inputs["k_fillr"] k_s = inputs["k_s"] m = discrete_inputs["m"] mu_0 = inputs["mu_0"] mu_r = inputs["mu_r"] p = inputs["p"] phi = inputs["phi"] q1 = discrete_inputs["q1"] q2 = discrete_inputs["q2"] ratio_mw2pp = inputs["ratio_mw2pp"] resist_Cu = inputs["resist_Cu"] sigma = inputs["sigma"] v = inputs["v"] y_tau_p = inputs["y_tau_p"] y_tau_pr = inputs["y_tau_pr"] """ # Assign values to universal constants sigma = 21.5e3 # shear stress (psi) what material? mu_0 = np.pi*4e-7 # permeability of free space in m * kg / (s**2 * A**2) cofi = 0.9 # power factor h_w = 0.005 # wedge height m = 3 # Number of phases resist_Cu = 1.8e-8 * 1.4 # Copper resistivity #Assign values to design constants b_so = 0.004 # Stator slot opening width b_ro = 0.004 # Rotor slot opening width q1 = 6 # Stator slots per pole per phase q2 = 4 # Rotor slots per pole per phase b_s_tau_s = 0.45 # Stator Slot width/Slot pitch ratio b_r_tau_r = 0.45 # Rotor Slot width/Slot pitch ratio y_tau_p = 12./15 # Coil span/pole pitch p = 3 # number of pole pairs freq = 60 # frequency in Hz k_fillr = 0.7 # Rotor slot fill factor P_Fe0h = 4 # specific hysteresis losses W / kg @ 1.5 T @50 Hz P_Fe0e = 1 # specific eddy losses W / kg @ 1.5 T @50 Hz S_N = -0.002 # Slip """ n_1 = shaft_rpm / (1 - S_N) # actual rotor speed (rpm) # Calculating winding factor k_y1 = np.sin(np.pi / 2 * y_tau_p) # winding chording factor k_q1 = np.sin(np.pi / 6) / (q1 * np.sin(np.pi / (6 * q1))) # zone factor k_wd = k_y1 * k_q1 # winding factor # Calculating air gap length ag_dia = 2 * rad_ag # air gap diameter ag_len = (0.1 + 0.012 * machine_rating ** (1.0 / 3)) * 0.001 # air gap length in m K_rad = len_s / ag_dia # Aspect ratio K_rad_LL = 0.5 # lower limit on aspect ratio K_rad_UL = 1.5 # upper limit on aspect ratio rad_r = rad_ag - ag_len # rotor radius tau_p = np.pi * ag_dia / (2 * p) # pole pitch S = 2 * p * q1 * m # Stator slots N_slots_pp = S / (m * p * 2) # Number of stator slots per pole per phase tau_s = tau_p / (m * q1) # Stator slot pitch b_s = b_s_tau_s * tau_s # Stator slot width b_t = tau_s - b_s # Stator tooth width Q_r = 2 * p * m * q2 # Rotor slots tau_r = np.pi * (ag_dia - 2 * ag_len) / Q_r # Rotor slot pitch b_r = b_r_tau_r * tau_r # Rotor slot width b_tr = tau_r - b_r # Rotor tooth width tau_r_min = np.pi * (ag_dia - 2 * (ag_len + h_0)) / Q_r b_trmin = tau_r_min - b_r_tau_r * tau_r_min # minumum rotor tooth width # Calculating equivalent slot openings mu_rs = 0.005 mu_rr = 0.005 W_s = (b_s / mu_rs) * 1e-3 # Stator, in m W_r = (b_r / mu_rr) * 1e-3 # Rotor, in m Slot_aspect_ratio1 = h_s / b_s # Stator slot aspect ratio Slot_aspect_ratio2 = h_0 / b_r # Rotor slot aspect ratio # Calculating Carter factor for stator,rotor and effective air gap length """ gamma_s = (2 * W_s / ag_len)**2 / (5 + 2 * W_s / ag_len) K_Cs = tau_s / (tau_s - ag_len * gamma_s * 0.5) # page 3-13 Boldea Induction machines Chapter 3 gamma_r = (2 * W_r / ag_len)**2 / (5 + 2 * W_r / ag_len) K_Cr = tau_r / (tau_r - ag_len * gamma_r * 0.5) # page 3-13 Boldea Induction machines Chapter 3 """ K_Cs = carterFactor(ag_len, W_s, tau_s) K_Cr = carterFactor(ag_len, W_r, tau_r) K_C = K_Cs * K_Cr g_eff = K_C * ag_len om_m = 2 * np.pi * shaft_rpm / 60 # mechanical frequency om_e = p * om_m # electrical frequency f = shaft_rpm * p / 60 # generator output freq K_s = 0.3 # saturation factor for Iron n_c = 2 # number of conductors per coil a1 = 2 # number of parallel paths # Calculating stator winding turns N_s = np.round(2 * p * N_slots_pp * n_c / a1) # Calculating Peak flux densities B_g1 = mu_0 * 3 * N_s * I_0 * np.sqrt(2) * k_y1 * k_q1 / (np.pi * p * g_eff * (1 + K_s)) B_g = B_g1 * K_C B_rymax = B_symax # calculating back iron thickness h_ys = B_g * tau_p / (B_symax * np.pi) h_yr = h_ys d_se = ag_dia + 2 * (h_ys + h_s + h_w) # stator outer diameter D_ratio = d_se / ag_dia # Diameter ratio # limits for Diameter ratio depending on pole pair if 2 * p == 2: D_ratio_LL = 1.65 D_ratio_UL = 1.69 elif 2 * p == 4: D_ratio_LL = 1.46 D_ratio_UL = 1.49 elif 2 * p == 6: D_ratio_LL = 1.37 D_ratio_UL = 1.4 elif 2 * p == 8: D_ratio_LL = 1.27 D_ratio_UL = 1.3 else: D_ratio_LL = 1.2 D_ratio_UL = 1.24 # Stator slot fill factor if ag_dia > 2: k_fills = 0.65 else: k_fills = 0.4 # Stator winding length and cross-section l_fs = 2 * (0.015 + y_tau_p * tau_p / 2 / np.cos(np.deg2rad(40))) + np.pi * h_s # end connection l_Cus = 2 * N_s * (l_fs + len_s) / a1 # shortpitch A_s = b_s * (h_s - h_w) # Slot area A_scalc = b_s * 1000 * (h_s - h_w) * 1000 # Conductor cross-section (mm^2) A_Cus = A_s * q1 * p * k_fills / N_s # Conductor cross-section (m^2) A_Cuscalc = A_scalc * q1 * p * k_fills / N_s # Stator winding resistance R_s = l_Cus * resist_Cu / A_Cus # Calculating no-load voltage om_s = shaft_rpm * 2 * np.pi / 60 # rated angular frequency P_e = machine_rating / (1 - S_N) # Electrical power E_p = om_s * N_s * k_wd * rad_ag * len_s * B_g1 * np.sqrt(2) S_GN = (1.0 - S_N) * machine_rating # same as P_e? T_e = p * S_GN / (2 * np.pi * freq * (1 - S_N)) I_srated = machine_rating / (3 * E_p * cofi) # Rotor design diff = h_0 - h_w A_bar = b_r * diff # bar cross section Beta_skin = np.sqrt(np.pi * mu_0 * freq / 2 / resist_Cu) # coefficient for skin effect correction k_rm = Beta_skin * h_0 # coefficient for skin effect correction J_b = 6e06 # Bar current density K_i = 0.864 I_b = 2 * m * N_s * k_wd * I_srated / Q_r # bar current # Calculating bar resistance R_rb = resist_Cu * k_rm * len_s / A_bar I_er = I_b / (2 * np.sin(np.pi * p / Q_r)) # End ring current J_er = 0.8 * J_b # End ring current density A_er = I_er / J_er # End ring cross-section b = h_0 # End ring dimension a = A_er / b # End ring dimension D_er = (rad_ag * 2 - 2 * ag_len) - 0.003 # End ring diameter l_er = np.pi * (D_er - b) / Q_r # End ring segment length if debug: sys.stderr.write("l_er {:.4f} A_er {:.4f} D_er {:.4f}\n".format(l_er[0], A_er[0], D_er[0])) # Calculating end ring resistance R_re = resist_Cu * l_er / (2 * A_er * (np.sin(np.pi * p / Q_r)) ** 2) # Calculating equivalent rotor resistance if debug: sys.stderr.write("R_rb {:.3e} R_re {:.3e} k_wd {:.4f} N_s {} Q_r {}\n".format(R_rb, R_re, k_wd, N_s, Q_r)) R_R = (R_rb + R_re) * 4 * m * (k_wd * N_s) ** 2 / Q_r # Calculating Rotor and Stator teeth flux density B_trmax = B_g * tau_r / b_trmin B_tsmax = B_g * tau_s / b_t # Calculating Equivalent core lengths l_r = len_s + 4 * ag_len # for axial cooling l_se = len_s + (2 / 3) * ag_len K_fe = 0.95 # Iron factor L_e = l_se * K_fe # radial cooling # Calculating leakage inductance in stator if debug: sys.stderr.write("b_s {:.3e} b_so {:.3e}\n".format(b_s[0], b_so[0])) L_ssigmas = ( 2 * mu_0 * len_s * N_s ** 2 / p / q1 * ((h_s - h_w) / (3 * b_s) + h_w / b_so) ) # slot leakage inductance L_ssigmaew = ( 2 * mu_0 * len_s * N_s ** 2 / p / q1 * 0.34 * q1 * (l_fs - 0.64 * tau_p * y_tau_p) / len_s ) # end winding leakage inductance L_ssigmag = ( 2 * mu_0 * len_s * N_s ** 2 / p / q1 * (5 * (ag_len * K_C / b_so) / (5 + 4 * (ag_len * K_C / b_so))) ) # tooth tip leakage inductance L_s = L_ssigmas + L_ssigmaew + L_ssigmag # stator leakage inductance L_sm = 6 * mu_0 * len_s * tau_p * (k_wd * N_s) ** 2 / (np.pi ** 2 * p * g_eff * (1 + K_s)) # Calculating leakage inductance in rotor lambda_ei = 2.3 * D_er / (4 * Q_r * len_s * (np.sin(np.pi * p / Q_r) ** 2)) * np.log(4.7 * ag_dia / (a + 2 * b)) lambda_b = h_0 / (3 * b_r) + h_w / b_ro L_i = np.pi * ag_dia / Q_r L_rsl = mu_0 * len_s * ((h_0 - h_w) / (3 * b_r) + h_w / b_ro) # slot leakage inductance L_rel = mu_0 * (len_s * lambda_b + 2 * lambda_ei * L_i) # end winding leakage inductance L_rtl = mu_0 * len_s * (0.9 * tau_r * 0.09 / g_eff) # tooth tip leakage inductance L_rsigma = (L_rsl + L_rtl + L_rel) * 4 * m * (k_wd * N_s) ** 2 / Q_r # rotor leakage inductance # Calculating rotor current if debug: sys.stderr.write( "S_N {} P_e {:.1f} m {} R_R {:.4f} = {:.1f}\n".format(S_N, P_e, m, R_R, -S_N * P_e / m / R_R) ) I_r = np.sqrt(-S_N * P_e / m / R_R) I_sm = E_p / (2 * np.pi * freq * L_sm) # Calculating stator currents and specific current loading I_s = np.sqrt((I_r ** 2 + I_sm ** 2)) A_1 = 2 * m * N_s * I_s / (np.pi * 2 * rad_ag) # Calculating masses of the electromagnetically active materials V_Cuss = m * l_Cus * A_Cus # Volume of copper in stator V_Cusr = Q_r * len_s * A_bar + np.pi * (D_er * A_er - A_er * b) # Volume of copper in rotor V_Fest = ( len_s * np.pi * ((rad_ag + h_s) ** 2 - rad_ag ** 2) - 2 * m * q1 * p * b_s * h_s * len_s ) # Volume of iron in stator teeth V_Fesy = len_s * np.pi * ((rad_ag + h_s + h_ys) ** 2 - (rad_ag + h_s) ** 2) # Volume of iron in stator yoke rad_r = rad_ag - ag_len # rotor radius V_Fert = ( np.pi * len_s * (rad_r ** 2 - (rad_r - h_0) ** 2) - 2 * m * q2 * p * b_r * h_0 * len_s ) # Volume of iron in rotor teeth V_Fery = np.pi * len_s * ((rad_r - h_0) ** 2 - (rad_r - h_0 - h_yr) ** 2) # Volume of iron in rotor yoke Copper = (V_Cuss + V_Cusr)[-1] * rho_Copper # Mass of Copper M_Fest = V_Fest * rho_Fe # Mass of stator teeth M_Fesy = V_Fesy * rho_Fe # Mass of stator yoke M_Fert = V_Fert * rho_Fe # Mass of rotor tooth M_Fery = V_Fery * rho_Fe # Mass of rotor yoke Iron = M_Fest + M_Fesy + M_Fert + M_Fery Active_mass = Copper + Iron L_tot = len_s Structural_mass = 0.0001 * Active_mass ** 2 + 0.8841 * Active_mass - 132.5 Mass = Active_mass + Structural_mass # Calculating Losses and efficiency # 1. Copper losses K_R = 1.2 # skin effect correction coefficient P_Cuss = m * I_s ** 2 * R_s * K_R # Copper loss - stator P_Cusr = m * I_r ** 2 * R_R # Copper loss - rotor P_Cusnom = P_Cuss + P_Cusr # Copper loss - total # Iron Losses ( from Hysteresis and eddy currents) P_Hyys = M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator yoke P_Ftys = ( M_Fesy * (B_symax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator yoke P_Hyd = M_Fest * (B_tsmax / 1.5) ** 2 * (P_Fe0h * om_e / (2 * np.pi * 60)) # Hysteresis losses in stator tooth P_Ftd = ( M_Fest * (B_tsmax / 1.5) ** 2 * (P_Fe0e * (om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in stator tooth P_Hyyr = ( M_Fery * (B_rymax / 1.5) ** 2 * (P_Fe0h * abs(S_N) * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in rotor yoke P_Ftyr = ( M_Fery * (B_rymax / 1.5) ** 2 * (P_Fe0e * (abs(S_N) * om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in rotor yoke P_Hydr = ( M_Fert * (B_trmax / 1.5) ** 2 * (P_Fe0h * abs(S_N) * om_e / (2 * np.pi * 60)) ) # Hysteresis losses in rotor tooth P_Ftdr = ( M_Fert * (B_trmax / 1.5) ** 2 * (P_Fe0e * (abs(S_N) * om_e / (2 * np.pi * 60)) ** 2) ) # Eddy losses in rotor tooth # Calculating Additional losses P_add = 0.5 * machine_rating / 100 P_Fesnom = P_Hyys + P_Ftys + P_Hyd + P_Ftd + P_Hyyr + P_Ftyr + P_Hydr + P_Ftdr Losses = P_Cusnom + P_Fesnom + P_add gen_eff = (P_e - Losses) / P_e # Calculating current densities in the stator and rotor J_s = I_s / A_Cuscalc J_r = I_r / A_bar / 1e6 # Calculating Tangential stress constraints TC1 = T_e / (2 * np.pi * sigma) TC2r = rad_ag ** 2 * len_s # Calculating mass moments of inertia and center of mass r_out = d_se * 0.5 outputs["R_out"] = r_out outputs["B_tsmax"] = B_tsmax outputs["B_trmax"] = B_trmax outputs["B_rymax"] = B_rymax outputs["B_g"] = B_g outputs["B_g1"] = B_g1 outputs["N_s"] = N_s outputs["S"] = S outputs["h_ys"] = h_ys outputs["b_s"] = b_s outputs["b_t"] = b_t outputs["D_ratio"] = D_ratio outputs["D_ratio_UL"] = D_ratio_UL outputs["D_ratio_LL"] = D_ratio_LL outputs["A_Cuscalc"] = A_Cuscalc outputs["Slot_aspect_ratio1"] = Slot_aspect_ratio1 outputs["h_yr"] = h_yr outputs["tau_p"] = tau_p outputs["Q_r"] = Q_r outputs["b_r"] = b_r outputs["b_trmin"] = b_trmin outputs["b_tr"] = b_tr outputs["rad_r"] = rad_r outputs["A_bar"] = A_bar outputs["Slot_aspect_ratio2"] = Slot_aspect_ratio2 outputs["E_p"] = E_p outputs["f"] = f outputs["I_s"] = I_s outputs["A_1"] = A_1 outputs["J_s"] = J_s outputs["J_r"] = J_r outputs["R_s"] = R_s outputs["R_R"] = R_R[-1] outputs["L_s"] = L_s outputs["L_sm"] = L_sm outputs["generator_mass"] = Mass outputs["K_rad"] = K_rad outputs["K_rad_UL"] = K_rad_UL outputs["K_rad_LL"] = K_rad_LL outputs["Losses"] = Losses outputs["eandm_efficiency"] = np.maximum(eps, gen_eff) outputs["Copper"] = Copper outputs["Iron"] = Iron outputs["Structural_mass"] = Structural_mass outputs["TC1"] = TC1 outputs["TC2r"] = TC2r # ---------------------------------------------------------------------------------------- class EESG(GeneratorBase): """ Estimates overall mass dimensions and Efficiency of Electrically Excited Synchronous generator. Parameters ---------- I_f : float, [A] Excitation current N_f : float field turns b_arm : float, [m] arm width h_yr : float, [m] rotor yoke height h_ys : float, [m] Yoke height tau_p : float, [m] Pole pitch self.tau_p Returns ------- n_brushes : float number of brushes h_p : float, [m] Pole height b_p : float, [m] Pole width L_m : float, [H] Stator synchronising inductance R_r : float, [ohm] Rotor resistance B_tmax : float, [T] Peak Teeth flux density B_gfm : float, [T] Average air gap flux density B_g B_pc : float, [T] Pole core flux density B_symax : float, [T] Peak Stator Yoke flux density B_ymax E_s : float, [V] Stator phase voltage J_f : float, [A*m**-2] rotor Current density Power_ratio : float Power_ratio Load_mmf_ratio : float mmf_ratio """ def initialize(self): super(EESG, self).initialize() def setup(self): super(EESG, self).setup() self.add_input("I_f", val=0.0, units="A") self.add_input("N_f", val=0.0) self.add_input("b_arm", val=0.0, units="m") self.add_input("h_yr", val=0.0, units="m") self.add_input("h_ys", val=0.0, units="m") self.add_input("tau_p", val=0.0, units="m") self.add_output("n_brushes", val=0.0) self.add_output("h_p", val=0.0, units="m") self.add_output("b_p", val=0.0, units="m") self.add_output("L_m", val=0.0, units="H") self.add_output("R_r", val=0.0, units="ohm") self.add_output("B_tmax", val=0.0, units="T") self.add_output("B_gfm", val=0.0, units="T") self.add_output("B_pc", val=0.0, units="T") self.add_output("B_symax", val=0.0, units="T") self.add_output("E_s", val=np.zeros(self.options["n_pc"]), units="V") self.add_output("J_f", val=0.0, units="A*m**-2") self.add_output("Power_ratio", val=0.0) self.add_output("Load_mmf_ratio", val=0.0) def compute(self, inputs, outputs, discrete_inputs, discrete_outputs): # Unpack inputs rad_ag = inputs["rad_ag"] len_s = inputs["len_s"] h_s = inputs["h_s"] tau_p = inputs["tau_p"] N_f = inputs["N_f"] I_f = inputs["I_f"] h_ys = inputs["h_ys"] h_yr = inputs["h_yr"] machine_rating = inputs["machine_rating"] shaft_rpm = inputs["shaft_rpm"] Torque = inputs["rated_torque"] b_st = inputs["b_st"] d_s = inputs["d_s"] t_ws = inputs["t_ws"] n_r = inputs["n_r"] n_s = inputs["n_s"] b_r = inputs["b_arm"] d_r = inputs["d_r"] t_wr = inputs["t_wr"] R_sh = 0.5 * inputs["D_shaft"] rho_Fe = inputs["rho_Fe"] rho_Copper = inputs["rho_Copper"] rho_Fes = inputs["rho_Fes"] # Grab constant values B_r = inputs["B_r"] E = inputs["E"] P_Fe0e = inputs["P_Fe0e"] P_Fe0h = inputs["P_Fe0h"] S_N = inputs["S_N"] alpha_p = inputs["alpha_p"] b_r_tau_r = inputs["b_r_tau_r"] b_ro = inputs["b_ro"] b_s_tau_s = inputs["b_s_tau_s"] b_so = inputs["b_so"] cofi = inputs["cofi"] freq = inputs["freq"] h_i = inputs["h_i"] h_sy0 = inputs["h_sy0"] h_w = inputs["h_w"] k_fes = inputs["k_fes"] k_fillr = inputs["k_fillr"] k_fills = inputs["k_fills"] k_s = inputs["k_s"] m = discrete_inputs["m"] mu_0 = inputs["mu_0"] mu_r = inputs["mu_r"] p = inputs["p"] phi = inputs["phi"] q1 = discrete_inputs["q1"] q2 = discrete_inputs["q2"] ratio_mw2pp = inputs["ratio_mw2pp"] resist_Cu = inputs["resist_Cu"] sigma = inputs["sigma"] v = inputs["v"] y_tau_p = inputs["y_tau_p"] y_tau_pr = inputs["y_tau_pr"] """ # Assign values to universal constants E = 2e11 # N / m^2 young's modulus sigma = 48.373e3 # shear stress of steel in psi (~333 MPa) mu_0 = np.pi * 4e-7 # permeability of free space in m * kg / (s**2 * A**2) phi = np.deg2rad(90) # Assign values to design constants h_w = 0.005 b_so = 0.004 # Stator slot opening m = 3 # number of phases q1 = 2 # no of stator slots per pole per phase b_s_tau_s = 0.45 # ratio of slot width to slot pitch P_Fe0h = 4 # specific hysteresis losses W / kg @ 1.5 T @50 Hz P_Fe0e = 1 # specific eddy losses W / kg @ 1.5 T @50 Hz resist_Cu = 1.8e-8 * 1.4 # resisitivity of copper # ohm-meter (Why the 1.4 factor?) k_fes = 0.9 # iron fill factor (not used) y_tau_p = 1 # coil span / pole pitch fullpitch k_fillr = 0.7 # rotor slot fill factor k_s = 0.2 # magnetic saturation factor for iron cofi = 0.85 # power factor """ T = Torque # back iron thickness for rotor and stator t_s = h_ys t = h_yr # Aspect ratio K_rad = len_s / (2 * rad_ag) ###################################################### Electromagnetic design############################################# alpha_p = np.pi / 2 * 0.7 # (not used) dia = 2 * rad_ag # air gap diameter # air gap length and minimum values g = 0.001 * dia if g < 0.005: g = 0.005 r_r = rad_ag - g # rotor radius d_se = dia + 2 * h_s + 2 * h_ys # stator outer diameter (not used) p = np.round(np.pi * dia / (2 * tau_p)) # number of pole pairs S = 2 * p * q1 * m # number of slots of stator phase winding N_conductors = S * 2 N_s = N_conductors / 2 / m # Stator turns per phase alpha = 180 / S / p # electrical angle (not used) tau_s = np.pi * dia / S # slot pitch h_ps = 0.1 * tau_p # height of pole shoe b_pc = 0.4 * tau_p # width of pole core h_pc = 0.6 * tau_p # height of pole core h_p = 0.7 * tau_p # pole height b_p = h_p b_s = tau_s * b_s_tau_s # slot width Slot_aspect_ratio = h_s / b_s b_t = tau_s - b_s # tooth width # Calculating Carter factor and effective air gap g_a = g K_C1 = (tau_s + 10 * g_a) / (tau_s - b_s + 10 * g_a) # salient pole rotor g_1 = K_C1 * g # calculating angular frequency om_m = 2 * np.pi * shaft_rpm / 60 om_e = 60 f = shaft_rpm * p / 60 # Slot fill factor according to air gap radius if 2 * rad_ag > 2: K_fills = 0.65 else: K_fills = 0.4 # Calculating Stator winding factor k_y1 =

np.sin(y_tau_p * np.pi / 2)

numpy.sin

# -------------------------------------------------------- # Licensed under The MIT License [see LICENSE for details] # -------------------------------------------------------- import random import os import time import sys import pybullet as p import numpy as np import IPython from env.tm5_gripper_hand_camera import Panda from transforms3d.quaternions import * import scipy.io as sio from core.utils import * import json from itertools import product import OMG.ycb_render.robotPose.robot_pykdl as robot_pykdl from OMG.omg.config import cfg as planner_cfg from OMG.omg.core import PlanningScene BASE_LINK = -1 MAX_DISTANCE = 0.000 def get_num_joints(body, CLIENT=None): return p.getNumJoints(body, physicsClientId=CLIENT) def get_links(body, CLIENT=None): return list(range(get_num_joints(body, CLIENT))) def get_all_links(body, CLIENT=None): return [BASE_LINK] + list(get_links(body, CLIENT)) def pairwise_link_collision(body1, link1, body2, link2=BASE_LINK, max_distance=MAX_DISTANCE, CLIENT=None): # 10000 return len(p.getClosestPoints(bodyA=body1, bodyB=body2, distance=max_distance, linkIndexA=link1, linkIndexB=link2, physicsClientId=CLIENT)) != 0 def any_link_pair_collision(body1, body2, links1=None, links2=None, CLIENT=None, **kwargs): if links1 is None: links1 = get_all_links(body1, CLIENT) if links2 is None: links2 = get_all_links(body2, CLIENT) for link1, link2 in product(links1, links2): if (body1 == body2) and (link1 == link2): continue if pairwise_link_collision(body1, link1, body2, link2, CLIENT=CLIENT, **kwargs): return True return False def body_collision(body1, body2, max_distance=MAX_DISTANCE, CLIENT=None): # 10000 return len(p.getClosestPoints(bodyA=body1, bodyB=body2, distance=max_distance, physicsClientId=CLIENT)) != 0 def pairwise_collision(body1, body2, **kwargs): if isinstance(body1, tuple) or isinstance(body2, tuple): body1, links1 = expand_links(body1) body2, links2 = expand_links(body2) return any_link_pair_collision(body1, body2, links1, links2, **kwargs) return body_collision(body1, body2, **kwargs) class PandaJointSpace(): def __init__(self): self.high = np.ones(7) * 0.25 self.low = np.ones(7) * -0.25 self.shape = [7] self.bounds = np.vstack([self.low, self.high]) class PandaTaskSpace6D(): def __init__(self): self.high = np.array([0.06, 0.06, 0.06, np.pi/6, np.pi/6, np.pi/6]) # , np.pi/10 self.low = np.array([-0.06, -0.06, -0.06, -np.pi/6, -np.pi/6, -np.pi/6]) # , -np.pi/3 self.shape = [6] self.bounds = np.vstack([self.low, self.high]) class PandaYCBEnv(): """ Class for franka panda environment with YCB objects. """ def __init__(self, renders=False, maxSteps=100, random_target=False, blockRandom=0.5, cameraRandom=0, action_space='configuration', use_expert_plan=False, accumulate_points=False, use_hand_finger_point=False, expert_step=20, expert_dynamic_timestep=False, data_type='RGB', filter_objects=[], img_resize=(224, 224), regularize_pc_point_count=False, egl_render=False, width=224, height=224, uniform_num_pts=1024, numObjects=7, termination_heuristics=True, domain_randomization=False, change_dynamics=False, pt_accumulate_ratio=0.95, initial_near=0.2, initial_far=0.5, disable_unnece_collision=True, omg_config=None): self._timeStep = 1. / 1000. self._observation = [] self._renders = renders self._maxSteps = maxSteps self._env_step = 0 self._resize_img_size = img_resize self._p = p self._window_width = width self._window_height = height self._blockRandom = blockRandom self._cameraRandom = cameraRandom self._numObjects = numObjects self._random_target = random_target self._accumulate_points = accumulate_points self._use_expert_plan = use_expert_plan self._expert_step = expert_step self._use_hand_finger_point = use_hand_finger_point self._data_type = data_type self._egl_render = egl_render self._action_space = action_space self._disable_unnece_collision = disable_unnece_collision self._pt_accumulate_ratio = pt_accumulate_ratio self._change_dynamics = change_dynamics self._domain_randomization = domain_randomization self._initial_near = initial_near self._initial_far = initial_far self._expert_dynamic_timestep = expert_dynamic_timestep self._termination_heuristics = termination_heuristics self._filter_objects = filter_objects self._omg_config = omg_config self._regularize_pc_point_count = regularize_pc_point_count self._uniform_num_pts = uniform_num_pts self.observation_dim = (self._window_width, self._window_height, 3) self.init_constant() self.connect() def init_constant(self): self._shift = [0.8, 0.8, 0.8] # to work without axis in DIRECT mode self._max_episode_steps = 50 self.root_dir = os.path.join(os.path.dirname(os.path.abspath(__file__)), '..') self.data_root_dir = os.path.join(self.root_dir, 'data/scenes') self._planner_setup = False self.retracted = False self._standoff_dist = 0.08 self.cam_offset = np.eye(4) self.cam_offset[:3, 3] = (np.array([0.1186, 0., 0.0191344123493])) # camera offset self.cam_offset[:3, :3] = euler2mat(0, 0, -np.pi/2) self.cur_goal = np.eye(4) self.target_idx = 0 self.objects_loaded = False self.parallel = False self.curr_acc_points = np.zeros([3, 0]) self.connected = False self.action_dim = 6 self.hand_finger_points = hand_finger_point self.action_space = PandaTaskSpace6D() def connect(self): """ Connect pybullet. """ if self._renders: self.cid = p.connect(p.SHARED_MEMORY) if (self.cid < 0): self.cid = p.connect(p.GUI) p.resetDebugVisualizerCamera(1.3, 180.0, -41.0, [-0.35, -0.58, -0.88]) else: self.cid = p.connect(p.DIRECT) if self._egl_render: import pkgutil egl = pkgutil.get_loader("eglRenderer") if egl: p.loadPlugin(egl.get_filename(), "_eglRendererPlugin") self.connected = True def disconnect(self): """ Disconnect pybullet. """ p.disconnect() self.connected = False def reset(self, save=False, init_joints=None, scene_file=None, data_root_dir=None, cam_random=0, reset_free=False, enforce_face_target=False): """ Environment reset called at the beginning of an episode. """ self.retracted = False if data_root_dir is not None: self.data_root_dir = data_root_dir self._cur_scene_file = scene_file if reset_free: return self.cache_reset(scene_file, init_joints, enforce_face_target) self.disconnect() self.connect() # Set the camera . look = [0.1 - self._shift[0], 0.2 - self._shift[1], 0 - self._shift[2]] distance = 2.5 pitch = -56 yaw = 245 roll = 0. fov = 20. aspect = float(self._window_width) / self._window_height self.near = 0.1 self.far = 10 self._view_matrix = p.computeViewMatrixFromYawPitchRoll(look, distance, yaw, pitch, roll, 2) self._proj_matrix = p.computeProjectionMatrixFOV(fov, aspect, self.near, self.far) self._light_position = np.array([-1.0, 0, 2.5]) p.resetSimulation() p.setTimeStep(self._timeStep) p.setPhysicsEngineParameter(enableConeFriction=0) p.setGravity(0, 0, -9.81) p.stepSimulation() # Set table and plane plane_file = os.path.join(self.root_dir, 'data/objects/floor/model_normalized.urdf') # _white table_file = os.path.join(self.root_dir, 'data/objects/table/models/model_normalized.urdf') self.obj_path = [plane_file, table_file] self.plane_id = p.loadURDF(plane_file, [0 - self._shift[0], 0 - self._shift[1], -.82 - self._shift[2]]) self.table_pos = np.array([0.5 - self._shift[0], 0.0 - self._shift[1], -.82 - self._shift[2]]) self.table_id = p.loadURDF(table_file, self.table_pos[0], self.table_pos[1], self.table_pos[2], 0.707, 0., 0., 0.707) # Intialize robot and objects if init_joints is None: self._panda = Panda(stepsize=self._timeStep, base_shift=self._shift) else: self._panda = Panda(stepsize=self._timeStep, init_joints=init_joints, base_shift=self._shift) for _ in range(1000): p.stepSimulation() if not self.objects_loaded: self._objectUids = self.cache_objects() if self._use_expert_plan: self.setup_expert_scene() if scene_file is None or not os.path.exists(os.path.join(self.data_root_dir, scene_file + '.mat')): self._randomly_place_objects(self._get_random_object(self._numObjects), scale=1) else: self.place_objects_from_scene(scene_file) self._objectUids += [self.plane_id, self.table_id] self._env_step = 0 self.collided = False self.collided_before = False self.obj_names, self.obj_poses = self.get_env_info() self.init_target_height = self._get_target_relative_pose()[2, 3] self.curr_acc_points = np.zeros([3, 0]) return None # observation def step(self, action, delta=False, obs=True, repeat=150, config=False, vis=False): """ Environment step. """ action = self.process_action(action, delta, config) self._panda.setTargetPositions(action) for _ in range(int(repeat)): p.stepSimulation() if self._renders: time.sleep(self._timeStep) observation = self._get_observation(vis=vis) test_termination_obs = observation[0][1] depth = test_termination_obs[[3]].T mask = test_termination_obs[[4]].T observation = self.input_selection(observation) done = self._termination(depth.copy(), mask, use_depth_heuristics=self._termination_heuristics) self.collision_check() reward = self._reward() info = {'grasp_success': reward, 'goal_dist': self._get_goal_dist(), 'point_num': self.curr_acc_points.shape[1], 'collided': self.collided, 'cur_ef_pose': self._get_ef_pose(mat=True)} self._env_step += 1 return observation, reward, done, info def _get_observation(self, pose=None, vis=False, acc=True): """ Get observation """ object_pose = self._get_target_relative_pose('ef') # self._get_relative_ef_pose() ef_pose = self._get_ef_pose('mat') joint_pos, joint_vel = self._panda.getJointStates() near, far = self.near, self.far view_matrix, proj_matrix = self._view_matrix, self._proj_matrix extra_overhead_camera = False camera_info = tuple(view_matrix) + tuple(proj_matrix) hand_cam_view_matrix, hand_proj_matrix, lightDistance, lightColor, lightDirection, near, far = self._get_hand_camera_view(pose) camera_info += tuple(hand_cam_view_matrix.flatten()) + tuple(hand_proj_matrix) _, _, rgba, depth, mask = p.getCameraImage(width=self._window_width, height=self._window_height, viewMatrix=tuple(hand_cam_view_matrix.flatten()), projectionMatrix=hand_proj_matrix, physicsClientId=self.cid, renderer=p.ER_BULLET_HARDWARE_OPENGL) depth = (far * near / (far - (far - near) * depth) * 5000).astype(np.uint16) # transform depth from NDC to actual depth mask[mask >= 0] += 1 # transform mask to have target id 0 target_idx = self.target_idx + 4 mask[mask == target_idx] = 0 mask[mask == -1] = 50 mask[mask != 0] = 1 obs = np.concatenate([rgba[..., :3], depth[..., None], mask[..., None]], axis=-1) obs = self.process_image(obs[..., :3], obs[..., [3]], obs[..., [4]], tuple(self._resize_img_size)) intrinsic_matrix = projection_to_intrinsics(hand_proj_matrix, self._window_width, self._window_height) point_state = backproject_camera_target(obs[3].T, intrinsic_matrix, obs[4].T) # obs[4].T point_state = self.cam_offset[:3, :3].dot(point_state) + self.cam_offset[:3, [3]] point_state[1] *= -1 point_state = self.process_pointcloud(point_state, vis, acc) obs = (point_state, obs) pose_info = (object_pose, ef_pose) return [obs, joint_pos, camera_info, pose_info] def retract(self, record=False): """ Move the arm to lift the object. """ cur_joint = np.array(self._panda.getJointStates()[0]) cur_joint[-1] = 0.8 # close finger observations = [self.step(cur_joint, repeat=300, config=True, vis=False)[0]] pos, orn = p.getLinkState(self._panda.pandaUid, self._panda.pandaEndEffectorIndex)[4:6] for i in range(10): pos = (pos[0], pos[1], pos[2] + 0.03) jointPoses = np.array(p.calculateInverseKinematics(self._panda.pandaUid, self._panda.pandaEndEffectorIndex, pos, maxNumIterations=500, residualThreshold=1e-8)) jointPoses[6] = 0.8 jointPoses = jointPoses[:7].copy() obs = self.step(jointPoses, config=True)[0] if record: observations.append(obs) self.retracted = True rew = self._reward() if record: return (rew, observations) return rew def _reward(self): """ Calculates the reward for the episode. """ reward = 0 if self.retracted and self.target_lifted(): print('target {} lifted !'.format(self.target_name)) reward = 1 return reward def _termination(self, depth_img, mask_img, use_depth_heuristics=False): """ Target depth heuristics for determining if grasp can be executed. The threshold is based on depth in the middle of the camera and the finger is near the bottom two sides """ depth_heuristics = False nontarget_mask = mask_img[..., 0] != 0 if use_depth_heuristics: depth_img = depth_img[..., 0] depth_img[nontarget_mask] = 10 # hard coded region depth_img_roi = depth_img[int(58. * self._window_height / 64):, int(21. * self._window_width / 64):int(42 * self._window_width / 64)] depth_img_roi_ = depth_img_roi[depth_img_roi < 0.21] if depth_img_roi_.shape[0] > 1: depth_heuristics = (depth_img_roi_ < 0.115).sum() > 10 return self._env_step >= self._maxSteps or depth_heuristics or self.target_fall_down() def cache_objects(self): """ Load all YCB objects and set up """ obj_path = os.path.join(self.root_dir, 'data/objects/') objects = self.obj_indexes obj_path = [obj_path + objects[i] for i in self._all_obj] self.target_obj_indexes = [self._all_obj.index(idx) for idx in self._target_objs] pose = np.zeros([len(obj_path), 3]) pose[:, 0] = -0.5 - np.linspace(0, 4, len(obj_path)) pos, orn = p.getBasePositionAndOrientation(self._panda.pandaUid) objects_paths = [p_.strip() + '/' for p_ in obj_path] objectUids = [] self.object_heights = [] self.obj_path = objects_paths + self.obj_path self.placed_object_poses = [] for i, name in enumerate(objects_paths): trans = pose[i] + np.array(pos) # fixed position self.placed_object_poses.append((trans.copy(), np.array(orn).copy())) uid = self._add_mesh(os.path.join(self.root_dir, name, 'model_normalized.urdf'), trans, orn) # xyzw if self._change_dynamics: p.changeDynamics(uid, -1, lateralFriction=0.15, spinningFriction=0.1, rollingFriction=0.1) point_z = np.loadtxt(os.path.join(self.root_dir, name, 'model_normalized.extent.txt')) half_height = float(point_z.max()) / 2 if len(point_z) > 0 else 0.01 self.object_heights.append(half_height) objectUids.append(uid) p.setCollisionFilterPair(uid, self.plane_id, -1, -1, 0) if self._disable_unnece_collision: for other_uid in objectUids: p.setCollisionFilterPair(uid, other_uid, -1, -1, 0) self.objects_loaded = True self.placed_objects = [False] * len(self.obj_path) return objectUids def cache_reset(self, scene_file, init_joints, enforce_face_target): """ Hack to move the loaded objects around to avoid loading multiple times """ self._panda.reset(init_joints) self.place_back_objects() if scene_file is None or not os.path.exists(os.path.join(self.data_root_dir, scene_file + '.mat')): self._randomly_place_objects(self._get_random_object(self._numObjects), scale=1) else: self.place_objects_from_scene(scene_file, self._objectUids) self._env_step = 0 self.retracted = False self.collided = False self.collided_before = False self.obj_names, self.obj_poses = self.get_env_info() self.init_target_height = self._get_target_relative_pose()[2, 3] self.curr_acc_points = np.zeros([3, 0]) if self._domain_randomization: self.load_textures() rand_tex_id = np.random.choice(len(self.table_textures)) p.changeVisualShape(self._objectUids[self.target_idx], -1, textureUniqueId=self.table_textures[rand_tex_id]) rand_tex_id = np.random.choice(len(self.table_textures)) p.changeVisualShape(self._objectUids[-2], -1, textureUniqueId=self.table_textures[rand_tex_id]) rand_tex_id = np.random.choice(len(self.table_textures)) p.changeVisualShape(self._objectUids[-1], -1, textureUniqueId=self.table_textures[rand_tex_id]) observation = self.enforce_face_target() if enforce_face_target else self._get_observation() observation = self.input_selection(observation) return observation def place_objects_from_scene(self, scene_file, objectUids=None): """ Place objects with poses based on the scene file """ if self.objects_loaded: objectUids = self._objectUids scene = sio.loadmat(os.path.join(self.data_root_dir, scene_file + '.mat')) poses = scene['pose'] path = scene['path'] pos, orn = p.getBasePositionAndOrientation(self._panda.pandaUid) new_objs = objectUids is None objects_paths = [p_.strip() + '/' for p_ in path] for i, name in enumerate(objects_paths[:-2]): pose = poses[i] trans = pose[:3, 3] + np.array(pos) # fixed position orn = ros_quat(mat2quat(pose[:3, :3])) full_name = os.path.join(self.root_dir, name) if full_name not in self.obj_path: continue k = self.obj_path.index(full_name) if self.objects_loaded else i self.placed_objects[k] = True p.resetBasePositionAndOrientation(objectUids[k], trans, orn) p.resetBaseVelocity( objectUids[k], (0.0, 0.0, 0.0), (0.0, 0.0, 0.0) ) rand_name = objects_paths[0] self.target_idx = self.obj_path.index(os.path.join(self.root_dir, rand_name)) self.target_name = rand_name.split('/')[-2] print('==== loaded scene: {} target: {} idx: {} init joint'.format(scene_file.split('/')[-1], self.target_name, self.target_idx)) if 'init_joints' in scene: self.reset_joint(scene['init_joints']) return objectUids def place_back_objects(self): for idx, obj in enumerate(self._objectUids): if self.placed_objects[idx]: p.resetBasePositionAndOrientation(obj, self.placed_object_poses[idx][0], self.placed_object_poses[idx][1]) self.placed_objects[idx] = False def load_textures(self): if hasattr(self, 'table_textures'): return texture_dir = os.path.join(self.root_dir, 'data/random_textures/textures') files = os.listdir(texture_dir) random_files = random.sample(files, 200) table_textures = [p.loadTexture(os.path.join(texture_dir, f)) for f in random_files] print('number of textures:', len(table_textures)) self.table_textures = table_textures def input_selection(self, observation): """ Select input channels based on data type """ return observation def update_curr_acc_points(self, new_points): """ Update accumulated points in world coordinate """ pos, rot = self._get_ef_pose() ef_pose = unpack_pose(np.hstack((pos, tf_quat(rot)))) new_points = ef_pose[:3, :3].dot(new_points) + ef_pose[:3, [3]] # accumulate points index = np.random.choice(range(new_points.shape[1]), size=int(self._pt_accumulate_ratio**self._env_step * new_points.shape[1]), replace=False).astype(np.int) self.curr_acc_points = np.concatenate((new_points[:, index], self.curr_acc_points), axis=1) def _get_init_info(self): return [self.obj_names, self.obj_poses, np.array(self._panda.getJointStates()[0])] def _add_mesh(self, obj_file, trans, quat, scale=1): """ Add a mesh with URDF file. """ bid = p.loadURDF(obj_file, trans, quat, globalScaling=scale, flags=p.URDF_ENABLE_CACHED_GRAPHICS_SHAPES) return bid def reset_joint(self, init_joints): if init_joints is not None: self._panda.reset(np.array(init_joints).flatten()) def process_action(self, action, delta=False, config=False): """ Process different action types """ if config: if delta: cur_joint = np.array(self._panda.getJointStates()[0]) action = cur_joint + action elif self._action_space == 'task6d': # transform to local coordinate cur_ef = np.array(self._panda.getJointStates()[0])[-3] pos, orn = p.getLinkState(self._panda.pandaUid, self._panda.pandaEndEffectorIndex)[4:6] pose = np.eye(4) pose[:3, :3] = quat2mat(tf_quat(orn)) pose[:3, 3] = pos pose_delta = np.eye(4) pose_delta[:3, :3] = euler2mat(action[3], action[4], action[5]) pose_delta[:3, 3] = action[:3] new_pose = pose.dot(pose_delta) orn = ros_quat(mat2quat(new_pose[:3, :3])) pos = new_pose[:3, 3] jointPoses = np.array(p.calculateInverseKinematics(self._panda.pandaUid, self._panda.pandaEndEffectorIndex, pos, orn, maxNumIterations=500, residualThreshold=1e-8)) jointPoses[6] = 0.0 action = jointPoses[:7] return action def _sample_ef(self, target, near=0.35, far=0.50): # sample a camera extrinsics count = 0 ik = None outer_loop_num = 20 inner_loop_num = 5 if not self._planner_setup: try: self.setup_expert_scene() except: print(f"{bcolors.FAIL}Expert Scene Setup Error.{bcolors.RESET}") pass for _ in range(outer_loop_num): theta = np.random.uniform(low=0, high=2*np.pi/3) phi = np.random.uniform(low=np.pi/2, high=3*np.pi/2) # top sphere r = np.random.uniform(low=self._initial_near, high=self._initial_far) # sphere radius pos = np.array([r*np.sin(theta)*np.cos(phi), r*np.sin(theta)*np.sin(phi), r*np.cos(theta)]) trans = pos + target + np.random.uniform(-0.03, 0.03, 3) trans[2] = np.clip(trans[2], 0.2, 0.6) trans[1] = np.clip(trans[1], -0.3, 0.3) trans[0] =

np.clip(trans[0], 0.0, 0.5)

numpy.clip

import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D # noqa: F401 from .. import style def make_axes(fig_width, wpad_edge=0, wpad_mid=0.05, hpad_top=0.05, hpad_bottom=0.05, small_sq_width=0.07): sq_width = (1. - 2 * wpad_edge - small_sq_width - 4 * wpad_mid) / 4. sq_height = 1. - hpad_top - hpad_bottom fig_height = sq_width * fig_width / sq_height small_sq_height = small_sq_width * fig_width / fig_height fig = plt.figure(figsize=(fig_width, fig_height)) # 2 small squares ax2 = fig.add_axes((wpad_edge, hpad_bottom, small_sq_width, small_sq_height)) ax1 = fig.add_axes((wpad_edge, 1. - hpad_top - small_sq_height, small_sq_width, small_sq_height)) # 3 big squares ax3 = fig.add_axes((wpad_edge + small_sq_width + wpad_mid, hpad_bottom, sq_width, sq_height)) ax4 = fig.add_axes((wpad_edge + small_sq_width + 2 * wpad_mid + sq_width, hpad_bottom, sq_width, sq_height)) ax5 = fig.add_axes((wpad_edge + small_sq_width + 3 * wpad_mid + 2 * sq_width, hpad_bottom, sq_width, sq_height)) ax6 = fig.add_axes((wpad_edge + small_sq_width + 4 * wpad_mid + 3 * sq_width, hpad_bottom, sq_width, sq_height)) axes = [ax1, ax2, ax3, ax4, ax5, ax6] for ax in axes: ax.set_xticks([]) ax.set_yticks([]) label_dx = -0.02 label_dy = 0.05 label_y = hpad_bottom + sq_height + label_dy fig.text(wpad_edge + label_dx, label_y, "A", va="bottom", ha="right", color="black", **style.panel_letter_fontstyle) fig.text(wpad_edge + small_sq_width + wpad_mid, label_y, "B", va="bottom", ha="center", color="black", **style.panel_letter_fontstyle) fig.text(wpad_edge + small_sq_width + 2 * wpad_mid + sq_width, label_y, "C", va="bottom", ha="center", color="black", **style.panel_letter_fontstyle) fig.text(wpad_edge + small_sq_width + 3 * wpad_mid + 2 * sq_width, label_y, "D", va="bottom", ha="center", color="black", **style.panel_letter_fontstyle) fig.text(wpad_edge + small_sq_width + 4 * wpad_mid + 3 * sq_width, label_y, "E", va="bottom", ha="center", color="black", **style.panel_letter_fontstyle) return axes def disp_heatmap(ax, heatmap, show_xlabels=True, show_ylabels=True, title=None): N_theta, N_phi = heatmap.shape ax.imshow(heatmap, origin="lower left", cmap="gray", aspect="equal") if show_xlabels: ax.set_xlabel("$\phi$", fontsize=style.axis_label_fontsize, labelpad=-8.5) ax.set_xticks([0, N_phi - 1]) ax.set_xticklabels(["0", "$\pi$"], fontsize=style.ticklabel_fontsize) else: ax.set_xticks([]) if show_ylabels: ax.set_ylabel("$\\theta$", fontsize=style.axis_label_fontsize, labelpad=-8.5) ax.set_yticks([0, N_theta - 1]) ax.set_yticklabels(["0", "$\pi$"], fontsize=style.ticklabel_fontsize) else: ax.set_yticks([]) ax.set_xlim([0, heatmap.shape[1] - 1]) ax.set_ylim([0, heatmap.shape[0] - 1]) if title is not None: ax.set_title(title, fontsize=style.axis_label_fontsize * 0.8, pad=1) def disp_scatter(ax, pi_gp, pi_knn, trajectories=None, diag_text=False, arrow=True, xlabel="full PI", ylabel="Gaussian PI"): # Note that gp=y and knn=x, but 0 index is gp and 1 is knn in data arrays! traj_color = "#C63F3A" all_gp_vals = [pi_gp] all_knn_vals = [pi_knn] if trajectories is not None: all_gp_vals += [traj[:, 0] for traj in trajectories] all_knn_vals += [traj[:, 1] for traj in trajectories] all_gp_vals =

np.concatenate(all_gp_vals)

numpy.concatenate

# this tells python to act as if though We are one folder up import sys sys.path.insert(0,'..') import pandas as pd import FixedEffectModelPyHDFE.api as FEM from FixedEffectModelPyHDFE.DemeanDataframe import get_np_columns #import FixedEffectModel.api as FEM import numpy as np from patsy import dmatrices import statsmodels.formula.api as smf import statsmodels.api as sm from fastreg import linear from datetime import datetime import unittest from math import isclose NLS_WORK = "./../data/test_dropped_na.dta" CEREAL = "./../data/cereal.dta" AUTO = "./../data/auto_drop_na.dta" TOLERANCE = 0.01 class FixedEffectsModelTestsVSfastreg(unittest.TestCase): def setup(self, data_directory, target, regressors, absorb, cluster): print(self._testMethodName) print("target: ", target) print("regressors: ", regressors) print("absorb: ", absorb) print("cluster: ", cluster) df = pd.read_stata(data_directory) df.reset_index(drop=True, inplace=True) fem_start = datetime.now() self.result = FEM.ols_high_d_category(df, regressors, target, absorb, cluster, formula=None, robust=False, epsilon = 1e-8, max_iter = 1e6) fem_end = datetime.now() print("FEM time taken: " + str(fem_end-fem_start)) self.result.summary() print() if absorb[0] == '0': absorb=None fastreg_start = datetime.now() fastreg = linear.ols(y=target[0], x=regressors, absorb=absorb, cluster=cluster, data=df) fastreg_end = datetime.now() print(fastreg) print("fastreg time taken: " + str(fastreg_end - fastreg_start)) print("\n\n\n\n\n") ######################################################################### ######################################################################### def test_just_absorb_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['idcode', 'birth_yr', 'fifty_clusts', 'sixty_clusts'], cluster=[]) def test_no_absorb_cluster_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['0'], cluster=['idcode', 'birth_yr', 'fifty_clusts', 'sixty_clusts']) # comparing fvalue def test_clustering_single_variable_no_absorb2_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['0'], cluster=['race']) # comparing fvalue assert(np.isclose(self.result.fvalue, 127593.72, atol=TOLERANCE)) # comparing standard errors assert(np.all(np.isclose(self.result.bse, np.asarray([.148934, .0065111, .0113615]), atol=TOLERANCE))) # comparing tvalues assert(np.all(np.isclose(self.result.tvalues, np.asarray([27.75, 2.32, 66.61]), atol=TOLERANCE))) def test_clustering_single_variable_no_absorb_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['0'], cluster=['fifty_clusts']) assert(np.isclose(self.result.fvalue, 10230.63, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.048274, .0044294, .0052923]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([85.60, 3.42, 143.00]), atol=TOLERANCE))) def test_clustering_two_variables_no_absorb_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['0'], cluster=['fifty_clusts', 'sixty_clusts']) assert(np.isclose(self.result.fvalue, 12347.24, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0518019, .0048228, .00492]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([79.77, 3.14, 153.82]), atol=TOLERANCE))) def test_clustering_many_variables_no_absorb_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['0'], cluster=['fifty_clusts', 'sixty_clusts', 'birth_yr', 'idcode']) assert(np.isclose(self.result.fvalue, 4664.62, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0551555, .0080815, .007881]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([74.92, 1.87, 96.03]), atol=TOLERANCE))) def test_just_absorb_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts', 'sixty_clusts', 'birth_yr', 'idcode'], cluster=[]) assert(np.isclose(self.result.fvalue, 3891.51, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0047052, .0096448]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([6.48, 88.22]), atol=TOLERANCE))) def test_cluster_1_absorb_1_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts'], cluster=['sixty_clusts']) assert(np.isclose(self.result.fvalue, 9884.24, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.004654, .0055812]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([3.18, 135.54]), atol=TOLERANCE))) def test_cluster_1_absorb_1_2_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts'], cluster=['fifty_clusts']) assert(np.isclose(self.result.fvalue, 10100.50, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0044538, .005324]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([3.33, 142.09]), atol=TOLERANCE))) def test_cluster_many_absorb_1_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts'], cluster=['fifty_clusts', 'sixty_clusts', 'idcode', 'year']) assert(np.isclose(self.result.fvalue, 86.89, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0189465, .0574001]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([0.78, 13.18]), atol=TOLERANCE))) def test_cluster_3_absorb_3_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts', 'sixty_clusts', 'ind_code'], cluster=['idcode', 'year', 'grade']) assert(np.isclose(self.result.fvalue, 113.61, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.0168144, .0501467]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([0.93, 15.03]), atol=TOLERANCE))) def test_cluster_3_absorb_3_2_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts', 'sixty_clusts', 'ind_code'], cluster=['fifty_clusts', 'sixty_clusts', 'ind_code']) assert(np.isclose(self.result.fvalue, 2525.34, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.004604, .0106474]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([3.41, 70.78]), atol=TOLERANCE))) def test_cluster_4_absorb_4_nls_work_dataset(self): self.setup(NLS_WORK, target=['ttl_exp'], regressors=['wks_ue', 'tenure'], absorb=['fifty_clusts', 'sixty_clusts', 'ind_code', 'idcode'], cluster=['fifty_clusts', 'sixty_clusts', 'ind_code', 'idcode']) assert(np.isclose(self.result.fvalue, 3191.76, atol=TOLERANCE)) assert(np.all(np.isclose(self.result.bse, np.asarray([.00498, .010914]), atol=TOLERANCE))) assert(np.all(np.isclose(self.result.tvalues, np.asarray([6.17, 77.85]), atol=TOLERANCE))) ######################################################################### ######################################################################### # Boston auto dataset def test_pure_regression_boston_auto_dataset(self): self.setup(AUTO, target=['price'], regressors=['weight', 'length', 'turn'], absorb=['0'], cluster=[]) # comparing fvalue assert(np.isclose(self.result.fvalue, 14.78, atol=TOLERANCE)) # comparing standard errors assert(np.all(np.isclose(self.result.bse, np.asarray([4667.441, 1.143408, 40.13139, 128.8455]), atol=TOLERANCE))) # comparing tvalues assert(np.all(np.isclose(self.result.tvalues, np.asarray([3.19, 4.67, -1.75, -2.28]), atol=TOLERANCE))) def test_clustering_one_variable_no_absorb_auto_dataset(self): self.setup(AUTO, target=['price'], regressors=['weight', 'length', 'turn'], absorb=['0'], cluster=['rep78']) # comparing fvalue assert(np.isclose(self.result.fvalue, 17.17, atol=TOLERANCE)) # comparing standard errors assert(np.all(np.isclose(self.result.bse, np.asarray([6132.17, .8258151, 24.15393, 191.4521]), atol=TOLERANCE))) # comparing tvalues assert(np.all(np.isclose(self.result.tvalues, np.asarray([2.42, 6.46, -2.91, -1.53]), atol=TOLERANCE))) def test_clustering_two_variables_no_absorb_auto_dataset(self): self.setup(AUTO, target=['price'], regressors=['weight', 'length', 'turn'], absorb=['0'], cluster=['rep78', 'headroom']) # comparing fvalue assert(np.isclose(self.result.fvalue, 27.03, atol=TOLERANCE)) # comparing standard errors assert(np.all(np.isclose(self.result.bse,

np.asarray([6037.897, 1.210828, 44.88812, 183.8683])

numpy.asarray

#!/bin/python import re import os import logging import yaml import pandas as pd import numpy as np import soundfile as sf from math import floor, ceil from pathlib import Path from dotenv import find_dotenv, load_dotenv def lengthAdjust(): logger = logging.getLogger(__name__) logger.info('adjusting length for label congruity') data_dir = 'data/raw/nips4b/wav/train/' out_dir = 'data/interim/nips4b/wav/train/' for filename in os.listdir(data_dir): [data, samplerate] = sf.read(data_dir + filename) desired_length = int(samplerate * N) logger.info('Processing ' + filename) logger.info("Number of Samples: " + str(desired_length)) logger.info("File length: " + str(desired_length/samplerate) + "s") data = np.asarray(data) zero_pad_length = desired_length - data.size zero_pad = np.zeros(zero_pad_length) data =

np.append(data, zero_pad)

numpy.append

"""test_rules - test the CPA rules parser """ import unittest from io import StringIO import numpy as np import cellprofiler_core.measurement import cellprofiler.utilities.rules as R OBJECT_NAME = "MyObject" M_FEATURES = ["Measurement%d" % i for i in range(1, 11)] class TestRules(unittest.TestCase): def test_01_01_load_rules(self): data = """IF (Nuclei_Intensity_UpperQuartileIntensity_CorrDend > 0.12762499999999999, [0.79607587785712131, -0.79607587785712131], [-0.94024303819690347, 0.94024303819690347]) IF (Nuclei_Intensity_MinIntensity_CorrAxon > 0.026831299999999999, [0.68998040630066426, -0.68998040630066426], [-0.80302016375137986, 0.80302016375137986]) IF (Nuclei_Intensity_UpperQuartileIntensity_CorrDend > 0.19306000000000001, [0.71934712791500899, -0.71934712791500899], [-0.47379648809429048, 0.47379648809429048]) IF (Nuclei_Intensity_UpperQuartileIntensity_CorrDend > 0.100841, [0.24553066971563919, -0.24553066971563919], [-1.0, 1.0]) IF (Nuclei_Location_Center_Y > 299.32499999999999, [-0.61833689824912363, 0.61833689824912363], [0.33384091087462237, -0.33384091087462237]) IF (Nuclei_Intensity_MaxIntensity_CorrNuclei > 0.76509499999999997, [-0.95683305069726121, 0.95683305069726121], [0.22816438860290775, -0.22816438860290775]) IF (Nuclei_Neighbors_NumberOfNeighbors_5 > 2.0, [-0.92848043428127192, 0.92848043428127192], [0.20751332434602923, -0.20751332434602923]) IF (Nuclei_Intensity_MedianIntensity_CorrDend > 0.15327499999999999, [0.79784566567342285, -0.79784566567342285], [-0.35665314560825129, 0.35665314560825129]) IF (Nuclei_Neighbors_SecondClosestXVector_5 > -11.5113, [-0.21859862538067179, 0.21859862538067179], [0.71270785008847592, -0.71270785008847592]) IF (Nuclei_Intensity_StdIntensity_CorrDend > 0.035382299999999998, [0.28838229530755011, -0.28838229530755011], [-0.75312050069265968, 0.75312050069265968]) IF (Nuclei_Intensity_MaxIntensityEdge_CorrNuclei > 0.63182899999999997, [-0.93629855522957672, 0.93629855522957672], [0.1710257492070047, -0.1710257492070047]) IF (Nuclei_Intensity_StdIntensityEdge_CorrNuclei > 0.037909400000000003, [0.28514731668218346, -0.28514731668218346], [-0.60783543053602795, 0.60783543053602795]) IF (Nuclei_Intensity_MedianIntensity_CorrAxon > 0.042631500000000003, [0.20227787378316109, -0.20227787378316109], [-0.78282539096589077, 0.78282539096589077]) IF (Nuclei_Intensity_MinIntensity_CorrDend > 0.042065400000000003, [0.52616744135942872, -0.52616744135942872], [-0.32613209033812068, 0.32613209033812068]) IF (Nuclei_Neighbors_FirstClosestYVector_5 > 3.8226100000000001, [0.69128399165300047, -0.69128399165300047], [-0.34874605597401531, 0.34874605597401531]) IF (Nuclei_Intensity_MeanIntensity_CorrNuclei > 0.283188, [-0.79881507037552979, 0.79881507037552979], [0.24825909570051025, -0.24825909570051025]) IF (Nuclei_Location_Center_Y > 280.154, [-0.50545174099468504, 0.50545174099468504], [0.3297202808867149, -0.3297202808867149]) IF (Nuclei_Intensity_UpperQuartileIntensity_CorrDend > 0.132241, [0.35771841831789791, -0.35771841831789791], [-0.63545019489162846, 0.63545019489162846]) IF (Nuclei_AreaShape_MinorAxisLength > 6.4944899999999999, [0.5755128363506562, -0.5755128363506562], [-0.41737581982462335, 0.41737581982462335]) IF (Nuclei_Intensity_LowerQuartileIntensity_CorrDend > 0.075424000000000005, [0.50557978238660795, -0.50557978238660795], [-0.35606081901385256, 0.35606081901385256]) """ fd = StringIO(data) rules = R.Rules() rules.parse(fd) self.assertEqual(len(rules.rules), 20) for rule in rules.rules: self.assertEqual(rule.object_name, "Nuclei") self.assertEqual(rule.comparitor, ">") rule = rules.rules[0] self.assertEqual(rule.feature, "Intensity_UpperQuartileIntensity_CorrDend") self.assertAlmostEqual(rule.threshold, 0.127625) self.assertAlmostEqual(rule.weights[0, 0], 0.79607587785712131) self.assertAlmostEqual(rule.weights[0, 1], -0.79607587785712131) self.assertAlmostEqual(rule.weights[1, 0], -0.94024303819690347) self.assertAlmostEqual(rule.weights[1, 1], 0.94024303819690347) def test_02_00_no_measurements(self): m = cellprofiler_core.measurement.Measurements() m.add_measurement(OBJECT_NAME, M_FEATURES[0], np.array([], float)) rules = R.Rules() rules.rules += [ R.Rules.Rule( OBJECT_NAME, M_FEATURES[0], ">", 0, np.array([[1.0, -1.0], [-1.0, 1.0]]) ) ] score = rules.score(m) self.assertEqual(score.shape[0], 0) self.assertEqual(score.shape[1], 2) def test_02_01_score_one_positive(self): m = cellprofiler_core.measurement.Measurements() m.add_measurement(OBJECT_NAME, M_FEATURES[0], np.array([1.5], float)) rules = R.Rules() rules.rules += [ R.Rules.Rule( OBJECT_NAME, M_FEATURES[0], ">", 0, np.array([[1.0, -0.5], [-2.0, 0.6]]) ) ] score = rules.score(m) self.assertEqual(score.shape[0], 1) self.assertEqual(score.shape[1], 2) self.assertAlmostEqual(score[0, 0], 1.0) self.assertAlmostEqual(score[0, 1], -0.5) def test_02_02_score_one_negative(self): m = cellprofiler_core.measurement.Measurements() m.add_measurement(OBJECT_NAME, M_FEATURES[0], np.array([1.5], float)) rules = R.Rules() rules.rules += [ R.Rules.Rule( OBJECT_NAME, M_FEATURES[0], ">", 2.0, np.array([[1.0, -0.5], [-2.0, 0.6]]), ) ] score = rules.score(m) self.assertEqual(score.shape[0], 1) self.assertEqual(score.shape[1], 2) self.assertAlmostEqual(score[0, 0], -2.0) self.assertAlmostEqual(score[0, 1], 0.6) def test_02_03_score_one_nan(self): m = cellprofiler_core.measurement.Measurements() m.add_measurement(OBJECT_NAME, M_FEATURES[0], np.array([np.NaN], float)) rules = R.Rules() rules.rules += [ R.Rules.Rule( OBJECT_NAME, M_FEATURES[0], ">", 2.0,

np.array([[1.0, -0.5], [-2.0, 0.6]])

numpy.array

from autoarray import exc from autoarray import util import numpy as np import pytest class TestMask1D: def test__total_image_pixels_1d_from(self): mask_1d = np.array([False, True, False, False, False, True]) assert util.mask_1d.total_pixels_1d_from(mask_1d=mask_1d) == 4 def test__total_sub_pixels_1d_from(self): mask_1d = np.array([False, True, False, False, False, True]) assert util.mask_1d.total_sub_pixels_1d_from(mask_1d=mask_1d, sub_size=2) == 8 def test__sub_native_index_for_sub_slim_index_1d_from(self): mask_1d = np.array([False, False, False, False]) sub_native_index_for_sub_slim_index_1d = util.mask_1d.native_index_for_slim_index_1d_from( mask_1d=mask_1d, sub_size=1 ) assert (sub_native_index_for_sub_slim_index_1d ==

np.array([0, 1, 2, 3])

numpy.array

""" Crystal class Class to store definition of a crystal, along with some analysis 1. geometric analysis (nearest neighbor displacements) 2. space group operations 3. point group operations for each basis position 4. Wyckoff position generation (for interstitials) """ __author__ = '<NAME>' import numpy as np import collections, copy, itertools from numbers import Number from math import gcd import yaml # use crystal.yaml to call--may need to change in the future from functools import reduce # YAML tags: # interfaces are either at the bottom, or staticmethods in the corresponding object NDARRAY_YAMLTAG = '!numpy.ndarray' GROUPOP_YAMLTAG = '!GroupOp' def gcdlist(lis): """Returns the GCD of a list of integers""" return reduce(gcd, lis) def incell(vec): """ Returns the vector inside the unit cell (in [0,1)**3) :param vec: 3-vector (unit coord) :return: 3-vector """ return vec - np.floor(vec + 1.0e-8) def inhalf(vec): """ Returns the vector inside the centered cell (in [-0.5,0.5)**3) :param vec: 3-vector (unit coord) :return: 3-vector """ return vec - np.floor(vec + 0.5) def maptranslation(oldpos, newpos, oldspins=None, newspins=None, threshold=1e-8): """ Given a list of transformed positions, identify if there's a translation vector that maps from the current positions to the new position. The mapping specifies the index that the *translated* atom corresponds to in the original position set. If unable to construct a mapping, the mapping return is None; the translation vector will be meaningless. If old/newspins are given then ONLY mappings that maintain spin are considered. This means that a loop is needed to consider possible spin phase factors. :param oldpos: list of list of array[3] :param newpos: list of list of array[3], same layout as oldpos :param oldspins: (optional) list of list of numbers/arrays :param newspins: (optional) list of list of numbers/arrays :return translation: array[3] :return mapping: list of list of indices """ # type-checking: if __debug__: if type(oldpos) is not list: raise TypeError('oldpos is not a list') if type(newpos) is not list: raise TypeError('newpos is not a list') if len(oldpos) != len(newpos): raise IndexError("{} and {} do not have the same length".format(oldpos, newpos)) for a, b in zip(oldpos, newpos): if type(a) is not list: raise TypeError("element of oldpos {} is not a list".format(a)) if type(b) is not list: raise TypeError("element of newpos {} is not a list".format(b)) if len(a) != len(b): raise IndexError("{} and {} do not have the same length".format(a, b)) if (oldspins is None) != (newspins is None): raise TypeError('give both or neither spin arguments') if oldspins is not None: if type(oldspins) is not list: raise TypeError('oldspins is not a list') if type(newspins) is not list: raise TypeError('newspins is not a list') if len(oldspins) != len(newspins): raise IndexError( "{} and {} do not have the same length".format(oldspins, newspins)) for a, b in zip(oldspins, newspins): if type(a) is not list: raise TypeError("element of oldspins {} is not a list".format(a)) if type(b) is not list: raise TypeError("element of newspins {} is not a list".format(b)) if len(a) != len(b): raise IndexError("{} and {} do not have the same length".format(a, b)) if oldspins is None: oldspins = [[0 for u in atomlist] for atomlist in oldpos] if newspins is None: newspins = oldspins # Work with the shortest possible list for identifying translations atomindex = 0 maxlen = len(oldpos[atomindex]) for i, ulist in enumerate(oldpos): if len(ulist) < maxlen: maxlen = len(ulist) atomindex = i ru0 = newpos[atomindex][0] for ub in oldpos[atomindex]: trans = inhalf(ub - ru0) foundmap = True # now check against all the others, and construct the mapping indexmap = [] for atomlist0, spinlist0, atomlist1, spinlist1 in zip(oldpos, oldspins, newpos, newspins): # work through the "new" positions if not foundmap: break maplist = [] for rua, sp1 in zip(atomlist1, spinlist1): for j, uj, sp0 in zip(itertools.count(), atomlist0, spinlist0): if not np.allclose(sp0, sp1, atol=threshold): continue # only allow maps that have same spin if np.allclose(inhalf(uj - rua - trans), 0, atol=threshold): maplist.append(j) break if len(maplist) != len(atomlist0): foundmap = False else: indexmap.append(tuple(maplist)) if foundmap: break if foundmap: return trans, tuple(indexmap) else: return None, None class GroupOp(collections.namedtuple('GroupOp', 'rot trans cartrot indexmap')): """ A class corresponding to a group operation. Based on namedtuple, so it is immutable. Intended to be used in combination with Crystal, we have a few operations that can be defined out-of-the-box. :param rot: np.array(3,3) integer idempotent matrix :param trans: np.array(3) real vector :param cartrot: np.array(3,3) real unitary matrix :param indexmap: tuples of tuples, containing the atom mapping """ def incell(self): """Return a version of groupop where the translation is in the unit cell""" return GroupOp(self.rot, incell(self.trans), self.cartrot, self.indexmap) def inhalf(self): """Return a version of groupop where the translation is in the centered unit cell""" return GroupOp(self.rot, inhalf(self.trans), self.cartrot, self.indexmap) @classmethod def ident(cls, basis): """Return a group operation corresponding to identity for a given basis""" return cls(rot=np.eye(3, dtype=int), trans=np.zeros(3), cartrot=np.eye(3), indexmap=tuple(tuple(i for i in range(len(atomlist))) for atomlist in basis)) def __str__(self): """Human-readable version of groupop""" str_rep = "#Rotation (lattice, cartesian):\n {}\t{}\n {}\t{}\n".format( self.rot[0], self.cartrot[0], self.rot[1], self.cartrot[1]) if self.rot.shape == (3,3): str_rep += " {}\t{}\n".format(self.rot[2], self.cartrot[2]) str_rep += "#Translation: {}\n#Indexmap:".format(self.trans) for chemind, atoms in enumerate(self.indexmap): for origind, finalind in enumerate(atoms): str_rep = str_rep + "\n {chem}.{o} -> {chem}.{f}".format(chem=chemind, o=origind, f=finalind) return str_rep def _asdict(self): """Return a proper dict""" return {'rot': self.rot, 'trans': self.trans, 'cartrot': self.cartrot, 'indexmap': self.indexmap} def __eq__(self, other): """Test for equality--we use numpy.isclose for comparison, since that's what we usually care about""" return isinstance(other, self.__class__) and \ np.all(self.rot == other.rot) and \ np.allclose(self.trans, other.trans) and \ np.allclose(self.cartrot, other.cartrot) and \ self.indexmap == other.indexmap def __ne__(self, other): """Inequality == not __eq__""" return not self.__eq__(other) def __hash__(self): """Hash, so that we can make sets of group operations""" ### we are a little conservative, and only use the rotation and indexmap to define the hash. This means ### we will get collisions for the same rotation but different unit cell translations. The reason is ### that __eq__ uses "isclose" on our translations, and we don't have a good way to handle ### that in a hash function. We lose a little bit on efficiency if we construct a set that ### has a whole lot of translation operations, but that's not usually what we will do. # return hash(self.rot.data.tobytes()) return hash(self.rot.data.tobytes()) ^ hash(self.indexmap) def __add__(self, other): """Add a translation to our group operation""" if __debug__: if type(other) is not np.ndarray: raise TypeError('Can only add a translation to a group operation') if other.shape != (self.rot.shape[0],): raise IndexError('Can only add a {} dimensional vector'.format(self.rot.shape[0])) if not np.issubdtype(other.dtype, np.integer): raise TypeError('Can only add a lattice vector translation') return GroupOp(self.rot, self.trans + other, self.cartrot, self.indexmap) def __sub__(self, other): """Add a (negative) translation to our group operation""" return self.__add__(-other) def __mul__(self, other): """Multiply two group operations to produce a new group operation""" if __debug__: if type(other) is not GroupOp: return NotImplemented return GroupOp(np.dot(self.rot, other.rot), np.dot(self.rot, other.trans) + self.trans, np.dot(self.cartrot, other.cartrot), tuple(tuple(atomlist0[i] for i in atomlist1) for atomlist0, atomlist1 in zip(self.indexmap, other.indexmap))) def __sane__(self): """Return true if the cartrot and rot are consistent and 'sane'""" tr = self.rot.trace() det = np.int(np.round(np.linalg.det(self.rot))) # consistency: if np.int(np.round(self.cartrot.trace())) != tr: return False if np.int(np.round(np.linalg.det(self.cartrot))) != det: return False # sanity: if abs(det) != 1: return False dimshift = 0 if self.rot.shape[0] == 3 else -1 if det * tr < (-1+dimshift) or det * tr > (3+dimshift): return False return True def inv(self): """Construct and return the inverse of the group operation""" inverse = (np.round(np.linalg.inv(self.rot))).astype(int) return GroupOp(inverse, -np.dot(inverse, self.trans), self.cartrot.T, tuple(tuple(x for i, x in sorted([(y, j) for j, y in enumerate(atomlist)])) for atomlist in self.indexmap)) @staticmethod def optype(rot): """Returns the type of group operation (single integer): 1 = identity 2, 3, 4, 6 = n- fold rotation around an axis negative = rotation + mirror operation, perpendicular to axis "special cases": -1 = mirror, -2 = inversion :param rot: rotation matrix (can be the integer rot) :return type: integer """ # dim = rot.shape[0] dimindexpos, dimindexneg = (1, 3) if rot.shape[0] == 3 else (2, 4) tr = np.int(rot.trace()) if np.linalg.det(rot) > 0: return (2, 3, 4, 6, 1)[tr + dimindexpos] # trace determines the rotation type [tr + 1] for 3d else: return (-2, -3, -4, -6, -1)[tr + dimindexneg] # trace determines the rotation type [tr + 3] fpr 3d def eigen(self): """Returns the type of group operation (single integer) and eigenvectors. 1 = identity 2, 3, 4, 6 = n- fold rotation around an axis negative = rotation + mirror operation, perpendicular to axis "special cases": -1 = mirror, -2 = inversion eigenvect[0] = axis of rotation / mirror eigenvect[1], eigenvect[2] = orthonormal vectors to define the plane giving a right-handed coordinate system and where rotation around [0] is positive, and the positive imaginary eigenvector for the complex eigenvalue is [1] + i [2]. :return type: integer :return eigenvectors: list of [ev0, ev1, ev2] """ if __debug__: if not self.__sane__(): raise ValueError('Bad GroupOp:\n{}'.format(self)) optype = self.optype(self.rot) det = 1 if optype > 0 else -1 tr = np.int(self.rot.trace()) # two trivial cases: identity, inversion: if optype == 1 or optype == -2: return optype, np.eye(self.rot.shape[0]) if self.rot.shape[0] == 2: if optype != -1: return optype, np.eye(self.rot.shape[0]) # only interesting case is how to deal with is the mirror plane; find the angle of the mirror phi = 0.5*np.arctan2(self.cartrot[0,1]+self.cartrot[1,0], self.cartrot[0,0]-self.cartrot[1,1]) return optype, np.array([[np.cos(phi), -np.sin(phi)], [np.sin(phi), np.cos(phi)]]) # otherwise, there's an axis to find: vmat = np.eye(3) vsum = np.zeros((3, 3)) if det > 0: for n in range(optype): vsum += vmat vmat = np.dot(self.cartrot, vmat) else: for n in range((0, 6, 4, 3, 2)[tr + 3]): # vsum += vmat vmat = -np.dot(self.cartrot, vmat) # vmat *should* equal identity if we didn't fail... if __debug__: if not np.allclose(vmat, np.eye(3)): raise ArithmeticError('eigenvalue analysis fail') vsum *= 1. / n # now the columns of vsum should either be (a) our rotation / mirror axis, or (b) zero eig0 = vsum[:, 0] magn0 = np.dot(eig0, eig0) if magn0 < 1e-2: eig0 = vsum[:, 1] magn0 = np.dot(eig0, eig0) if magn0 < 1e-2: eig0 = vsum[:, 2] magn0 = np.dot(eig0, eig0) eig0 /= np.sqrt(magn0) # now, construct the other two directions: if abs(eig0[2]) < 0.75: eig1 = np.array([eig0[1], -eig0[0], 0]) else: eig1 = np.array([-eig0[2], 0, eig0[0]]) eig1 /= np.sqrt(np.dot(eig1, eig1)) eig2 = np.cross(eig0, eig1) # we have a right-handed coordinate system; test that we have a positive rotation around the axis if abs(optype) > 2: if np.dot(eig2, np.dot(self.cartrot, eig1)) > 0: eig0 = -eig0 eig2 = -eig2 return optype, [eig0, eig1, eig2] @staticmethod def GroupOp_representer(dumper, data): """Output a GroupOp""" # asdict() returns an OrderedDictionary, so pass through dict() # had to rewrite _asdict() for some reason...? return dumper.represent_mapping(GROUPOP_YAMLTAG, data._asdict()) @staticmethod def GroupOp_constructor(loader, node): """Construct a GroupOp from YAML""" # ** turns the dictionary into parameters for GroupOp constructor return GroupOp(**loader.construct_mapping(node, deep=True)) def VectorBasis(rottype, eigenvect): """ Returns a vector basis corresponding to the optype and eigenvectors for a GroupOp :param rottype: output from eigen() :param eigenvect: eigenvectors :return dim: dimensionality, 0..3 :return vect: vector defining line direction (1) or plane normal (2) """ # 2d first if len(eigenvect) == 2: if rottype == 1: return (2, np.zeros(2)) # sphere (identity) if rottype == -1: return (1, eigenvect[0]) # plane (pure mirror) return (0, np.zeros(2)) # all others are rotation, which leaves nothing unchanged in 2d # edge cases first: if rottype == 1: return (3,

np.zeros(3)

numpy.zeros

""" rnn_lstm_cell_test_cy.py Test the correctness of the LSTM-cell implementation. """ import os import unittest from random import random from numpy import asarray, ones, zeros from torch import float64, FloatTensor, tensor from torch.nn import LSTMCell as PytorchLSTM from population.utils.rnn_cell_util.cy.lstm_cy import LSTMCellCy as LSTMCell EPSILON = 1e-5 def get_lstm(input_size): """Get a LSTM-cell of the requested input-size, completely initialized with zeros.""" bias_h = zeros((4,)) weight_hh = zeros((4, 1)) weight_xh = zeros((4, input_size)) return LSTMCell( input_size=input_size, bias=bias_h, weight_hh=weight_hh, weight_xh=weight_xh, ) def get_pytorch_lstm(input_size, used_lstm): """Load in a PyTorch LSTM that is a copy of the currently used LSTM.""" lstm = PytorchLSTM(input_size, 1) lstm.bias_hh[:] = tensor(zeros((4,)), dtype=float64)[:] lstm.bias_ih[:] = tensor(used_lstm.bias, dtype=float64)[:] lstm.weight_hh[:] = tensor(used_lstm.weight_hh, dtype=float64)[:] lstm.weight_ih[:] = tensor(used_lstm.weight_xh, dtype=float64)[:] return lstm # noinspection PyArgumentList class LSTM(unittest.TestCase): """Test the custom numpy implementation of the LSTM-cell.""" def test_single_input_single_batch(self): """> Test when only one input given and batch-size is only one.""" # Folder must be root to load in make_net properly if os.getcwd().split('\\')[-1] == 'tests': os.chdir('..') # Get 'empty' LSTM lstm = get_lstm(1) # Completely zero LSTM, all inputs get ignored self.assertEqual(lstm(asarray([[0]])), 0) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it self.assertEqual(lstm(asarray([[1]])), 0) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it # Modify the LSTM to have weight-arrays of one lstm.weight_hh = asarray(ones((4, 1))) lstm.weight_xh = asarray(ones((4, 1))) # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(1, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i]])) self.assertEqual(a.shape, b.shape) self.assertTrue(float(a) - EPSILON <= float(b) <= float(a) + EPSILON) # Set bias to minus ones lstm.bias = ones((4,)) * -1 # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(1, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i]])) self.assertEqual(a.shape, b.shape) self.assertTrue(float(a) - EPSILON <= float(b) <= float(a) + EPSILON) def test_single_input_multi_batch(self): """> Test when only one input given and batch-size is more than one.""" # Folder must be root to load in make_net properly if os.getcwd().split('\\')[-1] == 'tests': os.chdir('..') # Get 'empty' LSTM lstm = get_lstm(1) # Completely zero LSTM, all inputs get ignored result = lstm(asarray([[0], [0]])) for aa, bb in zip(result, asarray([[0], [0]])): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it result = lstm(asarray([[1], [1]])) for aa, bb in zip(result, asarray([[0], [0]])): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it # Modify the LSTM to have weight-arrays of one lstm.weight_hh = ones((4, 1)) lstm.weight_xh = ones((4, 1)) # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(1, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i], [i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i], [i]])) self.assertEqual(a.shape, b.shape) for aa, bb in zip(a, b): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) # Set bias to minus ones lstm.bias = ones((4,)) * -1 # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(1, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i], [i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i], [i]])) self.assertEqual(a.shape, b.shape) for aa, bb in zip(a, b): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) def test_multi_input_single_batch(self): """> Test when only one input given and batch-size is more than one.""" # Folder must be root to load in make_net properly if os.getcwd().split('\\')[-1] == 'tests': os.chdir('..') # Get 'empty' LSTM lstm = get_lstm(2) # Completely zero LSTM, all inputs get ignored self.assertEqual(lstm(asarray([[0, 0]])), 0) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it self.assertEqual(lstm(asarray([[1, 1]])), 0) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it # Modify the LSTM to have weight-arrays of one lstm.weight_hh = ones((4, 1)) lstm.weight_xh = ones((4, 2)) # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(2, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i, i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i, i]])) self.assertEqual(a.shape, b.shape) for aa, bb in zip(a, b): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) # Set bias to minus ones lstm.bias = ones((4,)) * -1 # Load in PyTorch native LSTM to compare with pytorch_lstm = get_pytorch_lstm(2, lstm) # Test if they continue to obtain the same results for _ in range(100): i = random() a = lstm(asarray([[i, i]])) lstm.hx, lstm.c = asarray([]), asarray([]) # LSTM keeps own state, reset it (b, _) = pytorch_lstm(FloatTensor([[i, i]])) self.assertEqual(a.shape, b.shape) for aa, bb in zip(a, b): self.assertTrue(float(aa) - EPSILON <= float(bb) <= float(aa) + EPSILON) def test_multi_input_multi_batch(self): """> Test when only one input given and batch-size is more than one.""" # Folder must be root to load in make_net properly if os.getcwd().split('\\')[-1] == 'tests': os.chdir('..') # Get 'empty' LSTM lstm = get_lstm(2) # Completely zero LSTM, all inputs get ignored result = lstm(asarray([[0, 0], [0, 0]])) for aa, bb in zip(result,

asarray([[0], [0]])

numpy.asarray

# -*- coding: utf-8 -*- # pylint: disable=invalid-name, too-many-arguments, too-many-instance-attributes """Copyright 2015 <NAME>. FilterPy library. http://github.com/rlabbe/filterpy Documentation at: https://filterpy.readthedocs.org Supporting book at: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python This is licensed under an MIT license. See the readme.MD file for more information. """ from __future__ import (absolute_import, division, unicode_literals) from copy import deepcopy from math import log, exp, sqrt import sys import warnings import numpy as np from numpy import dot, zeros, eye import scipy.linalg as linalg from filterpy.stats import logpdf from filterpy.common import pretty_str class FadingKalmanFilter(object): """ Fading memory Kalman filter. This implements a linear Kalman filter with a fading memory effect controlled by `alpha`. This is obsolete. The class KalmanFilter now incorporates the `alpha` attribute, and should be used instead. You are responsible for setting the various state variables to reasonable values; the defaults below will not give you a functional filter. Parameters ---------- alpha : float, >= 1 alpha controls how much you want the filter to forget past measurements. alpha==1 yields identical performance to the Kalman filter. A typical application might use 1.01 dim_x : int Number of state variables for the Kalman filter. For example, if you are tracking the position and velocity of an object in two dimensions, dim_x would be 4. This is used to set the default size of P, Q, and u dim_z : int Number of of measurement inputs. For example, if the sensor provides you with position in (x,y), dim_z would be 2. dim_u : int (optional) size of the control input, if it is being used. Default value of 0 indicates it is not used. Attributes ---------- You will have to assign reasonable values to all of these before running the filter. All must have dtype of float x : ndarray (dim_x, 1), default = [0,0,0...0] state of the filter P : ndarray (dim_x, dim_x), default identity matrix covariance matrix x_prior : numpy.array(dim_x, 1) Prior (predicted) state estimate. The *_prior and *_post attributes are for convienence; they store the prior and posterior of the current epoch. Read Only. P_prior : numpy.array(dim_x, dim_x) Prior (predicted) state covariance matrix. Read Only. x_post : numpy.array(dim_x, 1) Posterior (updated) state estimate. Read Only. P_post : numpy.array(dim_x, dim_x) Posterior (updated) state covariance matrix. Read Only. z : ndarray Last measurement used in update(). Read only. Q : ndarray (dim_x, dim_x), default identity matrix Process uncertainty matrix R : ndarray (dim_z, dim_z), default identity matrix measurement uncertainty H : ndarray (dim_z, dim_x) measurement function F : ndarray (dim_x, dim_x) state transition matrix B : ndarray (dim_x, dim_u), default 0 control transition matrix y : numpy.array Residual of the update step. Read only. K : numpy.array(dim_x, dim_z) Kalman gain of the update step. Read only. S : numpy.array System uncertainty (P projected to measurement space). Read only. S : numpy.array Inverse system uncertainty. Read only. log_likelihood : float log-likelihood of the last measurement. Read only. likelihood : float likelihood of last measurement. Read only. Computed from the log-likelihood. The log-likelihood can be very small, meaning a large negative value such as -28000. Taking the exp() of that results in 0.0, which can break typical algorithms which multiply by this value, so by default we always return a number >= sys.float_info.min. mahalanobis : float mahalanobis distance of the innovation. Read only. Examples -------- See my book Kalman and Bayesian Filters in Python https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python """ def __init__(self, alpha, dim_x, dim_z, dim_u=0): warnings.warn( "Use KalmanFilter class instead; it also provides the alpha attribute", DeprecationWarning) assert alpha >= 1 assert dim_x > 0 assert dim_z > 0 assert dim_u >= 0 self.alpha_sq = alpha**2 self.dim_x = dim_x self.dim_z = dim_z self.dim_u = dim_u self.x = zeros((dim_x, 1)) # state self.P = eye(dim_x) # uncertainty covariance self.Q = eye(dim_x) # process uncertainty self.B = 0. # control transition matrix self.F = np.eye(dim_x) # state transition matrix self.H = zeros((dim_z, dim_x)) # Measurement function self.R = eye(dim_z) # state uncertainty self.z = np.array([[None]*dim_z]).T # gain and residual are computed during the innovation step. We # save them so that in case you want to inspect them for various # purposes self.K = 0 # kalman gain self.y = zeros((dim_z, 1)) self.S = np.zeros((dim_z, dim_z)) # system uncertainty (measurement space) self.SI = np.zeros((dim_z, dim_z)) # inverse system uncertainty # identity matrix. Do not alter this. self.I = np.eye(dim_x) # Only computed only if requested via property self._log_likelihood = log(sys.float_info.min) self._likelihood = sys.float_info.min self._mahalanobis = None # these will always be a copy of x,P after predict() is called self.x_prior = self.x.copy() self.P_prior = self.P.copy() # these will always be a copy of x,P after update() is called self.x_post = self.x.copy() self.P_post = self.P.copy() def update(self, z, R=None): """ Add a new measurement (z) to the kalman filter. If z is None, nothing is changed. Parameters ---------- z : np.array measurement for this update. R : np.array, scalar, or None Optionally provide R to override the measurement noise for this one call, otherwise self.R will be used. """ if z is None: self.z = np.array([[None]*self.dim_z]).T self.x_post = self.x.copy() self.P_post = self.P.copy() return if R is None: R = self.R elif

np.isscalar(R)

numpy.isscalar

"""Define the DefaultAllocator class.""" from __future__ import division import warnings import numpy as np from six.moves import range from openmdao.proc_allocators.proc_allocator import ProcAllocator, ProcAllocationError from openmdao.utils.mpi import MPI class DefaultAllocator(ProcAllocator): """ Default processor allocator. """ def _divide_procs(self, req_procs, comm): """ Perform the parallel processor allocation. Parameters ---------- req_procs : list of (int, int) List of min/max usable procs for each subsystem. comm : MPI.Comm or <FakeComm> communicator of the owning system. Returns ------- isubs : [int, ...] indices of the owned local subsystems. sub_comm : MPI.Comm or <FakeComm> communicator to pass to the subsystems. sub_proc_range : (int, int) The range of processors that the subcomm owns, among those of comm. """ iproc = comm.rank nproc = comm.size nsub = len(req_procs) min_req_procs = [minproc for minproc, _ in req_procs] max_req_procs = [maxproc for _, maxproc in req_procs] assigned_procs = np.zeros(nsub, dtype=int) assigned = 0 total_req = np.sum(min_req_procs) if None in max_req_procs: limit = nproc max_requested = nproc else: max_requested = np.sum(max_req_procs) limit = min(nproc, max_requested) # first, just use simple round robin assignment of requested procs # until everybody has what they asked for or we run out if total_req: if nproc >= total_req: # we have enough for all subsystems while assigned < limit: for i, max_req in enumerate(max_req_procs): if max_req is None or assigned_procs[i] < max_req: assigned_procs[i] += 1 assigned += 1 if assigned == limit: break # create buckets (one sub per bucket) to be consistent in how # we split procs below buckets = [(n, [i]) for i, n in enumerate(assigned_procs)] else: # we don't have enough, so have to group subsystems remaining = nproc # sort req procs in descending order tups = sorted([(req[0], i) for i, req in enumerate(req_procs)], reverse=True) buckets = [] for i, (req, sub_idx) in enumerate(tups): if remaining >= req: buckets.append([req, [sub_idx]]) remaining -= req elif i == 0: # since we sorted in descending order by number of # requested procs, only in the first iteration is there # a chance that we've requested more procs than we have raise ProcAllocationError(sub_idx, req, remaining) else: # we already have at least one in the bucket list that's # big enough, so go through buckets, find all that are # big enough, and add the current sub to the one with # the fewest number of subs already in it. In the event # of a tie, take the bucket with the lowest number of # requested procs. lenlist = sorted([b for b in buckets if b[0] >= req], key=lambda t: len(t[1])) shortest = len(lenlist[0][1]) final = sorted(b for b in lenlist if len(b[1]) == shortest) final[0][1].append(sub_idx) warnings.warn("System requested %d processes to run fully " "in parallel, but it only got %d" % (total_req, nproc)) # if we have any procs left over, apply them to any sub that # can use them while remaining > 0: for i, max_req in enumerate(max_req_procs): procs, subs = buckets[i] for sub_idx in subs: if (max_req is None or max_req > procs): # add 1 to procs for this bucket buckets[i][0] += 1 remaining -= 1 break if remaining == 0: break assigned = nproc - remaining # a 'color' is assigned to each bucket, with # an entry for each processor it will be given # e.g. [0, 1, 1, 1, 1, 2, 2, 3, 3, 3, UND, UND] color = np.full(nproc, MPI.UNDEFINED, dtype=int) comm_sizes = np.empty(nproc, int) start, end = 0, 0 for i, b in enumerate(buckets): num_procs = b[0] end += num_procs color[start:end] = i comm_sizes[start:end] = num_procs start += num_procs # create a sub-communicator for each color and # get the one assigned to our color/process rank_color = color[iproc] sub_comm = comm.Split(rank_color) sub_proc_range = (np.sum(comm_sizes[:iproc]),

np.sum(comm_sizes[:iproc + 1])

numpy.sum

# -*- coding: utf-8 -*- """ Created on Tue Dec 18 20:56:46 2018 @author: nooteboom """ import numpy as np import matplotlib.pylab as plt import matplotlib from matplotlib.font_manager import FontProperties import seaborn as sns sns.set(style="darkgrid") font = {'family' : 'Helvetica', # 'weight' : 'bold', 'size' : 22} matplotlib.rc('font', **font) res = 10000 z = np.linspace(10,6000,res) c3 = np.full(res, 3) c6 = np.full(res, 6) c11 = np.full(res, 11) c25 = np.full(res, 25) c50 = np.full(res, 50) c100 = np.full(res, 100) c200 =

np.full(res, 200)

numpy.full

# Copyright (c) Facebook, Inc. and its affiliates # Copyright (c) MTRF authors import collections import numpy as np from typing import Any, Dict, Optional, NewType, Sequence, Union, Tuple from r3l.r3l_envs.inhand_env.base import ObjectType from r3l.r3l_envs.inhand_env.reposition import SawyerDhandInHandObjectRepositionFixed from r3l.robot.object import ObjectState from r3l.utils.quatmath import quat2euler, euler2quat from r3l.utils.range import get_range_from_params from r3l.utils.circle_math import circle_distance, circle_distance_mod from r3l.robot.default_configs import REORIENT_SAWYER_ROBOT_CONFIG class SawyerDhandInHandObjectReorientFixed(SawyerDhandInHandObjectRepositionFixed): DEFAULT_REWARD_KEYS_AND_WEIGHTS = { "object_to_target_circle_distance_reward": 1.0, "object_to_target_xy_distance_reward": 1.0, "object_to_hand_xyz_distance_reward": 1.0, # "span_dist": 1.0, "small_bonus": 1.0, "big_bonus": 1.0, } def __init__( self, object_type: ObjectType = ObjectType.Rod, random_init_angle: bool = False, random_target_angle: bool = False, symmetric_task: bool = True, reorient_only: bool = False, **kwargs ): if random_init_angle: init_euler_params = { "type": "UniformRange", "values": [np.array([0, 0, -np.pi]), np.array([0, 0, np.pi])], } else: init_euler_params = { "type": "DiscreteRange", "values": [np.array([0, 0, 0])], } target_xyz_params = { "type": "DiscreteRange", "values": [

np.array([0.72, 0.15, 0.76])

numpy.array

# ***** BEGIN GPL LICENSE BLOCK ***** # # # This program is free software; you can redistribute it and/or # modify it under the terms of the GNU General Public License # as published by the Free Software Foundation; either version 2 # of the License, or (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; if not, write to the Free Software Foundation, # Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. # # ***** END GPL LICENCE BLOCK ***** # # ----------------------------------------------------------------------- # Author: <NAME> (Clockmender), <NAME> (ermo) Copyright (c) 2019 # ----------------------------------------------------------------------- # import bmesh import numpy as np from math import sqrt, tan, pi from mathutils import Vector from mathutils.geometry import intersect_point_line from .pdt_functions import ( set_mode, oops, get_percent, dis_ang, check_selection, arc_centre, intersection, view_coords_i, view_coords, view_dir, set_axis, ) from . import pdt_exception PDT_SelectionError = pdt_exception.SelectionError PDT_InvalidVector = pdt_exception.InvalidVector PDT_ObjectModeError = pdt_exception.ObjectModeError PDT_InfRadius = pdt_exception.InfRadius PDT_NoObjectError = pdt_exception.NoObjectError PDT_IntersectionError = pdt_exception.IntersectionError PDT_InvalidOperation = pdt_exception.InvalidOperation PDT_VerticesConnected = pdt_exception.VerticesConnected PDT_InvalidAngle = pdt_exception.InvalidAngle from .pdt_msg_strings import ( PDT_ERR_BAD3VALS, PDT_ERR_BAD2VALS, PDT_ERR_BAD1VALS, PDT_ERR_CONNECTED, PDT_ERR_SEL_2_VERTS, PDT_ERR_EDOB_MODE, PDT_ERR_NO_ACT_OBJ, PDT_ERR_VERT_MODE, PDT_ERR_SEL_3_VERTS, PDT_ERR_SEL_3_OBJS, PDT_ERR_EDIT_MODE, PDT_ERR_NON_VALID, PDT_LAB_NOR, PDT_ERR_STRIGHT_LINE, PDT_LAB_ARCCENTRE, PDT_ERR_SEL_4_VERTS, PDT_ERR_INT_NO_ALL, PDT_LAB_INTERSECT, PDT_ERR_SEL_4_OBJS, PDT_INF_OBJ_MOVED, PDT_ERR_SEL_2_VERTIO, PDT_ERR_SEL_2_OBJS, PDT_ERR_SEL_3_VERTIO, PDT_ERR_TAPER_ANG, PDT_ERR_TAPER_SEL, PDT_ERR_INT_LINES, PDT_LAB_PLANE, ) def vector_build(context, pg, obj, operation, values, num_values): """Build Movement Vector from Input Fields. Args: context: Blender bpy.context instance. pg: PDT Parameters Group - our variables obj: The Active Object operation: The Operation e.g. Create New Vertex values: The paramters passed e.g. 1,4,3 for Cartesian Coordinates num_values: The number of values passed - determines the function Returns: Vector to position, or offset, items. """ scene = context.scene plane = pg.plane flip_angle = pg.flip_angle flip_percent= pg.flip_percent # Cartesian 3D coordinates if num_values == 3 and len(values) == 3: output_vector = Vector((float(values[0]), float(values[1]), float(values[2]))) # Polar 2D coordinates elif num_values == 2 and len(values) == 2: output_vector = dis_ang(values, flip_angle, plane, scene) # Percentage of imaginary line between two 3D coordinates elif num_values == 1 and len(values) == 1: output_vector = get_percent(obj, flip_percent, float(values[0]), operation, scene) else: if num_values == 3: pg.error = PDT_ERR_BAD3VALS elif num_values == 2: pg.error = PDT_ERR_BAD2VALS else: pg.error = PDT_ERR_BAD1VALS context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_InvalidVector return output_vector def placement_normal(context, operation): """Manipulates Geometry, or Objects by Normal Intersection between 3 points. Args: context: Blender bpy.context instance. operation: The Operation e.g. Create New Vertex Returns: Status Set. """ scene = context.scene pg = scene.pdt_pg extend_all = pg.extend obj = context.view_layer.objects.active if obj.mode == "EDIT": if obj is None: pg.error = PDT_ERR_NO_ACT_OBJ context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_ObjectModeError obj_loc = obj.matrix_world.decompose()[0] bm = bmesh.from_edit_mesh(obj.data) if len(bm.select_history) == 3: vector_a, vector_b, vector_c = check_selection(3, bm, obj) if vector_a is None: pg.error = PDT_ERR_VERT_MODE context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_FeatureError else: pg.error = f"{PDT_ERR_SEL_3_VERTIO} {len(bm.select_history)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError elif obj.mode == "OBJECT": objs = context.view_layer.objects.selected if len(objs) != 3: pg.error = f"{PDT_ERR_SEL_3_OBJS} {len(objs)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError objs_s = [ob for ob in objs if ob.name != obj.name] vector_a = obj.matrix_world.decompose()[0] vector_b = objs_s[-1].matrix_world.decompose()[0] vector_c = objs_s[-2].matrix_world.decompose()[0] vector_delta = intersect_point_line(vector_a, vector_b, vector_c)[0] if operation == "C": if obj.mode == "EDIT": scene.cursor.location = obj_loc + vector_delta elif obj.mode == "OBJECT": scene.cursor.location = vector_delta elif operation == "P": if obj.mode == "EDIT": pg.pivot_loc = obj_loc + vector_delta elif obj.mode == "OBJECT": pg.pivot_loc = vector_delta elif operation == "G": if obj.mode == "EDIT": if extend_all: for v in [v for v in bm.verts if v.select]: v.co = vector_delta bm.select_history.clear() bmesh.ops.remove_doubles(bm, verts=[v for v in bm.verts if v.select], dist=0.0001) else: bm.select_history[-1].co = vector_delta bm.select_history.clear() bmesh.update_edit_mesh(obj.data) elif obj.mode == "OBJECT": context.view_layer.objects.active.location = vector_delta elif operation == "N": if obj.mode == "EDIT": vertex_new = bm.verts.new(vector_delta) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() for v in [v for v in bm.verts if v.select]: v.select_set(False) vertex_new.select_set(True) else: pg.error = f"{PDT_ERR_EDIT_MODE} {obj.mode})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") return elif operation == "V" and obj.mode == "EDIT": vector_new = vector_delta vertex_new = bm.verts.new(vector_new) if extend_all: for v in [v for v in bm.verts if v.select]: bm.edges.new([v, vertex_new]) else: bm.edges.new([bm.select_history[-1], vertex_new]) for v in [v for v in bm.verts if v.select]: v.select_set(False) vertex_new.select_set(True) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() else: pg.error = f"{operation} {PDT_ERR_NON_VALID} {PDT_LAB_NOR}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") def placement_arc_centre(context, operation): """Manipulates Geometry, or Objects to an Arc Centre defined by 3 points on an Imaginary Arc. Args: context: Blender bpy.context instance. operation: The Operation e.g. Create New Vertex Returns: Status Set. """ scene = context.scene pg = scene.pdt_pg extend_all = pg.extend obj = context.view_layer.objects.active if obj.mode == "EDIT": if obj is None: pg.error = PDT_ERR_NO_ACT_OBJ context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_ObjectModeError obj = context.view_layer.objects.active obj_loc = obj.matrix_world.decompose()[0] bm = bmesh.from_edit_mesh(obj.data) verts = [v for v in bm.verts if v.select] if len(verts) != 3: pg.error = f"{PDT_ERR_SEL_3_VERTS} {len(verts)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError vector_a = verts[0].co vector_b = verts[1].co vector_c = verts[2].co vector_delta, radius = arc_centre(vector_a, vector_b, vector_c) if str(radius) == "inf": pg.error = PDT_ERR_STRIGHT_LINE context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_InfRadius pg.distance = radius if operation == "C": scene.cursor.location = obj_loc + vector_delta elif operation == "P": pg.pivot_loc = obj_loc + vector_delta elif operation == "N": vector_new = vector_delta vertex_new = bm.verts.new(vector_new) for v in [v for v in bm.verts if v.select]: v.select_set(False) vertex_new.select_set(True) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() vertex_new.select_set(True) elif operation == "G": if extend_all: for v in [v for v in bm.verts if v.select]: v.co = vector_delta bm.select_history.clear() bmesh.ops.remove_doubles(bm, verts=[v for v in bm.verts if v.select], dist=0.0001) else: bm.select_history[-1].co = vector_delta bm.select_history.clear() bmesh.update_edit_mesh(obj.data) elif operation == "V": vertex_new = bm.verts.new(vector_delta) if extend_all: for v in [v for v in bm.verts if v.select]: bm.edges.new([v, vertex_new]) v.select_set(False) vertex_new.select_set(True) bm.select_history.clear() bmesh.ops.remove_doubles(bm, verts=[v for v in bm.verts if v.select], dist=0.0001) bmesh.update_edit_mesh(obj.data) else: bm.edges.new([bm.select_history[-1], vertex_new]) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() else: pg.error = f"{operation} {PDT_ERR_NON_VALID} {PDT_LAB_ARCCENTRE}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") elif obj.mode == "OBJECT": if len(context.view_layer.objects.selected) != 3: pg.error = f"{PDT_ERR_SEL_3_OBJS} {len(context.view_layer.objects.selected)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError vector_a = context.view_layer.objects.selected[0].matrix_world.decompose()[0] vector_b = context.view_layer.objects.selected[1].matrix_world.decompose()[0] vector_c = context.view_layer.objects.selected[2].matrix_world.decompose()[0] vector_delta, radius = arc_centre(vector_a, vector_b, vector_c) pg.distance = radius if operation == "C": scene.cursor.location = vector_delta elif operation == "P": pg.pivot_loc = vector_delta elif operation == "G": context.view_layer.objects.active.location = vector_delta else: pg.error = f"{operation} {PDT_ERR_NON_VALID} {PDT_LAB_ARCCENTRE}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") def placement_intersect(context, operation): """Manipulates Geometry, or Objects by Convergance Intersection between 4 points, or 2 Edges. Args: context: Blender bpy.context instance. operation: The Operation e.g. Create New Vertex Returns: Status Set. """ scene = context.scene pg = scene.pdt_pg plane = pg.plane obj = context.view_layer.objects.active if obj.mode == "EDIT": if obj is None: pg.error = PDT_ERR_NO_ACT_OBJ context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_NoObjectError obj_loc = obj.matrix_world.decompose()[0] bm = bmesh.from_edit_mesh(obj.data) edges = [e for e in bm.edges if e.select] extend_all = pg.extend if len(edges) == 2: vertex_a = edges[0].verts[0] vertex_b = edges[0].verts[1] vertex_c = edges[1].verts[0] vertex_d = edges[1].verts[1] else: if len(bm.select_history) != 4: pg.error = ( PDT_ERR_SEL_4_VERTS + str(len(bm.select_history)) + " Vertices/" + str(len(edges)) + " Edges)" ) context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError vertex_a = bm.select_history[-1] vertex_b = bm.select_history[-2] vertex_c = bm.select_history[-3] vertex_d = bm.select_history[-4] vector_delta, done = intersection(vertex_a.co, vertex_b.co, vertex_c.co, vertex_d.co, plane) if not done: pg.error = f"{PDT_ERR_INT_LINES} {plane} {PDT_LAB_PLANE}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_IntersectionError if operation == "C": scene.cursor.location = obj_loc + vector_delta elif operation == "P": pg.pivot_loc = obj_loc + vector_delta elif operation == "N": vector_new = vector_delta vertex_new = bm.verts.new(vector_new) for v in [v for v in bm.verts if v.select]: v.select_set(False) for f in bm.faces: f.select_set(False) for e in bm.edges: e.select_set(False) vertex_new.select_set(True) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() elif operation in {"G", "V"}: vertex_new = None process = False if (vertex_a.co - vector_delta).length < (vertex_b.co - vector_delta).length: if operation == "G": vertex_a.co = vector_delta process = True else: vertex_new = bm.verts.new(vector_delta) bm.edges.new([vertex_a, vertex_new]) process = True else: if operation == "G" and extend_all: vertex_b.co = vector_delta elif operation == "V" and extend_all: vertex_new = bm.verts.new(vector_delta) bm.edges.new([vertex_b, vertex_new]) else: return if (vertex_c.co - vector_delta).length < (vertex_d.co - vector_delta).length: if operation == "G" and extend_all: vertex_c.co = vector_delta elif operation == "V" and extend_all: bm.edges.new([vertex_c, vertex_new]) else: return else: if operation == "G" and extend_all: vertex_d.co = vector_delta elif operation == "V" and extend_all: bm.edges.new([vertex_d, vertex_new]) else: return bm.select_history.clear() bmesh.ops.remove_doubles(bm, verts=bm.verts, dist=0.0001) if not process and not extend_all: pg.error = PDT_ERR_INT_NO_ALL context.window_manager.popup_menu(oops, title="Error", icon="ERROR") bmesh.update_edit_mesh(obj.data) return for v in bm.verts: v.select_set(False) for f in bm.faces: f.select_set(False) for e in bm.edges: e.select_set(False) if vertex_new is not None: vertex_new.select_set(True) for v in bm.select_history: if v is not None: v.select_set(True) bmesh.update_edit_mesh(obj.data) else: pg.error = f"{operation} {PDT_ERR_NON_VALID} {PDT_LAB_INTERSECT}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_InvalidOperation elif obj.mode == "OBJECT": if len(context.view_layer.objects.selected) != 4: pg.error = f"{PDT_ERR_SEL_4_OBJS} {len(context.view_layer.objects.selected)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError order = pg.object_order.split(",") objs = sorted(context.view_layer.objects.selected, key=lambda x: x.name) pg.error = ( "Original Object Order (1,2,3,4) was: " + objs[0].name + ", " + objs[1].name + ", " + objs[2].name + ", " + objs[3].name ) context.window_manager.popup_menu(oops, title="Info", icon="INFO") vector_a = objs[int(order[0]) - 1].matrix_world.decompose()[0] vector_b = objs[int(order[1]) - 1].matrix_world.decompose()[0] vector_c = objs[int(order[2]) - 1].matrix_world.decompose()[0] vector_d = objs[int(order[3]) - 1].matrix_world.decompose()[0] vector_delta, done = intersection(vector_a, vector_b, vector_c, vector_d, plane) if not done: pg.error = f"{PDT_ERR_INT_LINES} {plane} {PDT_LAB_PLANE}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_IntersectionError if operation == "C": scene.cursor.location = vector_delta elif operation == "P": pg.pivot_loc = vector_delta elif operation == "G": context.view_layer.objects.active.location = vector_delta pg.error = f"{PDT_INF_OBJ_MOVED} {context.view_layer.objects.active.name}" context.window_manager.popup_menu(oops, title="Info", icon="INFO") else: pg.error = f"{operation} {PDT_ERR_NON_VALID} {PDT_LAB_INTERSECT}" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") return else: return def join_two_vertices(context): """Joins 2 Free Vertices that do not form part of a Face. Note: Joins two vertices that do not form part of a single face It is designed to close open Edge Loops, where a face is not required or to join two disconnected Edges. Args: context: Blender bpy.context instance. Returns: Status Set. """ scene = context.scene pg = scene.pdt_pg obj = context.view_layer.objects.active if all([bool(obj), obj.type == "MESH", obj.mode == "EDIT"]): bm = bmesh.from_edit_mesh(obj.data) verts = [v for v in bm.verts if v.select] if len(verts) == 2: try: bm.edges.new([verts[-1], verts[-2]]) bmesh.update_edit_mesh(obj.data) bm.select_history.clear() return except ValueError: pg.error = PDT_ERR_CONNECTED context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_VerticesConnected else: pg.error = f"{PDT_ERR_SEL_2_VERTS} {len(verts)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError else: pg.error = f"{PDT_ERR_EDOB_MODE},{obj.mode})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_ObjectModeError def set_angle_distance_two(context): """Measures Angle and Offsets between 2 Points in View Plane. Note: Uses 2 Selected Vertices to set pg.angle and pg.distance scene variables also sets delta offset from these 2 points using standard Numpy Routines Works in Edit and Oject Modes. Args: context: Blender bpy.context instance. Returns: Status Set. """ scene = context.scene pg = scene.pdt_pg plane = pg.plane flip_angle = pg.flip_angle obj = context.view_layer.objects.active if obj is None: pg.error = PDT_ERR_NO_ACT_OBJ context.window_manager.popup_menu(oops, title="Error", icon="ERROR") return if obj.mode == "EDIT": bm = bmesh.from_edit_mesh(obj.data) verts = [v for v in bm.verts if v.select] if len(verts) == 2: if len(bm.select_history) == 2: vector_a, vector_b = check_selection(2, bm, obj) if vector_a is None: pg.error = PDT_ERR_VERT_MODE context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_FeatureError else: pg.error = f"{PDT_ERR_SEL_2_VERTIO} {len(bm.select_history)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError else: pg.error = f"{PDT_ERR_SEL_2_VERTIO} {len(verts)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError elif obj.mode == "OBJECT": objs = context.view_layer.objects.selected if len(objs) < 2: pg.error = f"{PDT_ERR_SEL_2_OBJS} {len(objs)})" context.window_manager.popup_menu(oops, title="Error", icon="ERROR") raise PDT_SelectionError objs_s = [ob for ob in objs if ob.name != obj.name] vector_a = obj.matrix_world.decompose()[0] vector_b = objs_s[-1].matrix_world.decompose()[0] if plane == "LO": vector_difference = vector_b - vector_a vector_b = view_coords_i(vector_difference.x, vector_difference.y, vector_difference.z) vector_a = Vector((0, 0, 0)) v0 = np.array([vector_a.x + 1, vector_a.y]) - np.array([vector_a.x, vector_a.y]) v1 = np.array([vector_b.x, vector_b.y]) - np.array([vector_a.x, vector_a.y]) else: a1, a2, _ = set_mode(plane) v0 = np.array([vector_a[a1] + 1, vector_a[a2]]) - np.array([vector_a[a1], vector_a[a2]]) v1 = np.array([vector_b[a1], vector_b[a2]]) - np.array([vector_a[a1], vector_a[a2]]) ang = np.rad2deg(np.arctan2(np.linalg.det([v0, v1]),

np.dot(v0, v1)

numpy.dot

import numpy as np import cv2 import matplotlib.pyplot as plt import matplotlib.image as mpimg ############################################################################################## #---------------------------CALIBRATION CAMERA + DISTORSION CORRECTION------------------------ def calculation_undistort(image, objpoints, imgpoints): # get image size img_size = (image.shape[1], image.shape[0]) # Camera Calibration ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, img_size, None, None) # Distorsion Correction undist = cv2.undistort(image,mtx,dist,None,mtx) return undist ################################################################################################ #--------------------------------------GRADIENT------------------------------------------------ def image_computing(image_undistorted): # Grayscale image to compute the gradient gray = cv2.cvtColor(image_undistorted, cv2.COLOR_RGB2GRAY) # HLS color space and separate the S channel for the color hls = cv2.cvtColor(image_undistorted, cv2.COLOR_RGB2HLS) l_channel = hls[:,:,1] s_channel = hls[:,:,2] #------------------------------------------------------------------------------------------- # Sobel x sobelx = cv2.Sobel(gray, cv2.CV_64F, 1, 0) abs_sobelx = np.absolute(sobelx) # x derivative accentuates lines away from horizontal scaled_sobelx = np.uint8(255*abs_sobelx/np.max(abs_sobelx)) # Sobel y sobely = cv2.Sobel(gray, cv2.CV_64F, 0, 1) abs_sobely = np.absolute(sobely) # y derivative accentuates lines away from horizontal scaled_sobely = np.uint8(255*abs_sobely/np.max(abs_sobely)) #--------------------------------------------------------------------------------------------- # x-gradient Thresholding thresh_min = 40 thresh_max = 100 sxbinary = np.zeros_like(scaled_sobelx) sxbinary[(scaled_sobelx >= thresh_min) & (scaled_sobelx <= thresh_max)] = 1 # y-gradient Thresholding thresh_min = 40 thresh_max = 100 sybinary = np.zeros_like(scaled_sobely) sybinary[(scaled_sobely >= thresh_min) & (scaled_sobely <= thresh_max)] = 1 #---------------------------------------------------------------------------------------------- # color channel Thresholding s_thresh_min = 150 s_thresh_max = 255 s_binary = np.zeros_like(s_channel) s_binary[(s_channel >= s_thresh_min) & (s_channel <= s_thresh_max)] = 1 l_thresh_min = 150 l_thresh_max = 255 l_binary = np.zeros_like(l_channel) l_binary[(l_channel >= l_thresh_min) & (l_channel <= l_thresh_max)] = 1 # Gradient direction thresholding thresh=(0.7, 1.3) direction = np.arctan2 (abs_sobely, abs_sobelx) # Calculate the direction dir_binary = np.zeros_like (direction) dir_binary[(direction >= thresh[0]) & (direction<=thresh[1])] =1 # Gradient magnitude thresholding mag_thresh=(30, 100) magnitude = np.sqrt((sobelx)**2 + (sobely)**2) # Calculate the magnitude scaled_magnitude = np.uint8 (255* magnitude/np.max(magnitude)) # Scale to 8-bit (0 - 255) and convert to type = np.uint8 mag_binary = np.zeros_like (scaled_magnitude) # Create a binary mask where mag thresholds are met mag_binary[(scaled_magnitude >= mag_thresh[0]) & (scaled_magnitude<=mag_thresh[1])] =1 #----------------------------------------------------------------------------------------------- #----------------------------------------------------------------------------------------------- # Combine the two binary thresholds : Only color and sobel x combined_binary = np.zeros_like(sxbinary) combined_binary[((s_binary == 1) & (l_binary == 1)) |(sxbinary == 1)] = 1 #----------------------------------------------------------------------------------------------- # Combine the two binary thresholds : color and sobel x + magnitude/direction gradient combined_binary_b = np.zeros_like(dir_binary) combined_binary_b[(sxbinary == 1 | ((mag_binary == 1) & (dir_binary == 1))) | s_binary == 1] = 1 #----------------------------------------------------------------------------------------------- # return the combinaison color and sobelx return sxbinary, sybinary, mag_binary, dir_binary, s_binary, l_binary, combined_binary, combined_binary_b ######################################################################################################### # ----------------------------PERPECTIVE TRANSFORM------------------------------------------------------- def warper(img, src, dst): img_size = (img.shape[1], img.shape[0]) M = cv2.getPerspectiveTransform(src, dst) Minv = cv2.getPerspectiveTransform(dst, src) warped = cv2.warpPerspective(img, M, img_size, flags=cv2.INTER_NEAREST) # keep same size as input image return warped,Minv ################################################################################################## #---------------------------------FIND LANE PIXEL - Methodic : Histrogramm and Window ------------ def find_lanes_pixels(binary_warped): # Take a histogram of the bottom half of the image # creation de l'histogramme avec les 2 pics, image coupé en 2 # et prendre en consideration que la demie-partie d'en bas --> shape[0] = axe y histogram = np.sum(binary_warped[binary_warped.shape[0]//2:,:], axis=0) #plt.plot(histogram) # Create an output image to draw on and visualize the result # creation d'une image resultat nommé out_img out_img = np.dstack((binary_warped, binary_warped, binary_warped)) # Find the peak of the left and right halves of the histogram # These will be the starting point for the left and right lines # analyse de d'histogramme : # 1) graphe histogramme coupe en 2 en x (partie droite et partie gauche) # 2) prise de la partie gauche en x et prendre le point le plus haut # 3) prise de la partie droite en x et prendre le point le plus haut midpoint = np.int(histogram.shape[0]//2) leftx_base = np.argmax(histogram[:midpoint]) rightx_base = np.argmax(histogram[midpoint:]) + midpoint #-------------------------------------------------------- # HYPERPARAMETERS # Choose the number of sliding windows # nombre de fenetres qui vont se succeder nwindows = 9 # Set the width of the windows +/- margin # tolerance en x margin = 50 # Set minimum number of pixels found to recenter window # nombre minimum de pixel trouve pour recentrer la fenetre minpix = 100 #------------------------------------------------------------ # DERNIERES PARAMETRAGES # definition de la hauteur des 9 fenetre : taille de la fenetre total / 9 # Set height of windows - based on nwindows above and image shape window_height = np.int(binary_warped.shape[0]//nwindows) # position x et y de tous les pixels actives dans l'image # Identify the x and y positions of all nonzero pixels in the image nonzero = binary_warped.nonzero() nonzeroy = np.array(nonzero[0]) # axe y nonzerox = np.array(nonzero[1]) # axe x # Current positions to be updated later for each window in nwindows #position courante des deux fenetres (gauche et droite), ici initalisation # donc fenetre (ligne) de base = fenetre (ligne) courante, qui va evoluer leftx_current = leftx_base rightx_current = rightx_base # Create empty lists to receive left and right lane pixel indices # creation de liste vide pour recevoir les indices des pixels des lignes (droite et gauche) left_lane_inds = [] right_lane_inds = [] #--------------------------------------------------------------- # Step through the windows one by one for window in range(nwindows): # iterer de 1 a 9 : # limites en y pour les fenetres : #hauteur de l'image/ ((hauteur_fenetre)*fenetre (0->9)), # Identify window boundaries in x and y (and right and left) win_y_low = binary_warped.shape[0] - (window+1)*window_height win_y_high = binary_warped.shape[0] - window*window_height # limite en x des fenetres : avec les tolerances margin en x a partir # du positionnement de la courbe ### TO-DO: Find the four below boundaries of the window ### win_xleft_low = leftx_current - margin win_xleft_high = leftx_current + margin win_xright_low = rightx_current - margin win_xright_high = rightx_current + margin # --------------------- # Draw the windows on the visualization image # tracage de la fenetre dans l'image de sortie avec les coodonnées donnés ci-dessus cv2.rectangle(out_img,(win_xleft_low,win_y_low), (win_xleft_high,win_y_high),(0,255,0), 2) cv2.rectangle(out_img,(win_xright_low,win_y_low), (win_xright_high,win_y_high),(0,255,0), 2) #------------------------ # identification des pixels activés en x et y dans la fenetre good_left_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xleft_low) & (nonzerox < win_xleft_high)).nonzero()[0] good_right_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xright_low) & (nonzerox < win_xright_high)).nonzero()[0] # Append these indices to the lists # ajout des indices des pixels activés left_lane_inds.append(good_left_inds) right_lane_inds.append(good_right_inds) # si le nombre de pixel dans la fentre est >50 # on calcule la moyenne des indices pour donner leftx_current # et recentrer la fenetre if len(good_left_inds) > minpix: leftx_current = np.int(

np.mean(nonzerox[good_left_inds])

numpy.mean

from __future__ import print_function import threading import multiprocessing from collections import namedtuple import os try: from queue import Queue, Full, Empty except ImportError: from Queue import Queue, Full, Empty try: import cPickle as pickle except ImportError: import pickle import numpy as np import h5py import tensorflow as tf from pybh import math_utils, hdf5_utils def write_samples_to_hdf5_file(filename, samples, attr_dict=None, **dataset_kwargs): stacked_samples = {} for key in samples[0]: stacked_samples[key] = np.empty((len(samples),) + samples[0][key].shape, dtype=samples[0][key].dtype) for key in samples[0]: for i, sample in enumerate(samples): stacked_samples[key][i, ...] = sample[key] hdf5_utils.write_numpy_dict_to_hdf5_file(filename, stacked_samples, attr_dict=attr_dict, **dataset_kwargs) def read_samples_from_hdf5_file(filename, field_dict=None, read_attributes=True): result = hdf5_utils.read_hdf5_file_to_numpy_dict(filename, field_dict, read_attributes) if read_attributes: data, attr_dict = result else: data = result key_list = list(data.keys()) sample_dict = {} for key in key_list: assert(data[key].shape[0] == data[key_list[0]].shape[0]) sample_dict[key] = [] for i in range(data[key].shape[0]): sample_dict[key].append(data[key][i, ...]) samples = [] for i in range(data[key_list[0]].shape[0]): samples.append({key: sample_dict[key][i] for key in sample_dict}) if read_attributes: return samples, attr_dict else: return samples Record = namedtuple("Record", ["obs_levels", "grid_3d", "rewards", "prob_rewards", "scores"]) RecordBatch = namedtuple("RecordBatch", ["obs_levels", "grid_3ds", "rewards", "prob_rewards", "scores"]) RecordV2 = namedtuple("RecordV2", ["obs_levels", "grid_3d", "rewards", "norm_rewards", "prob_rewards", "norm_prob_rewards", "scores"]) RecordV2Batch = namedtuple("RecordV2Batch", ["obs_levels", "grid_3ds", "rewards", "norm_rewards", "prob_rewards", "norm_prob_rewards", "scores"]) RecordV3 = namedtuple("RecordV3", ["obs_levels", "in_grid_3d", "out_grid_3d", "rewards", "scores"]) RecordV3Batch = namedtuple("RecordV3Batch", ["obs_levels", "in_grid_3ds", "out_grid_3ds", "rewards", "scores"]) RecordV4 = namedtuple("RecordV4", ["intrinsics", "map_resolution", "axis_mode", "forward_factor", "obs_levels", "in_grid_3d", "out_grid_3d", "rewards", "scores", "rgb_image", "depth_image", "normal_image"]) RecordV4Batch = namedtuple("RecordV4Batch", ["intrinsics", "map_resolution", "axis_mode", "forward_factor", "obs_levels", "in_grid_3ds", "out_grid_3ds", "rewards", "scores", "rgb_images", "depth_images", "normal_images"]) def write_hdf5_records(filename, records): f = h5py.File(filename, "w") (obs_levels, grid_3d, rewards, prob_rewards, scores) = records[0] assert(grid_3d.shape[-1] == 2 * len(obs_levels)) rewards_shape = (len(records),) + rewards.shape rewards_dset = f.create_dataset("rewards", rewards_shape, dtype='f') prob_rewards_shape = (len(records),) + prob_rewards.shape prob_rewards_dset = f.create_dataset("prob_rewards", prob_rewards_shape, dtype='f') scores_shape = (len(records),) + scores.shape scores_dset = f.create_dataset("scores", scores_shape, dtype='f') grid_3ds_shape = (len(records),) + grid_3d.shape grid_3ds_dset = f.create_dataset("grid_3ds", grid_3ds_shape, dtype='f') grid_3ds_dset.attrs["obs_levels"] = obs_levels grid_3ds_dset.attrs["obs_channels"] = grid_3ds_shape[-1] / len(obs_levels) for i, record in enumerate(records): (obs_levels, grid_3d, rewards, prob_rewards, scores) = record rewards_dset[i, ...] = rewards prob_rewards_dset[i, ...] = prob_rewards scores_dset[i, ...] = scores grid_3ds_dset[i, ...] = grid_3d f.close() def read_hdf5_records(filename): try: f = h5py.File(filename, "r") obs_levels = f["grid_3ds"].attrs["obs_levels"] obs_channels = f["grid_3ds"].attrs["obs_channels"] rewards = np.array(f["rewards"]) prob_rewards = np.array(f["prob_rewards"]) scores = np.array(f["scores"]) grid_3ds = np.array(f["grid_3ds"]) assert(rewards.shape[0] == grid_3ds.shape[0]) assert(prob_rewards.shape[0] == grid_3ds.shape[0]) assert(scores.shape[0] == grid_3ds.shape[0]) assert(grid_3ds.shape[-1] == len(obs_levels) * obs_channels) return RecordBatch(obs_levels, grid_3ds, rewards, prob_rewards, scores) except Exception as err: print("ERROR: Exception raised when reading as HDF5 v1 file \"{}\": {}".format(filename, err)) def write_hdf5_records_v2(filename, records): f = h5py.File(filename, "w") (obs_levels, grid_3d, rewards, norm_rewards, prob_rewards, norm_prob_rewards, scores) = records[0] assert(grid_3d.shape[-1] == 2 * len(obs_levels)) rewards_shape = (len(records),) + rewards.shape rewards_dset = f.create_dataset("rewards", rewards_shape, dtype='f') norm_rewards_shape = (len(records),) + norm_rewards.shape norm_rewards_dset = f.create_dataset("norm_rewards", norm_rewards_shape, dtype='f') prob_rewards_shape = (len(records),) + prob_rewards.shape prob_rewards_dset = f.create_dataset("prob_rewards", prob_rewards_shape, dtype='f') norm_prob_rewards_shape = (len(records),) + norm_prob_rewards.shape norm_prob_rewards_dset = f.create_dataset("norm_prob_rewards", norm_prob_rewards_shape, dtype='f') scores_shape = (len(records),) + scores.shape scores_dset = f.create_dataset("scores", scores_shape, dtype='f') grid_3ds_shape = (len(records),) + grid_3d.shape grid_3ds_dset = f.create_dataset("grid_3ds", grid_3ds_shape, dtype='f') grid_3ds_dset.attrs["obs_levels"] = obs_levels grid_3ds_dset.attrs["obs_channels"] = grid_3ds_shape[-1] / len(obs_levels) for i, record in enumerate(records): (obs_levels, grid_3d, rewards, norm_rewards, prob_rewards, norm_prob_rewards, scores) = record rewards_dset[i, ...] = rewards norm_rewards_dset[i, ...] = norm_rewards prob_rewards_dset[i, ...] = prob_rewards norm_prob_rewards_dset[i, ...] = norm_prob_rewards scores_dset[i, ...] = scores grid_3ds_dset[i, ...] = grid_3d f.close() def write_hdf5_records_v3(filename, records): f = h5py.File(filename, "w") (obs_levels, in_grid_3d, out_grid_3d, rewards, scores) = records[0] assert(in_grid_3d.shape[-1] == 2 * len(obs_levels)) assert(

np.all(in_grid_3d.shape == out_grid_3d.shape)

numpy.all

#!/usr/bin/env python # -*- coding: UTF-8 -*- """ Class of pytorch data loader --- <NAME> <EMAIL> Nanjing University of Science and Technology Aug 10, 2019 """ import glob import imageio import numpy as np import numpy.matlib import torch.utils.data from torchvision import transforms #from config import colorMap # C_NUM = 12 # number of classes # 'empty','ceiling','floor','wall','window','chair','bed','sofa','table','tvs','furn','objs' # 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 seg_class_map = [0, 1, 2, 3, 4, 11, 5, 6, 7, 8, 8, 10, 10, 10, 11, 11, 9, 8, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 10, 11, 8, 10, 11, 9, 11, 11, 11] # 0 - 11 # 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 class NYUDataset(torch.utils.data.Dataset): def __init__(self, root, istest=False): self.param = {'voxel_size': (240, 144, 240), 'voxel_unit': 0.02, # 0.02m, length of each grid == 20mm 'cam_k': [[518.8579, 0, 320], # K is [fx 0 cx; 0 fy cy; 0 0 1]; [0, 518.8579, 240], # cx = K(1,3); cy = K(2,3); [0, 0, 1]], # fx = K(1,1); fy = K(2,2); } # self.subfix = 'npz' self.istest = istest self.downsample = 4 # int, downsample = 4, in labeled data, get 1 voxel from each 4 self.filepaths = self.get_filelist(root, self.subfix) # Converts a PIL Image or numpy.ndarray (H x W x C) in the range [0, 255] \ # to a torch.FloatTensor of shape (C x H x W) in the range [0.0, 1.0]. self.transforms_rgb = transforms.Compose([ transforms.ToTensor(), transforms.Normalize(mean=[0.485, 0.456, 0.406], std=[0.229, 0.224, 0.225]), ]) print('Dataset:{} files'.format(len(self.filepaths))) def __getitem__(self, index): _name = self.filepaths[index][:-4] # print(_name) # --------------------------------------------------------------------------- # Processing repackaged data provided by DDRNet # --------------------------------------------------------------------------- if self.subfix == 'npz': with np.load(self.filepaths[index]) as npz_file: # print(npz_file.files) rgb_tensor = npz_file['rgb'] depth_tensor = npz_file['depth'] tsdf_hr = npz_file['tsdf_hr'] # flipped TSDF, (240, 144, 240, 1) # target_hr = npz_file['target_hr'] target_lr = npz_file['target_lr'] position = npz_file['position'] if self.istest: tsdf_lr = npz_file['tsdf_lr'] # ( 60, 36, 60) # nonempty = self.get_nonempty(tsdf, 'TSDF') nonempty = self.get_nonempty2(tsdf_lr, target_lr, 'TSDF') # 这个更符合SUNCG的做法 return rgb_tensor, depth_tensor, tsdf_hr, target_lr.T, nonempty.T, position, _name + '.png' return rgb_tensor, depth_tensor, tsdf_hr, target_lr.T, position, _name + '.png' # else: # # --------------------------------------------------------------------------- # Processing data provided by SSCNet # --------------------------------------------------------------------------- # --- read depth, shape: (h, w) depth = self._read_depth(_name + '.png') # depth_tensor = depth.reshape((1,) + depth.shape) # --- read rgb image, shape: (h, w, 3) # rgb = self._read_rgb(_name + '.jpg') # rgb = self._read_rgb(_name[:-4] + 'rgb.png') rgb_tensor = self.transforms_rgb(rgb) # channel first, shape: (3, h, w) # --- read ground truth vox_origin, cam_pose, rle = self._read_rle(_name + '.bin') target_hr = self._rle2voxel(rle, self.param['voxel_size'], _name + '.bin') target_lr = self._downsample_label(target_hr, self.param['voxel_size'], self.downsample) binary_vox, _, position, position4 = self._depth2voxel(depth, cam_pose, vox_origin, self.param) npz_file = np.load(_name + '.npz') tsdf_hr = npz_file['tsdf'] # SUNCG (W, H, D) if self.istest: tsdf_lr = self._downsample_tsdf(tsdf_hr, self.downsample) # nonempty = self.get_nonempty(tsdf, 'TSDF') nonempty = self.get_nonempty2(tsdf_lr, target_lr, 'TSDF') # 这个更符合SUNCG的做法 return rgb_tensor, depth_tensor, tsdf_hr, target_lr.T, nonempty.T, position, _name + '.png' return rgb_tensor, depth_tensor, tsdf_hr, target_lr.T, position, _name + '.png' def __len__(self): return len(self.filepaths) def get_filelist(self, root, subfix): if root is None: raise Exception("Oops! 'root' is None, please set the right file path.") _filepaths = list() if isinstance(root, list): # 将多个root for root_i in root: fp = glob.glob(root_i + '/*.' + subfix) fp.sort() _filepaths.extend(fp) elif isinstance(root, str): _filepaths = glob.glob(root + '/*.' + subfix) # List all files in data folder _filepaths.sort() if len(_filepaths) == 0: raise Exception("Oops! That was no valid data in '{}'.".format(root)) return _filepaths @staticmethod def _read_depth(depth_filename): r"""Read a depth image with size H x W and save the depth values (in millimeters) into a 2d numpy array. The depth image file is assumed to be in 16-bit PNG format, depth in millimeters. """ # depth = misc.imread(depth_filename) / 8000.0 # numpy.float64 depth = imageio.imread(depth_filename) / 8000.0 # numpy.float64 # assert depth.shape == (img_h, img_w), 'incorrect default size' depth = np.asarray(depth) return depth @staticmethod def _read_rgb(rgb_filename): # 0.01s r"""Read a RGB image with size H x W """ # rgb = misc.imread(rgb_filename) # <type 'numpy.ndarray'>, numpy.uint8, (480, 640, 3) rgb = imageio.imread(rgb_filename) # <type 'numpy.ndarray'>, numpy.uint8, (480, 640, 3) # rgb = np.rollaxis(rgb, 2, 0) # (H, W, 3)-->(3, H, W) return rgb @staticmethod def _read_rle(rle_filename): # 0.0005s r"""Read RLE compression data Return: vox_origin, cam_pose, vox_rle, voxel label data from file Shape: vox_rle, (240, 144, 240) """ fid = open(rle_filename, 'rb') vox_origin = np.fromfile(fid, np.float32, 3).T # Read voxel origin in world coordinates cam_pose = np.fromfile(fid, np.float32, 16).reshape((4, 4)) # Read camera pose vox_rle = np.fromfile(fid, np.uint32).reshape((-1, 1)).T # Read voxel label data from file vox_rle = np.squeeze(vox_rle) # 2d array: (1 x N), to 1d array: (N , ) fid.close() return vox_origin, cam_pose, vox_rle # this version takes 0.9s @classmethod def _rle2voxel(cls, rle, voxel_size=(240, 144, 240), rle_filename=''): r"""Read voxel label data from file (RLE compression), and convert it to fully occupancy labeled voxels. In the data loader of pytorch, only single thread is allowed. For multi-threads version and more details, see 'readRLE.py'. output: seg_label: 3D numpy array, size 240 x 144 x 240 """ # ---- Read RLE # vox_origin, cam_pose, rle = cls._read_rle(rle_filename) # ---- Uncompress RLE, 0.9s seg_label = np.zeros(voxel_size[0] * voxel_size[1] * voxel_size[2], dtype=np.uint8) # segmentation label vox_idx = 0 for idx in range(int(rle.shape[0] / 2)): check_val = rle[idx * 2] check_iter = rle[idx * 2 + 1] if check_val >= 37 and check_val != 255: # 37 classes to 12 classes print('RLE {} check_val: {}'.format(rle_filename, check_val)) # seg_label_val = 1 if check_val < 37 else 0 # 37 classes to 2 classes: empty or occupancy # seg_label_val = 255 if check_val == 255 else seg_class_map[check_val] seg_label_val = seg_class_map[check_val] if check_val != 255 else 255 # 37 classes to 12 classes seg_label[vox_idx: vox_idx + check_iter] = np.matlib.repmat(seg_label_val, 1, check_iter) vox_idx = vox_idx + check_iter seg_label = seg_label.reshape(voxel_size) # 3D array, size 240 x 144 x 240 return seg_label # this version takes 3s @classmethod # method 2, new def _depth2voxel(cls, depth, cam_pose, vox_origin, param): cam_k = param['cam_k'] voxel_size = param['voxel_size'] # (240, 144, 240) unit = param['voxel_unit'] # 0.02 # ---- Get point in camera coordinate H, W = depth.shape gx, gy = np.meshgrid(range(W), range(H)) pt_cam = np.zeros((H, W, 3), dtype=np.float32) pt_cam[:, :, 0] = (gx - cam_k[0][2]) * depth / cam_k[0][0] # x pt_cam[:, :, 1] = (gy - cam_k[1][2]) * depth / cam_k[1][1] # y pt_cam[:, :, 2] = depth # z, in meter # ---- Get point in world coordinate p = cam_pose pt_world = np.zeros((H, W, 3), dtype=np.float32) pt_world[:, :, 0] = p[0][0] * pt_cam[:, :, 0] + p[0][1] * pt_cam[:, :, 1] + p[0][2] * pt_cam[:, :, 2] + p[0][3] pt_world[:, :, 1] = p[1][0] * pt_cam[:, :, 0] + p[1][1] * pt_cam[:, :, 1] + p[1][2] * pt_cam[:, :, 2] + p[1][3] pt_world[:, :, 2] = p[2][0] * pt_cam[:, :, 0] + p[2][1] * pt_cam[:, :, 1] + p[2][2] * pt_cam[:, :, 2] + p[2][3] pt_world[:, :, 0] = pt_world[:, :, 0] - vox_origin[0] pt_world[:, :, 1] = pt_world[:, :, 1] - vox_origin[1] pt_world[:, :, 2] = pt_world[:, :, 2] - vox_origin[2] # ---- Aline the coordinates with labeled data (RLE .bin file) pt_world2 = np.zeros(pt_world.shape, dtype=np.float32) # (h, w, 3) # pt_world2 = pt_world pt_world2[:, :, 0] = pt_world[:, :, 0] # x 水平 pt_world2[:, :, 1] = pt_world[:, :, 2] # y 高低 pt_world2[:, :, 2] = pt_world[:, :, 1] # z 深度 # pt_world2[:, :, 0] = pt_world[:, :, 1] # x 原始paper方法 # pt_world2[:, :, 1] = pt_world[:, :, 2] # y # pt_world2[:, :, 2] = pt_world[:, :, 0] # z # ---- World coordinate to grid/voxel coordinate point_grid = pt_world2 / unit # Get point in grid coordinate, each grid is a voxel point_grid = np.rint(point_grid).astype(np.int32) # .reshape((-1, 3)) # (H*W, 3) (H, W, 3) # ---- crop depth to grid/voxel # binary encoding '01': 0 for empty, 1 for occupancy # voxel_binary = np.zeros(voxel_size, dtype=np.uint8) # (W, H, D) voxel_binary = np.zeros([_ + 1 for _ in voxel_size], dtype=np.float32) # (W, H, D) voxel_xyz = np.zeros(voxel_size + (3,), dtype=np.float32) # (W, H, D, 3) position = np.zeros((H, W), dtype=np.int32) position4 = np.zeros((H, W), dtype=np.int32) # position44 = np.zeros((H/4, W/4), dtype=np.int32) voxel_size_lr = (voxel_size[0] // 4, voxel_size[1] // 4, voxel_size[2] // 4) for h in range(H): for w in range(W): i_x, i_y, i_z = point_grid[h, w, :] if 0 <= i_x < voxel_size[0] and 0 <= i_y < voxel_size[1] and 0 <= i_z < voxel_size[2]: voxel_binary[i_x, i_y, i_z] = 1 # the bin has at least one point (bin is not empty) voxel_xyz[i_x, i_y, i_z, :] = point_grid[h, w, :] # position[h, w, :] = point_grid[h, w, :] # 记录图片上的每个像素对应的voxel位置 # 记录图片上的每个像素对应的voxel位置 position[h, w] = np.ravel_multi_index(point_grid[h, w, :], voxel_size) # TODO 这个project的方式可以改进 position4[h, ] = np.ravel_multi_index((point_grid[h, w, :] / 4).astype(np.int32), voxel_size_lr) # position44[h / 4, w / 4] = np.ravel_multi_index(point_grid[h, w, :] / 4, voxel_size_lr) # output --- 3D Tensor, 240 x 144 x 240 del depth, gx, gy, pt_cam, pt_world, pt_world2, point_grid # Release Memory return voxel_binary, voxel_xyz, position, position4 # (W, H, D), (W, H, D, 3) # this version takes about 0.6s on CPU @staticmethod def _downsample_label(label, voxel_size=(240, 144, 240), downscale=4): r"""downsample the labeled data, Shape: label, (240, 144, 240) label_downscale, if downsample==4, then (60, 36, 60) """ if downscale == 1: return label ds = downscale small_size = (voxel_size[0] // ds, voxel_size[1] // ds, voxel_size[2] // ds) # small size label_downscale = np.zeros(small_size, dtype=np.uint8) empty_t = 0.95 * ds * ds * ds # threshold s01 = small_size[0] * small_size[1] label_i = np.zeros((ds, ds, ds), dtype=np.int32) for i in range(small_size[0]*small_size[1]*small_size[2]): z = int(i / s01) y = int((i - z * s01) / small_size[0]) x = int(i - z * s01 - y * small_size[0]) # z, y, x = np.unravel_index(i, small_size) # 速度更慢了 # print(x, y, z) label_i[:, :, :] = label[x * ds:(x + 1) * ds, y * ds:(y + 1) * ds, z * ds:(z + 1) * ds] label_bin = label_i.flatten() # faltten 返回的是真实的数组，需要分配新的内存空间 # label_bin = label_i.ravel() # 将多维数组变成 1维数组，而ravel 返回的是数组的视图 # zero_count_0 = np.sum(label_bin == 0) # zero_count_255 = np.sum(label_bin == 255) zero_count_0 = np.array(np.where(label_bin == 0)).size # 要比sum更快 zero_count_255 = np.array(np.where(label_bin == 255)).size zero_count = zero_count_0 + zero_count_255 if zero_count > empty_t: label_downscale[x, y, z] = 0 if zero_count_0 > zero_count_255 else 255 else: # label_i_s = label_bin[np.nonzero(label_bin)] # get the none empty class labels label_i_s = label_bin[np.where(np.logical_and(label_bin > 0, label_bin < 255))] label_downscale[x, y, z] = np.argmax(np.bincount(label_i_s)) return label_downscale @staticmethod def _downsample_tsdf(tsdf, downscale=4): # 仅在Get None empty　时会用到 r""" Shape: tsdf, (240, 144, 240) tsdf_downscale, (60, 36, 60), (stsdf.shape[0]/4, stsdf.shape[1]/4, stsdf.shape[2]/4) """ if downscale == 1: return tsdf # TSDF_EMPTY = np.float32(0.001) # TSDF_SURFACE: 1, sign >= 0 # TSDF_OCCLUD: sign < 0 np.float32(-0.001) ds = downscale small_size = (int(tsdf.shape[0] / ds), int(tsdf.shape[1] / ds), int(tsdf.shape[2] / ds)) tsdf_downscale = np.ones(small_size, dtype=np.float32) * np.float32(0.001) # init 0.001 for empty s01 = small_size[0] * small_size[1] tsdf_sr = np.ones((ds, ds, ds), dtype=np.float32) # search region for i in range(small_size[0] * small_size[1] * small_size[2]): z = int(i / s01) y = int((i - z * s01) / small_size[0]) x = int(i - z * s01 - y * small_size[0]) tsdf_sr[:, :, :] = tsdf[x * ds:(x + 1) * ds, y * ds:(y + 1) * ds, z * ds:(z + 1) * ds] tsdf_bin = tsdf_sr.flatten() # none_empty_count = np.array(np.where(tsdf_bin != TSDF_EMPTY)).size none_empty_count = np.array(np.where(np.logical_or(tsdf_bin <= 0, tsdf_bin == 1))).size if none_empty_count > 0: # surface_count = np.array(np.where(stsdf_bin == 1)).size # occluded_count = np.array(np.where(stsdf_bin == -2)).size # surface_count = np.array(np.where(tsdf_bin > 0)).size # 这个存在问题 surface_count = np.array(np.where(tsdf_bin == 1)).size # occluded_count = np.array(np.where(tsdf_bin < 0)).size # tsdf_downscale[x, y, z] = 0 if surface_count > occluded_count else np.float32(-0.001) tsdf_downscale[x, y, z] = 1 if surface_count > 2 else np.float32(-0.001) # 1 or 0 ? # else: # tsdf_downscale[x, y, z] = empty # TODO 不应该将所有值均设为0.001 return tsdf_downscale @staticmethod def get_nonempty(voxels, encoding): # Get none empty from depth voxels data =

np.zeros(voxels.shape, dtype=np.float32)

numpy.zeros

""" Scaling of in and output """ import json import numpy as np class EnergyStandardScaler: def __init__(self): self.x_mean = np.zeros((1, 1, 1)) self.x_std = np.ones((1, 1, 1)) self.energy_mean = np.zeros((1, 1)) self.energy_std = np.ones((1, 1)) self._encountered_y_shape = None self._encountered_y_std = None def transform(self, x=None, y=None): x_res = x y_res = y if x is not None: x_res = (x - self.x_mean) / self.x_std if y is not None: y_res = (y - self.energy_mean) / self.energy_std return x_res, y_res def inverse_transform(self, x=None, y=None): energy = y x_res = x if y is not None: energy = y * self.energy_std + self.energy_mean if x is not None: x_res = x * self.x_std + self.x_mean return x_res, energy def fit(self, x=None, y=None, auto_scale=None): if auto_scale is None: auto_scale = {'x_mean': True, 'x_std': True, 'energy_std': True, 'energy_mean': True} npeps = np.finfo(float).eps if auto_scale['x_mean']: self.x_mean = np.mean(x) if auto_scale['x_std']: self.x_std = np.std(x) + npeps if auto_scale['energy_mean']: self.energy_mean = np.mean(y, axis=0, keepdims=True) if auto_scale['energy_std']: self.energy_std = np.std(y, axis=0, keepdims=True) + npeps self._encountered_y_shape = np.array(y.shape) self._encountered_y_std = np.std(y, axis=0) def fit_transform(self, x=None, y=None, auto_scale=None): self.fit(x=x,y=y,auto_scale=auto_scale) return self.transform(x=x,y=y) def save(self, filepath): outdict = {'x_mean': self.x_mean.tolist(), 'x_std': self.x_std.tolist(), 'energy_mean': self.energy_mean.tolist(), 'energy_std': self.energy_std.tolist() } with open(filepath, 'w') as f: json.dump(outdict, f) def load(self, filepath): with open(filepath, 'r') as f: indict = json.load(f) self.x_mean = np.array(indict['x_mean']) self.x_std = np.array(indict['x_std']) self.energy_mean = np.array(indict['energy_mean']) self.energy_std = np.array(indict['energy_std']) def get_params(self): outdict = {'x_mean': self.x_mean.tolist(), 'x_std': self.x_std.tolist(), 'energy_mean': self.energy_mean.tolist(), 'energy_std': self.energy_std.tolist(), } return outdict def set_params(self, indict): self.x_mean = np.array(indict['x_mean']) self.x_std = np.array(indict['x_std']) self.energy_mean = np.array(indict['energy_mean']) self.energy_std = np.array(indict['energy_std']) def print_params_info(self): print("Info: Total-Data energy std", self._encountered_y_shape, ":", self._encountered_y_std) print("Info: Using energy-std", self.energy_std.shape, ":", self.energy_std) print("Info: Using energy-mean", self.energy_mean.shape, ":", self.energy_mean) print("Info: Using x-scale", self.x_std.shape, ":", self.x_std) print("Info: Using x-offset", self.x_mean.shape, ":", self.x_mean) class EnergyGradientStandardScaler: def __init__(self): self.x_mean = np.zeros((1, 1, 1)) self.x_std = np.ones((1, 1, 1)) self.energy_mean = np.zeros((1, 1)) self.energy_std = np.ones((1, 1)) self.gradient_mean = np.zeros((1, 1, 1, 1)) self.gradient_std = np.ones((1, 1, 1, 1)) self._encountered_y_shape = [None, None] self._encountered_y_std = [None, None] def transform(self, x=None, y=None): x_res = x y_res = y if x is not None: x_res = (x - self.x_mean) / self.x_std if y is not None: energy = y[0] gradient = y[1] out_e = (energy - self.energy_mean) / self.energy_std out_g = gradient / self.gradient_std y_res = [out_e, out_g] return x_res, y_res def inverse_transform(self, x=None, y=None): x_res = x y_res = y if x is not None: x_res = x * self.x_std + self.x_mean if y is not None: energy = y[0] gradient = y[1] out_e = energy * self.energy_std + self.energy_mean out_g = gradient * self.gradient_std y_res = [out_e, out_g] return x_res, y_res def fit(self, x=None, y=None, auto_scale=None): if auto_scale is None: auto_scale = {'x_mean': True, 'x_std': True, 'energy_std': True, 'energy_mean': True} npeps = np.finfo(float).eps if auto_scale['x_mean']: self.x_mean = np.mean(x) if auto_scale['x_std']: self.x_std = np.std(x) + npeps if auto_scale['energy_mean']: y1 = y[0] self.energy_mean =

np.mean(y1, axis=0, keepdims=True)

numpy.mean

#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Jun 15 22:04:25 2020 @author: lukepinkel """ import numpy as np import pandas as pd from ..utilities.linalg_operations import vec, invec, vecl, vdg from ..utilities.special_mats import kmat, nmat, lmat class RotationMethod(object): def __init__(self, A, rotation_type="ortho"): self.p, self.m = A.shape self.A = A self.rotation_type = rotation_type self.Kmp = kmat(self.m, self.p) def rotate(self, T): if self.rotation_type == "ortho": L = np.dot(self.A, T) else: L = np.dot(self.A, np.linalg.inv(T.T)) return L def _d_rotate_oblique(self, T): A = self.A B = np.linalg.inv(T.T) L =

np.dot(A, B)

numpy.dot

import threading, queue, time, os, pickle # from queue import Queue import numpy as np import tensorflow as tf import sarnet_td3.common.tf_util as U from tensorflow.python.keras.backend import set_session lock = threading.Lock() class MultiTrainTD3(threading.Thread): def __init__(self, input_queue, output_queue, args=(), kwargs=None): threading.Thread.__init__(self, args=(), kwargs=None) self.input_queue = input_queue self.output_queue = output_queue self.daemon = True self.trainers = args[0] self.args = args[1] self.buffer_op = args[2] self.num_env = args[3] self.sess = args[4] self.num_agents = args[5] self.num_adversaries = args[6] self.ep_rewards = [[0.0] for _ in range(self.num_env)] self.ep_end_rewards = [[0.0] for _ in range(self.num_env)] self.ep_success = [[0.0] for _ in range(self.num_env)] self.agent_rewards = [[[0.0] for _ in range(self.num_agents)] for _ in range(self.num_env)] self.agent_info = [[[[]] for i in range(self.num_agents)] for _ in range(self.num_env)] # self.agent_info = [[[[]]] for _ in range(self.num_env)] self.final_ep_rewards = [] # Shape: (batch, #) sum of rewards for training curve self.final_ep_end_rewards = [] self.final_ep_ag_rewards = [] # agent rewards for training curve self.save_rate = self.args.max_episode_len * 100 self.save_n_ep = self.num_env * 10 self.print_step = -int(self.save_n_ep / self.num_env) self.q_h_init = np.zeros(shape=(self.num_env, self.args.critic_units)) self.mem_init = np.zeros(shape=(self.num_env, self.args.value_units)) self.time_prev = time.time() def run(self): # print(threading.currentThread().getName(), self.receive_messages) with self.sess.as_default(): # Freeze graph to avoid memory leaks # self.sess.graph.finalize() while True: try: action, p_index, data = self.input_queue.get() if action is "None": # If you send `None`, the thread will exit. return elif action is "get_action": out = self.get_action(data, p_index) self.output_queue.put(out) elif action is "get_qdebug": out = self.get_qdebug(data, p_index) self.output_queue.put(out) elif action is "get_loss": out = self.get_loss(data, p_index) self.output_queue.put(out) elif action is "write_tboard": self.write_tboard(data) elif action is "add_to_buffer": self.buffer_op.collect_exp(data) elif action is "save_rew_info": self.save_rew_info(data) elif action is "save_benchmark": out = self.save_benchmark(data) self.output_queue.put(out) elif action is "reset_rew_info": self.reset_rew_info() elif action is "save_model_rew": if not (self.args.benchmark or self.args.display): self.save_model(data) self.plot_rewards(data) except queue.Empty: continue def get_action(self, data, p_index): with lock: agent = self.trainers[p_index] obs_n_t, h_n_t, c_n_t, mem_n_t, q1_h_t, is_train = data obs_n_t = np.stack(obs_n_t, axis=-2) # This returns [agent, batch, dim] obs_n_t = np.expand_dims(obs_n_t, axis=1) # This adds [agent, time, batch, dim] p_input_j = agent.prep_input(obs_n_t, h_n_t, c_n_t, mem_n_t, q1_h_t[p_index], is_train) # print(np.shape(obs_n_t)) act_j_t, state_j_t1, mem_j_t1, attn_j_t = agent.action(p_input_j, is_train) if self.args.encoder_model == "LSTM" or self.args.encoder_model != "DDPG": c_j_t1, h_j_t1 = state_j_t1 else: h_j_t1 = state_j_t1 c_j_t1 = state_j_t1 if agent.comm_type in {"DDPG", "COMMNET", "IC3NET"}: mem_j_t1 = np.zeros(shape=(self.num_env, self.args.value_units)) return act_j_t, h_j_t1, c_j_t1, mem_j_t1, attn_j_t def get_qdebug(self, data, p_index): with lock: # with sess.as_default(): agent = self.trainers[p_index] obs_n_t, action_n_t, q1_h_n_t, q2_h_n_t = data obs_n_t = np.stack(obs_n_t, axis=-2) # This returns [agent, batch, dim] obs_n_t = np.expand_dims(obs_n_t, axis=1) # This adds [agent, time, batch, dim] q1_j_input = agent.prep_q_input(obs_n_t, action_n_t, q1_h_n_t[p_index]) _, q1_h_j_t1 = agent.q1_debug['q_values'](*(q1_j_input)) if self.args.td3: q2_input = agent.prep_q_input(obs_n_t, action_n_t, q2_h_n_t[p_index]) _, q2_h_j_t1 = agent.q2_debug['q_values'](*(q2_input)) else: q2_h_j_t1 = [] return q1_h_j_t1, q2_h_j_t1 def get_loss(self, data, p_index): with lock: # with sess.as_default(): agent = self.trainers[p_index] train_step = data loss = agent.update(self.trainers, self.buffer_op, train_step) return loss def write_tboard(self, data): with lock: loss, train_step, writer, summary_ops, summary_vars, num_agents = data # Tensorboard episode_b_rewards = [] for j in range(self.num_env): if self.args.env_type == "mpe": episode_b_rewards.append(np.mean(self.ep_rewards[j][self.print_step:])) else: episode_b_rewards.append(np.mean(self.ep_success[j][self.print_step:])) episode_b_rewards = np.mean(np.array(episode_b_rewards)) num_steps = train_step * self.num_env # Add to tensorboard only when actor agent is updated if loss[0][1] is not None: fd = {} for i, key in enumerate(summary_vars): if i == 0: fd[key] = episode_b_rewards else: agnt_idx = int((i - 1) / 5) if agnt_idx == num_agents: agnt_idx -= 1 if loss[agnt_idx] is not None: fd[key] = loss[agnt_idx][int((i - 1) % 5)] summary_str = U.get_session().run(summary_ops, feed_dict=fd) writer.add_summary(summary_str, num_steps) writer.flush() def save_rew_info(self, data): with lock: rew_n, info_n, ep_step = data # rew_n (num_env, num_agents) if self.args.env_type == "mpe": for j in range(self.num_env): for i, rew in enumerate(rew_n[j]): if ep_step >= self.args.max_episode_len - 10: # Compute only last 10 episode step rewards self.ep_end_rewards[j][-1] += rew self.ep_rewards[j][-1] += rew self.agent_rewards[j][i][-1] += rew elif self.args.env_type == "ic3net": for j in range(self.num_env): self.ep_success[j][-1] += info_n[j] if self.args.benchmark and self.args.env_type == "mpe": for j in range(self.num_env): for i, info in enumerate(info_n[j]): self.agent_info[j][i][-1].append(info) def reset_rew_info(self): with lock: for j in range(self.num_env): self.ep_rewards[j].append(0) self.ep_success[j].append(0) self.ep_end_rewards[j].append(0) for i in range(self.num_agents): self.agent_rewards[j][i].append(0) if self.args.benchmark: for j in range(self.num_env): for i in range(self.num_agents): self.agent_info[j][i].append([[]]) def save_benchmark(self, data): with lock: exp_name, exp_itr = data benchmark_dir = os.path.join('./exp_data', exp_name, exp_itr, self.args.benchmark_dir) if not os.path.exists(benchmark_dir): os.mkdir(benchmark_dir) file_name = './exp_data/' + exp_name + '/' + exp_itr + '/' + self.args.benchmark_dir + '/' + exp_name + '.pkl' print('Finished benchmarking, now saving...') # pickle_info = [self.agent_info[j] for j in range(self.num_env)] with open(file_name, 'wb') as fp: # Dump files as [num_env, [# agents, [#ep, [#stps, [dim]]]] pickle.dump(self.agent_info, fp) return "bench_saved" def save_model(self, data): with lock: # train_step = t_step * num_env train_step, num_episodes, time_taken, exp_name, exp_itr, data_file, saver = data # Policy File if num_episodes % (self.save_n_ep) == 0: save_dir = './exp_data/' + exp_name + '/' + exp_itr + '/' + self.args.save_dir + str(train_step) U.save_state(save_dir, self.sess, saver=saver) # episode_rewards, agent_rewards, final_ep_rewards, final_ep_ag_rewards = rewards if self.args.env_type == "mpe": # print statement depends on whether or not there are adversaries if self.num_adversaries == 0: episode_b_rewards = [] ep_end_b_rewards = [] ep_ag_b_rewards = [] for j in range(self.num_env): episode_b_rewards.append(np.mean(self.ep_rewards[j][self.print_step:])) ep_end_b_rewards.append(np.mean(self.ep_end_rewards[j][self.print_step:])) episode_b_rewards = np.mean(

np.array(episode_b_rewards)

numpy.array

#!/usr/bin/env python3 # -*- coding: utf-8 -*- import os import json import math import numpy class Wavefront(): def __init__(self, path, triangulateQuads = True): # These are the arrays we're going to produce, and which might # make sense to manipulate from the outside: self.vertexCoords = None # XYZ coordinated for each vertex self.vertexNormals = None # Normal (in XYZ form) for each vertex self.faces = None # Faces, specified by listing indexes for participating vertices # These are internal work arrays self._rawVertices = [] self._rawTexCo = [] self._rawVertexTexCo = []; self._rawFaces = [] self._vertexBelongsToFaces = None self._faceVertCache = None self.triangulateQuads = triangulateQuads if not os.path.exists(path): raise IOError(path + " does not exist") self.content = [] with open(path,'r') as file: self.content = file.readlines() # self._mode can be: # ONLYTRIS: The incoming mesh only contains tris (so no need to do anything) # TRIANGULATE: The incoming mesh contains quads (and may contain tris). Triangulate to get only tris. # ONLYQUADS: The incoming mesh contains only quads. Keep these rather than triangulating self._mode = None # Check if mesh contains quads and/or tris self._scanForMode() # Make a sweep for vertices as faces need that information self._extractVertices() # Make a sweep for texture coordinates, as faces need that too self._extractTextureCoordinates() # Make a sweep for faces self._extractFaces() # TODO: Find texture coordinates for vertices # create numpy arrays to contain vertices, faces and normals self._createVerticesNumpyArray() self._createFacesNumpyArray() # These two operations need to be redone if vertex coordinates # are changed self.recalculateFaceNormals() self.recalculateVertexNormals() def _scanForMode(self): containsTris = False containsQuads = False for line in self.content: strippedLine = line.strip() if not strippedLine is None and not strippedLine == "" and not strippedLine[0] == "#": parts = strippedLine.split(' ') if len(parts) > 4: containsQuads = True if len(parts) == 4: containsTris = True if len(parts) > 5: raise ValueError("Found a face with more than four vertices. N-gons are not supported.") # TODO: Check for n-gons? if containsQuads: if self.triangulateQuads: self._mode = "TRIANGULATE" else: if containsTris: raise ValueError("Since the mesh contains both tris and quads, requesting the mesh to not be triangulated is illegal") else: self._mode = "ONLYQUADS" else: if containsTris: self._mode = "ONLYTRIS" else: raise ValueError("The mesh didn't contain tris nor quads!?") if self._mode == "ONLYQUADS": raise ValueError("The ONLYQUADS mode is not implemented yet") print("Tris " + str(containsTris)) print("Quads " + str(containsQuads)) print(self._mode) def _extractVertices(self): for line in self.content: strippedLine = line.strip() if not strippedLine is None and not strippedLine == "" and not strippedLine[0] == "#": parts = strippedLine.split(' ') if len(parts) > 1: command = parts[0] if command == "v": x = float(parts[1]) y = float(parts[2]) z = float(parts[3]) vertex = [x, y, z] self._rawVertices.append(vertex) self._rawVertexTexCo.append([0,0]) def _extractTextureCoordinates(self): self.hasTexCo = False for line in self.content: strippedLine = line.strip() if not strippedLine is None and not strippedLine == "" and not strippedLine[0] == "#": parts = strippedLine.split(' ') if len(parts) > 1: command = parts[0] if command == "vt": x = float(parts[1]) y = float(parts[2]) texco = [x, y] self._rawTexCo.append(texco) def _distanceBetweenVerticesByIdx(self, idx1, idx2): vert1 = numpy.array(self._rawVertices[idx1]) vert2 = numpy.array(self._rawVertices[idx2]) difference = vert2 - vert1 x = difference[0] y = difference[1] z = difference[2] distance = math.sqrt( x*x + y*y + z*z ) return distance def _extractFaces(self): # Note that wavefront lists starts at 1, not 0 for line in self.content: strippedLine = line.strip() if not strippedLine is None and not strippedLine == "" and not strippedLine[0] == "#": parts = strippedLine.split(' ') if len(parts) > 1: command = parts[0] if command == "f": # Face info is vertIdx / texCoIdx / faceNormalIdx OR vertIdx / texCoIdx OR vertIdx vInfo1 = parts[1].split('/') vInfo2 = parts[2].split('/') vInfo3 = parts[3].split('/') # Find indexes of vertices making up the face. Note "-1" since wavefront indexes start # at 1 rather than 0 vidx1 = int(vInfo1[0]) - 1 vidx2 = int(vInfo2[0]) - 1 vidx3 = int(vInfo3[0]) - 1 if len(parts) == 4: if self._mode == "ONLYQUADS": raise ValueError("Found tri although mode was ONLYQUADS") face = [vidx1, vidx2, vidx3] self._rawFaces.append(face) else: vInfo4 = parts[4].split('/') vidx4 = int(vInfo4[0]) - 1 if self._mode == "ONLYTRIS": raise ValueError("Found quad although mode was ONLYTRIS") if self._mode == "ONLYQUADS": raise ValueError("ONLYQUADS mode not implemented yet") # Perform triangulation by splitting quad into two tris, using the shortest diagonal distance13 = self._distanceBetweenVerticesByIdx(vidx1, vidx3) distance24 = self._distanceBetweenVerticesByIdx(vidx2, vidx4) if distance13 > distance24: face = [vidx1, vidx2, vidx4] self._rawFaces.append(face) face = [vidx3, vidx4, vidx2] self._rawFaces.append(face) else: face = [vidx1, vidx3, vidx4] self._rawFaces.append(face) face = [vidx2, vidx3, vidx1] self._rawFaces.append(face) i = 1 while i < len(parts): f = parts[i].split('/') if len(f) > 1: vidx = int(f[0]) - 1 # Vertex index ti = f[1] # May be empty if no UV unwrap if ti != "": tidx = int(ti) - 1 # Texture coordinate index texco = self._rawTexCo[tidx] # Actual texture coordinats, x/y self._rawVertexTexCo[vidx] = texco self.hasTexCo = True i = i + 1 def _createFacesNumpyArray(self, assumeQuads = False): numberOfFaces = len(self._rawFaces) vertsPerFace = 3 if assumeQuads: vertsPerFace = 4 # Create a two-dimensional int array with shape (numFace/vertsPerFace) and # fill it values from the wavefront obj. This will contain vert indices. self.faces = numpy.array( self._rawFaces, dtype=int ) # Values will be copied from self._rawFaces # Create a two-dimensional float array with shape (numFace/ 3 ) and # fill it with zeros. This will contain faces normals, but needs to # be recalculated. self.faceNormals = numpy.zeros( (numberOfFaces, 3), dtype=float ) def _createVerticesNumpyArray(self): numberOfVertices = len(self._rawVertices) if numberOfVertices != len(self._rawVertexTexCo): raise ValueError("Not same number of elements in texco array") # Convert raw coords from wavefront into a 2d numpy array self.vertexCoords = numpy.array( self._rawVertices, dtype=float ) # Create a two-dimensional float array with shape (numVerts/3) and # fill it with zeros. This will contain vertex normals. self.vertexNormals = numpy.zeros( (numberOfVertices, 3), dtype=float ) # Create a two-dimensional float array with shape (numVerts/2) and # fill it with texture coordinates. self.vertexTexCo = numpy.array( self._rawVertexTexCo, dtype=float ) def recalculateVertexNormals(self, assumeQuads = False): # Build a cache where we, per vertex, list which faces are relevant # for it. We need this in order to calculate the vertex normal later, # as an average of the face normals surrounding it if self._vertexBelongsToFaces is None: self._vertexBelongsToFaces = [] numberOfFaces = len(self.faces) numberOfVertices = len(self.vertexCoords) vertsPerFace = 3 if assumeQuads: vertsPerFace = 4 currentVert = 0 while currentVert < numberOfVertices: self._vertexBelongsToFaces.append([]) currentVert = currentVert + 1 currentFace = 0 while currentFace < numberOfFaces: fv = self.faces[currentFace] currentVert = 0 while currentVert < vertsPerFace: vertexIndex = fv[currentVert] self._vertexBelongsToFaces[vertexIndex].append(currentFace) currentVert = currentVert + 1 currentFace = currentFace + 1 # Calculate vertex normals as an average of the surrounding face # normals. currentVert = 0 zeroNormal = numpy.array([0.0, 0.0, 0.0], dtype=float) while currentVert < numberOfVertices: faces = self._vertexBelongsToFaces[currentVert] numberOfFaces = len(faces) currentNormal = numpy.array([0,0,0], dtype=float) currentFace = 0 firstNormal = None while currentFace < numberOfFaces: fidx = faces[currentFace] fnormal = self.faceNormals[fidx] if firstNormal is None: firstNormal = fnormal currentNormal = currentNormal + fnormal currentFace = currentFace + 1 if numberOfFaces < 1: raise ValueError("Found a vertex (" + str(currentVert) + ") which did not belong to any face") averageNormal = currentNormal / numberOfFaces if numpy.array_equal(averageNormal, zeroNormal): print("WARNING: found zero vertex normal for vertex " + str(currentVert)) averageNormal = firstNormal self.vertexNormals[currentVert] = self._unitVector(averageNormal) currentVert = currentVert + 1 def recalculateFaceNormals(self): self._copyVertCoordsToCache() # Calculate the face normal from the first three vertices. This might produce # strange results if using quads. In that case we should probably triangulate and # and weight together the face normals of the resulting two tris. numberOfFaces = len(self.faces) currentFace = 0 while currentFace < numberOfFaces: U = self._faceVertCache[currentFace][1] - self._faceVertCache[currentFace][0] V = self._faceVertCache[currentFace][2] - self._faceVertCache[currentFace][0] cross =

numpy.cross(U,V)

numpy.cross

''' 本模块用于数据预处理 This module is used for data preproccessing ''' import numpy as np from maysics.utils import e_distances from matplotlib import pyplot as plt plt.rcParams['font.sans-serif'] = ['FangSong'] plt.rcParams['axes.unicode_minus'] = False from io import BytesIO from lxml import etree import base64 import math def _rc(arg): cov_mat = np.cov(arg) var_mat = np.diagonal(cov_mat)**0.5 var_mat[var_mat == 0] = 1 for i in range(cov_mat.shape[0]): cov_mat[i] /= var_mat[i] cov_mat[:, i] /= var_mat[i] return cov_mat def _preview_process(data, value_round): ''' 预览处理 ''' data = np.array(data, dtype=float) name_list = ['平均值', '中位数', '方差', '标准差', '最大值', '最小值', '偏度', '峰度'] value_list = [] mean_ = data.mean(axis=0) value_list.append(np.round(mean_, value_round)) value_list.append(np.round(np.median(data, axis=0), value_round)) value_list.append(np.round(data.var(axis=0), value_round)) value_list.append(np.round(data.std(axis=0), value_round)) value_list.append(np.round(data.max(axis=0), value_round)) value_list.append(np.round(data.min(axis=0), value_round)) value_list.append(np.round(((data - mean_)**3).mean(axis=0), value_round)) value_list.append(np.round(((data - mean_)**4).mean(axis=0), value_round)) value_list = np.array(value_list).flatten() style = ''' <style> table{ border-collapse: collapse; } table, table tr td { border:1px solid #ccc; } table tr td{ padding: 5px 10px; } </style> ''' table = '<h2 style="padding-left:50px; border-top:1px solid #ccc">数值特征</h2>' + style + '<table align="center"><caption></caption>' for i in range(8): table += '<tr><td>' + name_list[i] + '</td>' + '<td>%s</td>' * data.shape[1] + '</tr>' table = '<h1 style="padding-left:50px;">数据信息</h1>' + table % tuple(value_list) + '</table>' data = np.ascontiguousarray(data.T) num = data.shape[0] plt.figure(figsize=(9, 3 * num)) for i in range(num): q1, q2, q3 = np.percentile(data[i], [25, 50, 75]) plt.scatter(mean_[i], i+1, marker='o', color='white', s=30, zorder=3) plt.hlines(i+1, q1, q3, color='k', linestyle='-', lw=1) bx = plt.violinplot(data.tolist(), showextrema=False, vert=False) plt.title('分布图') buffer = BytesIO() plt.savefig(buffer) plt.close() plot_data = buffer.getvalue() imb = base64.b64encode(plot_data) ims = imb.decode() imd = 'data:image/png;base64,' + ims im1 = '<div align="center"><img src="%s"></div>' % imd im1 = '<br></br><h2 style="padding-left:50px; border-top:1px solid #ccc">密度分布</h2>' + im1 cov_mat = _rc(data) matrix = '<table border="0"><caption></caption>' for i in range(num): matrix += '<tr>' + '<td>%s</td>' * num + '</tr>' matrix = matrix % tuple(np.round(cov_mat.flatten(), value_round)) + '</table>' plt.figure(figsize=(8, 8)) plt.matshow(cov_mat, fignum=0, cmap='Blues') plt.colorbar() plt.title('相关系数图') buffer = BytesIO() plt.savefig(buffer) plt.close() plot_data = buffer.getvalue() imb = base64.b64encode(plot_data) ims = imb.decode() imd = 'data:image/png;base64,' + ims im2 = '<div style="display:flex;flex-direction:row;vertical-align:middle;justify-content:center;width:100%;height:80vh"><div style="margin:auto 0;white-space:pre-wrap;max-width:50%">' im2 = im2 +'相关矩阵：'+ matrix + '</div><img style="object-fit:contain;max-width:45%;max-height:80vh" src="{}"/></div>'.format(imd) im2 = '<br></br><h2 style="padding-left:50px; border-top:1px solid #ccc">相关性</h2>' + im2 plt.figure(figsize=(2.5 * num, 2.5 * num)) for i in range(num * num): ax = plt.subplot(num, num, i+1) ax.plot(data[i//num], data[i%num], 'o') buffer = BytesIO() plt.savefig(buffer) plt.close() plot_data = buffer.getvalue() imb = base64.b64encode(plot_data) ims = imb.decode() imd = "data:image/png;base64," + ims im3 = '<div align="center"><img src="%s"></div>' % imd im3 = '<br></br><h2 style="padding-left:50px; border-top:1px solid #ccc">散点关系</h2>' + im3 return '<title>数据信息预览</title>' + table + im1 + im2 + im3 def preview_file(filename, data, value_round=3): ''' 生成数据预览报告的html文件参数 ---- filename：字符串类型，文件名 data：二维数组，数据 value_round：整型，数字特征保留的小数点后的位数 Generate preview report with html file Parameters ---------- filename: str, file name data: 2-D array, data value_round: int, the number of digits after the decimal point retained by numeric features ''' root = _preview_process(data=data, value_round=value_round) html = etree.HTML(root) tree = etree.ElementTree(html) tree.write(filename) def preview(data, value_round=3): ''' 在jupyter中显示数据预览报告参数 ---- data：二维数组，数据 value_round：整型，数字特征保留的小数点后的位数 Display preview report in jupyter Parameters ---------- data: 2-D array, data value_round: int, the number of digits after the decimal point retained by numeric features ''' root = _preview_process(data=data, value_round=value_round) from IPython.core.display import display, HTML display(HTML(root)) def length_pad(seq, maxlen=None, value=0, padding='pre', dtype=float): ''' 填充二维列表，使得每行长度都为maxlen 参数 ---- seq：二维列表，需要填充的对象 maxlen：整型，可选，每行的最大长度，默认为原二维列表最大的长度 value：数类型，可选，填充值，默认为0 padding：字符串类型，可选，填充位置，'pre'代表从前面填充，'post'代表从后面填充，默认为'pre' dtype：可选，输出的元素类型，默认为float 返回 ---- 二维ndarray Pad the 2-D list so that every row is 'maxlen' in length Parameters ---------- seq: 2-D list, objects that need to be padded maxlen: int, callable, the maximum length of each row, default = the maximum length of the original 2-D list value: num, callable, padding value, default=0 padding: str, callable, padding location, 'pre' means padding from the front and 'post' from the back, default='pre' dtype: callable, the element type of the output, default=float Return ------ 2-D ndarray ''' seq = list(seq) if not maxlen: maxlen = 0 for i in seq: if len(i) > maxlen: maxlen = len(i) if padding == 'pre': for i in range(len(seq)): if maxlen > len(seq[i]): seq[i] = [value] * (maxlen - len(seq[i])) + seq[i] elif maxlen < len(seq[i]): seq[i] = seq[i][-1 * maxlen:] elif padding == 'post': for i in range(len(seq)): if maxlen > len(seq[i]): seq[i] += [value] * (maxlen - len(seq[i])) elif maxlen < len(seq[i]): seq[i] = seq[i][:maxlen] return np.array(seq, dtype=dtype) def sample_pad(data, index=0, padding=None): ''' 对二维数据进行样本填充先对data中的每个二维数据进行遍历，以各个index列的值作为全集，再对data的每个二维数据进行填充如：data1 = [[0, 1], [1, 2], [2, 3]] data2 = [[2, 3], [3, 4], [4, 5]] data = (data1, data2) 则得到输出： output = [array([[0, 1], [1, 2], [2, 3], [3, nan], [4, nan]]), array([[0, nan], [1,nan], [2, 3], [3, 4], [4, 5]])] data：元组或列表类型，数据 index：整型，作为扩充全集的标准列的索引 padding：填充值，可选，默认为None Sample filling for 2D data Values of each index column will be taken as the complete set, then each two-dimensional data of data is padded e.g. data1 = [[0, 1], [1, 2], [2, 3]] data2 = [[2, 3], [3, 4], [4, 5]] data = (data1, data2) output = [array([[0, 1], [1, 2], [2, 3], [3, nan], [4, nan]]), array([[0, nan], [1,nan], [2, 3], [3, 4], [4, 5]])] data: tuple or list, data index: int, the index of a standard column as an extended complete set padding: padding value, optional, default=None ''' time_set = set() result = [] if not padding: padding = [np.nan] * (len(data[0][0]) - 1) else: padding = list([padding]) for i in range(len(data)): data_part = np.array(data[i], dtype=np.object) result.append(data_part) time_set = time_set | set(data_part[:, index]) for i in range(len(result)): different_set_list = np.array([list(time_set - set(result[i][:, index]))], dtype=np.object).T num = len(different_set_list) padding_new = np.array(padding * num, dtype=np.object).reshape(num, -1) different_set_list = np.hstack((padding_new[:, :index], different_set_list, padding_new[:, index:])) result[i] = np.vstack((result[i], different_set_list)) return result def shuffle(*arg): ''' 打乱一个序列或以相同方法打乱多个序列返回 ---- 一个ndarray Shuffle a sequence or shuffle multiple sequences in the same way Return ------ a ndarray ''' state = np.random.get_state() a_new_list = [] for li in arg: np.random.set_state(state) np.random.shuffle(li) a_new_list.append(li) return np.array(a_new_list) def data_split(data, targets, train_size=None, test_size=None, shuffle=True, random_state=None): ''' 分离数据参数 ---- data：数据 targets：指标 train_size：浮点数类型，可选，训练集占总数据量的比，取值范围为(0, 1]，默认为0.75 test_size：浮点数类型，可选，测试集占总数据量的比，取值范围为[0, 1)，当train_size被定义时，该参数无效 shuffle：布尔类型，可选，True表示打乱数据，False表示不打乱数据，默认为True random_state：整型，可选，随机种子返回 ---- 元组，(数据测试集, 指标测试集, 数据验证集, 指标验证集) split the data Parameters ---------- data: data targets: targets train_size: float, callable, ratio of training set to total data, value range is (0, 1], default=0.75 test_size: float, callable, ratio of test set to total data, value range is [0, 1) shuffle: bool, callable, 'True' will shuffle the data, 'False' will not, default = True random_state: int, callable, random seed Return ------ tuple, (train_data, train_target, validation_data, validation_target) ''' data = np.array(data) targets = np.array(targets) if not (train_size or test_size): train_size = 0.75 elif test_size: train_size = 1 - test_size if train_size <= 0 or train_size > 1: raise Exception("'train_size' should be in (0, 1], 'test_size' should be in [0, 1)") if shuffle: np.random.seed(random_state) state = np.random.get_state() np.random.shuffle(data) np.random.set_state(state) np.random.shuffle(targets) num_of_data = len(data) train_data = data[:int(num_of_data * train_size)] train_target = targets[:int(num_of_data * train_size)] validation_data = data[int(num_of_data * train_size):] validation_target = targets[int(num_of_data * train_size):] return train_data, train_target, validation_data, validation_target def kfold(data, targets, n, k=5): ''' 参数 ---- data：数据 targets：指标 n：整型，表示将第n折作为验证集，从0开始 k：整型，可选，k折验证的折叠数，默认k=5 返回 ---- 元组，(数据测试集, 指标测试集, 数据验证集, 指标验证集) Parameters ---------- data: data targets: targets n: int, take the nth part as validation set, starting from 0 k: int, callable, the number of k-fold, default = 5 Return ------ tuple, (train_data, train_target, validation_data, validation_target) ''' data = np.array(data) targets = np.array(targets) num_validation_samples = len(data) // k validation_data = data[num_validation_samples * n: num_validation_samples * (n + 1)] validation_targets = targets[num_validation_samples * n: num_validation_samples * (n + 1)] train_data = np.concatenate([data[: num_validation_samples * n], data[num_validation_samples * (n + 1):]]) train_targets = np.concatenate([targets[: num_validation_samples * n], targets[num_validation_samples * (n + 1):]]) return train_data, train_targets, validation_data, validation_targets def dataloader(data, targets, choose_rate=0.3, shuffle=True, random_state=None): ''' 数据随机生成器参数 ---- data：数据 targets：指标 choose_rate：浮点数类型，可选，生成率，即一次生成数据量在原数据量的占比，范围为[0, 1]，默认为0.3 shuffle：布尔类型，可选，True表示打乱数据，False表示不打乱数据，默认为True random_state：整型，可选，随机种子返回 ---- 生成器 Data Random Generator Parameters ---------- data: data targets: targets choose_rate: float, callable, generation rate (the proportion of data generated at one time in the original data) whose range is [0, 1], default=0.3 shuffle: bool, callable, 'True' will shuffle the data, 'False' will not, default = True random_state: int, callable, random seed Return ------ generator ''' data = np.array(data) targets = np.array(targets) if shuffle: np.random.seed(random_state) state = np.random.get_state() np.random.shuffle(data) np.random.set_state(state)

np.random.shuffle(targets)

numpy.random.shuffle

import tensorflow as tf import numpy as np import sys tf.logging.set_verbosity(tf.logging.ERROR) class Judge: def __init__(self, N_to_mask, model_dir, binary_rewards=True): self.N_to_mask = N_to_mask self.binary_rewards = binary_rewards # Create the Estimator try: self.estimator = tf.estimator.Estimator( model_fn=self.model_fn, model_dir=model_dir, # directory to restore model from and save model to ) except AttributeError: raise Exception("Subclass needs to define a model_fn") # Create the predictor from the present model. Important when restoring a model. self.update_predictor() def update_predictor(self): # Predictors are used to get predictions fast once the model has been trained. # We create it from an estimator. self.predictor = tf.contrib.predictor.from_estimator( self.estimator, # The serving input receiver fn is witchcraft, which I don't quite understand. # It's supposed to set up the data in a way that tensorflow can handle. tf.estimator.export.build_raw_serving_input_receiver_fn( # The input is a dictionary that corresponds to the data we feed the predictor. # Each key stores a tensor that is replaced by data when the predictor is used. {"masked_x": tf.placeholder(shape=[None, 28, 28, 2], dtype=tf.float32)} ), ) def mask_image_batch(self, image_batch): """ Takes a batch of two-dimensional images, reshapes them, runs them through mask_batch, reshapes them back to images, and returns them. """ shape = tf.shape(image_batch) batch_flat = tf.reshape(image_batch, (shape[0], shape[1] * shape[2])) mask_flat = self.mask_batch(batch_flat) return tf.reshape(mask_flat, (shape[0], shape[1], shape[2], 2)) def mask_batch(self, batch): """ Create mask for each feature-vector in a batch, that contains N_to_mask nonzero features of the input vector. Combine this with the vector to create the input for the DNN. """ shape = tf.shape(batch) n_zero = tf.random.categorical(logits=self.zero_logits,num_samples=1,dtype=tf.int32) p = tf.random_uniform(shape, 0, 1) p = tf.where(batch > 0, p, -p) # each number is positive if > 0, else negative _, nonzero_indices = tf.nn.top_k(p, self.N_to_mask - n_zero[0][0]) # sample positive _, zero_indices = tf.nn.top_k(-p, n_zero[0][0]) # sample negative indices = tf.concat([nonzero_indices,zero_indices],1) mask = tf.one_hot(indices, shape[1], axis=1) mask = tf.reduce_sum(mask, axis=2) return tf.stack((mask, mask * batch), 2) def train(self, n_steps, n_zero=0): # Train the model train_input_fn = tf.estimator.inputs.numpy_input_fn( x={"x": self.train_data}, y=self.train_labels, batch_size=self.batch_size, num_epochs=None, shuffle=True, ) if type(n_zero) != list: self.zero_logits = [[0 if i == n_zero else -np.inf for i in range(self.N_to_mask + 1)]] else: assert len(n_zero) == self.N_to_mask + 1 self.zero_logits = np.log(n_zero).reshape((1,-1)) self.estimator.train(input_fn=train_input_fn, steps=n_steps) # Replace the old predictor with one created from the new estimator self.update_predictor() def evaluate_accuracy(self, n_zero=0): # Evaluate the accuracy on all the eval_data eval_input_fn = tf.estimator.inputs.numpy_input_fn( x={"x": self.eval_data}, y=self.eval_labels, num_epochs=1, shuffle=False ) if type(n_zero) != list: self.zero_logits = [[0 if i == n_zero else -np.inf for i in range(self.N_to_mask + 1)]] else: assert len(n_zero) == self.N_to_mask + 1 self.zero_logits = np.log(n_zero).reshape((1,-1)) return self.estimator.evaluate(input_fn=eval_input_fn) def evaluate_accuracy_using_predictor(self): """ Evaluates the test set accuracy using the tensorflow predictor instead of the estimator. Can be useful for debugging. """ correct = 0 count = 0 for i in range(len(self.eval_labels)): # print(i) image = self.eval_data[i].flat mask = np.zeros_like(image) while mask.sum() < self.N_to_mask: a = np.random.randint(mask.shape[0]) if image[a] > 0: mask[a] = 1 input = np.stack((mask, image * mask), axis=1) input =

np.reshape(input, self.shape)

numpy.reshape

#!/usr/bin/env python """ Perform the population demonstration test in Section IIIB. This will generate Figures 8 and 9. For more details on the method see https://arxiv.org/abs/2106.13785. For more details on the analysis see https://arxiv.org/abs/1712.00688. """ import os import dill import matplotlib.pyplot as plt import numpy as np import pandas as pd from bilby.core.utils import create_frequency_series from bilby.gw.conversion import convert_to_lal_binary_black_hole_parameters from bilby.gw.detector import PowerSpectralDensity from bilby.gw.source import lal_binary_black_hole from bilby.gw.waveform_generator import WaveformGenerator from scipy.signal.windows import tukey from scipy.special import logsumexp from tqdm.auto import trange from coarse_psd_matrix.utils import ( compute_psd_matrix, fetch_psd_data, regularized_inversion, ) from matplotlib import rcParams rcParams["font.family"] = "serif" rcParams["font.serif"] = "Computer Modern Roman" rcParams["font.size"] = 20 rcParams["text.usetex"] = True rcParams["grid.alpha"] = 0 def run_tbs(signal_model, signal_parameter, outdir): sampling_frequency = 2048 duration = 128 data_duration = 32 short_duration = 4 low_frequency = 16 minimum_frequency = 20 maximum_frequency = 800 tukey_alpha = 0.1 label = f"{signal_model}_{signal_parameter}" data = fetch_psd_data( interferometer_name="L1", event="GW170814", outdir="GW170814", medium_duration=duration, sampling_frequency=sampling_frequency, tukey_alpha=tukey_alpha, duration=short_duration, low_frequency=low_frequency, ) psd = data["psd"] freqs_ = data["frequencies"] del data psd_ = PowerSpectralDensity.from_power_spectral_density_array( frequency_array=freqs_, psd_array=psd ) short_window = tukey(sampling_frequency * short_duration, tukey_alpha) long_frequencies = np.fft.fftfreq( sampling_frequency * data_duration, 1 / sampling_frequency ) long_psd = psd_.power_spectral_density_interpolated(abs(long_frequencies)) print("PSD matrix") data = dict(frequencies=freqs_, medium_psd=long_psd) data_file = f"{outdir}/GW170814_data_coarse_{data_duration}_{sampling_frequency}_{tukey_alpha}_L1.pkl" with open(data_file, "wb") as ff: dill.dump(data, ff) _svd = compute_psd_matrix( interferometer_name="L1", event="GW170814", duration=short_duration, sampling_frequency=sampling_frequency, low_frequency=low_frequency, tukey_alpha=tukey_alpha, minimum_frequency=minimum_frequency, maximum_frequency=maximum_frequency, medium_duration=data_duration, outdir=outdir, ) finite_psd = abs((_svd[0] * _svd[1]) @ _svd[2]).diagonal() regularization_method = "window" cutoff = 0.1 regularized_inverse = regularized_inversion(_svd, (regularization_method, cutoff)) SIGNAL_MODELS = dict(cbc=generate_cbc_signal, gaussian=generate_gaussian_signal) short_frequencies = np.fft.rfftfreq( short_duration * sampling_frequency, 1 / sampling_frequency ) mask = (short_frequencies >= minimum_frequency) & ( short_frequencies <= maximum_frequency ) np.save(f"{outdir}/frequencies.npy", short_frequencies[mask]) np.save(f"{outdir}/finite_psd.npy", finite_psd) signal = SIGNAL_MODELS[signal_model]( signal_parameter, sampling_frequency=sampling_frequency, duration=short_duration, ) np.save(f"{outdir}/signal_{label}", normalize_signal(signal=signal[mask], psd=finite_psd)) signal = np.fft.rfft(np.fft.irfft(signal) * short_window)[mask] signal = normalize_signal(signal=signal, psd=finite_psd) data_file = f"{outdir}/ln_bfs_{label}.hdf5" if os.path.isfile(data_file): data = pd.read_hdf(data_file) else: data = run_tbs_test( signal=signal, psd=psd_, sampling_frequency=sampling_frequency, duration=duration, short_duration=short_duration, short_psd=finite_psd, mask=mask, inverse=regularized_inverse, tukey_alpha=tukey_alpha, n_average=5000, ) data.to_hdf(f"{outdir}/ln_bfs_{label}.hdf5", key="bayes_factors") data.to_hdf(f"{outdir}/ln_bfs_{label}.hdf5", key="bayes_factors") fig = plot_tbs_bayes_factors(data) fig.savefig(f"{outdir}/ln_bfs_{label}.png") plt.close(fig) fig = plot_tbs_posterior(data) fig.savefig(f"{outdir}/xi_post_{label}.png", transparent=True) plt.close(fig) def generate_cbc_signal(mass, sampling_frequency, duration): waveform_arguments = dict( waveform_approximant="IMRPhenomXPHM", minimum_frequency=10.0, reference_frequency=20.0, maximum_frequency=1024.0, ) waveform_generator = WaveformGenerator( duration=duration, sampling_frequency=sampling_frequency, frequency_domain_source_model=lal_binary_black_hole, parameter_conversion=convert_to_lal_binary_black_hole_parameters, waveform_arguments=waveform_arguments, ) injection_parameters = dict( mass_1=mass, mass_2=mass, a_1=0.0, a_2=0.0, tilt_1=0.0, tilt_2=0.0, phi_12=0.0, phi_jl=0.0, luminosity_distance=2000.0, theta_jn=0.4, phase=0, ) signal = waveform_generator.frequency_domain_strain(injection_parameters)["plus"] signal *= np.exp(1j * 2 * np.pi * waveform_generator.frequency_array * 2) return signal def generate_gaussian_signal(peak_frequency, sampling_frequency, duration): frequencies = create_frequency_series( sampling_frequency=sampling_frequency, duration=duration ) signal = np.exp(-((frequencies - peak_frequency) ** 2) / 2 / 10 ** 2) * np.exp( 1j * np.random.uniform(0, 2 * np.pi, len(frequencies)) ) return signal def normalize_signal(signal, psd, snr=4): signal /= np.sum(abs(signal) ** 2 / psd) ** 0.5 signal *= snr ** 0.5 return signal def run_tbs_test( signal, psd, sampling_frequency, duration, short_duration, mask, short_psd, inverse, tukey_alpha=0.1, n_average=50, ): short_window = tukey(sampling_frequency * short_duration, tukey_alpha) normalization = 2 / short_duration ln_bfs_1 = np.array([]) ln_bfs_2 = np.array([]) for _ in trange(n_average): noise, _ = psd.get_noise_realisation( sampling_frequency=sampling_frequency, duration=duration ) fd_noise = np.fft.rfft(

np.fft.irfft(noise)

numpy.fft.irfft

import numpy as np from typing import Tuple, Union, List import matplotlib.pyplot as plt class PPOReplayBuffer: def __init__(self, state_size, action_size, capacity, batch_size=64): self.state_size = state_size self.action_size = action_size self.capacity = capacity self.batch_size = batch_size self.size = 0 self.idx = 0 self._initialize_empty_buffers() def _initialize_empty_buffers(self) -> None: self.buffer_state = np.zeros(shape=(self.capacity, self.state_size)) self.buffer_action = np.zeros(shape=(self.capacity, self.action_size)) self.buffer_reward = np.zeros(shape=(self.capacity, 1)) self.buffer_mask = np.zeros(shape=(self.capacity, 1)) self.buffer_value = np.zeros(shape=(self.capacity, 1)) self.buffer_logp = np.zeros(shape=(self.capacity, 1)) self.buffer_adv = np.zeros(shape=(self.capacity, 1)) self.buffer_return = np.zeros(shape=(self.capacity, 1)) def store_transition(self, transition: Tuple) -> None: state, action, reward, mask, value, logp, adv, ret = transition # This will make sure to overwrite the oldest transition if full current_index = self.idx % self.capacity self.buffer_state[current_index] = state self.buffer_action[current_index] = action self.buffer_reward[current_index] = reward self.buffer_mask[current_index] = mask self.buffer_value[current_index] = value self.buffer_logp[current_index] = logp self.buffer_adv[current_index] = adv self.buffer_return[current_index] = ret # Increment counters if self.size < self.capacity: self.size += 1 self.idx += 1 def all(self) -> Union[None, Tuple]: # We can't sample if we don't have enough transitions if self.size < self.capacity: return return ( self.buffer_state, self.buffer_action, self.buffer_reward, self.buffer_mask, self.buffer_value, self.buffer_logp, self.buffer_adv, self.buffer_return ) def sample(self) -> Union[None, Tuple]: """ Returns a batch_size of random transitions from the buffer. If there are less than batch_size transitions in the buffer, this returns None. Note that sampling does not remove the transitions from the buffer so they could be sampled again. """ # We can't sample if we don't have enough transitions if self.size < self.capacity: return idxs = np.random.choice(self.size, self.batch_size) batch_state = self.buffer_state[idxs] batch_action = self.buffer_action[idxs] batch_reward = self.buffer_reward[idxs] batch_mask = self.buffer_mask[idxs] batch_value = self.buffer_value[idxs] batch_logp = self.buffer_logp[idxs] batch_adv = self.buffer_adv[idxs] batch_return = self.buffer_return[idxs] return (batch_state, batch_action, batch_reward, batch_mask, batch_value, batch_logp, batch_adv, batch_return) def flush(self) -> None: self.size = 0 self.idx = 0 self._initialize_empty_buffers() def __len__(self) -> int: return self.size def plot_training_results(rewards_history: List, running_rewards_history: List, steps_history: List, wallclock_history: List, test_freq: int = 1, save_dir: str = None): fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2, figsize=(12, 8)) fig.suptitle("Results", fontsize=16) # Epochs vs rewards num_epochs = len(rewards_history) ax1.plot(

np.arange(num_epochs)

numpy.arange

import pymbar from fe import endpoint_correction from collections import namedtuple import pickle import dataclasses import time import functools import copy import jax import numpy as np from md import minimizer from typing import Tuple, List, Any import os from fe import standard_state from fe.utils import sanitize_energies, extract_delta_Us_from_U_knk from timemachine.lib import potentials, custom_ops @dataclasses.dataclass class SimulationResult: xs: np.array boxes: np.array du_dps: np.array lambda_us: np.array def flatten(v): return tuple(), (v.xs, v.boxes, v.du_dps, v.lambda_us) def unflatten(aux_data, children): xs, boxes, du_dps, lambda_us = aux_data return SimulationResult(xs, boxes, du_dps, lambda_us) jax.tree_util.register_pytree_node(SimulationResult, flatten, unflatten) def run_model_simulations(model, sys_params): assert len(sys_params) == len(model.unbound_potentials) bound_potentials = [] for params, unbound_pot in zip(sys_params, model.unbound_potentials): bp = unbound_pot.bind(np.asarray(params)) bound_potentials.append(bp) all_args = [] for lamb_idx, lamb in enumerate(model.lambda_schedule): subsample_interval = 1000 all_args.append( ( lamb, model.box, model.x0, model.v0, bound_potentials, model.integrator, model.barostat, model.equil_steps, model.prod_steps, subsample_interval, subsample_interval, model.lambda_schedule, ) ) if model.endpoint_correct: assert isinstance(bound_potentials[-1], potentials.HarmonicBond) all_args.append( ( 1.0, model.box, model.x0, model.v0, bound_potentials[:-1], # strip out the restraints model.integrator, model.barostat, model.equil_steps, model.prod_steps, subsample_interval, subsample_interval, [], # no need to evaluate Us for the endpoint correction ) ) results = [] if model.client is None: for args in all_args: results.append(simulate(*args)) else: futures = [] for args in all_args: futures.append(model.client.submit(simulate, *args)) for future in futures: results.append(future.result()) return results def simulate( lamb, box, x0, v0, final_potentials, integrator, barostat, equil_steps, prod_steps, x_interval, u_interval, lambda_windows, ): """ Run a simulation and collect relevant statistics for this simulation. Parameters ---------- lamb: float lambda value used for the equilibrium simulation box: np.array 3x3 numpy array of the box, dtype should be np.float64 x0: np.array Nx3 numpy array of the coordinates v0: np.array Nx3 numpy array of the velocities final_potentials: list list of unbound potentials integrator: timemachine.Integrator integrator to be used for dynamics barostat: timemachine.Barostat barostat to be used for equilibration equil_steps: int number of equilibration steps prod_steps: int number of production steps x_interval: int how often we store coordinates. If x_interval == 0 then no frames are returned. u_interval: int how often we store energies. If u_interval == 0 then no energies are returned lambda_windows: list of float lambda windows we evaluate energies at. Returns ------- SimulationResult Results of the simulation. """ all_impls = [] # set up observables for du_dps here as well. du_dp_obs = [] for bp in final_potentials: impl = bp.bound_impl(np.float32) all_impls.append(impl) du_dp_obs.append(custom_ops.AvgPartialUPartialParam(impl, 25)) # fire minimize once again, needed for parameter interpolation x0 = minimizer.fire_minimize(x0, all_impls, box, np.ones(100, dtype=np.float64) * lamb) # sanity check that forces are well behaved for bp in all_impls: du_dx, du_dl, u = bp.execute(x0, box, lamb) norm_forces = np.linalg.norm(du_dx, axis=1) assert np.all(norm_forces < 25000), "Forces much greater than expected after minimization" if integrator.seed == 0: # this deepcopy is needed if we're running if client == None integrator = copy.deepcopy(integrator) integrator.seed = np.random.randint(np.iinfo(np.int32).max) if barostat.seed == 0: barostat = copy.deepcopy(barostat) barostat.seed = np.random.randint(np.iinfo(np.int32).max) intg_impl = integrator.impl() # technically we need to only pass in the nonbonded impl barostat_impl = barostat.impl(all_impls) # context components: positions, velocities, box, integrator, energy fxns ctxt = custom_ops.Context(x0, v0, box, intg_impl, all_impls, barostat_impl) # equilibration equil_schedule = np.ones(equil_steps) * lamb ctxt.multiple_steps(equil_schedule) # (ytz): intentionally hard-coded, I'd rather the end-user *not* # muck with this unless they have a good reason to. barostat_impl.set_interval(25) for obs in du_dp_obs: ctxt.add_observable(obs) full_us, xs, boxes = ctxt.multiple_steps_U(lamb, prod_steps, np.array(lambda_windows), u_interval, x_interval) # keep the structure of grads the same as that of final_potentials so we can properly # form their vjps. grads = [] for obs in du_dp_obs: grads.append(obs.avg_du_dp()) result = SimulationResult( xs=xs.astype("float32"), boxes=boxes.astype("float32"), du_dps=grads, lambda_us=full_us, ) return result FreeEnergyModel = namedtuple( "FreeEnergyModel", [ "unbound_potentials", "endpoint_correct", "client", "box", "x0", "v0", "integrator", "barostat", "lambda_schedule", "equil_steps", "prod_steps", "beta", "prefix", ], ) gradient = List[Any] # TODO: make this more descriptive of dG_grad structure def _deltaG_from_results(model, results, sys_params) -> Tuple[Tuple[float, List], np.array]: assert len(sys_params) == len(model.unbound_potentials) bound_potentials = [] for params, unbound_pot in zip(sys_params, model.unbound_potentials): bp = unbound_pot.bind(

np.asarray(params)

numpy.asarray

''' @file end_eff_lqr_gain_computation.py @package momentumopt @author <NAME> (<EMAIL>) @license License BSD-3-Clause @copyright Copyright (c) 2019, New York University and Max Planck Gesellschaft. @date 2019-06-05 Computes gains using lqr in the end_effector space for solo (assumes legs are weightless) and performs a backward pass to compute gains using a trajectory ''' ### ### ### Author: <NAME> ### Date:6/5/2019 import numpy as np from numpy.linalg import inv from matplotlib import pyplot as plt from scipy.spatial.transform import Rotation as Rot import scipy np.set_printoptions(linewidth=13000) class end_effector_lqr: def __init__(self, dir): self.dir = dir self.com_pos = np.loadtxt(dir + "/quadruped_com.dat", dtype=float)[:, [1,2,3]] self.com_vel = np.loadtxt(dir + "/quadruped_com_vel.dat", dtype=float)[:, [1,2,3]] self.com_ori = np.loadtxt(dir + "/quadruped_quaternion.dat", dtype=float)[:, [1,2,3,4]] self.com_ang_vel = np.loadtxt(dir + "/quadruped_base_ang_velocities.dat", dtype=float)[:, [1,2,3]] self.end_eff_forces = np.loadtxt(dir + "/quadruped_forces.dat", dtype=float)[:, 1:] self.end_eff_abs_pos = np.loadtxt(dir + "/quadruped_positions_abs_with_horizon_part.dat", dtype=float)[:, 1:] self.delta = 0.000001 self.dt = 0.001 self.mass = 2.17 self.inertia_com_frame = [[0.00578574, 0.0, 0.0], [0.0, 0.01938108, 0.0], [0.0, 0.0, 0.02476124]] def compute_r_cross(self, end_eff_abs_pos, com_pos): r_cross_mat = [[0, -(end_eff_abs_pos[2] - com_pos[2]), (end_eff_abs_pos[1] - com_pos[1])], [(end_eff_abs_pos[2] - com_pos[2]), 0, -(end_eff_abs_pos[0] - com_pos[0])], [-(end_eff_abs_pos[1] - com_pos[1]), -(end_eff_abs_pos[0] - com_pos[0]), 0]] return r_cross_mat def compute_dyn(self,t , x_t, u_t): ### quat_d = omega * quat omega = np.array([[0, x_t[: , 12], -1*x_t[:, 11], x_t[:, 10]], [-1*x_t[:,12], 0, x_t[:,10], x_t[:, 11]], [x_t[:,11], -1*x_t[:,10], 0, x_t[:,12]], [-1*x_t[:, 10], -1*x_t[:, 11], -1*x_t[:,12], 0]]) self.A_t = np.block([[np.zeros((3,3)), np.identity(3), np.zeros((3,4)), np.zeros((3,3))], [np.zeros((3,3)), np.zeros((3,3)), np.zeros((3,4)), np.zeros((3,3))], [np.zeros((4,3)),np.zeros((4,3)), 0.5*omega, np.zeros((4,3))], [np.zeros((3,3)), np.zeros((3,3)), np.zeros((3,4)), np.zeros((3,3))]]) rot_t = np.reshape(Rot.from_quat(x_t[:, [6,7,8,9]]).as_dcm(), (3,3)) inertia = np.matmul(np.matmul(np.transpose(rot_t),self.inertia_com_frame), rot_t) inv_inertia = inv(np.matrix(inertia)) r_cross_inv_inertia_fl = np.matmul(inv_inertia, self.compute_r_cross(self.end_eff_abs_pos[t][0:3], self.com_pos[t])) r_cross_inv_inertia_fr = np.matmul(inv_inertia, self.compute_r_cross(self.end_eff_abs_pos[t][3:6], self.com_pos[t])) r_cross_inv_inertia_hl = np.matmul(inv_inertia, self.compute_r_cross(self.end_eff_abs_pos[t][6:9], self.com_pos[t])) r_cross_inv_inertia_hr = np.matmul(inv_inertia, self.compute_r_cross(self.end_eff_abs_pos[t][9:12], self.com_pos[t])) self.B_t = np.block([[np.zeros((3,3)), np.zeros((3,3)),np.zeros((3,3)), np.zeros((3,3))], [(1/self.mass)*np.identity(3), (1/self.mass)*np.identity(3), (1/self.mass)*np.identity(3), (1/self.mass)*np.identity(3)], [np.zeros((4,3)), np.zeros((4,3)), np.zeros((4,3)), np.zeros((4,3))], [r_cross_inv_inertia_fl, r_cross_inv_inertia_fr, r_cross_inv_inertia_hl, r_cross_inv_inertia_hr]]) self.A_t = np.matrix(self.A_t) self.B_t = np.matrix(self.B_t) return np.matmul(self.A_t, np.transpose(x_t)) + np.matmul(self.B_t, np.transpose(u_t)) def compute_lin_dyn(self,t): ### computes linearized dymamics x_t = np.matrix(np.hstack((self.com_pos[t], self.com_vel[t], self.com_ori[t], self.com_ang_vel[t]))) u_t = np.matrix(self.end_eff_forces[t]) dyn_t = self.compute_dyn(t, x_t, u_t) # print(dyn_t) # partial derivative of a w.r.t x x_t1 = np.matrix(np.hstack((self.com_pos[t+1], self.com_vel[t+1], self.com_ori[t+1], self.com_ang_vel[t+1]))) u_t1 = np.matrix(self.end_eff_forces[t+1]) lin_A_t = np.zeros((13,13)) for i in range(13): pd_x_t = x_t.copy() delta_x = x_t1[: ,i].copy() - x_t[: ,i].copy() pd_x_t[: ,i] = x_t1[: ,i].copy() if delta_x == 0.0: delta_x = self.delta pd_x_t[:, i] += self.delta lin_A_t[:, i] = np.reshape(((self.compute_dyn(t, pd_x_t, u_t) - dyn_t.copy())/(delta_x)), (13,)) lin_B_t = np.zeros((13,12)) if np.linalg.norm(sum(u_t1)) < 0.001: lin_B_t = np.zeros((13,12)) else: for i in range(12): pd_u_t = u_t.copy() delta_u = u_t1[: ,i].copy() - u_t[:, i].copy() pd_u_t[: ,i] = u_t1[:, i].copy() if delta_u == 0: delta_u = self.delta pd_u_t[:, i] += self.delta lin_B_t[:, i] = np.reshape(((self.compute_dyn(t, x_t, pd_u_t) - dyn_t.copy())/(delta_u)), (13,)) return lin_A_t, lin_B_t def descretise_dynamics(self, lin_A_t, lin_B_t): ## descritizes the dynamics adn returns descritized lin_A, lin_B_t des_lin_A_t = lin_A_t*self.dt + np.identity(13) des_lin_B_t = lin_B_t*self.dt # print(des_lin_A_t) return des_lin_A_t, des_lin_B_t def compute_lqr_gains(self, Q, R, lin_A_t, lin_B_t, P_prev): ## input descritzed lin_A and lin_B ## solves ricati equation # print(lin_B_t) K = inv(R + np.matmul(np.matmul(

np.transpose(lin_B_t)

numpy.transpose

import argparse import pandas as pd import os import sys import numpy as np import torch from utils import computeMetricsAlt, evalThresholdAlt from ModelShokri import DataHandler, TrainWBAttacker from torch.utils.data import DataLoader parser = argparse.ArgumentParser(description='Analyse criteria obtained from different MIAs.') parser.add_argument('--model_type', type=str, help='Model Architecture to attack.') parser.add_argument('--num_iters', type=int, default=20, help='Number of iterations for empirical estimation.') parser.add_argument('--working_dir', type=str, default='./', help='Where to collect and store data.') exp_parameters = parser.parse_args() currdir = exp_parameters.working_dir num_runs_for_random = exp_parameters.num_iters model_type = exp_parameters.model_type # Extracting intermediate outputs and gradients of the model InterOuts_Grads0 = np.load(currdir + '/RawResults/NasrTrain0_' + model_type + '.npz') InterOuts_Grads1 = np.load(currdir + '/RawResults/NasrTrain1_' + model_type + '.npz') AdditionalInfo = np.load(currdir + '/RawResults/NasrAddInfo_' + model_type + '.npz') inter_outs0 = [] inter_outs1 = [] out_size_list = AdditionalInfo['arr_0'] layer_size_list = AdditionalInfo['arr_1'] kernel_size_list = AdditionalInfo['arr_2'] n_inter_outputs = len(out_size_list) n_layer_grads = len(kernel_size_list) for i in range(n_inter_outputs): inter_outs0.append(InterOuts_Grads0['arr_' + str(i)]) inter_outs1.append(InterOuts_Grads1['arr_' + str(i)]) lossval0 = InterOuts_Grads0['arr_' + str(n_inter_outputs)] lossval1 = InterOuts_Grads1['arr_' + str(n_inter_outputs)] labels1hot0 = InterOuts_Grads0['arr_' + str(n_inter_outputs + 1)] labels1hot1 = InterOuts_Grads1['arr_' + str(n_inter_outputs + 1)] grad_vals0 = [] grad_vals1 = [] for i in range(n_inter_outputs + 2, n_inter_outputs + 2 + n_layer_grads, 1): grad_vals0.append(InterOuts_Grads0['arr_' + str(i)]) grad_vals1.append(InterOuts_Grads1['arr_' + str(i)]) # Our Analysis FPR = np.linspace(0, 1, num=1001) try: dfMetricsBalanced = pd.read_csv(currdir + '/CompleteResults/BalancedMetrics_' + model_type + '.csv') dfTPRBalanced = pd.read_csv(currdir + '/CompleteResults/BalancedROC_' + model_type + '.csv') except FileNotFoundError: dfMetricsBalanced = pd.DataFrame(columns=['Attack Strategy', 'AUROC', 'AUROC STD', 'Best Accuracy', 'Best Accuracy STD', 'FPR at TPR80', 'FPR at TPR80 STD', 'FPR at TPR85', 'FPR at TPR85 STD', 'FPR at TPR90', 'FPR at TPR90 STD', 'FPR at TPR95', 'FPR at TPR95 STD']) dfTPRBalanced = pd.DataFrame(FPR, columns=['FPR']) aux_list_metrics = [] aux_list_TPR = [] for k in range(num_runs_for_random): np.random.seed(k) indx_train0 = np.random.choice(lossval0.shape[0], size=4000, replace=False) indx_train1 = np.random.choice(lossval1.shape[0], size=4000, replace=False) indx_test0 = np.setdiff1d(np.arange(lossval0.shape[0]), indx_train0) indx_test0 = np.random.choice(indx_test0, size=6000, replace=False) indx_test1 = np.setdiff1d(np.arange(lossval1.shape[0]), indx_train1) indx_test1 = np.random.choice(indx_test1, size=6000, replace=False) trainingData = DataHandler(inter_outs0, inter_outs1, lossval0, lossval1, labels1hot0, labels1hot1, grad_vals0, grad_vals1, indx_train0, indx_train1) Max = trainingData.Max Min = trainingData.Min testingData = DataHandler(inter_outs0, inter_outs1, lossval0, lossval1, labels1hot0, labels1hot1, grad_vals0, grad_vals1, indx_test0, indx_test1, Max=Max, Min=Min) AttackerShokri = TrainWBAttacker(trainingData, testingData, out_size_list, layer_size_list, kernel_size_list) dataloaderEval = DataLoader(testingData, batch_size=100, shuffle=False) scoresEval = [] EvalY = [] with torch.no_grad(): for i, batch in enumerate(dataloaderEval): example = batch[0] target = batch[1] scoresEval.append(AttackerShokri(*example).detach()) EvalY.append(target.cpu().data.numpy()) scoresEval = torch.cat(scoresEval, axis=0) scoresEval = torch.squeeze(scoresEval) scoresEval = scoresEval.cpu().data.numpy() EvalY = np.squeeze(np.concatenate(EvalY, axis=0)) TPR_, metrics_ = computeMetricsAlt(scoresEval, EvalY, FPR) aux_list_metrics.append(metrics_) aux_list_TPR.append(TPR_) metrics = np.stack(aux_list_metrics, 1) mean_metrics = np.mean(metrics, 1) std_metrics = np.std(metrics, 1) new_row = {"Attack Strategy": 'Nasr White-Box', 'AUROC': mean_metrics[0], 'AUROC STD': std_metrics[0], 'Best Accuracy': mean_metrics[1], 'Best Accuracy STD': std_metrics[1], 'FPR at TPR80': mean_metrics[2], 'FPR at TPR80 STD': std_metrics[2], 'FPR at TPR85': mean_metrics[3], 'FPR at TPR85 STD': std_metrics[3], 'FPR at TPR90': mean_metrics[4], 'FPR at TPR90 STD': std_metrics[4], 'FPR at TPR95': mean_metrics[5], 'FPR at TPR95 STD': std_metrics[5]} dfMetricsBalanced = dfMetricsBalanced.append(new_row, ignore_index=True) TPR = np.stack(aux_list_TPR, 1) mean_TPR = np.mean(TPR, 1) std_TPR = np.std(TPR, 1) dfTPRaux = pd.DataFrame(np.stack((mean_TPR, std_TPR), axis=1), columns=['Nasr White-Box TPR', 'Nasr White-Box TPR STD']) dfTPRBalanced = dfTPRBalanced.join(dfTPRaux) # Rezaei Analysis try: dfMetricsRezaei = pd.read_csv(currdir + '/CompleteResults/RezaeiMetrics_' + model_type + '.csv') except FileNotFoundError: dfMetricsRezaei = pd.DataFrame(columns=['Attack Strategy', 'Best Accuracy', 'Best Accuracy STD', 'FPR', 'FPR STD']) aux_list_metrics = [] for k in range(num_runs_for_random): np.random.seed(k) indx_train0 =

np.random.choice(lossval0.shape[0], size=8000, replace=False)

numpy.random.choice

""" Numpy是python很多科学计算与工程库的基础库，在量化数据分析中最常使用的Pandas 也是基于Numpy的封装。可以说Numpy就是量化数据分析领域中的基础数组，学会使用Numpy 是量化分析中关键的一步 Numpy底层实现中使用了C语言和Fortran语言的机制分配内存。可以理解为它的输出是一个非常大且联系的并且由同类型数据组成的内存区域，所以可以通过Numpy来构造一个比普通列表大的多的数组，并且灵活高效地对数组中所有的元素进行并行化操作 """ import timeit import time import numpy as np import matplotlib.pyplot as plt """ 使用timeit模块来计算构建10000个元素的列表循环求每个元素的平方所用的时间 timeit模块使用方法 timeit(stmt,number) stmt可以直接传简单的字符串表达式，也可以传变量，也可以传函数，接受匿名函数输入 """ '#######################################################################################################################' #1、使用普通方法构造列表 func1 = """ for i in range(10000): i**2 """ print(timeit.timeit(stmt=func1,number=1)) #结果：0.003410174186735481 """ 或者在jupyternotebook中执行 normal_list = range(10000) %timeit [i**2 for i in normal_list] 得到的时间为： 3.67 ms ± 67.1 µs per loop (mean ± std. dev. of 7 runs, 100 loops each) """ #2、使用numpy的arange模块来构造列表 """ 在jupyternotebook中执行下面代码， np_list = np.arange(10000) %timeit (np_list**2) 得到的时间为： 9.22 µs ± 24 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each) 可以看到使用numpy数组的速度远快于使用普通列表的速度 Numpy数组和普通列表的操作方式也是不同的，Numpy通过广播机制作用于每一个内部元素，是一种并行化执行的思想，普通list则作用于整体，示例如下： """ #注意：在numpy中*3的操作被作用于数组的每一个元素中 np_list = np.ones(5) * 3 print(np_list) # [3. 3. 3. 3. 3.] #普通列表则把*3操作认为是整体性操作 normal_list = [1,1,1,1,1] * 3 print(normal_list) # <class 'list'>: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] print(len(normal_list)) # 15 '#######################################################################################################################' #numpy的初始化操作 """ 一些numpy常用的初始化方式 """ #1、100个0 np.zeros(100) # array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., # 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., # 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., # 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., # 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., # 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]) #2、shape: 3行2列全是0

np.zeros((3,2))

numpy.zeros

#!/usr/bin/env python # vim: tabstop=2 shiftwidth=2 expandtab # Copyright 2020 Maintainers of PSegs-ROS-Ext # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. import collections import os import random import subprocess import sys import numpy as np ############################################################################### ### Utils def nanostamp_to_rostime(nanostamp): import rospy # For a good time see: # https://github.com/pgao/roscpp_core/commit/dffa31afe8d7f1268a3fa227408aeb6e04a28b87#diff-65b9485bd6b5d3fb4b7a84cd975c3967L157 return rospy.Time( secs=int(nanostamp / 1000000000), nsecs=int(nanostamp % 1000000000)) def to_ros_arr(arr): return arr.flatten(order='C').tolist() ############################################################################### ### ROS Message Generators def gen_transform(nanostamp): import tf from tf2_msgs.msg import TFMessage from geometry_msgs.msg import Transform from geometry_msgs.msg import TransformStamped tf_msg = TFMessage() tf_transform = TransformStamped() tf_transform.header.stamp = nanostamp_to_rostime(nanostamp) tf_transform.header.frame_id = 'src_frame' tf_transform.child_frame_id = 'child_frame' transform = Transform() r_4x4 = np.ones((4, 4)) q = tf.transformations.quaternion_from_matrix(r_4x4) transform.rotation.x = q[0] transform.rotation.y = q[1] transform.rotation.z = q[2] transform.rotation.w = q[3] transform.translation.x = 1 transform.translation.y = 2 transform.translation.z = 3 tf_transform.transform = transform tf_msg.transforms.append(tf_transform) return tf_msg def gen_camera_info(nanostamp): from sensor_msgs.msg import CameraInfo info = CameraInfo() info.header.frame_id = 'camera_frame' info.header.stamp = nanostamp_to_rostime(nanostamp) info.width = 100 info.height = 200 info.distortion_model = 'plumb_bob' K = np.ones((3, 3)) info.K = to_ros_arr(K) P = np.zeros((3, 4)) info.P = to_ros_arr(P) return info def gen_camera_image(nanostamp): import cv2 from cv_bridge import CvBridge bridge = CvBridge() # Create a fake image img = np.zeros((200, 100, 3), dtype=np.uint8) from PIL import Image p_img = Image.fromarray(img) from io import BytesIO with BytesIO() as output: p_img.save(output, 'PNG') img_bytes = bytearray(output.getvalue()) # Do a dance to get a CV Img, which has good interop with ROS img_arr = np.asarray(img_bytes, dtype=np.uint8) cv_img = cv2.imdecode(img_arr, cv2.IMREAD_UNCHANGED) ros_img_msg = bridge.cv2_to_imgmsg(cv_img, encoding='bgr8') ros_img_msg.header.frame_id = 'camera_frame' ros_img_msg.header.stamp = nanostamp_to_rostime(nanostamp) return ros_img_msg def gen_pcl_cloud(nanostamp): from sensor_msgs.msg import PointField from std_msgs.msg import Header import sensor_msgs.point_cloud2 as pcl2 header = Header() header.frame_id = 'pointsensor' header.stamp = nanostamp_to_rostime(nanostamp) points = np.zeros((10, 3), dtype=np.float32) fields = [PointField('x', 0, PointField.FLOAT32, 1), PointField('y', 4, PointField.FLOAT32, 1), PointField('z', 8, PointField.FLOAT32, 1)] pcl_msg = pcl2.create_cloud(header, fields, points) return pcl_msg def gen_ros_color(): """color in [0, 1] -> ROS color""" from std_msgs.msg import ColorRGBA r, g, b = (.5, .5, .5) ros_color = ColorRGBA() ros_color.r = r ros_color.g = g ros_color.b = b ros_color.a = 1. return ros_color def gen_marker(): from geometry_msgs.msg import Point from visualization_msgs.msg import Marker m = Marker() m.type = Marker.LINE_LIST # pairs of points create a line m.action = Marker.MODIFY # or add m.color = gen_ros_color() m.scale.x = 0.1 startp = Point() startp.x, startp.y, startp.z = (1, 2, 3) endp = Point() endp.x, endp.y, endp.z = (3, 4, 5) m.points += [startp, endp] return m def gen_marker_array(nanostamp): from visualization_msgs.msg import MarkerArray marray = MarkerArray() for obj_id in range(10): from std_msgs.msg import Header header = Header() header.frame_id = 'marker' header.stamp = nanostamp_to_rostime(nanostamp) markers = [gen_marker() for _ in range(10)] for mid, m in enumerate(markers): m.id = obj_id * 10 + mid m.ns = str(obj_id) m.header = header marray.markers += markers return marray # A container compatible with both ROSBag as well as ROS Publishers ROSMsgEntry = collections.namedtuple( 'ROSMsgEntry', ('topic', 'timestamp', 'msg')) def gen_msg_fixture(start_time_sec=1, end_time_sec=10): for t in

np.arange(start_time_sec, end_time_sec + 1, 0.5)

numpy.arange

import os import numpy import pytest from chainer import serializers, Variable, cuda from chainer_chemistry.links.scaler.standard_scaler import StandardScaler @pytest.fixture def data(): x = numpy.array( [[0.1, 10., 0.3], [0.2, 20., 0.1], [0.3, 30., 0.], [0.4, 40., 0.]], dtype=numpy.float32) expect_x_scaled = numpy.array( [[-1.3416407, -1.3416408, 1.6329931], [-0.44721353, -0.4472136, 0.], [0.44721368, 0.4472136, -0.8164965], [1.3416407, 1.3416408, -0.8164965]], dtype=numpy.float32) return x, expect_x_scaled @pytest.mark.parametrize('indices', [None, [0], [1, 2]]) def test_standard_scaler_transform(data, indices): x, expect_x_scaled = data scaler = StandardScaler() scaler.fit(x, indices=indices) x_scaled = scaler.transform(x) if indices is None: indices = numpy.arange(x.shape[1]) for index in range(x.shape[1]): if index in indices: assert numpy.allclose(x_scaled[:, index], expect_x_scaled[:, index]) else: assert numpy.allclose(x_scaled[:, index], x[:, index]) def test_standard_scaler_transform_variable(data): x, expect_x_scaled = data xvar = Variable(x) scaler = StandardScaler() scaler.fit(xvar) x_scaled = scaler.transform(xvar) assert isinstance(x_scaled, Variable) assert numpy.allclose(x_scaled.array, expect_x_scaled) @pytest.mark.gpu def test_standard_scaler_transform_gpu(data): x, expect_x_scaled = data scaler = StandardScaler() scaler.to_gpu() x = cuda.to_gpu(x) scaler.fit(x) x_scaled = scaler.transform(x) assert isinstance(x_scaled, cuda.cupy.ndarray) assert numpy.allclose(cuda.to_cpu(x_scaled), expect_x_scaled) @pytest.mark.parametrize('indices', [None, [0], [1, 2]]) def test_standard_scaler_inverse_transform(data, indices): x, expect_x_scaled = data scaler = StandardScaler() scaler.fit(x, indices=indices) x_inverse = scaler.inverse_transform(expect_x_scaled) if indices is None: indices = numpy.arange(x.shape[1]) for index in range(x.shape[1]): if index in indices: assert numpy.allclose(x_inverse[:, index], x[:, index]) else: assert numpy.allclose(x_inverse[:, index], expect_x_scaled[:, index]) def test_standard_scaler_fit_transform(data): x, expect_x_scaled = data scaler = StandardScaler() x_scaled = scaler.fit_transform(x) assert numpy.allclose(x_scaled, expect_x_scaled) @pytest.mark.parametrize('indices', [None, [0]]) def test_standard_scaler_serialize(tmpdir, data, indices): x, expect_x_scaled = data scaler = StandardScaler() scaler.fit(x, indices=indices) scaler_filepath = os.path.join(str(tmpdir), 'scaler.npz') serializers.save_npz(scaler_filepath, scaler) scaler2 = StandardScaler() serializers.load_npz(scaler_filepath, scaler2) # print('scaler2 attribs:', scaler2.mean, scaler2.std, scaler2.indices) assert numpy.allclose(scaler.mean, scaler2.mean) assert

numpy.allclose(scaler.std, scaler2.std)

numpy.allclose

import argparse import os import multiprocessing from multiprocessing import Process, Queue, Array import pickle import gym from gym.spaces import Box, Discrete from keras.models import Model from keras.layers import Input, TimeDistributed, Convolution2D, Flatten, LSTM, Dense from keras.objectives import categorical_crossentropy from keras.optimizers import Adam from keras.utils import np_utils import keras.backend as K import numpy as np from atari_utils import RandomizedResetEnv, AtariRescale42x42Env def create_env(env_id): env = gym.make(env_id) env = RandomizedResetEnv(env) env = AtariRescale42x42Env(env) return env def create_model(env, batch_size, num_steps): # network inputs are observations and advantages h = x = Input(batch_shape=(batch_size, num_steps) + env.observation_space.shape, name="x") A = Input(batch_shape=(batch_size, num_steps), name="A") # convolutional layers h = TimeDistributed(Convolution2D(32, 3, 3, subsample=(2, 2), border_mode="same", activation='elu', dim_ordering='tf'), name='c1')(h) h = TimeDistributed(Convolution2D(32, 3, 3, subsample=(2, 2), border_mode="same", activation='elu', dim_ordering='tf'), name='c2')(h) h = TimeDistributed(Convolution2D(32, 3, 3, subsample=(2, 2), border_mode="same", activation='elu', dim_ordering='tf'), name='c3')(h) h = TimeDistributed(Convolution2D(64, 3, 3, subsample=(2, 2), border_mode="same", activation='elu', dim_ordering='tf'), name='c4')(h) h = TimeDistributed(Flatten(), name="fl")(h) # recurrent layer h = LSTM(32, return_sequences=True, stateful=True, name="r1")(h) # policy network p = TimeDistributed(Dense(env.action_space.n, activation='softmax'), name="p")(h) # baseline network b = TimeDistributed(Dense(1), name="b")(h) # inputs to the model are observation and advantages, # outputs are action probabilities and baseline model = Model(input=[x, A], output=[p, b]) # policy gradient loss and entropy bonus def policy_gradient_loss(l_sampled, l_predicted): return K.mean(A * categorical_crossentropy(l_sampled, l_predicted), axis=1) \ - 0.01 * K.mean(categorical_crossentropy(l_predicted, l_predicted), axis=1) # baseline is optimized with MSE model.compile(optimizer='adam', loss=[policy_gradient_loss, 'mse']) return model def predict(model, observation): # create inputs for batch (and timestep) of size 1 x = np.array([[observation]]) A = np.zeros((1, 1)) # dummy advantage # predict action probabilities (and baseline state value) p, b = model.predict_on_batch([x, A]) # return action probabilities and baseline return p[0, 0], b[0, 0, 0] def discount(rewards, terminals, v, gamma): # calculate discounted future rewards for this trajectory returns = [] # start with the predicted value of the last state R = v for r, t in zip(reversed(rewards), reversed(terminals)): # if it was terminal state then restart from 0 if t: R = 0 R = r + R * gamma returns.insert(0, R) return returns def runner(shared_buffer, fifo, num_timesteps, monitor, args): proc_name = multiprocessing.current_process().name print("Runner %s started" % proc_name) # local environment for runner env = create_env(args.env_id) # start monitor to record statistics and videos if monitor: env.monitor.start(args.env_id) # copy of model model = create_model(env, batch_size=1, num_steps=1) # record episode lengths and rewards for statistics episode_rewards = [] episode_lengths = [] episode_reward = 0 episode_length = 0 observation = env.reset() for i in range(num_timesteps // args.num_local_steps): # copy weights from main network at the beginning of iteration # the main network's weights are only read, never modified # but we create our own model instance, because Keras is not thread-safe model.set_weights(pickle.loads(shared_buffer.raw)) observations = [] actions = [] rewards = [] terminals = [] baselines = [] for t in range(args.num_local_steps): if args.display: env.render() # predict action probabilities (and baseline state value) p, b = predict(model, observation) # sample action using those probabilities p /= np.sum(p) # ensure p-s sum up to 1 action =

np.random.choice(env.action_space.n, p=p)

numpy.random.choice

# This module has been generated automatically from space group information # obtained from the Computational Crystallography Toolbox # """ Space groups This module contains a list of all the 230 space groups that can occur in a crystal. The variable space_groups contains a dictionary that maps space group numbers and space group names to the corresponding space group objects. .. moduleauthor:: <NAME> <<EMAIL>> """ #----------------------------------------------------------------------------- # Copyright (C) 2013 The Mosaic Development Team # # Distributed under the terms of the BSD License. The full license is in # the file LICENSE.txt, distributed as part of this software. #----------------------------------------------------------------------------- import numpy as N class SpaceGroup(object): """ Space group All possible space group objects are created in this module. Other modules should access these objects through the dictionary space_groups rather than create their own space group objects. """ def __init__(self, number, symbol, transformations): """ :param number: the number assigned to the space group by international convention :type number: int :param symbol: the Hermann-Mauguin space-group symbol as used in PDB and mmCIF files :type symbol: str :param transformations: a list of space group transformations, each consisting of a tuple of three integer arrays (rot, tn, td), where rot is the rotation matrix and tn/td are the numerator and denominator of the translation vector. The transformations are defined in fractional coordinates. :type transformations: list """ self.number = number self.symbol = symbol self.transformations = transformations self.transposed_rotations = N.array([N.transpose(t[0]) for t in transformations]) self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2] for t in transformations])) def __repr__(self): return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol)) def __len__(self): """ :return: the number of space group transformations :rtype: int """ return len(self.transformations) def symmetryEquivalentMillerIndices(self, hkl): """ :param hkl: a set of Miller indices :type hkl: Scientific.N.array_type :return: a tuple (miller_indices, phase_factor) of two arrays of length equal to the number of space group transformations. miller_indices contains the Miller indices of each reflection equivalent by symmetry to the reflection hkl (including hkl itself as the first element). phase_factor contains the phase factors that must be applied to the structure factor of reflection hkl to obtain the structure factor of the symmetry equivalent reflection. :rtype: tuple """ hkls = N.dot(self.transposed_rotations, hkl) p = N.multiply.reduce(self.phase_factors**hkl, -1) return hkls, p space_groups = {} transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(1, 'P 1', transformations) space_groups[1] = sg space_groups['P 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(2, 'P -1', transformations) space_groups[2] = sg space_groups['P -1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(3, 'P 1 2 1', transformations) space_groups[3] = sg space_groups['P 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(4, 'P 1 21 1', transformations) space_groups[4] = sg space_groups['P 1 21 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(5, 'C 1 2 1', transformations) space_groups[5] = sg space_groups['C 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(6, 'P 1 m 1', transformations) space_groups[6] = sg space_groups['P 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(7, 'P 1 c 1', transformations) space_groups[7] = sg space_groups['P 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(8, 'C 1 m 1', transformations) space_groups[8] = sg space_groups['C 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(9, 'C 1 c 1', transformations) space_groups[9] = sg space_groups['C 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(10, 'P 1 2/m 1', transformations) space_groups[10] = sg space_groups['P 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(11, 'P 1 21/m 1', transformations) space_groups[11] = sg space_groups['P 1 21/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(12, 'C 1 2/m 1', transformations) space_groups[12] = sg space_groups['C 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(13, 'P 1 2/c 1', transformations) space_groups[13] = sg space_groups['P 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(14, 'P 1 21/c 1', transformations) space_groups[14] = sg space_groups['P 1 21/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(15, 'C 1 2/c 1', transformations) space_groups[15] = sg space_groups['C 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(16, 'P 2 2 2', transformations) space_groups[16] = sg space_groups['P 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(17, 'P 2 2 21', transformations) space_groups[17] = sg space_groups['P 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(18, 'P 21 21 2', transformations) space_groups[18] = sg space_groups['P 21 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(19, 'P 21 21 21', transformations) space_groups[19] = sg space_groups['P 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(20, 'C 2 2 21', transformations) space_groups[20] = sg space_groups['C 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(21, 'C 2 2 2', transformations) space_groups[21] = sg space_groups['C 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(22, 'F 2 2 2', transformations) space_groups[22] = sg space_groups['F 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(23, 'I 2 2 2', transformations) space_groups[23] = sg space_groups['I 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(24, 'I 21 21 21', transformations) space_groups[24] = sg space_groups['I 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(25, 'P m m 2', transformations) space_groups[25] = sg space_groups['P m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(26, 'P m c 21', transformations) space_groups[26] = sg space_groups['P m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(27, 'P c c 2', transformations) space_groups[27] = sg space_groups['P c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(28, 'P m a 2', transformations) space_groups[28] = sg space_groups['P m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(29, 'P c a 21', transformations) space_groups[29] = sg space_groups['P c a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(30, 'P n c 2', transformations) space_groups[30] = sg space_groups['P n c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(31, 'P m n 21', transformations) space_groups[31] = sg space_groups['P m n 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(32, 'P b a 2', transformations) space_groups[32] = sg space_groups['P b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(33, 'P n a 21', transformations) space_groups[33] = sg space_groups['P n a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(34, 'P n n 2', transformations) space_groups[34] = sg space_groups['P n n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(35, 'C m m 2', transformations) space_groups[35] = sg space_groups['C m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(36, 'C m c 21', transformations) space_groups[36] = sg space_groups['C m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(37, 'C c c 2', transformations) space_groups[37] = sg space_groups['C c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(38, 'A m m 2', transformations) space_groups[38] = sg space_groups['A m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(39, 'A b m 2', transformations) space_groups[39] = sg space_groups['A b m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(40, 'A m a 2', transformations) space_groups[40] = sg space_groups['A m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(41, 'A b a 2', transformations) space_groups[41] = sg space_groups['A b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(42, 'F m m 2', transformations) space_groups[42] = sg space_groups['F m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(43, 'F d d 2', transformations) space_groups[43] = sg space_groups['F d d 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(44, 'I m m 2', transformations) space_groups[44] = sg space_groups['I m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(45, 'I b a 2', transformations) space_groups[45] = sg space_groups['I b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(46, 'I m a 2', transformations) space_groups[46] = sg space_groups['I m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(47, 'P m m m', transformations) space_groups[47] = sg space_groups['P m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(48, 'P n n n :2', transformations) space_groups[48] = sg space_groups['P n n n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(49, 'P c c m', transformations) space_groups[49] = sg space_groups['P c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(50, 'P b a n :2', transformations) space_groups[50] = sg space_groups['P b a n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(51, 'P m m a', transformations) space_groups[51] = sg space_groups['P m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(52, 'P n n a', transformations) space_groups[52] = sg space_groups['P n n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(53, 'P m n a', transformations) space_groups[53] = sg space_groups['P m n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(54, 'P c c a', transformations) space_groups[54] = sg space_groups['P c c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(55, 'P b a m', transformations) space_groups[55] = sg space_groups['P b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(56, 'P c c n', transformations) space_groups[56] = sg space_groups['P c c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(57, 'P b c m', transformations) space_groups[57] = sg space_groups['P b c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(58, 'P n n m', transformations) space_groups[58] = sg space_groups['P n n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(59, 'P m m n :2', transformations) space_groups[59] = sg space_groups['P m m n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(60, 'P b c n', transformations) space_groups[60] = sg space_groups['P b c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(61, 'P b c a', transformations) space_groups[61] = sg space_groups['P b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(62, 'P n m a', transformations) space_groups[62] = sg space_groups['P n m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(63, 'C m c m', transformations) space_groups[63] = sg space_groups['C m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(64, 'C m c a', transformations) space_groups[64] = sg space_groups['C m c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(65, 'C m m m', transformations) space_groups[65] = sg space_groups['C m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(66, 'C c c m', transformations) space_groups[66] = sg space_groups['C c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(67, 'C m m a', transformations) space_groups[67] = sg space_groups['C m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(68, 'C c c a :2', transformations) space_groups[68] = sg space_groups['C c c a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(69, 'F m m m', transformations) space_groups[69] = sg space_groups['F m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(70, 'F d d d :2', transformations) space_groups[70] = sg space_groups['F d d d :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(71, 'I m m m', transformations) space_groups[71] = sg space_groups['I m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(72, 'I b a m', transformations) space_groups[72] = sg space_groups['I b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(73, 'I b c a', transformations) space_groups[73] = sg space_groups['I b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(74, 'I m m a', transformations) space_groups[74] = sg space_groups['I m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(75, 'P 4', transformations) space_groups[75] = sg space_groups['P 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(76, 'P 41', transformations) space_groups[76] = sg space_groups['P 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(77, 'P 42', transformations) space_groups[77] = sg space_groups['P 42'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(78, 'P 43', transformations) space_groups[78] = sg space_groups['P 43'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(79, 'I 4', transformations) space_groups[79] = sg space_groups['I 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(80, 'I 41', transformations) space_groups[80] = sg space_groups['I 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(81, 'P -4', transformations) space_groups[81] = sg space_groups['P -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(82, 'I -4', transformations) space_groups[82] = sg space_groups['I -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(83, 'P 4/m', transformations) space_groups[83] = sg space_groups['P 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(84, 'P 42/m', transformations) space_groups[84] = sg space_groups['P 42/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(85, 'P 4/n :2', transformations) space_groups[85] = sg space_groups['P 4/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(86, 'P 42/n :2', transformations) space_groups[86] = sg space_groups['P 42/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(87, 'I 4/m', transformations) space_groups[87] = sg space_groups['I 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(88, 'I 41/a :2', transformations) space_groups[88] = sg space_groups['I 41/a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(89, 'P 4 2 2', transformations) space_groups[89] = sg space_groups['P 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(90, 'P 4 21 2', transformations) space_groups[90] = sg space_groups['P 4 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(91, 'P 41 2 2', transformations) space_groups[91] = sg space_groups['P 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(92, 'P 41 21 2', transformations) space_groups[92] = sg space_groups['P 41 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(93, 'P 42 2 2', transformations) space_groups[93] = sg space_groups['P 42 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(94, 'P 42 21 2', transformations) space_groups[94] = sg space_groups['P 42 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(95, 'P 43 2 2', transformations) space_groups[95] = sg space_groups['P 43 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(96, 'P 43 21 2', transformations) space_groups[96] = sg space_groups['P 43 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(97, 'I 4 2 2', transformations) space_groups[97] = sg space_groups['I 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(98, 'I 41 2 2', transformations) space_groups[98] = sg space_groups['I 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(99, 'P 4 m m', transformations) space_groups[99] = sg space_groups['P 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(100, 'P 4 b m', transformations) space_groups[100] = sg space_groups['P 4 b m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(101, 'P 42 c m', transformations) space_groups[101] = sg space_groups['P 42 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(102, 'P 42 n m', transformations) space_groups[102] = sg space_groups['P 42 n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(103, 'P 4 c c', transformations) space_groups[103] = sg space_groups['P 4 c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(104, 'P 4 n c', transformations) space_groups[104] = sg space_groups['P 4 n c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(105, 'P 42 m c', transformations) space_groups[105] = sg space_groups['P 42 m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(106, 'P 42 b c', transformations) space_groups[106] = sg space_groups['P 42 b c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(107, 'I 4 m m', transformations) space_groups[107] = sg space_groups['I 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(108, 'I 4 c m', transformations) space_groups[108] = sg space_groups['I 4 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(109, 'I 41 m d', transformations) space_groups[109] = sg space_groups['I 41 m d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(110, 'I 41 c d', transformations) space_groups[110] = sg space_groups['I 41 c d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(111, 'P -4 2 m', transformations) space_groups[111] = sg space_groups['P -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(112, 'P -4 2 c', transformations) space_groups[112] = sg space_groups['P -4 2 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(113, 'P -4 21 m', transformations) space_groups[113] = sg space_groups['P -4 21 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(114, 'P -4 21 c', transformations) space_groups[114] = sg space_groups['P -4 21 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(115, 'P -4 m 2', transformations) space_groups[115] = sg space_groups['P -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(116, 'P -4 c 2', transformations) space_groups[116] = sg space_groups['P -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(117, 'P -4 b 2', transformations) space_groups[117] = sg space_groups['P -4 b 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(118, 'P -4 n 2', transformations) space_groups[118] = sg space_groups['P -4 n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(119, 'I -4 m 2', transformations) space_groups[119] = sg space_groups['I -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(120, 'I -4 c 2', transformations) space_groups[120] = sg space_groups['I -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(121, 'I -4 2 m', transformations) space_groups[121] = sg space_groups['I -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(122, 'I -4 2 d', transformations) space_groups[122] = sg space_groups['I -4 2 d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(123, 'P 4/m m m', transformations) space_groups[123] = sg space_groups['P 4/m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(124, 'P 4/m c c', transformations) space_groups[124] = sg space_groups['P 4/m c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(125, 'P 4/n b m :2', transformations) space_groups[125] = sg space_groups['P 4/n b m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot =

N.array([0,-1,0,-1,0,0,0,0,1])

numpy.array

from __future__ import division, print_function from typing import List import numpy import scipy class LinearRegression: def __init__(self, nb_features: int): self.nb_features = nb_features def train(self, features: List[List[float]], values: List[float]): # creating f(x) = W0 + sum((Wd)(Xd)) # finding W's # use LMS(least mean squared(minimizing residuals sum(mean squared error))) # LMS = ((X^tX)^-1) (X^tY) # make sure N > D+1 # features = X values = y y = numpy.array([values]).transpose() x = numpy.array(features) # add w0 x = numpy.append([[1]]*len(features),x, axis=1) xtx = x.transpose().dot(x) xty = x.transpose().dot(y) xtxInv = numpy.linalg.inv(xtx) self.weights = xtxInv.dot(xty) def phi(self, x: List[float]) -> List[float]: aug = [] for i in range(1,len(x)): for k in range(2,self.nb_features+1): aug.append(numpy.power(x[i],k)) return aug def predict(self, features: List[List[float]]) -> List[float]: # f(x) = wtx # x -> p(x) [1,x,x^2...x^d] x = numpy.array(features) x = numpy.append([[1]]*len(features),x, axis=1) return numpy.inner(self.weights.transpose(),x)[0] def get_weights(self) -> List[float]: """ for a model y = 1 + 3 * x_0 - 2 * x_1, the return value should be [1, 3, -2]. """ return self.weights class LinearRegressionWithL2Loss: '''Use L2 loss for weight regularization''' def __init__(self, nb_features: int, alpha: float): self.alpha = alpha self.nb_features = nb_features def train(self, features: List[List[float]], values: List[float]): # creating f(x) = W0 + sum((Wd)(Xd)) # finding W's # use LMS(least mean squared(minimizing residuals sum(mean squared error))) # LMS = ((X^tX)^-1) (X^tY) Now (X^tX -> X^tX + lI) # make sure N > D+1 # features = X values = y y = numpy.array([values]).transpose() x = numpy.array(features) # add w0 x = numpy.append([[1]]*len(features),x, axis=1) # xtx -> xtx + lI xtx = numpy.add(x.transpose().dot(x), self.alpha * numpy.identity(x.shape[1])) xty = x.transpose().dot(y) xtxInv = numpy.linalg.inv(xtx) self.weights = xtxInv.dot(xty) def phi(self, x: List[float]) -> List[float]: aug = [] for i in range(1,len(x)): for k in range(2,self.nb_features+1): aug.append(numpy.power(x[i],k)) return aug def predict(self, features: List[List[float]]) -> List[float]: # f(x) = wtx + l|w|^2 # x -> p(x) [1,x,x^2...x^d] x =

numpy.array(features)

numpy.array

""" Input/output utilities, adapted from https://github.com/vanderschaarlab/SyncTwin-NeurIPS-2021 """ # Author: <NAME> (<EMAIL>) # License: BSD 3 clause import os import pickle import numpy as np import torch def create_paths(*args): for base_path in args: if not os.path.exists(base_path): os.makedirs(base_path) def load_config(data_path, fold="train"): with open(data_path.format(fold, "config", "pkl"), "rb") as f: config = pickle.load(file=f) n_units = config["n_units"] n_treated = config["n_treated"] n_units_total = config["n_units_total"] step = config["step"] train_step = config["train_step"] control_sample = config["control_sample"] noise = config["noise"] n_basis = config["n_basis"] n_cluster = config["n_cluster"] return ( n_units, n_treated, n_units_total, step, train_step, control_sample, noise, n_basis, n_cluster, ) def load_tensor(data_path, fold="train", device="cpu"): x_full = torch.load( data_path.format(fold, "x_full", "pth"), map_location=torch.device(device) ) t_full = torch.load( data_path.format(fold, "t_full", "pth"), map_location=torch.device(device) ) mask_full = torch.load( data_path.format(fold, "mask_full", "pth"), map_location=torch.device(device) ) batch_ind_full = torch.load( data_path.format(fold, "batch_ind_full", "pth"), map_location=torch.device(device), ) y_full = torch.load( data_path.format(fold, "y_full", "pth"), map_location=torch.device(device) ) y_control = torch.load( data_path.format(fold, "y_control", "pth"), map_location=torch.device(device) ) y_mask_full = torch.load( data_path.format(fold, "y_mask_full", "pth"), map_location=torch.device(device) ) m = torch.load( data_path.format(fold, "m", "pth"), map_location=torch.device(device) ) sd = torch.load( data_path.format(fold, "sd", "pth"), map_location=torch.device(device) ) treatment_effect = torch.load( data_path.format(fold, "treatment_effect", "pth"), map_location=torch.device(device), ) return ( x_full, t_full, mask_full, batch_ind_full, y_full, y_control, y_mask_full, m, sd, treatment_effect, ) def load_data_dict(version=1): if version == 1: version = "" else: version = str(version) val_arr1 = np.load(f"real_data{version}/val_arr1.npy") val_mask_arr1 = np.load(f"real_data{version}/val_mask_arr1.npy") ts_arr1 = np.load(f"real_data{version}/ts_arr1.npy") ts_mask_arr1 = np.load(f"real_data{version}/ts_mask_arr1.npy") patid1 = np.load(f"real_data{version}/patid1.npy") val_arr0 = np.load(f"real_data{version}/val_arr0.npy") val_mask_arr0 = np.load(f"real_data{version}/val_mask_arr0.npy") ts_arr0 = np.load(f"real_data{version}/ts_arr0.npy") ts_mask_arr0 = np.load(f"real_data{version}/ts_mask_arr0.npy") patid0 = np.load(f"real_data{version}/patid0.npy") Y0 = np.load(f"real_data{version}/Y0.npy") Y1 = np.load(f"real_data{version}/Y1.npy") data1 = { "val_arr": val_arr1, "val_mask_arr": val_mask_arr1, "ts_arr": ts_arr1, "ts_mask_arr": ts_mask_arr1, "patid": patid1, "Y": Y1, } data0 = { "val_arr": val_arr0, "val_mask_arr": val_mask_arr0, "ts_arr": ts_arr0, "ts_mask_arr": ts_mask_arr0, "patid": patid0, "Y": Y0, } return data1, data0 def get_units(d1, d0): n_units = d0[0].shape[0] n_treated = d1[0].shape[0] return n_units, n_treated, n_units + n_treated def to_tensor(device, dtype, *args): return [torch.tensor(x, device=device, dtype=dtype) for x in args] def get_tensors(d1_train, d0_train, device): x_full =

np.concatenate([d0_train[0], d1_train[0]], axis=0)

numpy.concatenate

import numpy as np import numpy.random as npr import scipy as sc from operator import add from functools import reduce from sds.utils.general import Statistics as Stats from sds.utils.linalg import symmetrize class LinearGaussianWithPrecision: def __init__(self, column_dim, row_dim, A=None, lmbda=None, affine=True): self.column_dim = column_dim self.row_dim = row_dim self.A = A self.affine = affine self._lmbda = lmbda self._lmbda_chol = None self._lmbda_chol_inv = None @property def params(self): return self.A, self.lmbda @params.setter def params(self, values): self.A, self.lmbda = values @property def nb_params(self): return self.column_dim * self.row_dim \ + self.row_dim * (self.row_dim + 1) / 2 @property def input_dim(self): return self.column_dim - 1 if self.affine\ else self.column_dim @property def output_dim(self): return self.row_dim @property def lmbda(self): return self._lmbda @lmbda.setter def lmbda(self, value): self._lmbda = value self._lmbda_chol = None self._lmbda_chol_inv = None @property def lmbda_chol(self): if self._lmbda_chol is None: self._lmbda_chol = sc.linalg.cholesky(self.lmbda, lower=False) return self._lmbda_chol @property def lmbda_chol_inv(self): if self._lmbda_chol_inv is None: self._lmbda_chol_inv = sc.linalg.inv(self.lmbda_chol) return self._lmbda_chol_inv @property def sigma(self): return self.lmbda_chol_inv @ self.lmbda_chol_inv.T def predict(self, x): if self.affine: A, b = self.A[:, :-1], self.A[:, -1] y = np.einsum('dl,...l->...d', A, x, optimize=True) + b.T else: y = np.einsum('dl,...l->...d', self.A, x, optimize=True) return y def mean(self, x): return self.predict(x) def mode(self, x): return self.predict(x) def rvs(self, x): return self.mean(x) + npr.normal(size=self.output_dim).dot(self.lmbda_chol_inv.T) @property def base(self): return np.power(2. * np.pi, - self.output_dim / 2.) def log_base(self): return np.log(self.base) def statistics(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y = x[idx], y[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) contract = 'nd,nl->dl' yxT = np.einsum(contract, y, x, optimize=True) xxT = np.einsum(contract, x, x, optimize=True) yyT = np.einsum(contract, y, y, optimize=True) n = y.shape[0] return Stats([yxT, xxT, yyT, n]) else: stats = list(map(self.statistics, x, y)) return reduce(add, stats) def weighted_statistics(self, x, y, weights): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y, weights = x[idx], y[idx], weights[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) contract = 'nd,n,nl->dl' yxT = np.einsum(contract, y, weights, x, optimize=True) xxT = np.einsum(contract, x, weights, x, optimize=True) yyT = np.einsum(contract, y, weights, y, optimize=True) n = np.sum(weights) return Stats([yxT, xxT, yyT, n]) else: stats = list(map(self.weighted_statistics, x, y, weights)) return reduce(add, stats) def log_partition(self, x): mu = self.predict(x) return 0.5 * np.einsum('nd,dl,nl->n', mu, self.lmbda, mu)\ - np.sum(np.log(np.diag(self.lmbda_chol))) def log_likelihood(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): bads = np.logical_and(np.isnan(np.atleast_2d(x)).any(axis=1), np.isnan(np.atleast_2d(y)).any(axis=1)) x = np.nan_to_num(x, copy=False).reshape((-1, self.input_dim)) y = np.nan_to_num(y, copy=False).reshape((-1, self.output_dim)) mu = self.mean(x) log_lik = np.einsum('nd,dl,nl->n', mu, self.lmbda, y, optimize=True)\ - 0.5 * np.einsum('nd,dl,nl->n', y, self.lmbda, y, optimize=True) log_lik[bads] = 0. log_lik += - self.log_partition(x) + self.log_base() return log_lik else: return list(map(self.log_likelihood, x, y)) # Max likelihood def max_likelihood(self, x, y, weights=None): yxT, xxT, yyT, n = self.statistics(x, y) if weights is None\ else self.weighted_statistics(x, y, weights) self.A = np.linalg.solve(xxT, yxT.T).T sigma = (yyT - self.A.dot(yxT.T)) / n # numerical stabilization sigma = symmetrize(sigma) + 1e-16 * np.eye(self.output_dim) assert np.allclose(sigma, sigma.T) assert np.all(np.linalg.eigvalsh(sigma) > 0.) self.lmbda = np.linalg.inv(sigma) class StackedLinearGaussiansWithPrecision: def __init__(self, size, column_dim, row_dim, As=None, lmbdas=None, affine=True): self.size = size self.column_dim = column_dim self.row_dim = row_dim self.affine = affine As = [None] * self.size if As is None else As lmbdas = [None] * self.size if lmbdas is None else lmbdas self.dists = [LinearGaussianWithPrecision(column_dim, row_dim, As[k], lmbdas[k], affine=affine) for k in range(self.size)] @property def params(self): return self.As, self.lmbdas @params.setter def params(self, values): self.As, self.lmbdas = values @property def input_dim(self): return self.column_dim - 1 if self.affine\ else self.column_dim @property def output_dim(self): return self.row_dim @property def As(self): return np.array([dist.A for dist in self.dists]) @As.setter def As(self, value): for k, dist in enumerate(self.dists): dist.A = value[k] @property def lmbdas(self): return np.array([dist.lmbda for dist in self.dists]) @lmbdas.setter def lmbdas(self, value): for k, dist in enumerate(self.dists): dist.lmbda = value[k] @property def lmbdas_chol(self): return np.array([dist.lmbda_chol for dist in self.dists]) @property def lmbdas_chol_inv(self): return np.array([dist.lmbda_chol_inv for dist in self.dists]) @property def sigmas(self): return np.array([dist.sigma for dist in self.dists]) def predict(self, x): if self.affine: As, bs = self.As[:, :, :-1], self.As[:, :, -1] y = np.einsum('kdl,...l->...kd', As, x, optimize=True) + bs[None, ...] else: y = np.einsum('kdl,...l->...kd', self.As, x, optimize=True) return y def mean(self, x): return self.predict(x) def mode(self, x): return self.predict(x) def rvs(self, x): return np.array([dist.rvs(x) for dist in self.dists]) @property def base(self): return np.array([dist.base for dist in self.dists]) def log_base(self): return np.log(self.base) def statistics(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y = x[idx], y[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) contract = 'nd,nl->dl' yxT = np.einsum(contract, y, x, optimize=True) xxT = np.einsum(contract, x, x, optimize=True) yyT = np.einsum(contract, y, y, optimize=True) n = y.shape[0] yxTk = np.array([yxT for _ in range(self.size)]) xxTk = np.array([xxT for _ in range(self.size)]) yyTk = np.array([yyT for _ in range(self.size)]) nk = np.array([n for _ in range(self.size)]) return Stats([yxTk, xxTk, yyTk, nk]) else: stats = list(map(self.statistics, x, y)) return reduce(add, stats) def weighted_statistics(self, x, y, weights): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y, weights = x[idx], y[idx], weights[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) contract = 'nd,nk,nl->kdl' yxTk = np.einsum(contract, y, weights, x, optimize=True) xxTk = np.einsum(contract, x, weights, x, optimize=True) yyTk = np.einsum(contract, y, weights, y, optimize=True) nk = np.sum(weights, axis=0) return Stats([yxTk, xxTk, yyTk, nk]) else: stats = list(map(self.weighted_statistics, x, y, weights)) return reduce(add, stats) def log_partition(self, x): return np.array([dist.log_partition(x) for dist in self.dists]).T def log_likelihood(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): bads = np.logical_and(np.isnan(np.atleast_2d(x)).any(axis=1), np.isnan(np.atleast_2d(y)).any(axis=1)) x = np.nan_to_num(x, copy=False).reshape((-1, self.input_dim)) y = np.nan_to_num(y, copy=False).reshape((-1, self.output_dim)) mu = self.mean(x) log_lik = np.einsum('nkd,kdl,nl->nk', mu, self.lmbdas, y, optimize=True)\ - 0.5 * np.einsum('nd,kdl,nl->nk', y, self.lmbdas, y, optimize=True) log_lik[bads] = 0. log_lik += - self.log_partition(x) + self.log_base() return log_lik else: return list(map(self.log_likelihood, x, y)) # Max likelihood def max_likelihood(self, x, y, weights): yxTk, xxTk, yyTk, nk = self.weighted_statistics(x, y, weights) As = np.zeros((self.size, self.column_dim, self.row_dim)) lmbdas = np.zeros((self.size, self.output_dim, self.output_dim)) for k in range(self.size): As[k] = np.linalg.solve(xxTk[k], yxTk[k].T).T sigma = (yyTk[k] - As[k].dot(yxTk[k].T)) / nk[k] # numerical stabilization sigma = symmetrize(sigma) + 1e-16 * np.eye(self.output_dim) assert np.allclose(sigma, sigma.T) assert np.all(np.linalg.eigvalsh(sigma) > 0.) lmbdas[k] = np.linalg.inv(sigma) self.As = As self.lmbdas = lmbdas class TiedLinearGaussiansWithPrecision(StackedLinearGaussiansWithPrecision): def __init__(self, size, column_dim, row_dim, As=None, lmbdas=None, affine=True): super(TiedLinearGaussiansWithPrecision, self).__init__(size, column_dim, row_dim, As, lmbdas, affine) # Max likelihood def max_likelihood(self, x, y, weights): yxTk, xxTk, yyT, n = self.weighted_statistics(x, y, weights) As = np.zeros((self.size, self.column_dim, self.row_dim)) sigma = np.zeros((self.output_dim, self.output_dim)) sigma = yyT for k in range(self.size): As[k] = np.linalg.solve(xxTk[k], yxTk[k].T).T sigma -= As[k].dot(yxTk[k].T) sigma /= n # numerical stabilization sigma = symmetrize(sigma) + 1e-16 * np.eye(self.output_dim) assert np.allclose(sigma, sigma.T) assert np.all(np.linalg.eigvalsh(sigma) > 0.) self.As = As lmbda = np.linalg.inv(sigma) self.lmbdas = np.array(self.size * [lmbda]) class LinearGaussianWithDiagonalPrecision: def __init__(self, column_dim, row_dim, A=None, lmbda_diag=None, affine=True): self.column_dim = column_dim self.row_dim = row_dim self.A = A self.affine = affine self._lmbda_diag = lmbda_diag self._lmbda_chol = None self._lmbda_chol_inv = None @property def params(self): return self.A, self.lmbda_diag @params.setter def params(self, values): self.A, self.lmbda_diag = values @property def nb_params(self): return self.column_dim * self.row_dim + self.row_dim @property def input_dim(self): return self.column_dim - 1 if self.affine\ else self.column_dim @property def output_dim(self): return self.row_dim @property def lmbda_diag(self): return self._lmbda_diag @lmbda_diag.setter def lmbda_diag(self, value): self._lmbda_diag = value self._lmbda_chol = None self._lmbda_chol_inv = None @property def lmbda(self): assert self._lmbda_diag is not None return np.diag(self._lmbda_diag) @property def lmbda_chol(self): if self._lmbda_chol is None: self._lmbda_chol = np.diag(np.sqrt(self.lmbda_diag)) return self._lmbda_chol @property def lmbda_chol_inv(self): if self._lmbda_chol_inv is None: self._lmbda_chol_inv = np.diag(1. / np.sqrt(self.lmbda_diag)) return self._lmbda_chol_inv @property def sigma_diag(self): return 1. / self.lmbda_diag @property def sigma(self): return np.diag(self.sigma_diag) def predict(self, x): if self.affine: A, b = self.A[:, :-1], self.A[:, -1] y = np.einsum('dl,...l->...d', A, x, optimize=True) + b.T else: y = np.einsum('dl,...l->...d', self.A, x, optimize=True) return y def mean(self, x): return self.predict(x) def mode(self, x): return self.predict(x) def rvs(self, x): return self.mean(x) + npr.normal(size=self.output_dim).dot(self.lmbda_chol_inv.T) @property def base(self): return np.power(2. * np.pi, - self.output_dim / 2.) def log_base(self): return np.log(self.base) def statistics(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y = x[idx], y[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) xxT = np.einsum('nd,nl->dl', x, x, optimize=True) yxT = np.einsum('nd,nl->dl', y, x, optimize=True) yy = np.einsum('nd,nd->d', y, y, optimize=True) nd = np.broadcast_to(y.shape[0], (self.output_dim, )) return Stats([yxT, xxT, nd, yy]) else: stats = list(map(self.statistics, x, y)) return reduce(add, stats) def weighted_statistics(self, x, y, weights): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y, weights = x[idx], y[idx], weights[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) xxT = np.einsum('nd,n,nl->dl', x, weights, x, optimize=True) yxT = np.einsum('nd,n,nl->dl', y, weights, x, optimize=True) yy = np.einsum('nd,n,nd->d', y, weights, y, optimize=True) nd = np.broadcast_to(np.sum(weights), (self.output_dim, )) return Stats([yxT, xxT, nd, yy]) else: stats = list(map(self.weighted_statistics, x, y, weights)) return reduce(add, stats) def log_partition(self, x): mu = self.predict(x) return 0.5 * np.einsum('nd,dl,nl->n', mu, self.lmbda, mu)\ - np.sum(np.log(np.diag(self.lmbda_chol))) def log_likelihood(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): bads = np.logical_and(np.isnan(np.atleast_2d(x)).any(axis=1), np.isnan(np.atleast_2d(y)).any(axis=1)) x = np.nan_to_num(x, copy=False).reshape((-1, self.input_dim)) y = np.nan_to_num(y, copy=False).reshape((-1, self.output_dim)) mu = self.mean(x) log_lik = np.einsum('nd,dl,nl->n', mu, self.lmbda, y, optimize=True) \ - 0.5 * np.einsum('nd,dl,nl->n', y, self.lmbda, y, optimize=True) log_lik[bads] = 0. log_lik += - self.log_partition(x) + self.log_base() return log_lik else: return list(map(self.log_likelihood, x, y)) # Max likelihood def max_likelihood(self, x, y, weights=None): yxT, xxT, nd, yy = self.statistics(x, y) if weights is None\ else self.weighted_statistics(x, y, weights) self.A = np.linalg.solve(xxT, yxT.T).T sigmas = (yy - np.einsum('dl,dl->d', self.A, yxT)) / nd self.lmbda_diag = 1. / sigmas class StackedLinearGaussiansWithDiagonalPrecision: def __init__(self, size, column_dim, row_dim, As=None, lmbdas_diags=None, affine=True): self.size = size self.column_dim = column_dim self.row_dim = row_dim self.affine = affine As = [None] * self.size if As is None else As lmbdas_diags = [None] * self.size if lmbdas_diags is None else lmbdas_diags self.dists = [LinearGaussianWithDiagonalPrecision(column_dim, row_dim, As[k], lmbdas_diags[k], affine=affine) for k in range(self.size)] @property def params(self): return self.As, self.lmbdas_diags @params.setter def params(self, values): self.As, self.lmbdas_diags = values @property def input_dim(self): return self.column_dim - 1 if self.affine\ else self.column_dim @property def output_dim(self): return self.row_dim @property def As(self): return np.array([dist.A for dist in self.dists]) @As.setter def As(self, value): for k, dist in enumerate(self.dists): dist.A = value[k] @property def lmbdas_diags(self): return np.array([dist.lmbda_diag for dist in self.dists]) @lmbdas_diags.setter def lmbdas_diags(self, value): for k, dist in enumerate(self.dists): dist.lmbda_diag = value[k] @property def lmbdas(self): return np.array([dist.lmbda for dist in self.dists]) @property def lmbdas_chol(self): return np.array([dist.lmbda_chol for dist in self.dists]) @property def lmbdas_chol_inv(self): return np.array([dist.lmbda_chol_inv for dist in self.dists]) @property def sigmas_diag(self): return np.array([dist.sigma_diag for dist in self.dists]) @property def sigmas(self): return np.array([dist.sigma for dist in self.dists]) def predict(self, x): if self.affine: As, bs = self.As[:, :, :-1], self.As[:, :, -1] y = np.einsum('kdl,...l->...kd', As, x, optimize=True) + bs[None, ...] else: y = np.einsum('kdl,...l->...kd', self.As, x, optimize=True) return y def mean(self, x): return self.predict(x) def mode(self, x): return self.predict(x) def rvs(self, x): return np.array([dist.rvs(x) for dist in self.dists]) @property def base(self): return np.array([dist.base for dist in self.dists]) def log_base(self): return np.log(self.base) def statistics(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y = x[idx], y[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) xxT = np.einsum('nd,nl->dl', x, x, optimize=True) yxT = np.einsum('nd,nl->dl', y, x, optimize=True) yy = np.einsum('nd,nd->d', y, y, optimize=True) nd = np.broadcast_to(y.shape[0], (self.output_dim, )) xxTk = np.array([xxT for _ in range(self.size)]) yxTk = np.array([yxT for _ in range(self.size)]) yyk = np.array([yy for _ in range(self.size)]) ndk = np.array([nd for _ in range(self.size)]) return Stats([yxTk, xxTk, ndk, yyk]) else: stats = list(map(self.statistics, x, y)) return reduce(add, stats) def weighted_statistics(self, x, y, weights): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): idx = np.logical_and(~np.isnan(x).any(axis=1), ~np.isnan(y).any(axis=1)) x, y, weights = x[idx], y[idx], weights[idx] if self.affine: x = np.hstack((x, np.ones((x.shape[0], 1)))) xxTk = np.einsum('nd,nk,nl->kdl', x, weights, x, optimize=True) yxTk = np.einsum('nd,nk,nl->kdl', y, weights, x, optimize=True) yyk = np.einsum('nd,nk,nd->kd', y, weights, y, optimize=True) ndk = np.broadcast_to(np.sum(weights, axis=0, keepdims=True), (self.size, self.output_dim)) return Stats([yxTk, xxTk, ndk, yyk]) else: stats = list(map(self.weighted_statistics, x, y, weights)) return reduce(add, stats) def log_partition(self, x): return np.array([dist.log_partition(x) for dist in self.dists]).T def log_likelihood(self, x, y): if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): bads = np.logical_and(np.isnan(np.atleast_2d(x)).any(axis=1), np.isnan(np.atleast_2d(y)).any(axis=1)) x = np.nan_to_num(x, copy=False).reshape((-1, self.input_dim)) y = np.nan_to_num(y, copy=False).reshape((-1, self.output_dim)) mu = self.mean(x) log_lik =

np.einsum('nkd,kdl,nl->nk', mu, self.lmbdas, y, optimize=True)

numpy.einsum

from sys import getsizeof from typing import ( TYPE_CHECKING, Any, Callable, Hashable, Iterable, List, Optional, Sequence, Tuple, Union, ) import warnings import numpy as np from my_happy_pandas._config import get_option from my_happy_pandas._libs import algos as libalgos, index as libindex, lib from my_happy_pandas._libs.hashtable import duplicated_int64 from my_happy_pandas._typing import AnyArrayLike, Scalar from my_happy_pandas.compat.numpy import function as nv from my_happy_pandas.errors import InvalidIndexError, PerformanceWarning, UnsortedIndexError from my_happy_pandas.util._decorators import Appender, cache_readonly, doc from my_happy_pandas.core.dtypes.cast import coerce_indexer_dtype from my_happy_pandas.core.dtypes.common import ( ensure_int64, ensure_platform_int, is_categorical_dtype, is_hashable, is_integer, is_iterator, is_list_like, is_object_dtype, is_scalar, pandas_dtype, ) from my_happy_pandas.core.dtypes.dtypes import ExtensionDtype from my_happy_pandas.core.dtypes.generic import ABCDataFrame, ABCDatetimeIndex, ABCTimedeltaIndex from my_happy_pandas.core.dtypes.missing import array_equivalent, isna import my_happy_pandas.core.algorithms as algos from my_happy_pandas.core.arrays import Categorical from my_happy_pandas.core.arrays.categorical import factorize_from_iterables import my_happy_pandas.core.common as com import my_happy_pandas.core.indexes.base as ibase from my_happy_pandas.core.indexes.base import Index, _index_shared_docs, ensure_index from my_happy_pandas.core.indexes.frozen import FrozenList from my_happy_pandas.core.indexes.numeric import Int64Index import my_happy_pandas.core.missing as missing from my_happy_pandas.core.sorting import ( get_group_index, indexer_from_factorized, lexsort_indexer, ) from my_happy_pandas.io.formats.printing import ( format_object_attrs, format_object_summary, pprint_thing, ) if TYPE_CHECKING: from my_happy_pandas import Series # noqa:F401 _index_doc_kwargs = dict(ibase._index_doc_kwargs) _index_doc_kwargs.update( dict(klass="MultiIndex", target_klass="MultiIndex or list of tuples") ) class MultiIndexUIntEngine(libindex.BaseMultiIndexCodesEngine, libindex.UInt64Engine): """ This class manages a MultiIndex by mapping label combinations to positive integers. """ _base = libindex.UInt64Engine def _codes_to_ints(self, codes): """ Transform combination(s) of uint64 in one uint64 (each), in a strictly monotonic way (i.e. respecting the lexicographic order of integer combinations): see BaseMultiIndexCodesEngine documentation. Parameters ---------- codes : 1- or 2-dimensional array of dtype uint64 Combinations of integers (one per row) Returns ------- scalar or 1-dimensional array, of dtype uint64 Integer(s) representing one combination (each). """ # Shift the representation of each level by the pre-calculated number # of bits: codes <<= self.offsets # Now sum and OR are in fact interchangeable. This is a simple # composition of the (disjunct) significant bits of each level (i.e. # each column in "codes") in a single positive integer: if codes.ndim == 1: # Single key return np.bitwise_or.reduce(codes) # Multiple keys return np.bitwise_or.reduce(codes, axis=1) class MultiIndexPyIntEngine(libindex.BaseMultiIndexCodesEngine, libindex.ObjectEngine): """ This class manages those (extreme) cases in which the number of possible label combinations overflows the 64 bits integers, and uses an ObjectEngine containing Python integers. """ _base = libindex.ObjectEngine def _codes_to_ints(self, codes): """ Transform combination(s) of uint64 in one Python integer (each), in a strictly monotonic way (i.e. respecting the lexicographic order of integer combinations): see BaseMultiIndexCodesEngine documentation. Parameters ---------- codes : 1- or 2-dimensional array of dtype uint64 Combinations of integers (one per row) Returns ------- int, or 1-dimensional array of dtype object Integer(s) representing one combination (each). """ # Shift the representation of each level by the pre-calculated number # of bits. Since this can overflow uint64, first make sure we are # working with Python integers: codes = codes.astype("object") << self.offsets # Now sum and OR are in fact interchangeable. This is a simple # composition of the (disjunct) significant bits of each level (i.e. # each column in "codes") in a single positive integer (per row): if codes.ndim == 1: # Single key return np.bitwise_or.reduce(codes) # Multiple keys return np.bitwise_or.reduce(codes, axis=1) class MultiIndex(Index): """ A multi-level, or hierarchical, index object for pandas objects. Parameters ---------- levels : sequence of arrays The unique labels for each level. codes : sequence of arrays Integers for each level designating which label at each location. .. versionadded:: 0.24.0 sortorder : optional int Level of sortedness (must be lexicographically sorted by that level). names : optional sequence of objects Names for each of the index levels. (name is accepted for compat). copy : bool, default False Copy the meta-data. verify_integrity : bool, default True Check that the levels/codes are consistent and valid. Attributes ---------- names levels codes nlevels levshape Methods ------- from_arrays from_tuples from_product from_frame set_levels set_codes to_frame to_flat_index is_lexsorted sortlevel droplevel swaplevel reorder_levels remove_unused_levels get_locs See Also -------- MultiIndex.from_arrays : Convert list of arrays to MultiIndex. MultiIndex.from_product : Create a MultiIndex from the cartesian product of iterables. MultiIndex.from_tuples : Convert list of tuples to a MultiIndex. MultiIndex.from_frame : Make a MultiIndex from a DataFrame. Index : The base pandas Index type. Notes ----- See the `user guide <https://pandas.pydata.org/pandas-docs/stable/user_guide/advanced.html>`_ for more. Examples -------- A new ``MultiIndex`` is typically constructed using one of the helper methods :meth:`MultiIndex.from_arrays`, :meth:`MultiIndex.from_product` and :meth:`MultiIndex.from_tuples`. For example (using ``.from_arrays``): >>> arrays = [[1, 1, 2, 2], ['red', 'blue', 'red', 'blue']] >>> pd.MultiIndex.from_arrays(arrays, names=('number', 'color')) MultiIndex([(1, 'red'), (1, 'blue'), (2, 'red'), (2, 'blue')], names=['number', 'color']) See further examples for how to construct a MultiIndex in the doc strings of the mentioned helper methods. """ _deprecations = Index._deprecations | frozenset() # initialize to zero-length tuples to make everything work _typ = "multiindex" _names = FrozenList() _levels = FrozenList() _codes = FrozenList() _comparables = ["names"] rename = Index.set_names _tuples = None sortorder: Optional[int] # -------------------------------------------------------------------- # Constructors def __new__( cls, levels=None, codes=None, sortorder=None, names=None, dtype=None, copy=False, name=None, verify_integrity: bool = True, _set_identity: bool = True, ): # compat with Index if name is not None: names = name if levels is None or codes is None: raise TypeError("Must pass both levels and codes") if len(levels) != len(codes): raise ValueError("Length of levels and codes must be the same.") if len(levels) == 0: raise ValueError("Must pass non-zero number of levels/codes") result = object.__new__(MultiIndex) result._cache = {} # we've already validated levels and codes, so shortcut here result._set_levels(levels, copy=copy, validate=False) result._set_codes(codes, copy=copy, validate=False) result._names = [None] * len(levels) if names is not None: # handles name validation result._set_names(names) if sortorder is not None: result.sortorder = int(sortorder) else: result.sortorder = sortorder if verify_integrity: new_codes = result._verify_integrity() result._codes = new_codes if _set_identity: result._reset_identity() return result def _validate_codes(self, level: List, code: List): """ Reassign code values as -1 if their corresponding levels are NaN. Parameters ---------- code : list Code to reassign. level : list Level to check for missing values (NaN, NaT, None). Returns ------- new code where code value = -1 if it corresponds to a level with missing values (NaN, NaT, None). """ null_mask = isna(level) if np.any(null_mask): code = np.where(null_mask[code], -1, code) return code def _verify_integrity( self, codes: Optional[List] = None, levels: Optional[List] = None ): """ Parameters ---------- codes : optional list Codes to check for validity. Defaults to current codes. levels : optional list Levels to check for validity. Defaults to current levels. Raises ------ ValueError If length of levels and codes don't match, if the codes for any level would exceed level bounds, or there are any duplicate levels. Returns ------- new codes where code value = -1 if it corresponds to a NaN level. """ # NOTE: Currently does not check, among other things, that cached # nlevels matches nor that sortorder matches actually sortorder. codes = codes or self.codes levels = levels or self.levels if len(levels) != len(codes): raise ValueError( "Length of levels and codes must match. NOTE: " "this index is in an inconsistent state." ) codes_length = len(codes[0]) for i, (level, level_codes) in enumerate(zip(levels, codes)): if len(level_codes) != codes_length: raise ValueError( f"Unequal code lengths: {[len(code_) for code_ in codes]}" ) if len(level_codes) and level_codes.max() >= len(level): raise ValueError( f"On level {i}, code max ({level_codes.max()}) >= length of " f"level ({len(level)}). NOTE: this index is in an " "inconsistent state" ) if len(level_codes) and level_codes.min() < -1: raise ValueError(f"On level {i}, code value ({level_codes.min()}) < -1") if not level.is_unique: raise ValueError( f"Level values must be unique: {list(level)} on level {i}" ) if self.sortorder is not None: if self.sortorder > self._lexsort_depth(): raise ValueError( "Value for sortorder must be inferior or equal to actual " f"lexsort_depth: sortorder {self.sortorder} " f"with lexsort_depth {self._lexsort_depth()}" ) codes = [ self._validate_codes(level, code) for level, code in zip(levels, codes) ] new_codes = FrozenList(codes) return new_codes @classmethod def from_arrays(cls, arrays, sortorder=None, names=lib.no_default) -> "MultiIndex": """ Convert arrays to MultiIndex. Parameters ---------- arrays : list / sequence of array-likes Each array-like gives one level's value for each data point. len(arrays) is the number of levels. sortorder : int or None Level of sortedness (must be lexicographically sorted by that level). names : list / sequence of str, optional Names for the levels in the index. Returns ------- MultiIndex See Also -------- MultiIndex.from_tuples : Convert list of tuples to MultiIndex. MultiIndex.from_product : Make a MultiIndex from cartesian product of iterables. MultiIndex.from_frame : Make a MultiIndex from a DataFrame. Examples -------- >>> arrays = [[1, 1, 2, 2], ['red', 'blue', 'red', 'blue']] >>> pd.MultiIndex.from_arrays(arrays, names=('number', 'color')) MultiIndex([(1, 'red'), (1, 'blue'), (2, 'red'), (2, 'blue')], names=['number', 'color']) """ error_msg = "Input must be a list / sequence of array-likes." if not is_list_like(arrays): raise TypeError(error_msg) elif is_iterator(arrays): arrays = list(arrays) # Check if elements of array are list-like for array in arrays: if not is_list_like(array): raise TypeError(error_msg) # Check if lengths of all arrays are equal or not, # raise ValueError, if not for i in range(1, len(arrays)): if len(arrays[i]) != len(arrays[i - 1]): raise ValueError("all arrays must be same length") codes, levels = factorize_from_iterables(arrays) if names is lib.no_default: names = [getattr(arr, "name", None) for arr in arrays] return MultiIndex( levels=levels, codes=codes, sortorder=sortorder, names=names, verify_integrity=False, ) @classmethod def from_tuples(cls, tuples, sortorder=None, names=None): """ Convert list of tuples to MultiIndex. Parameters ---------- tuples : list / sequence of tuple-likes Each tuple is the index of one row/column. sortorder : int or None Level of sortedness (must be lexicographically sorted by that level). names : list / sequence of str, optional Names for the levels in the index. Returns ------- MultiIndex See Also -------- MultiIndex.from_arrays : Convert list of arrays to MultiIndex. MultiIndex.from_product : Make a MultiIndex from cartesian product of iterables. MultiIndex.from_frame : Make a MultiIndex from a DataFrame. Examples -------- >>> tuples = [(1, 'red'), (1, 'blue'), ... (2, 'red'), (2, 'blue')] >>> pd.MultiIndex.from_tuples(tuples, names=('number', 'color')) MultiIndex([(1, 'red'), (1, 'blue'), (2, 'red'), (2, 'blue')], names=['number', 'color']) """ if not is_list_like(tuples): raise TypeError("Input must be a list / sequence of tuple-likes.") elif is_iterator(tuples): tuples = list(tuples) if len(tuples) == 0: if names is None: raise TypeError("Cannot infer number of levels from empty list") arrays = [[]] * len(names) elif isinstance(tuples, (np.ndarray, Index)): if isinstance(tuples, Index): tuples = tuples._values arrays = list(lib.tuples_to_object_array(tuples).T) elif isinstance(tuples, list): arrays = list(lib.to_object_array_tuples(tuples).T) else: arrays = zip(*tuples) return MultiIndex.from_arrays(arrays, sortorder=sortorder, names=names) @classmethod def from_product(cls, iterables, sortorder=None, names=lib.no_default): """ Make a MultiIndex from the cartesian product of multiple iterables. Parameters ---------- iterables : list / sequence of iterables Each iterable has unique labels for each level of the index. sortorder : int or None Level of sortedness (must be lexicographically sorted by that level). names : list / sequence of str, optional Names for the levels in the index. .. versionchanged:: 1.0.0 If not explicitly provided, names will be inferred from the elements of iterables if an element has a name attribute Returns ------- MultiIndex See Also -------- MultiIndex.from_arrays : Convert list of arrays to MultiIndex. MultiIndex.from_tuples : Convert list of tuples to MultiIndex. MultiIndex.from_frame : Make a MultiIndex from a DataFrame. Examples -------- >>> numbers = [0, 1, 2] >>> colors = ['green', 'purple'] >>> pd.MultiIndex.from_product([numbers, colors], ... names=['number', 'color']) MultiIndex([(0, 'green'), (0, 'purple'), (1, 'green'), (1, 'purple'), (2, 'green'), (2, 'purple')], names=['number', 'color']) """ from my_happy_pandas.core.reshape.util import cartesian_product if not is_list_like(iterables): raise TypeError("Input must be a list / sequence of iterables.") elif is_iterator(iterables): iterables = list(iterables) codes, levels = factorize_from_iterables(iterables) if names is lib.no_default: names = [getattr(it, "name", None) for it in iterables] # codes are all ndarrays, so cartesian_product is lossless codes = cartesian_product(codes) return MultiIndex(levels, codes, sortorder=sortorder, names=names) @classmethod def from_frame(cls, df, sortorder=None, names=None): """ Make a MultiIndex from a DataFrame. .. versionadded:: 0.24.0 Parameters ---------- df : DataFrame DataFrame to be converted to MultiIndex. sortorder : int, optional Level of sortedness (must be lexicographically sorted by that level). names : list-like, optional If no names are provided, use the column names, or tuple of column names if the columns is a MultiIndex. If a sequence, overwrite names with the given sequence. Returns ------- MultiIndex The MultiIndex representation of the given DataFrame. See Also -------- MultiIndex.from_arrays : Convert list of arrays to MultiIndex. MultiIndex.from_tuples : Convert list of tuples to MultiIndex. MultiIndex.from_product : Make a MultiIndex from cartesian product of iterables. Examples -------- >>> df = pd.DataFrame([['HI', 'Temp'], ['HI', 'Precip'], ... ['NJ', 'Temp'], ['NJ', 'Precip']], ... columns=['a', 'b']) >>> df a b 0 HI Temp 1 HI Precip 2 NJ Temp 3 NJ Precip >>> pd.MultiIndex.from_frame(df) MultiIndex([('HI', 'Temp'), ('HI', 'Precip'), ('NJ', 'Temp'), ('NJ', 'Precip')], names=['a', 'b']) Using explicit names, instead of the column names >>> pd.MultiIndex.from_frame(df, names=['state', 'observation']) MultiIndex([('HI', 'Temp'), ('HI', 'Precip'), ('NJ', 'Temp'), ('NJ', 'Precip')], names=['state', 'observation']) """ if not isinstance(df, ABCDataFrame): raise TypeError("Input must be a DataFrame") column_names, columns = zip(*df.items()) names = column_names if names is None else names return cls.from_arrays(columns, sortorder=sortorder, names=names) # -------------------------------------------------------------------- @property def _values(self): # We override here, since our parent uses _data, which we don't use. return self.values @property def values(self): if self._tuples is not None: return self._tuples values = [] for i in range(self.nlevels): vals = self._get_level_values(i) if is_categorical_dtype(vals.dtype): vals = vals._internal_get_values() if isinstance(vals.dtype, ExtensionDtype) or isinstance( vals, (ABCDatetimeIndex, ABCTimedeltaIndex) ): vals = vals.astype(object) vals = np.array(vals, copy=False) values.append(vals) self._tuples = lib.fast_zip(values) return self._tuples @property def array(self): """ Raises a ValueError for `MultiIndex` because there's no single array backing a MultiIndex. Raises ------ ValueError """ raise ValueError( "MultiIndex has no single backing array. Use " "'MultiIndex.to_numpy()' to get a NumPy array of tuples." ) @property def shape(self): """ Return a tuple of the shape of the underlying data. """ # overriding the base Index.shape definition to avoid materializing # the values (GH-27384, GH-27775) return (len(self),) def __len__(self) -> int: return len(self.codes[0]) # -------------------------------------------------------------------- # Levels Methods @cache_readonly def levels(self): # Use cache_readonly to ensure that self.get_locs doesn't repeatedly # create new IndexEngine # https://github.com/pandas-dev/pandas/issues/31648 result = [ x._shallow_copy(name=name) for x, name in zip(self._levels, self._names) ] for level in result: # disallow midx.levels[0].name = "foo" level._no_setting_name = True return FrozenList(result) def _set_levels( self, levels, level=None, copy=False, validate=True, verify_integrity=False ): # This is NOT part of the levels property because it should be # externally not allowed to set levels. User beware if you change # _levels directly if validate: if len(levels) == 0: raise ValueError("Must set non-zero number of levels.") if level is None and len(levels) != self.nlevels: raise ValueError("Length of levels must match number of levels.") if level is not None and len(levels) != len(level): raise ValueError("Length of levels must match length of level.") if level is None: new_levels = FrozenList( ensure_index(lev, copy=copy)._shallow_copy() for lev in levels ) else: level_numbers = [self._get_level_number(lev) for lev in level] new_levels = list(self._levels) for lev_num, lev in zip(level_numbers, levels): new_levels[lev_num] = ensure_index(lev, copy=copy)._shallow_copy() new_levels = FrozenList(new_levels) if verify_integrity: new_codes = self._verify_integrity(levels=new_levels) self._codes = new_codes names = self.names self._levels = new_levels if any(names): self._set_names(names) self._tuples = None self._reset_cache() def set_levels(self, levels, level=None, inplace=False, verify_integrity=True): """ Set new levels on MultiIndex. Defaults to returning new index. Parameters ---------- levels : sequence or list of sequence New level(s) to apply. level : int, level name, or sequence of int/level names (default None) Level(s) to set (None for all levels). inplace : bool If True, mutates in place. verify_integrity : bool, default True If True, checks that levels and codes are compatible. Returns ------- new index (of same type and class...etc) Examples -------- >>> idx = pd.MultiIndex.from_tuples( ... [ ... (1, "one"), ... (1, "two"), ... (2, "one"), ... (2, "two"), ... (3, "one"), ... (3, "two") ... ], ... names=["foo", "bar"] ... ) >>> idx MultiIndex([(1, 'one'), (1, 'two'), (2, 'one'), (2, 'two'), (3, 'one'), (3, 'two')], names=['foo', 'bar']) >>> idx.set_levels([['a', 'b', 'c'], [1, 2]]) MultiIndex([('a', 1), ('a', 2), ('b', 1), ('b', 2), ('c', 1), ('c', 2)], names=['foo', 'bar']) >>> idx.set_levels(['a', 'b', 'c'], level=0) MultiIndex([('a', 'one'), ('a', 'two'), ('b', 'one'), ('b', 'two'), ('c', 'one'), ('c', 'two')], names=['foo', 'bar']) >>> idx.set_levels(['a', 'b'], level='bar') MultiIndex([(1, 'a'), (1, 'b'), (2, 'a'), (2, 'b'), (3, 'a'), (3, 'b')], names=['foo', 'bar']) If any of the levels passed to ``set_levels()`` exceeds the existing length, all of the values from that argument will be stored in the MultiIndex levels, though the values will be truncated in the MultiIndex output. >>> idx.set_levels([['a', 'b', 'c'], [1, 2, 3, 4]], level=[0, 1]) MultiIndex([('a', 1), ('a', 2), ('b', 1), ('b', 2), ('c', 1), ('c', 2)], names=['foo', 'bar']) >>> idx.set_levels([['a', 'b', 'c'], [1, 2, 3, 4]], level=[0, 1]).levels FrozenList([['a', 'b', 'c'], [1, 2, 3, 4]]) """ if is_list_like(levels) and not isinstance(levels, Index): levels = list(levels) if level is not None and not is_list_like(level): if not is_list_like(levels): raise TypeError("Levels must be list-like") if is_list_like(levels[0]): raise TypeError("Levels must be list-like") level = [level] levels = [levels] elif level is None or is_list_like(level): if not is_list_like(levels) or not is_list_like(levels[0]): raise TypeError("Levels must be list of lists-like") if inplace: idx = self else: idx = self._shallow_copy() idx._reset_identity() idx._set_levels( levels, level=level, validate=True, verify_integrity=verify_integrity ) if not inplace: return idx @property def nlevels(self) -> int: """ Integer number of levels in this MultiIndex. """ return len(self._levels) @property def levshape(self): """ A tuple with the length of each level. """ return tuple(len(x) for x in self.levels) # -------------------------------------------------------------------- # Codes Methods @property def codes(self): return self._codes def _set_codes( self, codes, level=None, copy=False, validate=True, verify_integrity=False ): if validate: if level is None and len(codes) != self.nlevels: raise ValueError("Length of codes must match number of levels") if level is not None and len(codes) != len(level): raise ValueError("Length of codes must match length of levels.") if level is None: new_codes = FrozenList( _coerce_indexer_frozen(level_codes, lev, copy=copy).view() for lev, level_codes in zip(self._levels, codes) ) else: level_numbers = [self._get_level_number(lev) for lev in level] new_codes = list(self._codes) for lev_num, level_codes in zip(level_numbers, codes): lev = self.levels[lev_num] new_codes[lev_num] = _coerce_indexer_frozen(level_codes, lev, copy=copy) new_codes = FrozenList(new_codes) if verify_integrity: new_codes = self._verify_integrity(codes=new_codes) self._codes = new_codes self._tuples = None self._reset_cache() def set_codes(self, codes, level=None, inplace=False, verify_integrity=True): """ Set new codes on MultiIndex. Defaults to returning new index. .. versionadded:: 0.24.0 New name for deprecated method `set_labels`. Parameters ---------- codes : sequence or list of sequence New codes to apply. level : int, level name, or sequence of int/level names (default None) Level(s) to set (None for all levels). inplace : bool If True, mutates in place. verify_integrity : bool (default True) If True, checks that levels and codes are compatible. Returns ------- new index (of same type and class...etc) Examples -------- >>> idx = pd.MultiIndex.from_tuples( ... [(1, "one"), (1, "two"), (2, "one"), (2, "two")], names=["foo", "bar"] ... ) >>> idx MultiIndex([(1, 'one'), (1, 'two'), (2, 'one'), (2, 'two')], names=['foo', 'bar']) >>> idx.set_codes([[1, 0, 1, 0], [0, 0, 1, 1]]) MultiIndex([(2, 'one'), (1, 'one'), (2, 'two'), (1, 'two')], names=['foo', 'bar']) >>> idx.set_codes([1, 0, 1, 0], level=0) MultiIndex([(2, 'one'), (1, 'two'), (2, 'one'), (1, 'two')], names=['foo', 'bar']) >>> idx.set_codes([0, 0, 1, 1], level='bar') MultiIndex([(1, 'one'), (1, 'one'), (2, 'two'), (2, 'two')], names=['foo', 'bar']) >>> idx.set_codes([[1, 0, 1, 0], [0, 0, 1, 1]], level=[0, 1]) MultiIndex([(2, 'one'), (1, 'one'), (2, 'two'), (1, 'two')], names=['foo', 'bar']) """ if level is not None and not is_list_like(level): if not is_list_like(codes): raise TypeError("Codes must be list-like") if is_list_like(codes[0]): raise TypeError("Codes must be list-like") level = [level] codes = [codes] elif level is None or is_list_like(level): if not is_list_like(codes) or not is_list_like(codes[0]): raise TypeError("Codes must be list of lists-like") if inplace: idx = self else: idx = self._shallow_copy() idx._reset_identity() idx._set_codes(codes, level=level, verify_integrity=verify_integrity) if not inplace: return idx # -------------------------------------------------------------------- # Index Internals @cache_readonly def _engine(self): # Calculate the number of bits needed to represent labels in each # level, as log2 of their sizes (including -1 for NaN): sizes = np.ceil(np.log2([len(l) + 1 for l in self.levels])) # Sum bit counts, starting from the _right_.... lev_bits = np.cumsum(sizes[::-1])[::-1] # ... in order to obtain offsets such that sorting the combination of # shifted codes (one for each level, resulting in a unique integer) is # equivalent to sorting lexicographically the codes themselves. Notice # that each level needs to be shifted by the number of bits needed to # represent the _previous_ ones: offsets = np.concatenate([lev_bits[1:], [0]]).astype("uint64") # Check the total number of bits needed for our representation: if lev_bits[0] > 64: # The levels would overflow a 64 bit uint - use Python integers: return MultiIndexPyIntEngine(self.levels, self.codes, offsets) return MultiIndexUIntEngine(self.levels, self.codes, offsets) @property def _constructor(self): return MultiIndex.from_tuples @doc(Index._shallow_copy) def _shallow_copy( self, values=None, name=lib.no_default, levels=None, codes=None, dtype=None, sortorder=None, names=lib.no_default, _set_identity: bool = True, ): if names is not lib.no_default and name is not lib.no_default: raise TypeError("Can only provide one of `names` and `name`") elif names is lib.no_default: names = name if name is not lib.no_default else self.names if values is not None: assert levels is None and codes is None and dtype is None return MultiIndex.from_tuples(values, sortorder=sortorder, names=names) levels = levels if levels is not None else self.levels codes = codes if codes is not None else self.codes result = MultiIndex( levels=levels, codes=codes, dtype=dtype, sortorder=sortorder, names=names, verify_integrity=False, _set_identity=_set_identity, ) result._cache = self._cache.copy() result._cache.pop("levels", None) # GH32669 return result def symmetric_difference(self, other, result_name=None, sort=None): # On equal symmetric_difference MultiIndexes the difference is empty. # Therefore, an empty MultiIndex is returned GH13490 tups = Index.symmetric_difference(self, other, result_name, sort) if len(tups) == 0: return MultiIndex( levels=[[] for _ in range(self.nlevels)], codes=[[] for _ in range(self.nlevels)], names=tups.name, ) return type(self).from_tuples(tups, names=tups.name) # -------------------------------------------------------------------- def copy( self, names=None, dtype=None, levels=None, codes=None, deep=False, name=None, _set_identity=False, ): """ Make a copy of this object. Names, dtype, levels and codes can be passed and will be set on new copy. Parameters ---------- names : sequence, optional dtype : numpy dtype or pandas type, optional levels : sequence, optional codes : sequence, optional deep : bool, default False name : Label Kept for compatibility with 1-dimensional Index. Should not be used. Returns ------- MultiIndex Notes ----- In most cases, there should be no functional difference from using ``deep``, but if ``deep`` is passed it will attempt to deepcopy. This could be potentially expensive on large MultiIndex objects. """ names = self._validate_names(name=name, names=names, deep=deep) if deep: from copy import deepcopy if levels is None: levels = deepcopy(self.levels) if codes is None: codes = deepcopy(self.codes) return self._shallow_copy( levels=levels, codes=codes, names=names, dtype=dtype, sortorder=self.sortorder, _set_identity=_set_identity, ) def __array__(self, dtype=None) -> np.ndarray: """ the array interface, return my values """ return self.values def view(self, cls=None): """ this is defined as a copy with the same identity """ result = self.copy() result._id = self._id return result @doc(Index.__contains__) def __contains__(self, key: Any) -> bool: hash(key) try: self.get_loc(key) return True except (LookupError, TypeError, ValueError): return False @cache_readonly def dtype(self) -> np.dtype: return np.dtype("O") def _is_memory_usage_qualified(self) -> bool: """ return a boolean if we need a qualified .info display """ def f(l): return "mixed" in l or "string" in l or "unicode" in l return any(f(l) for l in self._inferred_type_levels) @doc(Index.memory_usage) def memory_usage(self, deep: bool = False) -> int: # we are overwriting our base class to avoid # computing .values here which could materialize # a tuple representation unnecessarily return self._nbytes(deep) @cache_readonly def nbytes(self) -> int: """ return the number of bytes in the underlying data """ return self._nbytes(False) def _nbytes(self, deep: bool = False) -> int: """ return the number of bytes in the underlying data deeply introspect the level data if deep=True include the engine hashtable *this is in internal routine* """ # for implementations with no useful getsizeof (PyPy) objsize = 24 level_nbytes = sum(i.memory_usage(deep=deep) for i in self.levels) label_nbytes = sum(i.nbytes for i in self.codes) names_nbytes = sum(getsizeof(i, objsize) for i in self.names) result = level_nbytes + label_nbytes + names_nbytes # include our engine hashtable result += self._engine.sizeof(deep=deep) return result # -------------------------------------------------------------------- # Rendering Methods def _formatter_func(self, tup): """ Formats each item in tup according to its level's formatter function. """ formatter_funcs = [level._formatter_func for level in self.levels] return tuple(func(val) for func, val in zip(formatter_funcs, tup)) def _format_data(self, name=None): """ Return the formatted data as a unicode string """ return format_object_summary( self, self._formatter_func, name=name, line_break_each_value=True ) def _format_attrs(self): """ Return a list of tuples of the (attr,formatted_value). """ return format_object_attrs(self, include_dtype=False) def _format_native_types(self, na_rep="nan", **kwargs): new_levels = [] new_codes = [] # go through the levels and format them for level, level_codes in zip(self.levels, self.codes): level = level._format_native_types(na_rep=na_rep, **kwargs) # add nan values, if there are any mask = level_codes == -1 if mask.any(): nan_index = len(level) level = np.append(level, na_rep) assert not level_codes.flags.writeable # i.e. copy is needed level_codes = level_codes.copy() # make writeable level_codes[mask] = nan_index new_levels.append(level) new_codes.append(level_codes) if len(new_levels) == 1: # a single-level multi-index return Index(new_levels[0].take(new_codes[0]))._format_native_types() else: # reconstruct the multi-index mi = MultiIndex( levels=new_levels, codes=new_codes, names=self.names, sortorder=self.sortorder, verify_integrity=False, ) return mi._values def format( self, name: Optional[bool] = None, formatter: Optional[Callable] = None, na_rep: Optional[str] = None, names: bool = False, space: int = 2, sparsify=None, adjoin: bool = True, ) -> List: if name is not None: names = name if len(self) == 0: return [] stringified_levels = [] for lev, level_codes in zip(self.levels, self.codes): na = na_rep if na_rep is not None else _get_na_rep(lev.dtype.type) if len(lev) > 0: formatted = lev.take(level_codes).format(formatter=formatter) # we have some NA mask = level_codes == -1 if mask.any(): formatted = np.array(formatted, dtype=object) formatted[mask] = na formatted = formatted.tolist() else: # weird all NA case formatted = [ pprint_thing(na if isna(x) else x, escape_chars=("\t", "\r", "\n")) for x in algos.take_1d(lev._values, level_codes) ] stringified_levels.append(formatted) result_levels = [] for lev, lev_name in zip(stringified_levels, self.names): level = [] if names: level.append( pprint_thing(lev_name, escape_chars=("\t", "\r", "\n")) if lev_name is not None else "" ) level.extend(np.array(lev, dtype=object)) result_levels.append(level) if sparsify is None: sparsify = get_option("display.multi_sparse") if sparsify: sentinel = "" # GH3547 use value of sparsify as sentinel if it's "Falsey" assert isinstance(sparsify, bool) or sparsify is lib.no_default if sparsify in [False, lib.no_default]: sentinel = sparsify # little bit of a kludge job for #1217 result_levels = _sparsify( result_levels, start=int(names), sentinel=sentinel ) if adjoin: from my_happy_pandas.io.formats.format import _get_adjustment adj = _get_adjustment() return adj.adjoin(space, *result_levels).split("\n") else: return result_levels # -------------------------------------------------------------------- # Names Methods def _get_names(self): return FrozenList(self._names) def _set_names(self, names, level=None, validate=True): """ Set new names on index. Each name has to be a hashable type. Parameters ---------- values : str or sequence name(s) to set level : int, level name, or sequence of int/level names (default None) If the index is a MultiIndex (hierarchical), level(s) to set (None for all levels). Otherwise level must be None validate : boolean, default True validate that the names match level lengths Raises ------ TypeError if each name is not hashable. Notes ----- sets names on levels. WARNING: mutates! Note that you generally want to set this *after* changing levels, so that it only acts on copies """ # GH 15110 # Don't allow a single string for names in a MultiIndex if names is not None and not is_list_like(names): raise ValueError("Names should be list-like for a MultiIndex") names = list(names) if validate: if level is not None and len(names) != len(level): raise ValueError("Length of names must match length of level.") if level is None and len(names) != self.nlevels: raise ValueError( "Length of names must match number of levels in MultiIndex." ) if level is None: level = range(self.nlevels) else: level = [self._get_level_number(lev) for lev in level] # set the name for lev, name in zip(level, names): if name is not None: # GH 20527 # All items in 'names' need to be hashable: if not is_hashable(name): raise TypeError( f"{type(self).__name__}.name must be a hashable type" ) self._names[lev] = name # If .levels has been accessed, the names in our cache will be stale. self._reset_cache() names = property( fset=_set_names, fget=_get_names, doc="""\nNames of levels in MultiIndex.\n""" ) # -------------------------------------------------------------------- @doc(Index._get_grouper_for_level) def _get_grouper_for_level(self, mapper, level): indexer = self.codes[level] level_index = self.levels[level] if mapper is not None: # Handle group mapping function and return level_values = self.levels[level].take(indexer) grouper = level_values.map(mapper) return grouper, None, None codes, uniques = algos.factorize(indexer, sort=True) if len(uniques) > 0 and uniques[0] == -1: # Handle NAs mask = indexer != -1 ok_codes, uniques = algos.factorize(indexer[mask], sort=True) codes = np.empty(len(indexer), dtype=indexer.dtype) codes[mask] = ok_codes codes[~mask] = -1 if len(uniques) < len(level_index): # Remove unobserved levels from level_index level_index = level_index.take(uniques) else: # break references back to us so that setting the name # on the output of a groupby doesn't reflect back here. level_index = level_index.copy() if level_index._can_hold_na: grouper = level_index.take(codes, fill_value=True) else: grouper = level_index.take(codes) return grouper, codes, level_index @cache_readonly def inferred_type(self) -> str: return "mixed" def _get_level_number(self, level) -> int: count = self.names.count(level) if (count > 1) and not is_integer(level): raise ValueError( f"The name {level} occurs multiple times, use a level number" ) try: level = self.names.index(level) except ValueError as err: if not is_integer(level): raise KeyError(f"Level {level} not found") from err elif level < 0: level += self.nlevels if level < 0: orig_level = level - self.nlevels raise IndexError( f"Too many levels: Index has only {self.nlevels} levels, " f"{orig_level} is not a valid level number" ) from err # Note: levels are zero-based elif level >= self.nlevels: raise IndexError( f"Too many levels: Index has only {self.nlevels} levels, " f"not {level + 1}" ) from err return level @property def _has_complex_internals(self) -> bool: # used to avoid libreduction code paths, which raise or require conversion return True @cache_readonly def is_monotonic_increasing(self) -> bool: """ return if the index is monotonic increasing (only equal or increasing) values. """ if any(-1 in code for code in self.codes): return False if all(level.is_monotonic for level in self.levels): # If each level is sorted, we can operate on the codes directly. GH27495 return libalgos.is_lexsorted( [x.astype("int64", copy=False) for x in self.codes] ) # reversed() because lexsort() wants the most significant key last. values = [ self._get_level_values(i)._values for i in reversed(range(len(self.levels))) ] try: sort_order = np.lexsort(values) return Index(sort_order).is_monotonic except TypeError: # we have mixed types and np.lexsort is not happy return Index(self._values).is_monotonic @cache_readonly def is_monotonic_decreasing(self) -> bool: """ return if the index is monotonic decreasing (only equal or decreasing) values. """ # monotonic decreasing if and only if reverse is monotonic increasing return self[::-1].is_monotonic_increasing @cache_readonly def _inferred_type_levels(self): """ return a list of the inferred types, one for each level """ return [i.inferred_type for i in self.levels] @doc(Index.duplicated) def duplicated(self, keep="first"): shape = map(len, self.levels) ids = get_group_index(self.codes, shape, sort=False, xnull=False) return duplicated_int64(ids, keep) def fillna(self, value=None, downcast=None): """ fillna is not implemented for MultiIndex """ raise NotImplementedError("isna is not defined for MultiIndex") @doc(Index.dropna) def dropna(self, how="any"): nans = [level_codes == -1 for level_codes in self.codes] if how == "any": indexer = np.any(nans, axis=0) elif how == "all": indexer = np.all(nans, axis=0) else: raise ValueError(f"invalid how option: {how}") new_codes = [level_codes[~indexer] for level_codes in self.codes] return self.copy(codes=new_codes, deep=True) def _get_level_values(self, level, unique=False): """ Return vector of label values for requested level, equal to the length of the index **this is an internal method** Parameters ---------- level : int level unique : bool, default False if True, drop duplicated values Returns ------- values : ndarray """ lev = self.levels[level] level_codes = self.codes[level] name = self._names[level] if unique: level_codes = algos.unique(level_codes) filled = algos.take_1d(lev._values, level_codes, fill_value=lev._na_value) return lev._shallow_copy(filled, name=name) def get_level_values(self, level): """ Return vector of label values for requested level. Length of returned vector is equal to the length of the index. Parameters ---------- level : int or str ``level`` is either the integer position of the level in the MultiIndex, or the name of the level. Returns ------- values : Index Values is a level of this MultiIndex converted to a single :class:`Index` (or subclass thereof). Examples -------- Create a MultiIndex: >>> mi = pd.MultiIndex.from_arrays((list('abc'), list('def'))) >>> mi.names = ['level_1', 'level_2'] Get level values by supplying level as either integer or name: >>> mi.get_level_values(0) Index(['a', 'b', 'c'], dtype='object', name='level_1') >>> mi.get_level_values('level_2') Index(['d', 'e', 'f'], dtype='object', name='level_2') """ level = self._get_level_number(level) values = self._get_level_values(level) return values @doc(Index.unique) def unique(self, level=None): if level is None: return super().unique() else: level = self._get_level_number(level) return self._get_level_values(level=level, unique=True) def _to_safe_for_reshape(self): """ convert to object if we are a categorical """ return self.set_levels([i._to_safe_for_reshape() for i in self.levels]) def to_frame(self, index=True, name=None): """ Create a DataFrame with the levels of the MultiIndex as columns. Column ordering is determined by the DataFrame constructor with data as a dict. .. versionadded:: 0.24.0 Parameters ---------- index : bool, default True Set the index of the returned DataFrame as the original MultiIndex. name : list / sequence of str, optional The passed names should substitute index level names. Returns ------- DataFrame : a DataFrame containing the original MultiIndex data. See Also -------- DataFrame : Two-dimensional, size-mutable, potentially heterogeneous tabular data. """ from my_happy_pandas import DataFrame if name is not None: if not is_list_like(name): raise TypeError("'name' must be a list / sequence of column names.") if len(name) != len(self.levels): raise ValueError( "'name' should have same length as number of levels on index." ) idx_names = name else: idx_names = self.names # Guarantee resulting column order - PY36+ dict maintains insertion order result = DataFrame( { (level if lvlname is None else lvlname): self._get_level_values(level) for lvlname, level in zip(idx_names, range(len(self.levels))) }, copy=False, ) if index: result.index = self return result def to_flat_index(self): """ Convert a MultiIndex to an Index of Tuples containing the level values. .. versionadded:: 0.24.0 Returns ------- pd.Index Index with the MultiIndex data represented in Tuples. Notes ----- This method will simply return the caller if called by anything other than a MultiIndex. Examples -------- >>> index = pd.MultiIndex.from_product( ... [['foo', 'bar'], ['baz', 'qux']], ... names=['a', 'b']) >>> index.to_flat_index() Index([('foo', 'baz'), ('foo', 'qux'), ('bar', 'baz'), ('bar', 'qux')], dtype='object') """ return Index(self._values, tupleize_cols=False) @property def is_all_dates(self) -> bool: return False def is_lexsorted(self) -> bool: """ Return True if the codes are lexicographically sorted. Returns ------- bool Examples -------- In the below examples, the first level of the MultiIndex is sorted because a<b<c, so there is no need to look at the next level. >>> pd.MultiIndex.from_arrays([['a', 'b', 'c'], ['d', 'e', 'f']]).is_lexsorted() True >>> pd.MultiIndex.from_arrays([['a', 'b', 'c'], ['d', 'f', 'e']]).is_lexsorted() True In case there is a tie, the lexicographical sorting looks at the next level of the MultiIndex. >>> pd.MultiIndex.from_arrays([[0, 1, 1], ['a', 'b', 'c']]).is_lexsorted() True >>> pd.MultiIndex.from_arrays([[0, 1, 1], ['a', 'c', 'b']]).is_lexsorted() False >>> pd.MultiIndex.from_arrays([['a', 'a', 'b', 'b'], ... ['aa', 'bb', 'aa', 'bb']]).is_lexsorted() True >>> pd.MultiIndex.from_arrays([['a', 'a', 'b', 'b'], ... ['bb', 'aa', 'aa', 'bb']]).is_lexsorted() False """ return self.lexsort_depth == self.nlevels @cache_readonly def lexsort_depth(self): if self.sortorder is not None: return self.sortorder return self._lexsort_depth() def _lexsort_depth(self) -> int: """ Compute and return the lexsort_depth, the number of levels of the MultiIndex that are sorted lexically Returns ------- int """ int64_codes = [ensure_int64(level_codes) for level_codes in self.codes] for k in range(self.nlevels, 0, -1): if libalgos.is_lexsorted(int64_codes[:k]): return k return 0 def _sort_levels_monotonic(self): """ This is an *internal* function. Create a new MultiIndex from the current to monotonically sorted items IN the levels. This does not actually make the entire MultiIndex monotonic, JUST the levels. The resulting MultiIndex will have the same outward appearance, meaning the same .values and ordering. It will also be .equals() to the original. Returns ------- MultiIndex Examples -------- >>> mi = pd.MultiIndex(levels=[['a', 'b'], ['bb', 'aa']], ... codes=[[0, 0, 1, 1], [0, 1, 0, 1]]) >>> mi MultiIndex([('a', 'bb'), ('a', 'aa'), ('b', 'bb'), ('b', 'aa')], ) >>> mi.sort_values() MultiIndex([('a', 'aa'), ('a', 'bb'), ('b', 'aa'), ('b', 'bb')], ) """ if self.is_lexsorted() and self.is_monotonic: return self new_levels = [] new_codes = [] for lev, level_codes in zip(self.levels, self.codes): if not lev.is_monotonic: try: # indexer to reorder the levels indexer = lev.argsort() except TypeError: pass else: lev = lev.take(indexer) # indexer to reorder the level codes indexer = ensure_int64(indexer) ri = lib.get_reverse_indexer(indexer, len(indexer)) level_codes = algos.take_1d(ri, level_codes) new_levels.append(lev) new_codes.append(level_codes) return MultiIndex( new_levels, new_codes, names=self.names, sortorder=self.sortorder, verify_integrity=False, ) def remove_unused_levels(self): """ Create new MultiIndex from current that removes unused levels. Unused level(s) means levels that are not expressed in the labels. The resulting MultiIndex will have the same outward appearance, meaning the same .values and ordering. It will also be .equals() to the original. Returns ------- MultiIndex Examples -------- >>> mi = pd.MultiIndex.from_product([range(2), list('ab')]) >>> mi MultiIndex([(0, 'a'), (0, 'b'), (1, 'a'), (1, 'b')], ) >>> mi[2:] MultiIndex([(1, 'a'), (1, 'b')], ) The 0 from the first level is not represented and can be removed >>> mi2 = mi[2:].remove_unused_levels() >>> mi2.levels FrozenList([[1], ['a', 'b']]) """ new_levels = [] new_codes = [] changed = False for lev, level_codes in zip(self.levels, self.codes): # Since few levels are typically unused, bincount() is more # efficient than unique() - however it only accepts positive values # (and drops order): uniques = np.where(np.bincount(level_codes + 1) > 0)[0] - 1 has_na = int(len(uniques) and (uniques[0] == -1)) if len(uniques) != len(lev) + has_na: # We have unused levels changed = True # Recalculate uniques, now preserving order. # Can easily be cythonized by exploiting the already existing # "uniques" and stop parsing "level_codes" when all items # are found: uniques = algos.unique(level_codes) if has_na: na_idx = np.where(uniques == -1)[0] # Just ensure that -1 is in first position: uniques[[0, na_idx[0]]] = uniques[[na_idx[0], 0]] # codes get mapped from uniques to 0:len(uniques) # -1 (if present) is mapped to last position code_mapping = np.zeros(len(lev) + has_na) # ... and reassigned value -1: code_mapping[uniques] = np.arange(len(uniques)) - has_na level_codes = code_mapping[level_codes] # new levels are simple lev = lev.take(uniques[has_na:]) new_levels.append(lev) new_codes.append(level_codes) result = self.view() if changed: result._reset_identity() result._set_levels(new_levels, validate=False) result._set_codes(new_codes, validate=False) return result # -------------------------------------------------------------------- # Pickling Methods def __reduce__(self): """Necessary for making this object picklable""" d = dict( levels=list(self.levels), codes=list(self.codes), sortorder=self.sortorder, names=list(self.names), ) return ibase._new_Index, (type(self), d), None # -------------------------------------------------------------------- def __getitem__(self, key): if is_scalar(key): key = com.cast_scalar_indexer(key, warn_float=True) retval = [] for lev, level_codes in zip(self.levels, self.codes): if level_codes[key] == -1: retval.append(np.nan) else: retval.append(lev[level_codes[key]]) return tuple(retval) else: if com.is_bool_indexer(key): key = np.asarray(key, dtype=bool) sortorder = self.sortorder else: # cannot be sure whether the result will be sorted sortorder = None if isinstance(key, Index): key = np.asarray(key) new_codes = [level_codes[key] for level_codes in self.codes] return MultiIndex( levels=self.levels, codes=new_codes, names=self.names, sortorder=sortorder, verify_integrity=False, ) @Appender(_index_shared_docs["take"] % _index_doc_kwargs) def take(self, indices, axis=0, allow_fill=True, fill_value=None, **kwargs): nv.validate_take(tuple(), kwargs) indices = ensure_platform_int(indices) taken = self._assert_take_fillable( self.codes, indices, allow_fill=allow_fill, fill_value=fill_value, na_value=-1, ) return MultiIndex( levels=self.levels, codes=taken, names=self.names, verify_integrity=False ) def _assert_take_fillable( self, values, indices, allow_fill=True, fill_value=None, na_value=None ): """ Internal method to handle NA filling of take """ # only fill if we are passing a non-None fill_value if allow_fill and fill_value is not None: if (indices < -1).any(): msg = ( "When allow_fill=True and fill_value is not None, " "all indices must be >= -1" ) raise ValueError(msg) taken = [lab.take(indices) for lab in self.codes] mask = indices == -1 if mask.any(): masked = [] for new_label in taken: label_values = new_label label_values[mask] = na_value masked.append(np.asarray(label_values)) taken = masked else: taken = [lab.take(indices) for lab in self.codes] return taken def append(self, other): """ Append a collection of Index options together Parameters ---------- other : Index or list/tuple of indices Returns ------- appended : Index """ if not isinstance(other, (list, tuple)): other = [other] if all( (isinstance(o, MultiIndex) and o.nlevels >= self.nlevels) for o in other ): arrays = [] for i in range(self.nlevels): label = self._get_level_values(i) appended = [o._get_level_values(i) for o in other] arrays.append(label.append(appended)) return MultiIndex.from_arrays(arrays, names=self.names) to_concat = (self._values,) + tuple(k._values for k in other) new_tuples = np.concatenate(to_concat) # if all(isinstance(x, MultiIndex) for x in other): try: return MultiIndex.from_tuples(new_tuples, names=self.names) except (TypeError, IndexError): return Index(new_tuples) def argsort(self, *args, **kwargs) -> np.ndarray: return self._values.argsort(*args, **kwargs) @Appender(_index_shared_docs["repeat"] % _index_doc_kwargs) def repeat(self, repeats, axis=None): nv.validate_repeat(tuple(), dict(axis=axis)) repeats = ensure_platform_int(repeats) return MultiIndex( levels=self.levels, codes=[ level_codes.view(np.ndarray).astype(np.intp).repeat(repeats) for level_codes in self.codes ], names=self.names, sortorder=self.sortorder, verify_integrity=False, ) def where(self, cond, other=None): raise NotImplementedError(".where is not supported for MultiIndex operations") def drop(self, codes, level=None, errors="raise"): """ Make new MultiIndex with passed list of codes deleted Parameters ---------- codes : array-like Must be a list of tuples level : int or level name, default None errors : str, default 'raise' Returns ------- dropped : MultiIndex """ if level is not None: return self._drop_from_level(codes, level, errors) if not isinstance(codes, (np.ndarray, Index)): try: codes = com.index_labels_to_array(codes, dtype=object) except ValueError: pass inds = [] for level_codes in codes: try: loc = self.get_loc(level_codes) # get_loc returns either an integer, a slice, or a boolean # mask if isinstance(loc, int): inds.append(loc) elif isinstance(loc, slice): inds.extend(range(loc.start, loc.stop)) elif com.is_bool_indexer(loc): if self.lexsort_depth == 0: warnings.warn( "dropping on a non-lexsorted multi-index " "without a level parameter may impact performance.", PerformanceWarning, stacklevel=3, ) loc = loc.nonzero()[0] inds.extend(loc) else: msg = f"unsupported indexer of type {type(loc)}" raise AssertionError(msg) except KeyError: if errors != "ignore": raise return self.delete(inds) def _drop_from_level(self, codes, level, errors="raise"): codes = com.index_labels_to_array(codes) i = self._get_level_number(level) index = self.levels[i] values = index.get_indexer(codes) mask = ~algos.isin(self.codes[i], values) if mask.all() and errors != "ignore": raise KeyError(f"labels {codes} not found in level") return self[mask] def swaplevel(self, i=-2, j=-1): """ Swap level i with level j. Calling this method does not change the ordering of the values. Parameters ---------- i : int, str, default -2 First level of index to be swapped. Can pass level name as string. Type of parameters can be mixed. j : int, str, default -1 Second level of index to be swapped. Can pass level name as string. Type of parameters can be mixed. Returns ------- MultiIndex A new MultiIndex. See Also -------- Series.swaplevel : Swap levels i and j in a MultiIndex. Dataframe.swaplevel : Swap levels i and j in a MultiIndex on a particular axis. Examples -------- >>> mi = pd.MultiIndex(levels=[['a', 'b'], ['bb', 'aa']], ... codes=[[0, 0, 1, 1], [0, 1, 0, 1]]) >>> mi MultiIndex([('a', 'bb'), ('a', 'aa'), ('b', 'bb'), ('b', 'aa')], ) >>> mi.swaplevel(0, 1) MultiIndex([('bb', 'a'), ('aa', 'a'), ('bb', 'b'), ('aa', 'b')], ) """ new_levels = list(self.levels) new_codes = list(self.codes) new_names = list(self.names) i = self._get_level_number(i) j = self._get_level_number(j) new_levels[i], new_levels[j] = new_levels[j], new_levels[i] new_codes[i], new_codes[j] = new_codes[j], new_codes[i] new_names[i], new_names[j] = new_names[j], new_names[i] return MultiIndex( levels=new_levels, codes=new_codes, names=new_names, verify_integrity=False ) def reorder_levels(self, order): """ Rearrange levels using input order. May not drop or duplicate levels. Parameters ---------- order : list of int or list of str List representing new level order. Reference level by number (position) or by key (label). Returns ------- MultiIndex """ order = [self._get_level_number(i) for i in order] if len(order) != self.nlevels: raise AssertionError( f"Length of order must be same as number of levels ({self.nlevels}), " f"got {len(order)}" ) new_levels = [self.levels[i] for i in order] new_codes = [self.codes[i] for i in order] new_names = [self.names[i] for i in order] return MultiIndex( levels=new_levels, codes=new_codes, names=new_names, verify_integrity=False ) def _get_codes_for_sorting(self): """ we categorizing our codes by using the available categories (all, not just observed) excluding any missing ones (-1); this is in preparation for sorting, where we need to disambiguate that -1 is not a valid valid """ def cats(level_codes): return np.arange(

np.array(level_codes)

numpy.array

#! /usr/bin/env python import sys import time import random import argparse import itertools import numpy as np import baldor as br import raveutils as ru import robotsp as rtsp import openravepy as orpy from scipy.spatial import ConvexHull from lenny_openrave.manager import EnvironmentManager from lenny_openrave.scheduler import PDPScheduler from lenny_openrave.bimanual import BimanualPlanner def parse_args(): # Remove extra IPython notebook args clean_argv = sys.argv if "-f" in clean_argv: clean_argv = clean_argv[1:] # Parse format_class = argparse.RawDescriptionHelpFormatter parser = argparse.ArgumentParser(description="Lenny RoboTSP bimanual") parser.add_argument("-r", "--reachability", action="store_true", help="If set, will only show reachability") parser.add_argument("-s", "--seed", type=int, default=123, help="Seed for the random yaw of the cubes") parser.add_argument("-v", "--viewer", action="store_true", help="If set, will show the qtcoin viewer") parser.add_argument("--ik", action="store_true", help="If set, will only show the found IK solutions") return parser.parse_args() args = parse_args() np.set_printoptions(precision=6, suppress=True) # Load the environment env = orpy.Environment() world_xml = "worlds/bimanual_pick_and_place.env.xml" if not env.Load(world_xml): raise Exception("Failed to load world: {}".format(world_xml)) robot = env.GetRobot("robot") robot.SetDOFValues(np.zeros(robot.GetDOF())) # Environment manager eman = EnvironmentManager(env, num_cubes=8, seed=args.seed) cubes = eman.get_cubes() bins = eman.get_bins() # Initialize the bimanual planner bimanual = BimanualPlanner(robot) bimanual.set_left_manipulator("arm_left_tool0") bimanual.set_right_manipulator("arm_right_tool0") bimanual.set_torso_joint("torso_joint_b1") if not bimanual.load_ikfast(freeinc=np.pi / 6.): print("Failed to load IKFast. Run the generate_robot_databases.sh script.") exit(0) # Start and configure the viewer if args.viewer: viewer_name = "qtcoin" print("Starting viewer: {0}".format(viewer_name)) eman.start_viewer(viewer_name) if args.reachability: # Reachability. One arm is enough due to symmetry print ("Computing reachable workspace...") indices = np.zeros(3) indices[1:] = bimanual.left_indices[:2] manip = bimanual.left_manip Toffset =

np.eye(4)

numpy.eye

import os, glob import subprocess from os import listdir from os.path import isfile, join import time import traceback import shutil import numpy as np import csv import time def checkForUpdate(count, lastUpdate): sn = os.environ['SERVERNUM'] hdfs = os.environ['HDFS'] updateCount = -1 print("UPDATE CHECK: SERVER") print([count, lastUpdate]) while(updateCount == -1): time.sleep(10) print('Checking') for i in range(lastUpdate+1, count): print([i,count]) print("In Check "+str(i)) out = os.popen('/opt/hadoop/bin/hadoop fs -test -e hdfs://'+hdfs+':9000/server_'+ sn+'/run_'+str(i)+'/knndata && echo $?').read() try: if(int(out) == 0): updateCount = i print("Update Ready: "+str(i)) except: traceback.print_exc() print("Update Not Ready") break; if(updateCount > -1): try: os.remove('knndatasetGI') except: pass out = os.popen('/opt/hadoop/bin/hadoop fs -copyToLocal hdfs://'+hdfs+':9000/server_'+ sn+'/run_'+str(updateCount)+'/knndata knndatasetGI').read() return updateCount def updateLocal(): pwd = os.getcwd() print(pwd) knndata = np.genfromtxt('knndatasetGI',delimiter=',') os.chdir(pwd+'/tmp/') for f in glob.glob('*'): print(f) for f in glob.glob('*.JPG'): fname = f.split('.')[0] #cmd = 'bash '+pwd+'/Parser/runParser.sh '+pwd+'/tmp/'+str(i)+'/'+f #print(cmd) #out = os.popen(cmd).read().rstrip()[1:-1].split(',') #line = [] #for feat in out: # line.append(float(feat.split('=')[1])) data = [] with open(pwd+'/tmp/'+fname+'.csv') as csvf: reader = csv.reader(csvf) data = list(reader)[0] line = [] for d in data: line.append(float(d)) #print(line) npl =

np.asarray(line)

numpy.asarray

"""Unit tests for probsevere_io.py.""" import copy import unittest import numpy import pandas from gewittergefahr.gg_io import probsevere_io from gewittergefahr.gg_utils import storm_tracking_utils as tracking_utils TOP_DIRECTORY_NAME = 'foo' FTP_DIRECTORY_NAME = 'bar' VALID_TIME_UNIX_SEC = 1507181187 # 052627 5 Oct 2017 PATHLESS_JSON_FILE_NAME = 'SSEC_AWIPS_PROBSEVERE_20171005_052627.json' PATHLESS_ASCII_FILE_NAME = 'SSEC_AWIPS_PROBSEVERE_20171005_052627.ascii' JSON_FILE_NAME = ( 'foo/201710/20171005/SSEC_AWIPS_PROBSEVERE_20171005_052627.json' ) ASCII_FILE_NAME = ( 'foo/201710/20171005/SSEC_AWIPS_PROBSEVERE_20171005_052627.ascii' ) ALTERNATIVE_JSON_FILE_NAME = ( 'foo/201710/20171005/SSEC_AWIPS_CONVECTPROB_20171005_052627.json' ) ALTERNATIVE_ASCII_FILE_NAME = ( 'foo/201710/20171005/SSEC_AWIPS_CONVECTPROB_20171005_052627.ascii' ) JSON_FILE_NAME_ON_FTP = 'bar/SSEC_AWIPS_PROBSEVERE_20171005_052627.json' # The following constants are used to test # _get_dates_needed_for_renaming_storms. NUM_DATES_IN_PERIOD = 20 WORKING_DATE_INDEX_MIDDLE = 10 DATE_NEEDED_INDICES_START = numpy.array([0, 1], dtype=int) DATE_NEEDED_INDICES_END = numpy.array([18, 19], dtype=int) DATE_NEEDED_INDICES_MIDDLE = numpy.array([9, 10, 11], dtype=int) # The following constants are used to test _rename_storms_one_original_id. STORM_TIMES_UNIX_SEC = numpy.array( [0, 1, 2, 3, 6, 7, 8, 9, 12, 15], dtype=int ) NEXT_ID_NUMBER = 5 MAX_DROPOUT_TIME_SECONDS = 2 STORM_ID_STRINGS = [ '5probSevere', '5probSevere', '5probSevere', '5probSevere', '6probSevere', '6probSevere', '6probSevere', '6probSevere', '7probSevere', '8probSevere' ] NEXT_ID_NUMBER_AFTER_ONE_ORIG_ID = 9 # The following constants are used to test _rename_storms_one_table. WORKING_DATE_INDEX_FOR_TABLE = 1 THESE_ID_STRINGS = [ 'a', 'b', 'c', 'b', 'd', 'a', 'b', 'd', 'a', 'b', 'c' ] THESE_TIMES_UNIX_SEC =

numpy.array([0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3], dtype=int)

numpy.array

""" Copyright (C) 2018-2020 Intel Corporation Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. """ import numpy as np from mo.front.common.partial_infer.utils import int64_array from mo.front.extractor import FrontExtractorOp from mo.ops.pooling import Pooling from extensions.ops.adaptive_avg_pooling import AdaptiveAvgPooling from mo.utils.error import Error from .common import get_pads class MaxPool2dFrontExtractor(FrontExtractorOp): op = 'MaxPool2d' enabled = True @classmethod def extract(cls, node): # Extract pads attribute final_pads = get_pads(node.module) # Extract strides attribute strides = [node.module.stride, node.module.stride] final_strides = np.array([1, 1, *strides], dtype=np.int64) kernel_shape = [node.module.kernel_size, node.module.kernel_size] final_kernel_shape = np.array([1, 1, *kernel_shape], dtype=np.int64) attrs = { 'op': node.op, 'window': final_kernel_shape, 'stride': final_strides, 'pad': final_pads, 'pool_method': 'max', 'channel_dims': np.array([1], dtype=np.int64), 'batch_dims': np.array([0], dtype=np.int64), 'layout': 'NCHW', } if (node.module.ceil_mode): attrs['rounding_type'] = 'ceil' # update the attributes of the node Pooling.update_node_stat(node, attrs) return cls.enabled class AdaptiveAvgPool2dFrontExtractor(FrontExtractorOp): op = 'AdaptiveAvgPool2d' enabled = True @classmethod def extract(cls, node): output_size = node.module.output_size # If a single integer but not a tuple or list if not hasattr(output_size, '__contains__'): output_size = [output_size, output_size] data = { 'output_size': output_size, } AdaptiveAvgPooling.update_node_stat(node, data) return cls.enabled class AvgPool2dFrontExtractor(FrontExtractorOp): op = 'AvgPool2d' enabled = True @classmethod def extract(cls, node): # Extract pads attribute final_pads = get_pads(node.module) # Extract strides attribute strides = [node.module.stride, node.module.stride] final_strides = np.array([1, 1, *strides], dtype=np.int64) kernel_shape = [node.module.kernel_size, node.module.kernel_size] final_kernel_shape =

np.array([1, 1, *kernel_shape], dtype=np.int64)

numpy.array

# ---------------------------------------------------------------------------- # Copyright 2014-2016 Nervana Systems Inc. # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ---------------------------------------------------------------------------- """ Our CPU based backend interface and tensor data structure. Our implementation wraps :mod:`numpy` ndarray and related operations """ from __future__ import division from builtins import object, round, str, zip import numpy as np import logging import time from neon.backends.backend import Tensor, Backend, OpTreeNode, OpCollection from neon.backends.layer_cpu import ConvLayer, DeconvLayer, PoolLayer from neon.util.compat import xrange _none_slice = slice(None, None, None) logger = logging.getLogger(__name__) # TODO: enable this flag to find numerical problems # np.seterr(all='raise') class CPUTensor(Tensor): """ The n-dimensional array data structure that resides in host memory, and is meant to be manipulated on the CPU. wrapped `numpy.ndarray` tensor. Arguments: dtype (numpy.ndtype, optional): underlying data type of the elements. ary (data array, optional): optionally it can be instantiated with a data array persist_values (bool, optional): If set to True (the default), the values assigned to this Tensor will persist across multiple begin and end calls. Setting to False may provide a performance increase if values do not need to be maintained across such calls See also: :class:`NervanaCPU` class """ _tensor = None def __init__(self, backend, shape=None, dtype=np.float32, ary=None, name=None, persist_values=True, base=None): super(CPUTensor, self).__init__(backend, shape, dtype, name, persist_values) # supported dtypes assert dtype in (np.float16, np.float32, np.float64, np.uint8, np.int8, np.uint16, np.int16, np.uint32, np.int32) dtype = np.dtype(dtype) if type(ary) != np.ndarray: self._tensor = np.array(ary, dtype) elif ary.dtype != dtype: self._tensor = ary.astype(dtype) else: self._tensor = ary while self._tensor.ndim < self._min_dims: self._tensor = self._tensor.reshape(self._tensor.shape + (1, )) if shape is not None and len(shape) < self._min_dims: self.shape = shape + (1, )*(self._min_dims - len(shape)) else: self.shape = self._tensor.shape shape_ = [] size = 1 for dim in self.shape: if int(dim) != dim: raise TypeError('shape dims must be integer values [%s]' % str(dim)) dim = int(dim) shape_.append(dim) size *= dim self.shape = tuple(shape_) self.size = size self.base = base self.dtype = dtype self.is_contiguous = self._tensor.flags.c_contiguous def __str__(self): """ Returns a string representation of this Tensor. Returns: str: the representation. """ if self._tensor.base is not None: base_id = id(self._tensor.base) else: base_id = id(self._tensor) return ("CPUTensor(base 0x%x) name:%s shape:%s dtype:%s strides:%s" " is_c_contiguous:%s" % (base_id, self.name, self.shape, self.dtype, self._tensor.strides, self._tensor.flags.c_contiguous)) def __repr__(self): """ Returns a more unambiguous string representation of the Tensor. Returns: str: the representation. """ return self.__str__() def __len__(self): """ Return the size of the leading dimension of self. """ if len(self.shape): return self.shape[0] else: return 0 def __setitem__(self, key, value): """ Assign the specified value to a subset of elements found via slice style indexing along each dimension. e.g. A[5:10, :] = 4.5. Each slice consists of start_idx:stop_idx:step_size triplets. If step_size isn't specified it defaults to 1. If start_idx isn't specified it defaults to 0. If stop_idx isn't specified it defaults to the total number of elements along that dimension. As such a slice value of ':' allows one to select all elements along that dimension. Arguments: key (int, slice, tuple): indices of each dimension's slice. value (numeric array, CPUTensor): values to be assigned to the extracted element subset. If an array it should be the same shape as what key indexes (or be broadcastable as such). """ self.__getitem__(key)._assign(value) return self def __getitem__(self, key): """ Extract a subset view of the items via slice style indexing along each dimension. e.g. A[5:10, :]. Each slice consists of start_idx:stop_idx:step_size triplets. If step_size isn't specified it defaults to 1. If start_idx isn't specified it defaults to 0. If stop_idx isn't specified it defaults to the total number of elements along that dimension. As such a slice value of ':' allows one to select all elements along that dimension. To be consistent with GPU Tensors, CPU Tensors remove the axis that has size 1 unless it needs to maintain 2D. Arguments: key (int, slice, tuple): indices of each dimension's slice. Returns: CPUTensor: view of self corresponding to the subset items. """ # speed up common case of [:] if not isinstance(key, tuple): if key == _none_slice: return self key = (key,) # ensure we return a view # exact same behavior as cpu # let a.shape = (3,4) # a[1,1] = 10 # cpu, gpu and numpy # type(a[1,1]) # for cpu and gpu type is Tensor; for numpy type is float key_list = list(key) for idx, k in enumerate(key): if type(k) is int: k = self.shape[idx] + k if k < 0 else k key_list[idx] = slice(k, k + 1, None) key = tuple(key_list) new_shape = list(self._tensor[key].shape) for idx, k in enumerate(new_shape): if len(new_shape) > 2 and k is 1: new_shape.remove(k) # return a view of the tensor return self.__class__( backend=self.backend, ary=self._tensor[key].reshape(new_shape), dtype=self._tensor.dtype, base=self) def _assign(self, value): """ Assign an input value to the CPU tensor. The NervanaCPU does clipping for int and uint types, when overflow happens Arguments: value (CPUTensor, OpTreeNode, numeric): the value to be assigned. """ if isinstance(value, (CPUTensor, OpTreeNode)): OpTreeNode.build("assign", self, value) elif isinstance(value, (int, float, np.ndarray)): self.set(value) else: raise TypeError("Invalid type for assignment: %s" % type(value)) return self def set(self, value): """ Wrap the value into NervanaCPU tensor. Arguments: value: Array or single input. If it is array, check and Convert the dtype and shape. If it is single value, broadcast to the memory Returns: self """ if isinstance(value, np.ndarray): if value.dtype is not self.dtype: value = value.astype(self.dtype) assert value.size == self.size if value.ndim < self._min_dims: value = value.reshape(self.shape) self._tensor[:] = value return self def get(self): """ Return the array. """ return self._tensor.copy() def raw(self): """ Access the raw buffer. Returns: pointer: A device specific pointer """ return self._tensor.ctypes.data def asnumpyarray(self): """ Deprecated. Scheduled to be removed in 2.0. Use get() instead. """ return self._tensor def take(self, indices, axis=None): """ Select a subset of elements from an array across an axis. Arguments: indices (Tensor, numpy ndarray): indicies of elements to select axis (int): axis across which to select the values Returns: Tensor: Tensor with selected values """ if type(indices) == self.__class__: indices = indices._tensor # if indices are nx1 or 1xn, much of our code assumes these dims are # collapsed, hence the squeeze call. if type(indices) == np.ndarray: indices = indices.squeeze() new_shape = list(self.shape) new_shape[axis] = indices.size return self.__class__( backend=self.backend, ary=self._tensor.take(indices, axis).reshape(new_shape), dtype=self._tensor.dtype, base=self) def fill(self, value): """ Assign specified value to each element of this CPUTensor. Arguments: value (numeric): The value to be assigned to each element. Return: CPUTensor: updated view of the data. """ self._tensor.fill(value) return self def copy(self, a): """ Construct and return a deep copy of the Tensor passed. Arguments: a (Tensor): the object to copy Returns: Tensor: new array object with the same values as input tensor """ return self._assign(a) def copy_from(self, a): """ Alias of copy. Arguments: a (Tensor): the object to copy Returns: Tensor: new array object with the same values as input tensor """ return self._assign(a) def reshape(self, *shape): """ Return a reshaped view. """ if isinstance(shape[0], (tuple, list)): shape = tuple(shape[0]) if shape == self.shape: return self return self.__class__( backend=self.backend, ary=self._tensor.reshape(shape), dtype=self._tensor.dtype, base=self) @property def T(self): """ Return a transposed view. For 2D tensor, will do a normal transpose For 3D tensor, will keep the 0 dim, swap the 1 and 2 dimensions """ if len(self.shape) <= 2: ary = self._tensor.transpose() else: # support for batched dot. # perserve outer dimension but reverse inner dims # shape = np.concatenate((shape[-1:], shape[:-1]) ary = self._tensor.swapaxes(1, 2) return self.__class__( backend=self.backend, ary=ary, dtype=self._tensor.dtype, base=self) def transpose(self, out=None): """ Return a transposed view of the data. Alias of .T property """ if out: return OpTreeNode.build("assign", out, self.T) return self.T def share(self, shape, dtype=None, name=None): """ Return a view: ary, where ary.size <= self.size. Allows easy sharing of temporary memory This is mostly provided for compatibility, -- dtype is ignored """ size =

np.prod(shape)

numpy.prod

from typing import Dict, Tuple import pandas as pd import numpy as np import attr from itertools import chain @attr.s(slots=True) class MScanLineValidator: sig_val = attr.ib() # SignalValidator def __getattr__(self, item): return getattr(self.sig_val, item) def run(self) -> Tuple[Dict, np.uint64]: """ Interpolate MScan-specific line signals :return: Dictionary containing the data and the mean difference between subsequent lines """ lines = self.dict_of_data["Lines"].loc[:, "abs_time"].copy() rel_idx, delta = self.__calc_line_parameters(lines=lines) lines, rel_idx, delta = self.__filter_extra_lines(lines=lines, delta=delta) if len(rel_idx) > 0: # missing lines, not just extra theo_lines = self.__gen_line_model(lines=lines, m=delta) lines = self.__diff_vec_analysis(lines=lines, y=theo_lines, delta=delta) lines = self.__finalize_lines(lines=lines, delta=delta) if self.bidir: lines = self.sig_val.add_phase_to_bidir_lines(lines=lines) self.dict_of_data["Lines"] = pd.DataFrame( lines, dtype=np.uint64, columns=["abs_time"] ) return self.dict_of_data, delta def __calc_line_parameters(self, lines: pd.Series) -> Tuple[np.ndarray, np.uint64]: """ Generate general parameters of the given acquisition """ rel_idx = np.where( np.abs(lines.diff().pct_change(periods=1)) > self.change_thresh )[0] delta = np.uint64( lines.drop(rel_idx) .reindex(np.arange(len(lines))) .interpolate() .diff() .mean() ) return rel_idx[::2], delta def __filter_extra_lines( self, lines: pd.Series, delta: np.uint64 ) -> Tuple[pd.Series, pd.Series, np.uint64]: """ Kick out excess line signals :param lines: :param delta: :return: Tuple of valid lines, missing lines and new delta of lines """ diffs = lines.diff() rel_idx = np.where(np.abs(diffs.pct_change(periods=1)) > self.change_thresh)[0] recurring = np.where(np.diff(rel_idx) == 1)[0] idx_to_keep = np.ones_like(rel_idx, dtype=bool) for idx, _ in enumerate(recurring[1:], 1): try: if recurring[idx] - recurring[idx - 1] == 1: idx_to_keep[recurring[idx] + 1] = False except IndexError: pass rel_idx_new = pd.Series(rel_idx[idx_to_keep][::2], dtype=np.uint64) missing_lines = [] extra_lines = [] for idx in rel_idx_new: if diffs[idx] < (delta / 2): # excess lines extra_lines.append(idx) else: missing_lines.append(idx) valid_lines = lines.drop(extra_lines).reset_index(drop=True) delta = np.uint64(valid_lines.drop(missing_lines).diff().mean()) # Get rid of lines that came after the last frame num_of_extra_lines = len(valid_lines) % self.num_of_lines valid_lines = valid_lines[:-num_of_extra_lines] return valid_lines, pd.Series(missing_lines), delta def __gen_line_model(self, lines: pd.Series, m: np.uint64) -> np.ndarray: """ Using linear approximation generate a model for the "correct" line signal """ const = lines.iloc[0] x = np.arange(start=0, stop=len(lines), dtype=np.uint64) y = m * x + const if len(lines) > 1500: # correct simulated lines idx_range = np.arange(1500, len(lines), step=1500, dtype=np.uint64) for idx in idx_range: x = np.arange(0, len(lines) - idx, dtype=np.uint64) y[idx:] = m * x + lines.iloc[idx] # MScan's lines are evenly separated first_diff = np.uint64(lines.iloc[2:110].diff()[1::2].median()) delta_diff = np.int32((m - first_diff) / 2) if first_diff < m: y[1::2] -= delta_diff y[::2] += delta_diff else: y[1::2] += delta_diff y[::2] -= delta_diff return y def __diff_vec_analysis( self, y: np.ndarray, lines: pd.Series, delta: np.uint64 ) -> pd.Series: diff_vec = np.abs(np.subtract(y, lines, dtype=np.int64)) missing_val = np.where(diff_vec > delta / 20)[0] while missing_val.shape[0] > 0: if np.abs(diff_vec[missing_val[0]] - delta) / delta < 0.1: # double line lines = np.concatenate( (lines[: missing_val[0]], lines[missing_val[0] + 1 :]) ) else: lines = np.concatenate( ( lines[: missing_val[0]], np.atleast_1d(y[missing_val[0]]), lines[missing_val[0] :], ) ) # Restart the loop y = self.__gen_line_model(pd.Series(lines), delta) diff_vec = np.abs(

np.subtract(y, lines, dtype=np.int64)

numpy.subtract

from pathlib import Path from typing import Optional import numpy as np from cclib.io import ccopen from cclib.parser.utils import convertor import pyscf from pyresponse import cphf, operators, solvers, utils from pyresponse.core import AO2MOTransformationType, Hamiltonian, Spin from pyresponse.dalton.utils import dalton_label_to_operator from pyresponse.pyscf.ao2mo import AO2MOpyscf try: from daltools import mol as dalmol from daltools import sirifc except: pass def calculate_disk_rhf( testcasedir: Path, hamiltonian: str, spin: str, frequency: str, label_1: str, label_2: str, ) -> float: occupations = utils.read_file_occupations(testcasedir / "occupations") nocc_alph, nvirt_alph, nocc_beta, nvirt_beta = occupations assert nocc_alph == nocc_beta assert nvirt_alph == nvirt_beta norb = nocc_alph + nvirt_alph C = utils.read_file_3(testcasedir / "C") assert C.shape[0] == 1 assert C.shape[2] == norb nbasis = C.shape[1] moene = utils.read_file_2(testcasedir / "moene") assert moene.shape == (norb, 1) moints_iajb_aaaa = utils.read_file_4(testcasedir / "moints_iajb_aaaa") moints_ijab_aaaa = utils.read_file_4(testcasedir / "moints_ijab_aaaa") assert moints_iajb_aaaa.shape == (nocc_alph, nvirt_alph, nocc_alph, nvirt_alph) assert moints_ijab_aaaa.shape == (nocc_alph, nocc_alph, nvirt_alph, nvirt_alph) operator_1 = dalton_label_to_operator(label_1) operator_2 = dalton_label_to_operator(label_2) operator_1_integrals_mn = utils.read_file_3(testcasedir / f"operator_mn_{operator_1.label}") operator_2_integrals_mn = utils.read_file_3(testcasedir / f"operator_mn_{operator_2.label}") # The first dimension can"t be checked since there may be multiple # components. assert operator_1_integrals_mn.shape[1:] == (nbasis, nbasis) assert operator_2_integrals_mn.shape[1:] == (nbasis, nbasis) # Only take the component/slice from the integral as determined # from the DALTON operator label. operator_1_integrals_mn = operator_1_integrals_mn[operator_1.slice_idx] operator_2_integrals_mn = operator_2_integrals_mn[operator_2.slice_idx] # However, this eliminates an axis, which needs to be added back. operator_1_integrals_mn = operator_1_integrals_mn[np.newaxis, ...] operator_2_integrals_mn = operator_2_integrals_mn[np.newaxis, ...] operator_1.ao_integrals = operator_1_integrals_mn operator_2.ao_integrals = operator_2_integrals_mn moene = np.diag(moene[:, 0])[np.newaxis, ...] assert moene.shape == (1, norb, norb) solver = solvers.ExactInv(C, moene, occupations) solver.tei_mo = (moints_iajb_aaaa, moints_ijab_aaaa) solver.tei_mo_type = AO2MOTransformationType.partial driver = cphf.CPHF(solver) driver.add_operator(operator_1) driver.add_operator(operator_2) driver.set_frequencies([float(frequency)]) driver.run( hamiltonian=Hamiltonian[hamiltonian.upper()], spin=Spin[spin], program=None, program_obj=None, ) assert len(driver.frequencies) == len(driver.results) == 1 res = driver.results[0] assert res.shape == (2, 2) bl = res[1, 0] tr = res[0, 1] diff = abs(abs(bl) - abs(tr)) # Results should be symmetric w.r.t. interchange between operators # in the LR equations. thresh = 1.0e-13 assert diff < thresh return bl def calculate_disk_uhf( testcasedir: Path, hamiltonian: str, spin: str, frequency: str, label_1: str, label_2: str, ) -> float: occupations = utils.read_file_occupations(testcasedir / "occupations") nocc_alph, nvirt_alph, nocc_beta, nvirt_beta = occupations norb = nocc_alph + nvirt_alph C = utils.read_file_3(testcasedir / "C") assert C.shape[0] == 2 assert C.shape[2] == norb nbasis = C.shape[1] moene = utils.read_file_2(testcasedir / "moene") assert moene.shape == (norb, 2) moints_iajb_aaaa = utils.read_file_4(testcasedir / "moints_iajb_aaaa") moints_iajb_aabb = utils.read_file_4(testcasedir / "moints_iajb_aabb") moints_iajb_bbaa = utils.read_file_4(testcasedir / "moints_iajb_bbaa") moints_iajb_bbbb = utils.read_file_4(testcasedir / "moints_iajb_bbbb") moints_ijab_aaaa = utils.read_file_4(testcasedir / "moints_ijab_aaaa") moints_ijab_bbbb = utils.read_file_4(testcasedir / "moints_ijab_bbbb") assert moints_iajb_aaaa.shape == (nocc_alph, nvirt_alph, nocc_alph, nvirt_alph) assert moints_iajb_aabb.shape == (nocc_alph, nvirt_alph, nocc_beta, nvirt_beta) assert moints_iajb_bbaa.shape == (nocc_beta, nvirt_beta, nocc_alph, nvirt_alph) assert moints_iajb_bbbb.shape == (nocc_beta, nvirt_beta, nocc_beta, nvirt_beta) assert moints_ijab_aaaa.shape == (nocc_alph, nocc_alph, nvirt_alph, nvirt_alph) assert moints_ijab_bbbb.shape == (nocc_beta, nocc_beta, nvirt_beta, nvirt_beta) operator_1 = dalton_label_to_operator(label_1) operator_2 = dalton_label_to_operator(label_2) operator_1_integrals_mn = utils.read_file_3(testcasedir / f"operator_mn_{operator_1.label}") operator_2_integrals_mn = utils.read_file_3(testcasedir / f"operator_mn_{operator_2.label}") # The first dimension can"t be checked since there may be multiple # components. assert operator_1_integrals_mn.shape[1:] == (nbasis, nbasis) assert operator_2_integrals_mn.shape[1:] == (nbasis, nbasis) # Only take the component/slice from the integral as determined # from the DALTON operator label. operator_1_integrals_mn = operator_1_integrals_mn[operator_1.slice_idx] operator_2_integrals_mn = operator_2_integrals_mn[operator_2.slice_idx] # However, this eliminates an axis, which needs to be added back. operator_1_integrals_mn = operator_1_integrals_mn[np.newaxis, ...] operator_2_integrals_mn = operator_2_integrals_mn[np.newaxis, ...] operator_1.ao_integrals = operator_1_integrals_mn operator_2.ao_integrals = operator_2_integrals_mn moene_alph =

np.diag(moene[:, 0])

numpy.diag

# This module has been generated automatically from space group information # obtained from the Computational Crystallography Toolbox # """ Space groups This module contains a list of all the 230 space groups that can occur in a crystal. The variable space_groups contains a dictionary that maps space group numbers and space group names to the corresponding space group objects. .. moduleauthor:: <NAME> <<EMAIL>> """ #----------------------------------------------------------------------------- # Copyright (C) 2013 The Mosaic Development Team # # Distributed under the terms of the BSD License. The full license is in # the file LICENSE.txt, distributed as part of this software. #----------------------------------------------------------------------------- import numpy as N class SpaceGroup(object): """ Space group All possible space group objects are created in this module. Other modules should access these objects through the dictionary space_groups rather than create their own space group objects. """ def __init__(self, number, symbol, transformations): """ :param number: the number assigned to the space group by international convention :type number: int :param symbol: the Hermann-Mauguin space-group symbol as used in PDB and mmCIF files :type symbol: str :param transformations: a list of space group transformations, each consisting of a tuple of three integer arrays (rot, tn, td), where rot is the rotation matrix and tn/td are the numerator and denominator of the translation vector. The transformations are defined in fractional coordinates. :type transformations: list """ self.number = number self.symbol = symbol self.transformations = transformations self.transposed_rotations = N.array([N.transpose(t[0]) for t in transformations]) self.phase_factors = N.exp(N.array([(-2j*N.pi*t[1])/t[2] for t in transformations])) def __repr__(self): return "SpaceGroup(%d, %s)" % (self.number, repr(self.symbol)) def __len__(self): """ :return: the number of space group transformations :rtype: int """ return len(self.transformations) def symmetryEquivalentMillerIndices(self, hkl): """ :param hkl: a set of Miller indices :type hkl: Scientific.N.array_type :return: a tuple (miller_indices, phase_factor) of two arrays of length equal to the number of space group transformations. miller_indices contains the Miller indices of each reflection equivalent by symmetry to the reflection hkl (including hkl itself as the first element). phase_factor contains the phase factors that must be applied to the structure factor of reflection hkl to obtain the structure factor of the symmetry equivalent reflection. :rtype: tuple """ hkls = N.dot(self.transposed_rotations, hkl) p = N.multiply.reduce(self.phase_factors**hkl, -1) return hkls, p space_groups = {} transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(1, 'P 1', transformations) space_groups[1] = sg space_groups['P 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(2, 'P -1', transformations) space_groups[2] = sg space_groups['P -1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(3, 'P 1 2 1', transformations) space_groups[3] = sg space_groups['P 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(4, 'P 1 21 1', transformations) space_groups[4] = sg space_groups['P 1 21 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(5, 'C 1 2 1', transformations) space_groups[5] = sg space_groups['C 1 2 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(6, 'P 1 m 1', transformations) space_groups[6] = sg space_groups['P 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(7, 'P 1 c 1', transformations) space_groups[7] = sg space_groups['P 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(8, 'C 1 m 1', transformations) space_groups[8] = sg space_groups['C 1 m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(9, 'C 1 c 1', transformations) space_groups[9] = sg space_groups['C 1 c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(10, 'P 1 2/m 1', transformations) space_groups[10] = sg space_groups['P 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(11, 'P 1 21/m 1', transformations) space_groups[11] = sg space_groups['P 1 21/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(12, 'C 1 2/m 1', transformations) space_groups[12] = sg space_groups['C 1 2/m 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(13, 'P 1 2/c 1', transformations) space_groups[13] = sg space_groups['P 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(14, 'P 1 21/c 1', transformations) space_groups[14] = sg space_groups['P 1 21/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(15, 'C 1 2/c 1', transformations) space_groups[15] = sg space_groups['C 1 2/c 1'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(16, 'P 2 2 2', transformations) space_groups[16] = sg space_groups['P 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(17, 'P 2 2 21', transformations) space_groups[17] = sg space_groups['P 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(18, 'P 21 21 2', transformations) space_groups[18] = sg space_groups['P 21 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(19, 'P 21 21 21', transformations) space_groups[19] = sg space_groups['P 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(20, 'C 2 2 21', transformations) space_groups[20] = sg space_groups['C 2 2 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(21, 'C 2 2 2', transformations) space_groups[21] = sg space_groups['C 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(22, 'F 2 2 2', transformations) space_groups[22] = sg space_groups['F 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(23, 'I 2 2 2', transformations) space_groups[23] = sg space_groups['I 2 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(24, 'I 21 21 21', transformations) space_groups[24] = sg space_groups['I 21 21 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(25, 'P m m 2', transformations) space_groups[25] = sg space_groups['P m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(26, 'P m c 21', transformations) space_groups[26] = sg space_groups['P m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(27, 'P c c 2', transformations) space_groups[27] = sg space_groups['P c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(28, 'P m a 2', transformations) space_groups[28] = sg space_groups['P m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(29, 'P c a 21', transformations) space_groups[29] = sg space_groups['P c a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(30, 'P n c 2', transformations) space_groups[30] = sg space_groups['P n c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(31, 'P m n 21', transformations) space_groups[31] = sg space_groups['P m n 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(32, 'P b a 2', transformations) space_groups[32] = sg space_groups['P b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(33, 'P n a 21', transformations) space_groups[33] = sg space_groups['P n a 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(34, 'P n n 2', transformations) space_groups[34] = sg space_groups['P n n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(35, 'C m m 2', transformations) space_groups[35] = sg space_groups['C m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(36, 'C m c 21', transformations) space_groups[36] = sg space_groups['C m c 21'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(37, 'C c c 2', transformations) space_groups[37] = sg space_groups['C c c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(38, 'A m m 2', transformations) space_groups[38] = sg space_groups['A m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(39, 'A b m 2', transformations) space_groups[39] = sg space_groups['A b m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(40, 'A m a 2', transformations) space_groups[40] = sg space_groups['A m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(41, 'A b a 2', transformations) space_groups[41] = sg space_groups['A b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(42, 'F m m 2', transformations) space_groups[42] = sg space_groups['F m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(43, 'F d d 2', transformations) space_groups[43] = sg space_groups['F d d 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(44, 'I m m 2', transformations) space_groups[44] = sg space_groups['I m m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(45, 'I b a 2', transformations) space_groups[45] = sg space_groups['I b a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(46, 'I m a 2', transformations) space_groups[46] = sg space_groups['I m a 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(47, 'P m m m', transformations) space_groups[47] = sg space_groups['P m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(48, 'P n n n :2', transformations) space_groups[48] = sg space_groups['P n n n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(49, 'P c c m', transformations) space_groups[49] = sg space_groups['P c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(50, 'P b a n :2', transformations) space_groups[50] = sg space_groups['P b a n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(51, 'P m m a', transformations) space_groups[51] = sg space_groups['P m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(52, 'P n n a', transformations) space_groups[52] = sg space_groups['P n n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(53, 'P m n a', transformations) space_groups[53] = sg space_groups['P m n a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(54, 'P c c a', transformations) space_groups[54] = sg space_groups['P c c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(55, 'P b a m', transformations) space_groups[55] = sg space_groups['P b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(56, 'P c c n', transformations) space_groups[56] = sg space_groups['P c c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(57, 'P b c m', transformations) space_groups[57] = sg space_groups['P b c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(58, 'P n n m', transformations) space_groups[58] = sg space_groups['P n n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(59, 'P m m n :2', transformations) space_groups[59] = sg space_groups['P m m n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(60, 'P b c n', transformations) space_groups[60] = sg space_groups['P b c n'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(61, 'P b c a', transformations) space_groups[61] = sg space_groups['P b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(62, 'P n m a', transformations) space_groups[62] = sg space_groups['P n m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(63, 'C m c m', transformations) space_groups[63] = sg space_groups['C m c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(64, 'C m c a', transformations) space_groups[64] = sg space_groups['C m c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(65, 'C m m m', transformations) space_groups[65] = sg space_groups['C m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(66, 'C c c m', transformations) space_groups[66] = sg space_groups['C c c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(67, 'C m m a', transformations) space_groups[67] = sg space_groups['C m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(68, 'C c c a :2', transformations) space_groups[68] = sg space_groups['C c c a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(69, 'F m m m', transformations) space_groups[69] = sg space_groups['F m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,3,3]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,0,3]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([4,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,1]) trans_den = N.array([4,4,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,3,1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([3,1,1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([2,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,-1]) trans_den = N.array([4,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([4,4,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(70, 'F d d d :2', transformations) space_groups[70] = sg space_groups['F d d d :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(71, 'I m m m', transformations) space_groups[71] = sg space_groups['I m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(72, 'I b a m', transformations) space_groups[72] = sg space_groups['I b a m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(73, 'I b c a', transformations) space_groups[73] = sg space_groups['I b c a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(74, 'I m m a', transformations) space_groups[74] = sg space_groups['I m m a'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(75, 'P 4', transformations) space_groups[75] = sg space_groups['P 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(76, 'P 41', transformations) space_groups[76] = sg space_groups['P 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(77, 'P 42', transformations) space_groups[77] = sg space_groups['P 42'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(78, 'P 43', transformations) space_groups[78] = sg space_groups['P 43'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(79, 'I 4', transformations) space_groups[79] = sg space_groups['I 4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(80, 'I 41', transformations) space_groups[80] = sg space_groups['I 41'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(81, 'P -4', transformations) space_groups[81] = sg space_groups['P -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(82, 'I -4', transformations) space_groups[82] = sg space_groups['I -4'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(83, 'P 4/m', transformations) space_groups[83] = sg space_groups['P 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(84, 'P 42/m', transformations) space_groups[84] = sg space_groups['P 42/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(85, 'P 4/n :2', transformations) space_groups[85] = sg space_groups['P 4/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,-1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,-1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(86, 'P 42/n :2', transformations) space_groups[86] = sg space_groups['P 42/n :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(87, 'I 4/m', transformations) space_groups[87] = sg space_groups['I 4/m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-3,-3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,5,5]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([3,3,3]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,-1,-1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([4,4,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(88, 'I 41/a :2', transformations) space_groups[88] = sg space_groups['I 41/a :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(89, 'P 4 2 2', transformations) space_groups[89] = sg space_groups['P 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(90, 'P 4 21 2', transformations) space_groups[90] = sg space_groups['P 4 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(91, 'P 41 2 2', transformations) space_groups[91] = sg space_groups['P 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(92, 'P 41 21 2', transformations) space_groups[92] = sg space_groups['P 41 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(93, 'P 42 2 2', transformations) space_groups[93] = sg space_groups['P 42 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(94, 'P 42 21 2', transformations) space_groups[94] = sg space_groups['P 42 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,3]) trans_den = N.array([1,1,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(95, 'P 43 2 2', transformations) space_groups[95] = sg space_groups['P 43 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([2,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(96, 'P 43 21 2', transformations) space_groups[96] = sg space_groups['P 43 21 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(97, 'I 4 2 2', transformations) space_groups[97] = sg space_groups['I 4 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(98, 'I 41 2 2', transformations) space_groups[98] = sg space_groups['I 41 2 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(99, 'P 4 m m', transformations) space_groups[99] = sg space_groups['P 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(100, 'P 4 b m', transformations) space_groups[100] = sg space_groups['P 4 b m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(101, 'P 42 c m', transformations) space_groups[101] = sg space_groups['P 42 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(102, 'P 42 n m', transformations) space_groups[102] = sg space_groups['P 42 n m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(103, 'P 4 c c', transformations) space_groups[103] = sg space_groups['P 4 c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(104, 'P 4 n c', transformations) space_groups[104] = sg space_groups['P 4 n c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(105, 'P 42 m c', transformations) space_groups[105] = sg space_groups['P 42 m c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(106, 'P 42 b c', transformations) space_groups[106] = sg space_groups['P 42 b c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(107, 'I 4 m m', transformations) space_groups[107] = sg space_groups['I 4 m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(108, 'I 4 c m', transformations) space_groups[108] = sg space_groups['I 4 c m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(109, 'I 41 m d', transformations) space_groups[109] = sg space_groups['I 41 m d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,3]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(110, 'I 41 c d', transformations) space_groups[110] = sg space_groups['I 41 c d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(111, 'P -4 2 m', transformations) space_groups[111] = sg space_groups['P -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(112, 'P -4 2 c', transformations) space_groups[112] = sg space_groups['P -4 2 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(113, 'P -4 21 m', transformations) space_groups[113] = sg space_groups['P -4 21 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(114, 'P -4 21 c', transformations) space_groups[114] = sg space_groups['P -4 21 c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(115, 'P -4 m 2', transformations) space_groups[115] = sg space_groups['P -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(116, 'P -4 c 2', transformations) space_groups[116] = sg space_groups['P -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(117, 'P -4 b 2', transformations) space_groups[117] = sg space_groups['P -4 b 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(118, 'P -4 n 2', transformations) space_groups[118] = sg space_groups['P -4 n 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(119, 'I -4 m 2', transformations) space_groups[119] = sg space_groups['I -4 m 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(120, 'I -4 c 2', transformations) space_groups[120] = sg space_groups['I -4 c 2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(121, 'I -4 2 m', transformations) space_groups[121] = sg space_groups['I -4 2 m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,3]) trans_den = N.array([2,1,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,5]) trans_den = N.array([1,2,4]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(122, 'I -4 2 d', transformations) space_groups[122] = sg space_groups['I -4 2 d'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(123, 'P 4/m m m', transformations) space_groups[123] = sg space_groups['P 4/m m m'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,-1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(124, 'P 4/m c c', transformations) space_groups[124] = sg space_groups['P 4/m c c'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,-1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([-1,-1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) sg = SpaceGroup(125, 'P 4/n b m :2', transformations) space_groups[125] = sg space_groups['P 4/n b m :2'] = sg transformations = [] rot = N.array([1,0,0,0,1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,0,0]) trans_den = N.array([1,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,0,0]) trans_den = N.array([2,1,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,-1,0,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([0,1,0]) trans_den = N.array([1,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([1,0,0,0,-1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,1,1]) trans_den = N.array([1,2,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,1,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,0,1]) trans_den = N.array([2,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([-1,0,0,0,-1,0,0,0,1]) rot.shape = (3, 3) trans_num = N.array([1,1,0]) trans_den = N.array([2,2,1]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,1,0,1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([0,0,1]) trans_den = N.array([1,1,2]) transformations.append((rot, trans_num, trans_den)) rot = N.array([0,-1,0,-1,0,0,0,0,-1]) rot.shape = (3, 3) trans_num = N.array([1,1,1]) trans_den = N.array([2,2,2]) transformations.append((rot, trans_num, trans_den)) rot =

N.array([-1,0,0,0,-1,0,0,0,-1])

numpy.array

import geopandas as gpd import numpy as np import pygeos import pytest from xugrid import conversion as cv @pytest.fixture(scope="function") def line(): x = np.array([0.0, 1.0, 2.0]) y = np.array([0.0, 0.0, 0.0]) edge_node_connectivity = np.array( [ [0, 1], [1, 2], ] ) return x, y, edge_node_connectivity @pytest.fixture(scope="function") def line_gdf(): x = np.array([0.0, 1.0, 2.0]) y = np.array([0.0, 0.0, 0.0]) gdf = gpd.GeoDataFrame(geometry=[pygeos.creation.linestrings(x, y)]) return gdf @pytest.fixture(scope="function") def triangle_mesh(): x = np.array([0.0, 1.0, 1.0, 2.0]) y =

np.array([0.0, 0.0, 1.0, 0.0])

numpy.array

import jax.numpy as jnp from jax import grad, vmap, hessian, jit import jax.ops as jop from jax.config import config; config.update("jax_enable_x64", True) # numpy import numpy as onp from numpy import random import scipy.io import argparse import logging import datetime from time import time import os def get_parser(): parser = argparse.ArgumentParser(description='Allen Cahn equation GP solver') parser.add_argument("--nu", type=float, default = 1e-4) parser.add_argument("--kernel", type=str, default="gaussian", choices=["gaussian","inv_quadratics"]) parser.add_argument("--sigma", type = float, default = 0.02) parser.add_argument("--dt", type = float, default = 0.04) parser.add_argument("--T", type = float, default = 1.0) parser.add_argument("--N_domain", type = int, default = 512) parser.add_argument("--nugget", type = float, default = 1e-13) parser.add_argument("--GNsteps", type = int, default = 2) parser.add_argument("--logroot", type=str, default='./logs/') parser.add_argument("--randomseed", type=int, default=9999) args = parser.parse_args() return args def sample_points(num_pts, dt, T, option = 'grid'): Nt = int(T/dt)+1 X_domain = onp.zeros((Nt,num_pts,2)) if option == 'grid': for i in range(Nt): X_domain[i,:,0] = i*dt X_domain[i,:,1] = onp.linspace(-1.0,1.0, num_pts) return X_domain def assembly_Theta(X_domain, sigma): N_domain = onp.shape(X_domain)[0] N_boundary = 0 Theta = onp.zeros((3*N_domain+N_boundary, 3*N_domain+N_boundary)) # auxiliary vector for construncting Theta # domain-domain XdXd = onp.tile(X_domain, (N_domain,1)) XdXd_T = onp.transpose(XdXd) XdXb1 = onp.transpose(onp.tile(X_domain,(N_domain+N_boundary,1))) X_all = X_domain XdXb2 = onp.tile(X_all,(N_domain,1)) XdbXdb = onp.tile(X_all,(N_domain+N_boundary,1)) XdbXdb_T = onp.transpose(XdbXdb) val = vmap(lambda x1,y1: Delta_x1_Delta_y1_kappa(x1,y1, sigma))(XdXd_T.flatten(), XdXd.flatten()) Theta[:N_domain,:N_domain] = onp.reshape(val, (N_domain,N_domain)) val = vmap(lambda x1,y1: Delta_x1_D_y1_kappa(x1,y1, sigma))(XdXd_T.flatten(), XdXd.flatten()) Theta[:N_domain,N_domain:2*N_domain] = onp.reshape(val, (N_domain,N_domain)) Theta[N_domain:2*N_domain,:N_domain] = onp.transpose(onp.reshape(val, (N_domain,N_domain))) val = vmap(lambda x1,y1: Delta_x1_kappa(x1,y1, sigma))(XdXb1.flatten(), XdXb2.flatten()) Theta[:N_domain,2*N_domain:] = onp.reshape(val,(N_domain,N_domain+N_boundary)) Theta[2*N_domain:,:N_domain] = onp.transpose(onp.reshape(val,(N_domain,N_domain+N_boundary))) val = vmap(lambda x1,y1: D_x1_D_y1_kappa(x1,y1, sigma))(XdXd_T.flatten(), XdXd.flatten()) Theta[N_domain:2*N_domain,N_domain:2*N_domain] = onp.reshape(val, (N_domain,N_domain)) val = vmap(lambda x1,y1: D_x1_kappa(x1,y1, sigma))(XdXb1.flatten(), XdXb2.flatten()) Theta[N_domain:2*N_domain,2*N_domain:] = onp.reshape(val,(N_domain,N_domain+N_boundary)) Theta[2*N_domain:,N_domain:2*N_domain] = onp.transpose(onp.reshape(val,(N_domain,N_domain+N_boundary))) val = vmap(lambda x1,y1: kappa(x1,y1, sigma))(XdbXdb_T.flatten(), XdbXdb.flatten()) Theta[2*N_domain:,2*N_domain:] = onp.reshape(val, (N_domain+N_boundary,N_domain+N_boundary)) return Theta @jit def J_loss(v, rhs_f, L,dt): N_domain = onp.shape(rhs_f)[0] vec_u = jnp.append(v[:N_domain-1],v[0]) vec_u_x = jnp.append(v[N_domain-1:],v[N_domain-1]) vec_u_xx = (2/dt*vec_u+5*vec_u**3-5*vec_u-rhs_f)/nu vv = jnp.append(vec_u_xx,vec_u_x) vv = jnp.append(vv,vec_u) temp = jnp.linalg.solve(L,vv) return jnp.dot(temp, temp) grad_J = grad(J_loss) @jit def GN_J(v, rhs_f, L, dt, v_old): N_domain = onp.shape(rhs_f)[0] vec_u_old = jnp.append(v_old[:N_domain-1],v_old[0]) vec_u = jnp.append(v[:N_domain-1],v[0]) vec_u_x = jnp.append(v[N_domain-1:],v[N_domain-1]) vec_u_xx = (2/dt*vec_u+15*vec_u_old**2*vec_u-5*vec_u-rhs_f)/nu vv = jnp.append(vec_u_xx,vec_u_x) vv = jnp.append(vv,vec_u) temp = jnp.linalg.solve(L,vv) return jnp.dot(temp, temp) Hessian_GN=jit(hessian(GN_J)) def time_steping_solve(X_domain, dt,T,num_pts, step_size = 1, nugget = 1e-10, sigma=0.2, GN_iteration = 4): Nt = int(T/dt)+1 sol_u = onp.zeros((Nt,num_pts)) sol_u_x = onp.zeros((Nt,num_pts)) sol_u_xx =

onp.zeros((Nt,num_pts))

numpy.zeros

# -*- coding: utf-8 -*- """ Created on Tue Mar 16 11:13:37 2021 @author: dv516 """ import numpy as np import pickle import pyro pyro.enable_validation(True) # can help with debugging pyro.set_rng_seed(1) from algorithms.PyBobyqa_wrapped.Wrapper_for_pybobyqa import PyBobyqaWrapper from algorithms.Bayesian_opt_Pyro.utilities_full import BayesOpt from algorithms.nesterov_random.nesterov_random import nesterov_random from algorithms.simplex.simplex_method import simplex_method from algorithms.CUATRO.CUATRO import CUATRO from algorithms.Finite_differences.Finite_differences import finite_Diff_Newton from algorithms.Finite_differences.Finite_differences import Adam_optimizer from algorithms.Finite_differences.Finite_differences import BFGS_optimizer from algorithms.SQSnobfit_wrapped.Wrapper_for_SQSnobfit import SQSnobFitWrapper from algorithms.DIRECT_wrapped.Wrapper_for_Direct import DIRECTWrapper from test_functions import rosenbrock_constrained, quadratic_constrained import matplotlib.pyplot as plt import pickle def trust_fig(oracle, bounds): N = 200 lim = 2 x = np.linspace(-lim, lim, N) y = np.linspace(-lim, lim, N) X,Y = np.meshgrid(x, y) Z = oracle.sample_obj(X,Y) constr = oracle.sample_constr(X,Y) level_list = np.logspace(-0.5, 4, 10) fig = plt.figure(figsize = (6,4)) ax = fig.add_subplot() ax.contour(X,Y,Z*constr, levels = level_list) ax.plot([bounds[0,0], bounds[0, 1]], [bounds[1,0], bounds[1, 0]], c = 'k') ax.plot([bounds[0,0], bounds[0, 1]], [bounds[1,1], bounds[1, 1]], c = 'k') ax.plot([bounds[0,0], bounds[0, 0]], [bounds[1,0], bounds[1, 1]], c = 'k') ax.plot([bounds[0,1], bounds[0, 1]], [bounds[1,0], bounds[1, 1]], c = 'k') return ax, fig def average_from_list(solutions_list): N = len(solutions_list) f_best_all = np.zeros((N, 100)) for i in range(N): f_best = np.array(solutions_list[i]['f_best_so_far']) x_ind = np.array(solutions_list[i]['samples_at_iteration']) for j in range(100): ind = np.where(x_ind <= j+1) if len(ind[0]) == 0: f_best_all[i, j] = f_best[0] else: f_best_all[i, j] = f_best[ind][-1] f_median = np.median(f_best_all, axis = 0) # f_av = np.average(f_best_all, axis = 0) # f_std = np.std(f_best_all, axis = 0) f_min = np.min(f_best_all, axis = 0) f_max = np.max(f_best_all, axis = 0) return f_best_all, f_median, f_min, f_max class RB: def __init__(self, objective, ineq = []): self.obj = objective ; self.ieq = ineq def sample_obj(self, x, y): return self.obj(x, y) def sample_constr(self, x, y): if self.ieq == []: if (type(x) == float) or (type(x) == int): return 1 else: return np.ones(len(x)) elif (type(x) == float) or (type(x) == int): temporary = [int(g(x, y)) for g in self.ieq] return np.product(

np.array(temporary)

numpy.array

import theano import theano.tensor as T import numpy as np from util import * class Autoencoder_1obj(): # each render_var gets its own l2 layer def __init__(self, scene, n_visible, n_hidden_l1, n_hidden_l2, n_hidden_l3): self.scene = scene self.n_visible = n_visible self.n_hidden_l1 = n_hidden_l1 self.n_hidden_l2 = n_hidden_l2 self.l1_biases = theano.shared(np.zeros(n_hidden_l1), borrow=True) self.l2_biases = theano.shared(np.zeros(n_hidden_l2), borrow=True) self.l3_biases = theano.shared(np.zeros(n_hidden_l3), borrow=True) numpy_rng = np.random.RandomState(1234) self.vis_to_l1 = initialize_weight(n_visible, n_hidden_l1, "vis_to_l1", numpy_rng, 'uniform') self.l1_to_l2 = initialize_weight(n_hidden_l1, n_hidden_l2, "vis_to_l1", numpy_rng, 'uniform') self.l2_to_l3 = initialize_weight(n_hidden_l2, n_hidden_l3, "vis_to_l1", numpy_rng, 'uniform') self.params0 = [self.vis_to_l1, self.l1_to_l2, self.l2_to_l3, self.l1_biases, self.l2_biases,self.l3_biases] #Adding Capsules self.l3_to_rvar1 = theano.shared(self.init_capsule_param(n_hidden_l3),borrow=True) self.rvar1_biases = theano.shared(np.asarray([0,0,2.5,1,1,1]), borrow=True) self.params1 = [self.l3_to_rvar1, self.rvar1_biases] #self.l3_to_rvar2, self.rvar2_biases] self.params= self.params0+self.params1 def init_capsule_param(self, n_hidden_l3): #return 0.07*np.asarray( np.random.uniform(\ # low=-4 * np.sqrt(6. / 6+n_hidden_l3), # high=4 * np.sqrt(6. / 6+n_hidden_l3), # size=(n_hidden_l3, 6)), dtype=theano.config.floatX) l3_to_center = 0.07*np.asarray( np.random.uniform( low=-4 * np.sqrt(6. / 6+n_hidden_l3), high=4 *

np.sqrt(6. / 6+n_hidden_l3)

numpy.sqrt

import numpy as onp import jax import jax.numpy as np import random import os import scipy.interpolate import astropy.io.fits as pyfits from redrock.templates import Template from redrock.archetypes import Archetype from chex import assert_shape key = jax.random.PRNGKey(42) mask_std_val = 1e2 def create_mask(x, x_var, indices, val=0.0): mask = onp.ones(x.shape) # mask[x == 0] = val ind = np.where(np.logical_or(x_var <= 0, x_var == mask_std_val ** 2.0)) mask[ind] = val fullindices = onp.asarray(indices)[:, None] + onp.arange(x.shape[1])[None, :] mask[fullindices < 0] = val # offs = - np.maximum(indices, np.zeros_like(indices)) # for io, off in enumerate(offs): # mask[io, 0:off] = 0 return np.asarray(mask) def interp(x_new, x, y): return scipy.interpolate.interp1d( x, y, fill_value="extrapolate", kind="linear", bounds_error=False )(x_new) def draw_uniform(samples, bins, desired_size): """ Draw uniform set of samples """ hist, bin_edges = np.histogram(samples, bins=bins) avg_nb = int(desired_size / float(bins)) numbers = np.repeat(avg_nb, bins) for j in range(4): numbers[hist <= numbers] = hist[hist <= numbers] nb_rest = desired_size - np.sum(numbers[hist <= numbers]) # * bins avg_nb = round(nb_rest / np.sum(hist > numbers)) numbers[hist > numbers] = avg_nb result = [] count = 0 for i in range(bin_edges.size - 1): ind = samples >= bin_edges[i] ind &= samples <= bin_edges[i + 1] if ind.sum() > 0: positions = np.where(ind)[0] nb = min([numbers[i], ind.sum()]) result.append(jax.random.choice(positions, nb, replace=False)) return np.concatenate(result) class DataPipeline: """ Pipeline for loading data """ def load_spectrophotometry( self, input_dir="./", write_subset=False, use_subset=False, subsampling=1, spec=True, phot=True, ): if use_subset: suffix = "2.npy" else: suffix = ".npy" self.input_dir = input_dir self.lamgrid = onp.load(self.input_dir + "lamgrid.npy") self.lam_phot_eff = onp.load(self.input_dir + "lam_phot_eff.npy") self.lam_phot_size_eff = onp.load(self.input_dir + "lam_phot_size_eff.npy") self.redshifts = onp.load(self.input_dir + "redshifts" + suffix) n_obj = self.redshifts.size self.n_obj = n_obj assert_shape(self.redshifts, (n_obj,)) if phot: self.transferfunctions = ( onp.load(self.input_dir + "transferfunctions.npy") * 1e-16 ) self.transferfunctions_zgrid = onp.load( self.input_dir + "transferfunctions_zgrid.npy" ) assert self.transferfunctions.shape[0] == self.transferfunctions_zgrid.size assert self.transferfunctions.shape[1] == self.lamgrid.size self.index_transfer_redshift = onp.load( self.input_dir + "index_transfer_redshift" + suffix ) self.interprightindices_transfer = onp.load( self.input_dir + "interprightindices_transfer" + suffix ) self.interpweights_transfer = onp.load( self.input_dir + "interpweights_transfer" + suffix ) self.phot = fluxes = onp.load(self.input_dir + "phot" + suffix) self.phot_invvar = flux_ivars = onp.load( self.input_dir + "phot_invvar" + suffix ) assert_shape(self.index_transfer_redshift, (n_obj,)) assert_shape(self.interprightindices_transfer, (n_obj,)) assert_shape(self.interpweights_transfer, (n_obj,)) n_pix_phot = self.phot.shape[1] assert_shape(self.phot, (n_obj, n_pix_phot)) assert_shape(self.phot_invvar, (n_obj, n_pix_phot)) self.n_pix_phot = self.phot.shape[1] if spec: self.chi2s_sdss = onp.load(self.input_dir + "chi2s_sdss" + suffix) self.lamspec_waveoffset = int( onp.load(self.input_dir + "lamspec_waveoffset" + suffix) ) self.index_wave = onp.load(self.input_dir + "index_wave" + suffix) self.interprightindices = onp.load( self.input_dir + "interprightindices" + suffix ) self.interpweights = onp.load(self.input_dir + "interpweights" + suffix) self.specmod_sdss = onp.load(self.input_dir + "spec_mod" + suffix) if True: self.spec = onp.load(self.input_dir + "spec" + suffix) self.spec_invvar = onp.load(self.input_dir + "spec_invvar" + suffix) else: self.spec = onp.load(self.input_dir + "spec_mod" + suffix) self.spec_invvar = ( onp.load(self.input_dir + "spec_invvar" + suffix) * 0 + 1 ) self.n_pix_spec = self.spec.shape[1] assert_shape(self.chi2s_sdss, (n_obj,)) assert_shape(self.index_wave, (n_obj,)) n_pix_spec = self.spec.shape[1] assert_shape(self.spec, (n_obj, n_pix_spec)) assert_shape(self.specmod_sdss, (n_obj, n_pix_spec)) assert_shape(self.spec_invvar, (n_obj, n_pix_spec)) if write_subset: M = 50000 suffix = "2.npy" self.index_wave = self.index_wave[:M] self.redshifts = self.redshifts[:M] self.chi2s_sdss = self.chi2s_sdss[:M] self.phot_invvar = self.phot_invvar[:M, :] self.index_transfer_redshift = self.index_transfer_redshift[:M] np.save(self.input_dir + "index_wave" + suffix, self.index_wave[:M]) np.save( self.input_dir + "interprightindices_transfer" + suffix, self.interprightindices_transfer[:M, :], ) np.save( self.input_dir + "interpweights_transfer" + suffix, self.interpweights_transfer[:M, :], ) np.save( self.input_dir + "index_transfer_redshift2.npy", self.index_transfer_redshift, ) np.save(self.input_dir + "redshifts" + suffix, self.redshifts) np.save(self.input_dir + "spec" + suffix, self.spec) np.save(self.input_dir + "chi2s_sdss" + suffix, self.chi2s_sdss) np.save(self.input_dir + "spec_invvar" + suffix, self.spec_invvar) np.save(self.input_dir + "phot" + suffix, self.phot) np.save(self.input_dir + "phot_invvar" + suffix, self.phot_invvar) np.save(self.input_dir + "spec_mod" + suffix, self.specmod_sdss) if subsampling > 1: self.lamgrid = self.lamgrid[::subsampling] self.transferfunctions = self.transferfunctions[:, ::subsampling, :][ ::subsampling, :, : ] self.transferfunctions_zgrid = self.transferfunctions_zgrid[::subsampling] self.lamspec_waveoffset = self.lamspec_waveoffset // subsampling self.spec = self.spec[:, ::subsampling] self.specmod_sdss = self.specmod_sdss[:, ::subsampling] self.spec_invvar = self.spec_invvar[:, ::subsampling] self.index_wave = self.index_wave // subsampling self.index_transfer_redshift = self.index_transfer_redshift // subsampling self.interprightindices = ( self.interprightindices[:, ::subsampling] // subsampling ) self.interpweights = ( self.interpweights[:, ::subsampling] / subsampling ) # dilution self.interprightindices_transfer = ( self.interprightindices_transfer // subsampling ) # is it correct? self.interpweights_transfer = ( self.interpweights_transfer / subsampling ) # is it correct? @staticmethod def save_fake_data(n_obj, n_pix_sed, n_pix_spec, n_pix_phot, n_pix_transfer): root = "data/fake/fake_" from jax.random import uniform, randint np.save(root + "lamgrid.npy", 8.1e2 + np.arange(n_pix_sed)) np.save(root + "lam_phot_eff.npy", np.arange(n_pix_phot)) np.save(root + "lam_phot_size_eff.npy", np.arange(n_pix_phot)) np.save( root + "transferfunctions.npy", uniform(key, (n_pix_transfer, n_pix_sed, n_pix_phot)), ) np.save(root + "transferfunctions_zgrid.npy", np.arange(n_pix_transfer)) np.save(root + "chi2s_sdss.npy", uniform(key, (n_obj,))) np.save( root + "lamspec_waveoffset.npy", randint(key, (1,), 0, n_pix_sed - n_pix_spec - 1), ) np.save( root + "index_wave.npy", randint(key, (n_obj,), 0, n_pix_sed - n_pix_spec - 1), ) np.save( root + "index_transfer_redshift.npy", randint(key, (n_obj,), 0, n_pix_transfer), ) np.save( root + "interprightindices.npy", randint(key, (n_obj, n_pix_spec), 0, n_pix_transfer), ) np.save( root + "interpweights.npy", uniform(key, (n_obj, n_pix_spec)), ) np.save( root + "interprightindices_transfer.npy", randint(key, (n_obj,), 0, n_pix_transfer), ) np.save( root + "interpweights_transfer.npy", uniform(key, (n_obj,)), ) np.save(root + "spec.npy", uniform(key, (n_obj, n_pix_spec))) np.save(root + "spec_mod.npy", uniform(key, (n_obj, n_pix_spec))) np.save(root + "spec_invvar.npy", uniform(key, (n_obj, n_pix_spec))) np.save(root + "phot.npy", uniform(key, (n_obj, n_pix_phot))) np.save(root + "phot_invvar.npy", uniform(key, (n_obj, n_pix_phot))) np.save(root + "redshifts.npy", uniform(key, (n_obj,))) def __init__( self, input_dir="./", subsampling=1, npix_min=1, write_subset=False, use_subset=False, spec=True, phot=True, ): self.load_spectrophotometry( input_dir=input_dir, write_subset=write_subset, use_subset=use_subset, subsampling=subsampling, spec=spec, phot=phot, ) self.indices = np.arange(self.n_obj) self.batch = 0 self.subsampling = subsampling self.npix_min = npix_min if phot: # Multiplying by delta lambda in preparation for integral over lambda xbounds = onp.zeros(self.lamgrid.size + 1) xbounds[1:-1] = (self.lamgrid[1:] + self.lamgrid[:-1]) / 2 xbounds[0] = self.lamgrid[0] - (xbounds[1] - self.lamgrid[0]) xbounds[-1] = self.lamgrid[-1] + (self.lamgrid[-1] - xbounds[-2]) xsizes = np.asarray(np.diff(xbounds)) self.transferfunctions = self.transferfunctions * xsizes[None, :, None] print("Initial lamgrid shape:", self.lamgrid.shape) if spec: print("Initial spec shape:", self.spec.shape) # spec[spec <= 0] = np.nan self.spec_invvar[~onp.isfinite(self.spec)] = 0 self.spec_invvar[self.spec == 0] = 0 self.spec_invvar[~onp.isfinite(self.spec_invvar)] = 0 self.spec_invvar[self.spec_invvar < 0] = 0 self.spec_invvar[self.interpweights < 0] = 0 self.spec_invvar[self.interprightindices < 0] = 0 self.spec[~onp.isfinite(self.spec)] = 0 # Masking sky lines lamsize_spec = self.spec.shape[1] print( "lamspec_waveoffset", self.lamspec_waveoffset, self.lamgrid[self.lamspec_waveoffset], ) print("lamsize_spec", lamsize_spec) print("lamgrid", self.lamgrid.size) # Floor spectroscopic errors ind = self.spec_invvar ** -0.5 < 1e-4 * np.abs(self.spec) # ind &= self.spec_invvar != 0 # ind &= self.spec != 0 print("How many spec errors are floored?", np.sum(ind), "out of", ind.size) # ind = np.where(ind)[0] self.spec_invvar[ind] = (1e-4 * np.abs(self.spec)[ind]) ** -2.0 if ( np.sum(~np.isfinite(self.spec)) > 0 or np.sum(~np.isfinite(self.spec_invvar)) > 0 ): print( "nans?", np.sum(~np.isfinite(self.spec)), np.sum(~np.isfinite(self.spec_invvar)), ) stop # Calculated after changing the data self.chi2s_sdss = np.sum( (self.specmod_sdss - self.spec) ** 2 * self.spec_invvar, axis=-1 ) print("Revised data shape:", self.spec.shape) # masks = create_mask(self.spec, self.spec_invvar, self.index_wave) masks = ~(self.spec_invvar == 0) npix = np.sum(masks, axis=1) print("Number of objects with 0 valid pixels:", np.sum(npix == 0)) print("Number of objects with <10 valid pixels:", np.sum(npix <= 10)) print("Number of objects with <100 valid pixels:", np.sum(npix <= 100)) self.indices = onp.where(npix > npix_min)[0] onp.random.shuffle(self.indices) print("Number of objects with valid pixels:", self.indices.size) self.specphotscalings = np.ones((self.spec.shape[0],)) if phot: ind = ~np.isfinite(self.phot_invvar) ind |= self.phot_invvar < 0 # ind = np.where(ind)[0] self.phot_invvar[ind] = 0 print("Initial phot shape:", self.phot.shape) # Floor photometric errors ind = self.phot_invvar ** -0.5 < 1e-2 * self.phot print("How many phot errors are floored?", np.sum(ind), "out of", ind.size) # ind = np.where(ind)[0] self.phot_invvar[ind] = (1e-2 * self.phot[ind]) ** -2.0 print("Finished pre-processing data.") def get_grids(self): n_pix_sed = self.lamgrid.size n_pix_spec = self.spec.shape[1] n_pix_phot = self.phot.shape[1] # lamgrid_spec = self.lamgrid[ # self.lamspec_waveoffset : self.lamspec_waveoffset + n_pix_spec # ] return ( self.lamgrid, self.lam_phot_eff, self.lam_phot_size_eff, self.transferfunctions, self.transferfunctions_zgrid, n_pix_sed, n_pix_spec, n_pix_phot, ) def next_batch_specandphot(self, indices, batchsize): length = indices.size startindex = self.batch * batchsize batch_indices = indices[startindex : startindex + batchsize] # print('batch_indices', batch_indices.size, batch_indices[0], batch_indices[-1]) batch_index_wave = np.take(self.index_wave, batch_indices) batch_index_transfer_redshift = np.take( self.index_transfer_redshift, batch_indices ) batch_spec = np.take(self.spec, batch_indices, axis=0) batch_spec_invvar = np.take(self.spec_invvar, batch_indices, axis=0) # batch_sed_mask = create_mask(batch_spec, batch_spec_invvar, batch_index_wave) batch_phot = np.take(self.phot, batch_indices, axis=0) batch_phot_invvar = np.take(self.phot_invvar, batch_indices, axis=0) batch_redshifts = np.take(self.redshifts, batch_indices) batch_specphotscaling = np.take(self.specphotscalings, batch_indices) batch_interpweights = np.take(self.interpweights, batch_indices, axis=0) batch_interprightindices = np.take( self.interprightindices, batch_indices, axis=0 ) self.batch += 1 nextbatch_startindex = self.batch * batchsize if nextbatch_startindex >= length: self.batch = 0 actualbatchsize = min([batchsize, length - startindex]) # si, _ = startindex, batchsize # sh = (batch_spec.shape[0], wavesize) # batch_transferfunctions = np.zeros((batch_spec.shape[0], wavesize, batch_phot.shape[1])) batch_transferfunctions = self.transferfunctions[ batch_index_transfer_redshift, :, : ] batch_index_wave_ext = batch_index_wave[:, None] + np.arange( batch_spec.shape[1] ) if np.sum(batch_index_wave_ext < 0) > 0: print( "Number of negative wave indices:", np.sum(batch_index_wave < 0), np.sum(batch_index_wave_ext < 0), ) exit(1) # batch_index_wave_ext[batch_index_wave_ext < 0] = 0 batch_spec_loginvvar = np.where( batch_spec_invvar == 0, 0, np.log(batch_spec_invvar) ) batch_phot_loginvvar = np.where( batch_phot_invvar == 0, 0, np.log(batch_phot_invvar) ) if ( np.sum(~np.isfinite(batch_spec)) > 0 or np.sum(~np.isfinite(batch_spec_invvar)) > 0 or np.sum(~np.isfinite(batch_spec_loginvvar)) > 0 ): print( "nans?", np.sum(~np.isfinite(batch_spec)), np.sum(~np.isfinite(batch_spec_invvar)), np.sum(~np.isfinite(batch_spec_loginvvar)), ) exit(1) return ( startindex, actualbatchsize, batch_index_wave, batch_index_transfer_redshift, batch_spec, batch_spec_invvar, batch_spec_loginvvar, # batch_sed_mask, batch_specphotscaling, batch_phot, batch_phot_invvar, batch_phot_loginvvar, batch_redshifts, batch_transferfunctions, batch_index_wave_ext, batch_interprightindices, batch_interpweights, ) def next_batch_photonly(self, indices, batchsize): length = indices.size startindex = self.batch * batchsize batch_indices = indices[startindex : startindex + batchsize] batch_phot = np.take(self.phot, batch_indices, axis=0) batch_phot_invvar = np.take(self.phot_invvar, batch_indices, axis=0) batch_redshifts = np.take(self.redshifts, batch_indices) batch_interpweights_transfer = np.take( self.interpweights_transfer, batch_indices, axis=0 ) batch_interprightindices_transfer = np.take( self.interprightindices_transfer, batch_indices, axis=0 ) self.batch += 1 nextbatch_startindex = self.batch * batchsize if nextbatch_startindex >= length: self.batch = 0 actualbatchsize = min([batchsize, length - startindex]) batch_phot_loginvvar = np.where( batch_phot_invvar == 0, 0, np.log(batch_phot_invvar) ) return ( startindex, actualbatchsize, batch_phot, batch_phot_invvar, batch_phot_loginvvar, batch_redshifts, self.transferfunctions, batch_interprightindices_transfer, batch_interpweights_transfer, ) def get_nbatches(self, indices, batchsize): self.batchsize = batchsize return (indices.shape[0] // self.batchsize) + 1 def change_redshift(self, iz, zstep, data_batch): ( si, bs, batch_index_wave, batch_index_transfer_redshift, spec, spec_invvar, spec_loginvvar, # batch_spec_mask, specphotscaling, phot, phot_invvar, phot_loginvvar, batch_redshifts, batch_transferfunctions, batch_index_wave_ext, batch_interprightindices, batch_interpweights, ) = data_batch batch_transferfunctions = self.transferfunctions[ None, iz * zstep, :, : ] * onp.ones((bs, 1, 1)) # batch_index_wave = np.repeat(self.lamspec_waveoffset - iz * zstep, bs) # not correct with new arrays batch_index_wave_z0 = batch_index_wave + batch_index_transfer_redshift batch_interprightindices_z0 = ( batch_interprightindices + batch_index_transfer_redshift[:, None] ) batch_index_wave = batch_index_wave_z0 - iz * zstep batch_interprightindices = batch_interprightindices_z0 - iz * zstep batch_index_wave_ext = batch_index_wave[:, None] + onp.arange(spec.shape[1]) # batch_index_wave_ext[batch_index_wave_ext < 0] = 0 # TODO: is this a problem? # TODO: something to do about the specphotscaling? return ( si, bs, batch_index_wave, batch_index_transfer_redshift, spec, spec_invvar, spec_loginvvar, # batch_spec_mask, specphotscaling, phot, phot_invvar, phot_loginvvar, batch_redshifts, batch_transferfunctions, batch_index_wave_ext, batch_interprightindices, batch_interpweights, ) class ResultsPipeline: def __init__( self, prefix, suffix, n_archetypes, n_components, dataPipeline, indices=None ): n_pix_sed = dataPipeline.lamgrid.size n_pix_spec = dataPipeline.spec.shape[1] n_pix_phot = dataPipeline.phot.shape[1] self.dataPipeline = dataPipeline self.prefix = prefix self.suffix = suffix if indices is not None: n_obj = indices.size self.indices = indices self.logfml = onp.zeros((n_obj, n_archetypes)) self.specmod = onp.zeros((n_obj, n_pix_spec)) self.photmod = onp.zeros((n_obj, n_pix_phot)) self.thetamap = onp.zeros((n_obj, n_archetypes, n_components)) self.thetastd = onp.zeros((n_obj, n_archetypes, n_components)) self.ellfactors = onp.zeros((n_obj, n_archetypes)) def write_batch( self, data_batch, logfml, thetamap, thetastd, specmod, photmod, ellfactors ): si, bs = data_batch[0], data_batch[1] best = np.argmax(logfml, axis=1) fac = np.ones((bs, specmod.shape[2]), dtype=int) i0 = np.arange(bs, dtype=int)[:, None] * fac i1 = best[:, None] * fac i2 = fac * np.arange(specmod.shape[2], dtype=int)[None, :] self.specmod[si : si + bs, :] = specmod[i0, i1, i2] fac = np.ones((bs, photmod.shape[2]), dtype=int) i0 = np.arange(bs, dtype=int)[:, None] * fac i1 = best[:, None] * fac i2 = fac * np.arange(photmod.shape[2], dtype=int)[None, :] self.photmod[si : si + bs, :] = photmod[i0, i1, i2] self.logfml[si : si + bs, :] = logfml self.thetamap[si : si + bs, :, :] = thetamap self.thetastd[si : si + bs, :, :] = thetastd self.ellfactors[si : si + bs, :] = ellfactors def load_reconstructions(self): self.indices = onp.load(self.prefix + "indices" + self.suffix + ".npy") self.logfml =

onp.load(self.prefix + "logfml" + self.suffix + ".npy")

numpy.load

#!/usr/bin/env python ############################################################################# ## # This file is part of Taurus ## # http://taurus-scada.org ## # Copyright 2011 CELLS / ALBA Synchrotron, Bellaterra, Spain ## # Taurus is free software: you can redistribute it and/or modify # it under the terms of the GNU Lesser General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. ## # Taurus is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU Lesser General Public License for more details. ## # You should have received a copy of the GNU Lesser General Public License # along with Taurus. If not, see <http://www.gnu.org/licenses/>. ## ############################################################################# """ arrayedit.py: Widget for editing a spectrum/array via control points """ from __future__ import absolute_import from builtins import range import numpy from taurus.external.qt import Qt, Qwt5 from taurus.qt.qtgui.util.ui import UILoadable from .curvesAppearanceChooserDlg import CurveAppearanceProperties @UILoadable class ControllerBox(Qt.QWidget): selected = Qt.pyqtSignal(int) def __init__(self, parent=None, x=0, y=0, corr=0): Qt.QWidget.__init__(self, parent) self.loadUi() self._x = x self.setY(y) self.box.setTitle('x=%6g' % self._x) self.corrSB.setValue(corr) self.ctrlObj = self.corrSB.ctrlObj = self.lCopyBT.ctrlObj = self.rCopyBT.ctrlObj = self.lScaleBT.ctrlObj = self.rScaleBT.ctrlObj = self # reimplementing the focusInEvent method for the spinbox self.corrSB.focusInEvent = self.corrSB_focusInEvent self.box.mousePressEvent = self.mousePressEvent #self.connect(self.corrSB, Qt.SIGNAL('valueChanged(double)'), self.enableScale) def mousePressEvent(self, event): self.selected.emit(self._x) # print 'SELECTED', self #Qt.QDoubleSpinBox.focusInEvent(self.corrSB, event) def corrSB_focusInEvent(self, event): self.selected.emit(self._x) # print 'GOT FOCUS', self Qt.QDoubleSpinBox.focusInEvent(self.corrSB, event) def setY(self, y): self._y = y self.enableScale() def enableScale(self, *args): enable = (self._y + self.corrSB.value()) != 0 self.lScaleBT.setEnabled(enable) self.rScaleBT.setEnabled(enable) @UILoadable class EditCPointsDialog(Qt.QDialog): def __init__(self, parent=None, x=0): Qt.QDialog.__init__(self, parent) self.loadUi() @UILoadable class AddCPointsDialog(Qt.QDialog): def __init__(self, parent=None, x=0): Qt.QDialog.__init__(self, parent) self.loadUi() @UILoadable class ArrayEditor(Qt.QWidget): def __init__(self, parent=None): Qt.QWidget.__init__(self, parent) self.loadUi() self._controllers = [] # construct the layout for controllers container self.ctrlLayout = Qt.QHBoxLayout(self.controllersContainer) self.ctrlLayout.setContentsMargins(5, 0, 5, 0) self.ctrlLayout.setSpacing(1) # implement scroll bars for the controllers container self.scrollArea = Qt.QScrollArea(self) self.scrollArea.setWidget(self.controllersContainer) self.scrollArea.setVerticalScrollBarPolicy(Qt.Qt.ScrollBarAlwaysOff) self.scrollArea.setWidgetResizable(True) self.cpointsGroupBox.layout().insertWidget(0, self.scrollArea) # initialize data cpoints = 2 self.x = numpy.arange(256, dtype='double') self.y = numpy.zeros(256, dtype='double') self.xp = numpy.linspace(self.x[0], self.x[-1], cpoints) self.corrp = numpy.zeros(cpoints) self.yp = numpy.interp(self.xp, self.x, self.y) self.corr = numpy.zeros(self.x.size) # markers self.markerPos = self.xp[0] self.marker1 = Qwt5.QwtPlotMarker() self.marker1.setSymbol(Qwt5.QwtSymbol(Qwt5.QwtSymbol.Rect, Qt.QBrush(Qt.Qt.NoBrush), Qt.QPen(Qt.Qt.green), Qt.QSize(8, 8))) self.marker1.attach(self.plot1) self.marker2 = Qwt5.QwtPlotMarker() self.marker2.setSymbol(Qwt5.QwtSymbol(Qwt5.QwtSymbol.Rect, Qt.QBrush(Qt.Qt.NoBrush), Qt.QPen(Qt.Qt.green), Qt.QSize(8, 8))) self.marker2.attach(self.plot2) # cpointsPickers self._cpointMovingIndex = None self._cpointsPicker1 = Qwt5.QwtPicker(self.plot1.canvas()) self._cpointsPicker1.setSelectionFlags(Qwt5.QwtPicker.PointSelection) self._cpointsPicker2 = Qwt5.QwtPicker(self.plot2.canvas()) self._cpointsPicker2.setSelectionFlags(Qwt5.QwtPicker.PointSelection) self._cpointsPicker1.widgetMousePressEvent = self.plot1MousePressEvent self._cpointsPicker1.widgetMouseReleaseEvent = self.plot1MouseReleaseEvent self._cpointsPicker2.widgetMousePressEvent = self.plot2MousePressEvent self._cpointsPicker2.widgetMouseReleaseEvent = self.plot2MouseReleaseEvent self._cpointsPicker1.widgetMouseDoubleClickEvent = self.plot1MouseDoubleClickEvent self._cpointsPicker2.widgetMouseDoubleClickEvent = self.plot2MouseDoubleClickEvent self._populatePlots() self.resetCorrection() self._selectedController = self._controllers[0] self._addCPointsDialog = AddCPointsDialog(self) # Launch low-priority initializations (to speed up load time) # Qt.QTimer.singleShot(0, <method>) # connections self.addCPointsBT.clicked.connect(self._addCPointsDialog.show) self._addCPointsDialog.editBT.clicked.connect(self.showEditCPointsDialog) self._addCPointsDialog.cleanBT.clicked.connect(self.resetCorrection) self._addCPointsDialog.addSingleCPointBT.clicked.connect(self.onAddSingleCPointBT) self._addCPointsDialog.addRegEspCPointsBT.clicked.connect(self.onAddRegEspCPointsBT) def plot1MousePressEvent(self, event): self.plotMousePressEvent(event, self.plot1) def plot2MousePressEvent(self, event): self.plotMousePressEvent(event, self.plot2) def plotMousePressEvent(self, event, taurusplot): picked, pickedCurveName, pickedIndex = taurusplot.pickDataPoint( event.pos(), scope=20, showMarker=False, targetCurveNames=['Control Points']) if picked is not None: self.changeCPointSelection(picked.x()) self.makeControllerVisible(self._controllers[pickedIndex]) self._cpointMovingIndex = pickedIndex self._movingStartYPos = event.y() taurusplot.canvas().setCursor(Qt.Qt.SizeVerCursor) def plot1MouseReleaseEvent(self, event): self.plotMouseReleaseEvent(event, self.plot1) def plot2MouseReleaseEvent(self, event): self.plotMouseReleaseEvent(event, self.plot2) def plotMouseReleaseEvent(self, event, taurusplot): if self._cpointMovingIndex is None: return # if no cpoint was picked, do nothing on release # no motion s performed if the y position is unchanged or if the mouse # release is out of the canvas validMotion = (self._movingStartYPos != event.pos().y() ) and taurusplot.canvas().rect().contains(event.pos()) if validMotion: # calculate the new correction newCorr = taurusplot.invTransform( taurusplot.getCurve('Control Points').yAxis(), event.y()) if taurusplot is self.plot1: newCorr -= self.yp[self._cpointMovingIndex] # apply new correction self._controllers[self._cpointMovingIndex].corrSB.setValue(newCorr) # reset the moving state self._cpointMovingIndex = None taurusplot.canvas().setCursor(Qt.Qt.CrossCursor) def plot1MouseDoubleClickEvent(self, event): self.plotMouseDoubleClickEvent(event, self.plot1) def plot2MouseDoubleClickEvent(self, event): self.plotMouseDoubleClickEvent(event, self.plot2) def plotMouseDoubleClickEvent(self, event, taurusplot): picked, pickedCurveName, pickedIndex = taurusplot.pickDataPoint( event.pos(), scope=20, showMarker=False, targetCurveNames=['Control Points']) if picked is not None: return # we dont want to create a control point too close of an existing one xp = taurusplot.invTransform(taurusplot.getCurve( 'Control Points').xAxis(), event.x()) if xp < self.xp[0] or xp > self.xp[-1]: return # we dont want to create control points out of the curve range if Qt.QMessageBox.question(self, 'Create Control Point?', 'Insert a new control point at x=%g?' % xp, 'Yes', 'No') == 0: self.insertController(xp) self.changeCPointSelection(xp) # singleshot is used as a hack to get out of the eventhandler Qt.QTimer.singleShot(1, self.makeControllerVisible) def makeControllerVisible(self, ctrl=None): if ctrl is None: ctrl = self._selectedController self.scrollArea.ensureWidgetVisible(ctrl) def connectToController(self, ctrl): ctrl.selected.connect(self.changeCPointSelection) ctrl.corrSB.valueChanged.connect(self.onCorrSBChanged) ctrl.lCopyBT.clicked.connect(self.onLCopy) ctrl.rCopyBT.clicked.connect(self.onRCopy) ctrl.lScaleBT.clicked.connect(self.onLScale) ctrl.rScaleBT.clicked.connect(self.onRScale) def onAddSingleCPointBT(self): x = self._addCPointsDialog.singleCPointXSB.value() self.insertController(x) def onAddRegEspCPointsBT(self): cpoints = self._addCPointsDialog.regEspCPointsSB.value() positions = numpy.linspace(self.x[0], self.x[-1], cpoints + 2)[1:-1] for xp in positions: self.insertController(xp) def showEditCPointsDialog(self): dialog = EditCPointsDialog(self) table = dialog.tableTW table.setRowCount(self.xp.size) for i, (xp, corrp) in enumerate(zip(self.xp, self.corrp)): table.setItem(i, 0, Qt.QTableWidgetItem(str(xp))) table.setItem(i, 1, Qt.QTableWidgetItem(str(corrp))) # show dialog and update values if it is accepted if dialog.exec_(): # delete previous controllers for c in self._controllers: c.setParent(None) c.deleteLater() self._controllers = [] # and create them anew new_xp = numpy.zeros(table.rowCount()) new_corrp = numpy.zeros(table.rowCount()) try: for i in range(table.rowCount()): new_xp[i] = float(table.item(i, 0).text()) new_corrp[i] = float(table.item(i, 1).text()) self.setCorrection(new_xp, new_corrp) except: Qt.QMessageBox.warning( self, 'Invalid data', 'Some values were not valid. Edition is ignored.') def _getInsertionIndex(self, xp): i = 0 while (self.xp[i] < xp): i += 1 return i def insertControllers(self, xplist): for xp in xplist: self.insertController(xp) def insertController(self, xp, index=None): if xp in self.xp: return None if index is None: index = self._getInsertionIndex(xp) # updating data (not in the most efficient way, but at least is clean) old_xp = self.xp self.xp = numpy.concatenate((self.xp[:index], (xp,), self.xp[index:])) self.yp = numpy.interp(self.xp, self.x, self.y) # the new correction is obtained by interpolation from the neighbouring # ones self.corrp = numpy.interp(self.xp, old_xp, self.corrp) # creating the controller ctrl = ControllerBox(parent=None, x=xp, y=self.yp[ index], corr=self.corrp[index]) self.ctrlLayout.insertWidget(index, ctrl) self._controllers.insert(index, ctrl) self.connectToController(ctrl) self.updatePlots() return index def delController(self, index): c = self._controllers.pop(index) c.setParent(None) c.deleteLater() self.xp = numpy.concatenate((self.xp[:index], self.xp[index + 1:])) self.yp = numpy.interp(self.xp, self.x, self.y) self.corrp = numpy.concatenate( (self.corrp[:index], self.corrp[index + 1:])) def _populatePlots(self): # Curves appearance self._yAppearance = CurveAppearanceProperties( sStyle=Qwt5.QwtSymbol.NoSymbol, lStyle=Qt.Qt.SolidLine, lWidth=2, lColor='black', cStyle=Qwt5.QwtPlotCurve.Lines, yAxis=Qwt5.QwtPlot.yLeft) self._correctedAppearance = CurveAppearanceProperties( sStyle=Qwt5.QwtSymbol.NoSymbol, lStyle=Qt.Qt.DashLine, lWidth=1, lColor='blue', cStyle=Qwt5.QwtPlotCurve.Lines, yAxis=Qwt5.QwtPlot.yLeft) self._cpointsAppearance = CurveAppearanceProperties( sStyle=Qwt5.QwtSymbol.Rect, sSize=5, sColor='blue', sFill=True, lStyle=Qt.Qt.NoPen, yAxis=Qwt5.QwtPlot.yLeft) self._corrAppearance = CurveAppearanceProperties( sStyle=Qwt5.QwtSymbol.NoSymbol, lStyle=Qt.Qt.SolidLine, lWidth=1, lColor='blue', cStyle=Qwt5.QwtPlotCurve.Lines, yAxis=Qwt5.QwtPlot.yLeft) self.plot1.attachRawData({'x': self.x, 'y': self.y, 'title': 'Master'}) self.plot1.setCurveAppearanceProperties({'Master': self._yAppearance}) self.plot1.attachRawData( {'x': self.xp, 'y': self.yp + self.corrp, 'title': 'Control Points'}) self.plot1.setCurveAppearanceProperties( {'Control Points': self._cpointsAppearance}) self.plot1.attachRawData( {'x': self.x, 'y': self.y + self.corr, 'title': 'Corrected'}) self.plot1.setCurveAppearanceProperties( {'Corrected': self._correctedAppearance}) self.plot2.attachRawData( {'x': self.x, 'y': self.corr, 'title': 'Correction'}) self.plot2.setCurveAppearanceProperties( {'Correction': self._corrAppearance}) self.plot2.attachRawData( {'x': self.xp, 'y': self.corrp, 'title': 'Control Points'}) self.plot2.setCurveAppearanceProperties( {'Control Points': self._cpointsAppearance}) def updatePlots(self): self.plot1.getCurve('Control Points').setData( self.xp, self.yp + self.corrp) self.plot1.getCurve('Corrected').setData(self.x, self.y + self.corr) self.plot2.getCurve('Correction').setData(self.x, self.corr) self.plot2.getCurve('Control Points').setData(self.xp, self.corrp) index = self._getInsertionIndex(self.markerPos) self.marker1.setValue(self.xp[index], self.yp[ index] + self.corrp[index]) self.marker2.setValue(self.xp[index], self.corrp[index]) self.plot1.replot() self.plot2.replot() def onLCopy(self, checked): sender = self.sender().ctrlObj index = self._getInsertionIndex(sender._x) v = sender.corrSB.value() for ctrl in self._controllers[:index]: ctrl.corrSB.setValue(v) def onRCopy(self, checked): sender = self.sender().ctrlObj index = self._getInsertionIndex(sender._x) v = sender.corrSB.value() for ctrl in self._controllers[index + 1:]: ctrl.corrSB.setValue(v) def onLScale(self, checked): sender = self.sender().ctrlObj index = self._getInsertionIndex(sender._x) # y=numpy.interp(self.xp, self.x, self.y) #values of the master at the # control points if self.yp[index] == 0: Qt.QMessageBox.warning( self, 'Scaling Error', 'The master at this control point is zero-valued. This point cannot be used as reference for scaling') return v = sender.corrSB.value() / (self.yp[index]) for i in range(0, index): self._controllers[i].corrSB.setValue(v * self.yp[i]) def onRScale(self, checked): sender = self.sender().ctrlObj index = self._getInsertionIndex(sender._x) # y=numpy.interp(self.xp, self.x, self.y) #values of the master at the # control points if self.yp[index] == 0: Qt.QMessageBox.warning( self, 'Scaling Error', 'The master at this control point is zero-valued. This point cannot be used as reference for scaling') return v = sender.corrSB.value() / (self.yp[index]) for i in range(index + 1, self.xp.size): self._controllers[i].corrSB.setValue(v * self.yp[i]) def changeCPointSelection(self, newpos): index = self._getInsertionIndex(newpos) old_index = self._getInsertionIndex(self.markerPos) self.markerPos = self.xp[index] self.marker1.setValue(self.xp[index], self.yp[ index] + self.corrp[index]) self.marker2.setValue(self.xp[index], self.corrp[index]) self.plot1.replot() self.plot2.replot() self._controllers[old_index].corrSB.setStyleSheet('') self._controllers[index].corrSB.setStyleSheet('background:lightgreen') self._selectedController = self._controllers[index] def onCorrSBChanged(self, value=None): '''recalculates the position and value of the control points (self.xp and self.corrp) as well as the correction curve (self.corr)''' ctrl = self.sender().ctrlObj self.corrp[self._getInsertionIndex(ctrl._x)] = value # recalculate the correction curve self.corr = numpy.interp(self.x, self.xp, self.corrp) self.updatePlots() def setMaster(self, x, y, keepCP=False, keepCorr=False): # make sure that x,y are numpy arrays and that the values are sorted # for x x, y = numpy.array(x), numpy.array(y) if x.shape != y.shape or x.size == 0 or y.size == 0: raise ValueError('The master curve is not valid') sortedindexes =

numpy.argsort(x)

numpy.argsort

import os import pickle import numpy as np from tqdm import tqdm import torch from self_supervised.data.io import loadmat FILENAMES = { ('mihi', 1): 'full-mihi-03032014', ('mihi', 2): 'full-mihi-03062014', ('chewie', 1): 'full-chewie-10032013', ('chewie', 2): 'full-chewie-12192013', } class ReachNeuralDataset: def __init__(self, path, primate='mihi', day=1, binning_period=0.1, binning_overlap=0.0, train_split=0.8, scale_firing_rates=False, scale_velocity=False, sort_by_reach=True): self.path = path # get path to data assert primate in ['mihi', 'chewie'] assert day in [1, 2] self.primate = primate self.filename = FILENAMES[(self.primate, day)] self.raw_path = os.path.join(self.path, 'raw/%s.mat') % self.filename self.processed_path = os.path.join(self.path, 'processed/%s.pkl') % (self.filename + '-%.2f' % binning_period) # get binning parameters self.binning_period = binning_period self.binning_overlap = binning_overlap if self.binning_overlap != 0: raise NotImplemented # train/val split self.train_split = train_split # initialize some parameters self.dataset_ = {} self.subset = 'train' # default selected subset ### Process data # load data if not os.path.exists(self.processed_path): data_train_test = self._process_data() else: data_train_test = self._load_processed_data() # split data data_train, data_test = self._split_data(data_train_test) self._num_trials = {'train': len(data_train['firing_rates']), 'test': len(data_test['firing_rates'])} # compute mean and std of firing rates self.mean, self.std = self._compute_mean_std(data_train, feature='firing_rates') # remove neurons with no variance data_train, data_test = self._remove_static_neurons(data_train, data_test) # scale data if scale_firing_rates: data_train, data_test = self._scale_data(data_train, data_test, feature='firing_rates') if scale_velocity: data_train, data_test = self._scale_data(data_train, data_test, feature='velocity') # sort by reach direction if sort_by_reach: data_train = self._sort_by_reach_direction(data_train) data_test = self._sort_by_reach_direction(data_test) # build sequences trial_lengths_train = [seq.shape[0] for seq in data_train['firing_rates']] # merge everything for feature in data_train.keys(): data_train[feature] = np.concatenate(data_train[feature]).squeeze() data_test[feature] = np.concatenate(data_test[feature]).squeeze() data_train['trial_lengths'] = trial_lengths_train data_train['reach_directions'] = np.unique(data_train['labels']).tolist() data_train['reach_lengths'] = [np.sum(data_train['labels'] == reach_id) for reach_id in data_train['reach_directions']] # map labels to 0 .. N-1 for training data_train['raw_labels'] = data_train['labels'].copy() data_test['raw_labels'] = data_test['labels'].copy() data_train['labels'] = self._map_labels(data_train) data_test['labels'] = self._map_labels(data_test) self.dataset_['train'] = data_train self.dataset_['test'] = data_test @property def dataset(self): return self.dataset_[self.subset] def __getattr__(self, item): return self.dataset[item] def train(self): self.subset = 'train' def test(self): self.subset = 'test' @property def num_trials(self): return self._num_trials[self.subset] @property def num_neurons(self): return self[0]['firing_rates'].shape[1] def _process_data(self): print('Preparing dataset: Binning data.') # load data mat_dict = loadmat(self.raw_path) # bin data data = self._bin_data(mat_dict) self._save_processed_data(data) return data def _save_processed_data(self, data): with open(self.processed_path, 'wb') as output: pickle.dump({'data': data}, output) def _load_processed_data(self): with open(self.processed_path, "rb") as fp: data = pickle.load(fp)['data'] return data def _bin_data(self, mat_dict): # load matrix trialtable = mat_dict['trial_table'] neurons = mat_dict['out_struct']['units'] pos = np.array(mat_dict['out_struct']['pos']) vel = np.array(mat_dict['out_struct']['vel']) acc = np.array(mat_dict['out_struct']['acc']) force =

np.array(mat_dict['out_struct']['force'])

numpy.array

# Copyright 2018 <NAME> # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. from typed_python import ( Bool, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Float32, Float64, NoneType, TupleOf, ListOf, OneOf, Tuple, NamedTuple, Dict, ConstDict, Alternative, serialize, deserialize, Value, Class, Member, TypeFilter, UndefinedBehaviorException, Function ) from typed_python.test_util import currentMemUsageMb import typed_python._types as _types import psutil import unittest import traceback import time import numpy import os import sys def typeFor(t): assert not isinstance(t, list), t return type(t) def typeForSeveral(t): ts = set(typeFor(a) for a in t) if len(ts) == 1: return list(ts)[0] return OneOf(*ts) def makeTupleOf(*args): if not args: return TupleOf(int)() return TupleOf(typeForSeveral(args))(args) def makeNamedTuple(**kwargs): if not kwargs: return NamedTuple()() return NamedTuple(**{k:typeFor(v) for k,v in kwargs.items()})(**kwargs) def makeTuple(*args): if not args: return Tuple()() return Tuple(*[typeFor(v) for v in args])(args) def makeDict(d): if not d: return ConstDict(int,int)() return ConstDict(typeForSeveral(d.keys()), typeForSeveral(d.values()))(d) def makeAlternative(severalDicts): types = list( set( tuple( (k,typeFor(v)) for k,v in ntDict.items() ) for ntDict in severalDicts ) ) alt = Alternative("Alt", **{ "a_%s" % i: dict(types[i]) for i in range(len(types)) }) res = [] for thing in severalDicts: did = False for i in range(len(types)): try: res.append(getattr(alt,"a_%s" % i)(**thing)) did = True except Exception: pass if did: break assert len(res) == len(severalDicts) return res def choice(x): #numpy.random.choice([1,(1,2)]) blows up because it looks 'multidimensional' #so we have to pick from a list of indices if not isinstance(x,list): x = list(x) return x[numpy.random.choice(list(range(len(x))))] class RandomValueProducer: def __init__(self): self.levels = {0: [b'1', b'', '2', '', 0, 1, 0.0, 1.0, None, False, True, "a ", "a string", "b string", "b str"]} def addEvenly(self, levels, count): for level in range(1, levels+1): self.addValues(level, count) def all(self): res = [] for valueList in self.levels.values(): res.extend(valueList) return res def addValues(self, level, count, sublevels = None): assert level > 0 if sublevels is None: sublevels = list(range(level)) sublevels = [x for x in sublevels if x in self.levels] assert sublevels def picker(): whichLevel = choice(sublevels) try: return choice(self.levels[whichLevel]) except Exception: print(self.levels[whichLevel]) raise for _ in range(count): val = self.randomValue(picker) if not isinstance(val,list): val = [val] self.levels.setdefault(level, []).extend(val) def randomValue(self, picker): def randomTuple(): return makeTuple(*[picker() for i in range(choice([0,1,2,3,4]))]) def randomNamedTupleDict(): return {"x_%s" % i: picker() for i in range(choice([0,1,2,3,4]))} def randomNamedTuple(): return makeNamedTuple(**randomNamedTupleDict()) def randomDict(): return makeDict({picker():picker() for i in range(choice([0,1,2,3,4]))}) def randomTupleOf(): return makeTupleOf(*[picker() for i in range(choice([0,1,2,3,4]))]) def randomAlternative(): return makeAlternative([randomNamedTupleDict() for i in range(choice([1,2,3,4]))]) return choice([randomTuple,randomNamedTuple,randomDict,randomTupleOf,randomAlternative,picker])() def pickRandomly(self): return choice(self.levels[choice(list(self.levels))]) class NativeTypesTests(unittest.TestCase): def check_expected_performance(self, elapsed, expected=1.0): if os.environ.get('TRAVIS_CI', None) is not None: expected = 2 * expected self.assertTrue( elapsed < expected, "Slow Performance: expected to take {expected} sec, but took {elapsed}" .format(expected=expected, elapsed=elapsed) ) def test_objects_are_singletons(self): self.assertTrue(Int8 is Int8) self.assertTrue(NoneType is NoneType) def test_object_binary_compatibility(self): ibc = _types.isBinaryCompatible self.assertTrue(ibc(NoneType, NoneType)) self.assertTrue(ibc(Int8, Int8)) NT = NamedTuple(a=int,b=int) class X(NamedTuple(a=int,b=int)): pass class Y(NamedTuple(a=int,b=int)): pass self.assertTrue(ibc(X, X)) self.assertTrue(ibc(X, Y)) self.assertTrue(ibc(X, NT)) self.assertTrue(ibc(Y, NT)) self.assertTrue(ibc(NT, Y)) self.assertFalse(ibc(OneOf(int, float), OneOf(float, int))) self.assertTrue(ibc(OneOf(int, X), OneOf(int, Y))) self.assertIsInstance(OneOf(None, X)(Y()), X) self.assertIsInstance(NamedTuple(x=OneOf(None, X))(x=Y()).x, X) def test_binary_compatibility_incompatible_alternatives(self): ibc = _types.isBinaryCompatible A1 = Alternative("A1", X={'a': int}, Y={'b': float}) A2 = Alternative("A2", X={'a': int}, Y={'b': str}) self.assertTrue(ibc(A1, A1.X)) self.assertTrue(ibc(A1, A1.Y)) self.assertTrue(ibc(A1.Y, A1.Y)) self.assertTrue(ibc(A1.Y, A1)) self.assertTrue(ibc(A1.X, A1)) self.assertFalse(ibc(A1.X, A1.Y)) self.assertFalse(ibc(A1, A2)) self.assertFalse(ibc(A1.X, A2.X)) self.assertFalse(ibc(A1.Y, A2.Y)) def test_binary_compatibility_compatible_alternatives(self): ibc = _types.isBinaryCompatible A1 = Alternative("A1", X={'a': int}, Y={'b': float}) A2 = Alternative("A2", X={'a': int}, Y={'b': float}) self.assertTrue(ibc(A1.X, A2.X)) self.assertTrue(ibc(A1.Y, A2.Y)) self.assertFalse(ibc(A1.X, A2.Y)) self.assertFalse(ibc(A1.Y, A2.X)) def test_object_bytecounts(self): self.assertEqual(_types.bytecount(NoneType), 0) self.assertEqual(_types.bytecount(Int8), 1) self.assertEqual(_types.bytecount(Int64), 8) def test_type_stringification(self): for t in ['Int8', 'NoneType']: self.assertEqual(str(getattr(_types,t)()), "<class '%s'>" % t) def test_tuple_of(self): tupleOfInt = TupleOf(int) i = tupleOfInt(()) i = tupleOfInt((1,2,3)) self.assertEqual(len(i), 3) self.assertEqual(tuple(i), (1,2,3)) for x in range(10): self.assertEqual( tuple(tupleOfInt(tuple(range(x)))), tuple(range(x)) ) with self.assertRaisesRegex(AttributeError, "do not accept attributes"): tupleOfInt((1,2,3)).x = 2 def test_one_of_alternative(self): X = Alternative("X", V={'a': int}) O = OneOf(None, X) self.assertEqual(O(X.V(a=10)), X.V(a=10)) def test_one_of_py_subclass(self): class X(NamedTuple(x=int)): def f(self): return self.x O = OneOf(None, X) self.assertEqual(NamedTuple(x=int)(x=10).x, 10) self.assertEqual(X(x=10).f(), 10) self.assertEqual(O(X(x=10)).f(), 10) def test_tuple_of_tuple_of(self): tupleOfInt = TupleOf(int) tupleOfTupleOfInt = TupleOf(tupleOfInt) pyVersion = (1,2,3),(1,2,3,4) nativeVersion = tupleOfTupleOfInt(pyVersion) self.assertEqual(len(nativeVersion), 2) self.assertEqual(len(nativeVersion[0]), 3) self.assertEqual(tuple(tuple(x) for x in nativeVersion), pyVersion) bigTup = tupleOfInt(list(range(1000))) t0 = time.time() t = (bigTup,bigTup,bigTup,bigTup,bigTup) for i in range(1000000): tupleOfTupleOfInt(t) elapsed = time.time() - t0 print("Took ", elapsed, " to do 1mm") self.check_expected_performance(elapsed) def test_default_initializer_oneof(self): x = OneOf(None, int) self.assertTrue(x() is None, repr(x())) def test_tuple_of_various_things(self): for thing, typeOfThing in [("hi", str), (b"somebytes", bytes), (1.0, float), (2, int), (None, type(None)) ]: tupleType = TupleOf(typeOfThing) t = tupleType((thing,)) self.assertTrue(type(t[0]) is typeOfThing) self.assertEqual(t[0], thing) def test_tuple_assign_fails(self): with self.assertRaisesRegex(TypeError, "does not support item assignment"): (1,2,3)[10] = 20 with self.assertRaisesRegex(TypeError, "does not support item assignment"): TupleOf(int)((1,2,3))[10] = 20 def test_list_of(self): L = ListOf(int) self.assertEqual(L.__qualname__, "ListOf(Int64)") l = L([1,2,3,4]) self.assertEqual(l[0], 1) self.assertEqual(l[-1], 4) l[0] = 10 self.assertEqual(l[0], 10) l[-1] = 11 self.assertEqual(l[3], 11) with self.assertRaisesRegex(IndexError, "index out of range"): l[100] = 20 l2 = L((10,2,3,11)) self.assertEqual(l,l2) self.assertNotEqual(l,(10,2,3,11)) self.assertEqual(l,[10,2,3,11]) self.assertEqual(str(l),str([10,2,3,11])) l3 = l + l2 self.assertEqual(l3, [10,2,3,11,10,2,3,11]) l3.append(23) self.assertEqual(l3, [10,2,3,11,10,2,3,11, 23]) def test_list_resize(self): l = ListOf(TupleOf(int))() l.resize(10) self.assertEqual(l.reserved(), 10) self.assertEqual(len(l), 10) emptyTup = TupleOf(int)() aTup = TupleOf(int)((1,2,3)) self.assertEqual(list(l), [emptyTup] * 10) l.resize(20, aTup) self.assertEqual(list(l), [emptyTup] * 10 + [aTup] * 10) self.assertEqual(_types.refcount(aTup), 11) self.assertEqual(l.pop(15), aTup) self.assertEqual(l.pop(5), emptyTup) self.assertEqual(_types.refcount(aTup), 10) l.resize(15) with self.assertRaises(IndexError): l.pop(100) self.assertEqual(_types.refcount(aTup), 7) #6 in the list because we popped at '5' l.pop() self.assertEqual(_types.refcount(aTup), 6) #this pops one of the empty tuples l.pop(-10) self.assertEqual(_types.refcount(aTup), 6) l.clear() self.assertEqual(len(l), 0) def test_one_of(self): o = OneOf(None, str) self.assertEqual(o("hi"), "hi") self.assertTrue(o(None) is None) o = OneOf(None, "hi", 1.5, 1, True, b"hi2") self.assertTrue(o(None) is None) self.assertTrue(o("hi") == "hi") self.assertTrue(o(b"hi2") == b"hi2") self.assertTrue(o(1.5) == 1.5) self.assertTrue(o(1) is 1) self.assertIs(o(True), True) with self.assertRaises(TypeError): o("hi2") with self.assertRaises(TypeError): o(b"hi") with self.assertRaises(TypeError): o(3) with self.assertRaises(TypeError): o(False) def test_ordering(self): o = OneOf(None, "hi", 1.5, 1, True, b"hi2") self.assertIs(o(True), True) def test_one_of_flattening(self): self.assertEqual(OneOf(OneOf(None, 1.0), OneOf(2.0, 3.0)), OneOf(None, 1.0, 2.0, 3.0)) def test_one_of_order_matters(self): self.assertNotEqual(OneOf(1.0, 2.0), OneOf(2.0, 1.0)) def test_type_filter(self): EvenInt = TypeFilter(int, lambda i: i % 2 == 0) self.assertTrue(isinstance(2, EvenInt)) self.assertFalse(isinstance(1, EvenInt)) self.assertFalse(isinstance(2.0, EvenInt)) EvenIntegers = TupleOf(EvenInt) e = EvenIntegers(()) e2 = e + (2,4,0) with self.assertRaises(TypeError): EvenIntegers((1,)) with self.assertRaises(TypeError): e2 + (1,) def test_tuple_of_one_of_fixed_size(self): t = TupleOf(OneOf(0,1,2,3,4)) ints = tuple([x % 5 for x in range(1000000)]) typedInts = t(ints) self.assertEqual(len(serialize(t, typedInts)), len(ints) + 8) #4 bytes for size of list, 4 bytes for frame size self.assertEqual(tuple(typedInts), ints) def test_tuple_of_one_of_multi(self): t = TupleOf(OneOf(int, bool)) someThings = tuple([100 + x % 5 if x % 17 != 0 else bool(x%19) for x in range(1000000)]) typedThings = t(someThings) self.assertEqual( len(serialize(t, typedThings)), sum(2 if isinstance(t,bool) else 9 for t in someThings) + 8 ) self.assertEqual(tuple(typedThings), someThings) def test_compound_oneof(self): producer = RandomValueProducer() producer.addEvenly(1000, 2) for _ in range(1000): vals = (producer.pickRandomly(), producer.pickRandomly(), producer.pickRandomly()) a = OneOf(vals[0], vals[1], type(vals[2])) for v in vals: self.assertEqual(a(v), v, (a(v),v)) tup = TupleOf(a) tupInst = tup(vals) for i in range(len(vals)): self.assertEqual(tupInst[i], vals[i], vals) def test_one_of_conversion_failure(self): o = OneOf(None, str) with self.assertRaises(TypeError): o(b"bytes") def test_one_of_in_tuple(self): t = Tuple(OneOf(None, str), str) self.assertEqual(t(("hi","hi2"))[0], "hi") self.assertEqual(t(("hi","hi2"))[1], "hi2") self.assertEqual(t((None,"hi2"))[1], "hi2") self.assertEqual(t((None,"hi2"))[0], None) with self.assertRaises(TypeError): t((None,None)) with self.assertRaises(IndexError): t((None,"hi2"))[2] def test_one_of_composite(self): t = OneOf(TupleOf(str), TupleOf(float)) self.assertIsInstance(t((1.0,2.0)), TupleOf(float)) self.assertIsInstance(t(("1.0","2.0")), TupleOf(str)) with self.assertRaises(TypeError): t((1.0,"2.0")) def test_named_tuple(self): t = NamedTuple(a=int, b=int) with self.assertRaisesRegex(AttributeError, "object has no attribute"): t().asdf with self.assertRaisesRegex(AttributeError, "immutable"): t().a = 1 self.assertEqual(t()[0], 0) self.assertEqual(t().a, 0) self.assertEqual(t()[1], 0) self.assertEqual(t(a=1,b=2).a, 1) self.assertEqual(t(a=1,b=2).b, 2) def test_named_tuple_construction(self): t = NamedTuple(a=int, b=int) self.assertEqual(t(a=10).a, 10) self.assertEqual(t(a=10).b, 0) self.assertEqual(t(a=10,b=2).a, 10) self.assertEqual(t(a=10,b=2).b, 2) self.assertEqual(t({'a': 10,'b':2}).a, 10) self.assertEqual(t({'a': 10,'b':2}).b, 2) self.assertEqual(t({'b':2}).a, 0) self.assertEqual(t({'b':2}).b, 2) with self.assertRaises(TypeError): t({'c':10}) with self.assertRaises(TypeError): t(c=10) def test_named_tuple_str(self): t = NamedTuple(a=str, b=str) self.assertEqual(t(a='1',b='2').a, '1') self.assertEqual(t(a='1',b='2').b, '2') self.assertEqual(t(b='2').a, '') self.assertEqual(t(b='2').b, '2') self.assertEqual(t().a, '') self.assertEqual(t().b, '') def test_tuple_of_string_perf(self): t = NamedTuple(a=str, b=str) t0 = time.time() for i in range(1000000): t(a="a", b="b").a elapsed = time.time() - t0 print("Took ", elapsed, " to do 1mm") self.check_expected_performance(elapsed) def test_comparisons_in_one_of(self): t = OneOf(None, float) def map(x): if x is None: return -1000000.0 else: return x lt = lambda a,b: map(a) < map(b) le = lambda a,b: map(a) <= map(b) eq = lambda a,b: map(a) == map(b) ne = lambda a,b: map(a) != map(b) gt = lambda a,b: map(a) > map(b) ge = lambda a,b: map(a) >= map(b) funcs = [lt,le,eq,ne,gt,ge] ts = [None,1.0,2.0,3.0] for f in funcs: for t1 in ts: for t2 in ts: self.assertTrue(f(t1,t2) is f(t(t1),t(t2))) def test_comparisons_equivalence(self): t = TupleOf(OneOf(None, str, bytes, float, int, bool, TupleOf(int)),) def lt(a,b): return a < b def le(a,b): return a <= b def eq(a,b): return a == b def ne(a,b): return a != b def gt(a,b): return a > b def ge(a,b): return a >= b funcs = [lt,le,eq,ne,gt,ge] tgroups = [ [1.0,2.0,3.0], [1,2,3], [True,False], ["a","b","ab","bb","ba","aaaaaaa","","asdf"], ["1","2","3","12","13","23","24","123123", "0", ""], [b"a",b"b",b"ab",b"bb",b"ba",b"aaaaaaa",b"",b"asdf"], [(1,2),(1,2,3),(),(1,1),(1,)] ] for ts in tgroups: for f in funcs: for t1 in ts: for t2 in ts: self.assertTrue(f(t1,t2) is f(t((t1,)),t((t2,))), (f, t1,t2, f(t1,t2), f(t((t1,)),t((t2,)))) ) def test_const_dict(self): t = ConstDict(str,str) self.assertEqual(len(t()), 0) self.assertEqual(len(t({})), 0) self.assertEqual(len(t({'a':'b'})), 1) self.assertEqual(t({'a':'b'})['a'], 'b') self.assertEqual(t({'a':'b','b':'c'})['b'], 'c') self.assertTrue("a" in deserialize(t,serialize(t, t({'a':'b'})))) self.assertTrue("a" in deserialize(t,serialize(t, t({'a':'b','b':'c'})))) self.assertTrue("a" in deserialize(t,serialize(t, t({'a':'b','b':'c','c':'d'})))) self.assertTrue("a" in deserialize(t,serialize(t, t({'a':'b','b':'c','c':'d','d':'e'})))) self.assertTrue("c" in deserialize(t,serialize(t, t({'a':'b','b':'c','c':'d','def':'e'})))) self.assertTrue("def" in deserialize(t,serialize(t, t({'a':'b','b':'c','c':'d','def':'e'})))) def test_const_dict_get(self): a = ConstDict(str,str)({'a':'b','c':'d'}) self.assertEqual(a.get('a'),'b') self.assertEqual(a.get('asdf'),None) self.assertEqual(a.get('asdf',20),20) def test_const_dict_items_keys_and_values(self): a = ConstDict(str,str)({'a':'b','c':'d'}) self.assertEqual(sorted(a.items()), [('a','b'),('c','d')]) self.assertEqual(sorted(a.keys()), ['a','c']) self.assertEqual(sorted(a.values()), ['b','d']) def test_empty_string(self): a = ConstDict(str,str)({'a':''}) print(a['a']) def test_dict_to_oneof(self): t = ConstDict(str,OneOf("A","B","ABCDEF")) a = t({'a':'A','b':'ABCDEF'}) self.assertEqual(a['a'], "A") self.assertEqual(a['b'], "ABCDEF") self.assertEqual(a, deserialize(t,serialize(t,a))) def test_deserialize_primitive(self): x = deserialize(str, serialize(str, "a")) self.assertTrue(isinstance(x,str)) def test_dict_containment(self): for _ in range(100): producer = RandomValueProducer() producer.addEvenly(20, 2) values = producer.all() for v in values: if str(type(v))[:17] == "<class 'ConstDict": v = deserialize(type(v), serialize(type(v), v)) for k in v: self.assertTrue(k in v) def test_named_tuple_from_dict(self): N = NamedTuple(x=int, y=str,z=OneOf(None,"hihi")) self.assertEqual(N().x, 0) self.assertEqual(N().y, "") self.assertEqual(N().z, None) self.assertEqual(N({}).x, 0) self.assertEqual(N({}).y, "") self.assertEqual(N({}).z, None) self.assertEqual(N({'x': 20}).x, 20) self.assertEqual(N({'x': 20, 'y': "30"}).y, "30") self.assertEqual(N({'y': "30", 'x': 20}).y, "30") self.assertEqual(N({'z': "hihi"}).z, "hihi") with self.assertRaises(Exception): N({'r': 'hi'}) N({'y': 'hi', 'z': "not hihi"}) N({'a': 0, 'b': 0, 'c': 0, 'd': 0}) def test_const_dict_mixed(self): t = ConstDict(str,int) self.assertTrue(t({"a":10})["a"] == 10) t = ConstDict(int, str) self.assertTrue(t({10:"a"})[10] == "a") def test_const_dict_comparison(self): t = ConstDict(str,str) self.assertEqual(t({'a':'b'}), t({'a':'b'})) self.assertLess(t({}), t({'a':'b'})) def test_const_dict_lookup(self): for type_to_use, vals in [ (int, list(range(20))), (bytes, [b'1', b'2', b'3', b'4', b'5']) ]: t = ConstDict(type_to_use, type_to_use) for _ in range(10): ks = list(vals) vs = list(vals) numpy.random.shuffle(ks) numpy.random.shuffle(vs) py_d = {} for i in range(len(ks)): py_d[ks[i]] = vs[i] typed_d = t(py_d) for k in py_d: self.assertEqual(py_d[k], typed_d[k]) last_k = None for k in typed_d: assert last_k is None or k > last_k, (k,last_k) last_k = k def test_const_dict_lookup_time(self): int_dict = ConstDict(int, int) d = int_dict({k:k for k in range(1000000)}) for k in range(1000000): self.assertTrue(k in d) self.assertTrue(d[k] == k) def test_const_dict_of_dict(self): int_dict = ConstDict(int, int) int_dict_2 = ConstDict(int_dict,int_dict) d = int_dict({1:2}) d2 = int_dict({1:2,3:4}) big = int_dict_2({d:d2}) self.assertTrue(d in big) self.assertTrue(d2 not in big) self.assertTrue(big[d] == d2) def test_dict_hash_perf(self): str_dict = ConstDict(str, str) s = str_dict({'a' * 1000000: 'b' * 1000000}) t0 = time.time() for k in range(1000000): hash(s) elapsed = time.time() - t0 print(elapsed, " to do 1mm") self.check_expected_performance(elapsed) def test_const_dict_str_perf(self): t = ConstDict(str,str) t0 = time.time() for i in range(100000): t({str(k): str(k+1) for k in range(10)}) elapsed = time.time() - t0 print("Took ", elapsed, " to do 1mm") self.check_expected_performance(elapsed) def test_const_dict_int_perf(self): t = ConstDict(int,int) t0 = time.time() for i in range(100000): t({k:k+1 for k in range(10)}) elapsed = time.time() - t0 print("Took ", elapsed, " to do 1mm") self.check_expected_performance(elapsed) def test_const_dict_iter_int(self): t = ConstDict(int,int) aDict = t({k:k+1 for k in range(100)}) for k in aDict: self.assertEqual(aDict[k], k+1) def test_const_dict_iter_str(self): t = ConstDict(str,str) aDict = t({str(k):str(k+1) for k in range(100)}) for k in aDict: self.assertEqual(aDict[str(k)], str(int(k)+1)) def test_alternatives_with_Bytes(self): alt = Alternative( "Alt", x_0={'a':bytes} ) self.assertEqual(alt.x_0(a=b''), alt.x_0(a=b'')) def test_alternatives_with_str_func(self): alt = Alternative( "Alt", x_0={'a':bytes}, f=lambda self: 1, __str__=lambda self: "not_your_usual_str" ) self.assertEqual(alt.x_0().f(), 1) self.assertEqual(str(alt.x_0()), "not_your_usual_str") def test_named_tuple_subclass_magic_methods(self): class X(NamedTuple(x=int,y=int)): def __str__(self): return "str override" def __repr__(self): return "repr override" self.assertEqual(repr(X()), "repr override") self.assertEqual(str(X()), "str override") def test_empty_alternatives(self): a = Alternative( "Alt", A={}, B={} ) self.assertEqual(a.A(), a.A()) self.assertIsInstance(deserialize(a, serialize(a, a.A())), a.A) self.assertEqual(a.A(), deserialize(a, serialize(a, a.A()))) self.assertEqual(a.B(), a.B()) self.assertNotEqual(a.A(), a.B()) self.assertNotEqual(a.B(), a.A()) def test_extracted_alternatives_have_correct_type(self): Alt = Alternative( "Alt", A={}, B={} ) tOfAlt = TupleOf(Alt) a = Alt.A() aTup = tOfAlt((a,)) self.assertEqual(a, aTup[0]) self.assertTrue(type(a) is type(aTup[0])) def test_alternatives(self): alt = Alternative( "Alt", child_ints={'x': int, 'y': int}, child_strings={'x': str, 'y': str} ) self.assertTrue(issubclass(alt.child_ints, alt)) self.assertTrue(issubclass(alt.child_strings, alt)) a = alt.child_ints(x=10,y=20) a2 = alt.child_ints(x=10,y=20) self.assertEqual(a,a2) self.assertTrue(isinstance(a, alt)) self.assertTrue(isinstance(a, alt.child_ints)) self.assertEqual(a.x, 10) self.assertEqual(a.y, 20) self.assertTrue(a.matches.child_ints) self.assertFalse(a.matches.child_strings) with self.assertRaisesRegex(AttributeError, "immutable"): a.x = 20 def test_alternatives_comparison(self): empty = Alternative("X", A={}, B={}) self.assertEqual(empty.A(), empty.A()) self.assertEqual(empty.B(), empty.B()) self.assertNotEqual(empty.A(), empty.B()) a = Alternative("X", A={'a': int}, B={'b': int}, C={'c': str}, D={'d': bytes}, ) self.assertEqual(a.A(a=10), a.A(a=10)) self.assertNotEqual(a.A(a=10), a.A(a=11)) self.assertNotEqual(a.C(c=""), a.C(c="hi")) self.assertFalse(a.C(c="") == a.C(c="hi")) self.assertNotEqual(a.D(d=b""), a.D(d=b"hi")) def test_alternatives_add_operator(self): alt = Alternative( "Alt", child_ints={'x': int, 'y': int}, __add__=lambda l,r: (l,r) ) a = alt.child_ints(x=0,y=2) self.assertEqual(a+a,(a,a)) def test_alternatives_perf(self): alt = Alternative( "Alt", child_ints={'x': int, 'y': int}, child_strings={'x': str, 'y': str} ) t0 = time.time() for i in range(1000000): a = alt.child_ints(x=10,y=20) a.matches.child_ints a.x elapsed = time.time() - t0 print("Took ", elapsed, " to do 1mm") self.check_expected_performance(elapsed, expected=2.0) def test_object_hashing_and_equality(self): for _ in range(100): producer = RandomValueProducer() producer.addEvenly(20, 2) values = producer.all() for v1 in values: for v2 in values: if hash(v1) != hash(v2) and v1 == v2: print(v1,v2, type(v1), type(v2)) for v1 in values: for v2 in values: if type(v1) == type(v2) and v1 == v2: self.assertEqual(hash(v1), hash(v2), (v1, v2)) if type(v1) is type(v2): self.assertEqual(repr(v1), repr(v2), (v1, v2, type(v1),type(v2))) values = sorted([makeTuple(v) for v in values]) for i in range(len(values)-1): self.assertTrue(values[i] <= values[i+1]) self.assertTrue(values[i+1] >= values[i]) def test_bytes_repr(self): for _ in range(100000): #always start with a '"' because otherwise python keeps chosing different #initial characters. someBytes = b'"' + numpy.random.uniform(size=2).tostring() self.assertEqual(repr(makeTuple(someBytes)), repr((someBytes,))) def test_equality_with_native_python_objects(self): tups = [(1,2,3), (), ("2",), (b"2",), (1,2,3, "b"), (2,), (None,)] for tup1 in tups: self.assertEqual( makeTuple(*tup1), tup1 ) for tup2 in tups: if tup1 != tup2: self.assertNotEqual( makeTuple(*tup1), tup2 ) for tup1 in tups: self.assertEqual( makeTupleOf(*tup1), tup1 ) for tup2 in tups: if tup1 != tup2: self.assertNotEqual( makeTupleOf(*tup1), tup2 ) def test_add_tuple_of(self): tupleOfInt = TupleOf(int) tups = [(),(1,2),(1,),(1,2,3,4)] for tup1 in tups: for tup2 in tups: self.assertEqual(tupleOfInt(tup1) + tupleOfInt(tup2), tupleOfInt(tup1+tup2)) self.assertEqual(tupleOfInt(tup1) + tup2, tupleOfInt(tup1+tup2)) def test_slice_tuple_of(self): tupleOfInt = TupleOf(int) ints = tuple(range(20)) aTuple = tupleOfInt(ints); for i in range(-21,21): for i2 in range(-21, 21): for step in range(-3, 3): if step != 0: self.assertEqual(aTuple[i:i2:step], ints[i:i2:step]) try: ints[i] self.assertEqual(aTuple[i], ints[i]) except IndexError: with self.assertRaises(IndexError): aTuple[i] def test_dictionary_subtraction_basic(self): intDict = ConstDict(int,int) self.assertEqual(intDict({1:2}) - (1,), intDict({})) self.assertEqual(intDict({1:2, 3:4}) - (1,), intDict({3:4})) self.assertEqual(intDict({1:2, 3:4}) - (3,), intDict({1:2})) def test_dictionary_addition_and_subtraction(self): someDicts = [{i:choice([1,2,3,4,5]) for i in range(choice([4,6,10,20]))} for _ in range(20)] intDict = ConstDict(int,int) for d1 in someDicts: for d2 in someDicts: addResult = dict(d1) addResult.update(d2) self.assertEqual(intDict(d1) + intDict(d2), intDict(addResult)) res = intDict(addResult) while len(res): toRemove = [] for i in range(choice(list(range(len(res))))+1): key = choice(list(addResult)) del addResult[key] toRemove.append(key) res = res - toRemove self.assertEqual(res, intDict(addResult)) def test_subclassing(self): BaseTuple = NamedTuple(x=int,y=float) class NTSubclass(BaseTuple): def f(self): return self.x + self.y def __repr__(self): return "ASDF" inst = NTSubclass(x=10,y=20) self.assertTrue(isinstance(inst, BaseTuple)) self.assertTrue(isinstance(inst, NTSubclass)) self.assertTrue(type(inst) is NTSubclass) self.assertEqual(repr(inst), "ASDF") self.assertNotEqual(BaseTuple.__repr__(inst), "ASDF") self.assertEqual(inst.x, 10) self.assertEqual(inst.f(), 30) TupleOfSubclass = TupleOf(NTSubclass) instTup = TupleOfSubclass((inst,BaseTuple(x=20,y=20.0))) self.assertTrue(isinstance(instTup[0], NTSubclass)) self.assertTrue(isinstance(instTup[1], NTSubclass)) self.assertEqual(instTup[0].f(), 30) self.assertEqual(instTup[1].f(), 40) self.assertEqual(BaseTuple(inst).x, 10) self.assertTrue(OneOf(None, NTSubclass)(None) is None) self.assertTrue(OneOf(None, NTSubclass)(inst) == inst) def test_serialization(self): ints = TupleOf(int)((1,2,3,4)) self.assertEqual( len(serialize(TupleOf(int), ints)), 40 ) while len(ints) < 1000000: ints = ints + ints t0 = time.time() self.assertEqual(len(serialize(TupleOf(int), ints)), len(ints) * 8 + 8) print(time.time() - t0, " for ", len(ints)) def test_serialization_roundtrip(self): badlen = None for _ in range(100): producer = RandomValueProducer() producer.addEvenly(30, 3) values = producer.all() for v in values: ser = serialize(type(v), v) v2 = deserialize(type(v), ser) ser2 = serialize(type(v), v2) self.assertTrue(type(v2) is type(v)) self.assertEqual(ser,ser2) self.assertEqual(str(v), str(v2)) self.assertEqual(v, v2) def test_serialize_doesnt_leak(self): T = TupleOf(int) def getMem(): return psutil.Process().memory_info().rss / 1024 ** 2 m0 = getMem() for passIx in range(100): for i in range(1000): t = T(list(range(i))) deserialize(T, serialize(T,t)) self.assertTrue(getMem() < m0 + 100) def test_const_dict_of_tuple(self): K = NamedTuple(a=OneOf(float, int), b=OneOf(float, int)) someKs = [K(a=0,b=0), K(a=1), K(a=10), K(b=10), K()] T = ConstDict(K, K) indexDict = {} x = T() numpy.random.seed(42) for _ in range(100): i1 = numpy.random.choice(len(someKs)) i2 = numpy.random.choice(len(someKs)) add = numpy.random.choice([False, True]) if add: indexDict[i1] = i2 x = x + {someKs[i1]: someKs[i2]} else: if i1 in indexDict: del indexDict[i1] x = x - (someKs[i1],) self.assertEqual(x, T({someKs[i]:someKs[v] for i,v in indexDict.items()})) for k in x: self.assertTrue(k in x) x[k] def test_conversion_of_binary_compatible(self): class T1(NamedTuple(a=int)): pass class T2(NamedTuple(a=int)): pass class T1Comp(NamedTuple(d=ConstDict(str, T1))): pass class T2Comp(NamedTuple(d=ConstDict(str, T1))): pass aT1C = T1Comp(d={'a': T1(a=10)}) self.assertEqual(T2Comp(aT1C).d['a'].a, 10) self.assertEqual(aT1C, deserialize(T1Comp, serialize(T2Comp, aT1C))) def test_conversion_of_binary_compatible_nested(self): def make(): class Interior(NamedTuple(a=int)): pass class Exterior(NamedTuple(a=Interior)): pass return Exterior E1 = make() E2 = make() OneOf(None, E2)(E1()) def test_python_objects_in_tuples(self): class NormalPyClass(object): pass class NormalPySubclass(NormalPyClass): pass NT = NamedTuple(x=NormalPyClass, y=NormalPySubclass) nt = NT(x=NormalPyClass(),y=NormalPySubclass()) self.assertIsInstance(nt.x, NormalPyClass) self.assertIsInstance(nt.y, NormalPySubclass) def test_construct_alternatives_with_positional_arguments(self): a = Alternative("A", HasOne = {'a': str}, HasTwo = {'a': str, 'b': str}) with self.assertRaises(TypeError): a.HasTwo("hi") self.assertEqual(a.HasOne("hi"), a.HasOne(a="hi")) hasOne = a.HasOne("hi") self.assertEqual(a.HasOne(hasOne), hasOne) with self.assertRaises(TypeError): a.HasOne(a.HasTwo(a='1',b='b')) def test_recursive_classes_repr(self): class ASelfRecursiveClass(Class): x = Member(OneOf(None, lambda: ASelfRecursiveClass)) a = ASelfRecursiveClass() a.x = a b = ASelfRecursiveClass() b.x = b print(repr(a)) def test_unsafe_pointers_to_list_internals(self): x = ListOf(int)() x.resize(100) for i in range(len(x)): x[i] = i aPointer = x.pointerUnsafe(0) self.assertTrue(str(aPointer).startswith("(Int64*)0x")) self.assertEqual(aPointer.get(), x[0]) aPointer.set(100) self.assertEqual(aPointer.get(), 100) self.assertEqual(x[0], 100) aPointer = aPointer + 10 self.assertEqual(aPointer.get(), x[10]) self.assertEqual(aPointer[10], x[20]) aPointer.set(20) self.assertEqual(aPointer.get(), 20) self.assertEqual(x[10], 20) #this is OK because ints are POD. aPointer.initialize(30) self.assertEqual(x[10], 30) def test_unsafe_pointers_to_uninitialized_list_items(self): #because this is testing unsafe operations, the test is #really just that we don't segfault! for _ in range(100): x = ListOf(TupleOf(int))() x.reserve(10) for i in range(x.reserved()): x.pointerUnsafe(i).initialize((i,)) x.setSizeUnsafe(10) #now check that if we fail to set the size we'll leak the tuple aLeakedTuple = TupleOf(int)((1,2,3)) x = ListOf(TupleOf(int))() x.reserve(1) x.pointerUnsafe(0).initialize(aLeakedTuple) x = None self.assertEqual(_types.refcount(aLeakedTuple), 2) def test_list_copy_operation_duplicates_list(self): T = ListOf(int) x = T([1,2,3]) y = T(x) x[0] = 100 self.assertNotEqual(y[0], 100) def test_list_and_tuple_conversion_to_numpy(self): for T in [ListOf(bool), TupleOf(bool)]: for arr in [

numpy.array([])

numpy.array

#!/usr/bin/python ''' Improved Minima Controlled Recursive Averaging (IMCRA) single channel noise estmation after [1] Israel Cohen, Noise Spectrum estimation in Adverse Environments: Improved Minima Controlled Recursive Averaging. IEEE. Trans. Acoust. Speech Signal Process. VOL. 11, NO. 5, Sep 2003. <NAME> Feb2015 ''' import numpy as np import sys import os # Add the path of the toolbox root # from ns import MMSE_LSA # For debugging purposes #import ipdb #np.seterr(divide='ignore',invalid='raise') def post_speech_prob(Y_l, q, Gamma, xi): ''' Posterior speech probability given prior speech absence and the complex Gaussian model of speech distortion Input: Y_l [K, 1] STFT frame Input: q [K, 1] a priori speech presence Input: Gamma [K, 1] A posteriori SNR Input: xi [K, 1] A priori SNR ''' nu = Gamma*xi/(1+xi) p = np.zeros(Y_l.shape) p[q < 1] = 1./(1+(q[q < 1]/(1-q[q < 1]))*(1+xi[q < 1])*np.exp(-nu[q < 1])) return p def sym_hanning(n): ''' Same Hanning as the matlab default ''' # to float n = float(n) if np.mod(n, 2) == 0: # Even length window half = n/2; else: # Odd length window half = (n+1)/2; w = .5*(1 - np.cos(2*np.pi*np.arange(1,half+1)/(n+1))) return np.concatenate((w, w[:-1])); # Default buffer size L_MAX = 1000 class imcra_se(): ''' Simple class for enhancement using IMCRA ''' def __init__(self, nfft, Lambda_D=None, Bmin=3.2, alpha =0.92, xi_min=10**(-25./20), IS=10): # Decision directed smoothing factor self.alpha = alpha # Decision directed a priori SNR floor self.xi_min = xi_min self.nfft = int(nfft/2+1) # self.store = {} self.store['Lambda_D'] = np.zeros((self.nfft, L_MAX)) self.store['p'] = np.zeros((self.nfft, L_MAX)) self.store['xi'] = np.zeros((self.nfft, L_MAX)) self.store['MSE'] = np.zeros((self.nfft, L_MAX)) self.l = 0 # IMCRA initial background segment (frames) # Initialization self.imcra = imcra(nfft, IS=IS, Bmin=Bmin) self.G = 1 self.p = np.zeros([self.nfft, 1]) # Initial noise estimate if Lambda_D is None: self.Lambda_D = 1e-6*np.ones([self.nfft, 1]) else: self.Lambda_D = Lambda_D def update(self, Y): hat_X = np.zeros(Y.shape, dtype=complex) G = self.G Gamma = G Lambda_D = self.Lambda_D p = self.p K, L = Y.shape if self.l + L > L_MAX: # If maximum size surpassed, add a new batch of zeroes self.store['Lambda_D'] = np.concatenate((self.store['Lambda_D'], np.zeros((K, L_MAX))), 1) self.store['p'] = np.concatenate((self.store['p'], np.zeros((K, L_MAX))), 1) self.store['xi'] = np.concatenate((self.store['xi'], np.zeros((K, L_MAX))), 1) self.store['MSE'] = np.concatenate((self.store['MSE'], np.zeros((K, L_MAX))), 1) for l in np.arange(0, L): # A priori SNR, stationary parameter estimate (uses last Gamma) xi_G = (G**2)*Gamma # A posterori SNR Gamma = (np.abs(Y[:, l:l+1])**2)/Lambda_D # A priori SNR, maximum likelihood estimate xi_ML = Gamma - 1 xi_ML[xi_ML<1e-6] = 1e-6 # Decision directed rule xi = self.alpha*xi_G + (1-self.alpha)*xi_ML # Flooring xi[xi<self.xi_min] = self.xi_min # MMSE-LSA # Get Wiener gain G = xi/(1 + xi) hat_X[:, l:l+1] = MMSE_LSA(G*Y[:, l:l+1], G*Lambda_D) # Residual MSE of Wiener filter MSE = G*Lambda_D # TODO: Store additional variables if solicited self.store['Lambda_D'][:, self.l:self.l+1] = Lambda_D self.store['p'][:, self.l:self.l+1] = p self.store['xi'][:, self.l:self.l+1] = xi self.store['MSE'][:, self.l:self.l+1] = MSE self.l += 1 # IMCRA noise estimate and posterior speech probability for the # next iteration Lambda_D, p = self.imcra.update(Y[:, l:l+1], Gamma, xi) # Keep these for the next iteration self.G = G self.Lambda_D = Lambda_D[:, -2:] self.p = p return hat_X def get_param(self, param_list): ''' Return stored parameters ''' val_list = [] for par in param_list: if par not in self.store: raise(ValueError, "Parameter %s was not recorded" % par) val_list.append(self.store[par][:, :self.l]) return val_list class imcra(): ''' IMCRA class ''' def __init__(self, nfft, Bmin=None, **kwargs): # IMCRA DEFAULT CONFIGURATION # Consult [1] on how to set the parameters # Number of initial frames of the signal assumed to be noise self.IS = 15 # How many adjacent bins (before and after bin k) are used to smooth # spectrogram in frecuency (S_f[k,l]) self.w = 1 # Adaptation rate for the spectrogram smoothing in time self.alpha_s = 0.9 # Adaptation rate for speech probability dependent time smoothing # paramater self.alpha_d = 0.85 # U spectrogram values are stored to perform minimum tracking self.U = 8 # 8 # Each V frames minimum tracking will take place self.V = 15 # 15 # Number of frames before the actual frame considered in minimum # traking. (Irrelevant its included in Bmin) self.D = self.U*self.V # Significance levels # Significance level for the first VAD self.epsilon = 0.01 # Significance level for the second VAD self.epsilon1 = 0.05 # Overload defaults for par in kwargs.keys(): # If parameter is one of the defaults, overload it if par in self.__dict__: setattr(self, par, kwargs[par]) else: raise ValueError("%s is not an imcra parameter" % par) # If the standard significance levels and smoothing parameters not used # we need to recompute everything if ((self.epsilon == 0.01) & (self.epsilon1 == 0.05) & (self.alpha_s == 0.9) & (self.w == 1)): # VAD is attained through hypothesis test assuming distributions # for ratios related to the minimum statistics, these are the # parameteres # Treshold to achieve 0.01 significance in first VAD speech absence # hypothesis test self.Gamma0 = 4.6 # Treshold to achieve 0.05 significance in second VAD speech # presence hypothesis test self.Gamma1 = 3 # Treshold to achieve 0.05 significance in second VAD speech # presence hypothesis test self.zeta0 = 1.67 # Noise variance estimate bias for speech absence (depends only # on the last three parameters though [1, Eq. 31]) self.beta = 1.47 else: # Note: This STILL assumes that we use the posterior probability # as defined by [1, Eq. 7], see [1, App. II] # This will need SCIPY! import scipy.stats.chi2 as chi2 # Approx degrees of freedom of Eq. 20, see App. II mu = (1+self.alpha_s)/(1-self.alha_s)*(1 + 0.7*w) # Treshold to achieve 0.01 significance in first VAD speech absence # hypothesis test self.Gamma0 = -np.log(epsilon) self.zeta0 = chi2.ppf(1-epsilon,mu)/mu self.Gamma1 = -np.log(epsilon1) # Treshold to achieve 0.05 significance in second VAD speech # presence hypothesis test [1, Eq. 31]) self.beta = ((gamma1 - 1 -np.exp(-1) + np.exp(-gamma1))/ (gamma1 -1 - 3*np.exp(-1) + (gamma1+2)*np.exp(-gamma1))) # Check for smoothed spectrogram bias set if Bmin is None: import warnings warnings.warn("Minimum statistic bias Bmin is not set. Run " "imcra.setBmin(), until then 2.1 used.", DeprecationWarning) self.Bmin = 2.1 # This is for my config! else: self.Bmin = Bmin self.K = int(nfft/2+1) # Number of frequency bins under Nyquist self.l = -1 # Set frame index. -1 is no frame processed self.j = 0 # Set counter for the buffer update self.u = 0 # Set copunter for buffer last filled position # To do the smoothing in frequency fast, we create indices to expand # each frame (column) to a matrix with that column on the center and # neighbouring frequencies on each row. Thay way we can smooth with # One single loop # Create matrix of indices self.sm_idx = np.arange(0,self.K)[:,None] + np.arange(-self.w,self.w+1)[None,:] # Create coresponding matrix of hamming windows self.sm_win = np.tile(sym_hanning(2*self.w+1),(self.K,1)) # Ignore indices out of bounds self.sm_win[self.sm_idx<0] = 0 self.sm_win[self.sm_idx>self.K-1] = 0 self.sm_idx[self.sm_idx<0] = 0 self.sm_idx[self.sm_idx>self.K-1] = self.K-1 # Normalize self.sm_win = self.sm_win/np.sum(self.sm_win, 1, keepdims=True) # BUFFERS # They will be propperly initialized when the first frame is processed # Smoothed Spectrogram first iteration self.S = np.zeros([self.K, 1]) # Smoothed Spectrogram minimum first iteration self.Smin = np.zeros([self.K, 1]) # Smoothed Spectrogram second iteration self.tilde_S = np.zeros([self.K, 1]) # Smoothed Spectrogram second iteration self.tilde_Smin = np.zeros([self.K, 1]) # Smoothed Spectrogram minimum running minimum self.Smin_sw = np.zeros([self.K, 1]) # Second smoothed Spectrogram minimum running minimum self.tilde_Smin_sw = np.zeros([self.K, 1]) # Smoothed Spectrogram minimum first iteration store buffer self.Storing = np.zeros([self.K, self.U]) # Smoothed Spectrogram minimum second iteration store buffer self.tilde_Storing = np.zeros([self.K, self.U]) # Biased noise variance estimate self.ov_Lambda_D = np.zeros([self.K, 1]) # Unbiased noise variance estimate self.Lambda_D = np.zeros([self.K, 1]) # A posteriori speech presence probability self.q = np.ones([self.K, 1]) # A posteriori speech presence probability self.p = np.zeros([self.K, 1]) # Speech presence prob upbound self.p_upthr = 0.9 def reset(self, nfft=512, Bmin=3.2): self.__init__(self, nfft, Bmin) def setBmin(self, N): ''' Computes Bmin given the stft of a white noise signal as obtained e.g n = np.random.randn(1e5) N = stft(n, windowsize, shift, nfft) Bmin = imcra.computeBmin(N) ''' # SANITY CHECK: Enough samples if N.shape[1] < 3*self.U*self.V: raise ValueError("Not enough samples, pick a langer white noise signal") Bmin = np.zeros(N.shape) for l in np.arange(0,N.shape[1]): # Init if l == 0: self.init_params(N[:,l:l+1]) # Get minimum statistics Bmin = (np.abs(N[:,l:l+1])**2)/self.Smin # [3,eq.18] #zeta[:,l:l+1] = imcra.S/(imcra.Bmin*imcra.Smin) # [3,eq.21] #tilde_Gamma_min[:,l:l+1] = (np.abs(Y[:,l:l+1])**2)/(imcra.Bmin*imcra.tilde_Smin) # [3,eq.18] #tilde_zeta[:,l:l+1] = imcra.S/(imcra.Bmin*imcra.tilde_Smin) # [3,eq.21] # Compute mean as average self.Bmin = np.mean(Bmin) return self.Bmin ''' Fast frequency smoothing ''' def fsmooth(self, P_l): return np.sum(self.sm_win*P_l[self.sm_idx][:, :, 0], 1)[:,None] def init_params(self,Y_l): # Smoothed spectrograms # Smoothed Spectrogram first iteration self.S = self.fsmooth(np.abs(Y_l)**2) # Smoothed Spectrogram second iteration self.tilde_S = self.S.copy() # Smoothed Spectrogram minimum first iteration self.Smin = self.S.copy() # Smoothed Spectrogram minimum first second iteration self.tilde_Smin = self.S.copy() # Smoothed Spectrogram minimum running minimum self.Smin_sw = self.S.copy() # Second smoothed Spectrogram minimum running minimum self.tilde_Smin_sw = self.S.copy() # Other parameters # Biased noise variance estimate self.ov_Lambda_D = np.abs(Y_l)**2 # Unbiased noise variance estimate self.Lambda_D = self.ov_Lambda_D # A posteriori speech presence probability self.p = np.zeros(Y_l.shape) def update(self, Y_l, Gamma, xi): ''' This calls the components of IMCRA as in the original paper. These are A priori speech absence probability estimator A posteriori speech probability estimator Probabilistic recursive smoothing For the initialization period (only noise assumed) it uses normal smoothing ''' # Increase frame counter self.l += 1 # If in first frame, initialize buffers with observed frame if self.l == 0: # print('first frame!') self.init_params(Y_l) # If in initialization segment, update noise stats only # Note: Keep in mind that IS might be zero if self.l < self.IS: # Frequency smoothing [3,eq.14] Sf = self.fsmooth(np.abs(Y_l)**2) # Frequency and time smoothing [3,eqs.15] self.S = self.alpha_s*self.S + (1-self.alpha_s)*Sf # Update running minimum self.Smin = np.min(np.concatenate((self.Smin,self.S),1),1)[:,None] self.Smin_sw = np.min(np.concatenate((self.Smin_sw,self.S),1),1)[:,None] # Compute smoothed spectrogram for p = 0 self.Lambda_D = self.alpha_d*self.Lambda_D + (1-self.alpha_d)*np.abs(Y_l)**2 # Set a priori background probability to one self.q[:] = 1 # Set a posteriori speech probability to zero self.p[:] = 0 else: # FIRST MINIMA CONTROLLED VAD # This provides a rough VAD to eliminate relatively strong speech # components towards the second power spectrum estimation Sf = self.fsmooth(np.abs(Y_l)**2) # [3,eq.14] # Time smoothing self.S = self.alpha_s*self.S+(1-self.alpha_s)*Sf # [3,eq.15] # update running minimum self.Smin = np.min(np.concatenate((self.Smin,self.S),1),1)[:,None] self.Smin_sw = np.min(np.concatenate((self.Smin_sw,self.S),1),1)[:,None] # Indicator function for VAD Gamma_min = (np.abs(Y_l)**2)/(self.Bmin*self.Smin) # [3,eq.18] zeta = self.S/(self.Bmin*self.Smin) # [3,eq.21] I = np.zeros([self.K, 1]) I[(Gamma_min < self.Gamma0 ) & (zeta < self.zeta0)] = 1 # [3,eq.21] # SECOND MINIMA CONTROLLED VAD # This provides the speech probability needed to compute the final # noise estimation. The hard VAD index I, computed in the previous # estimation, is here used to exclude strong speech components. norm = self.fsmooth(I) self.tilde_Sf = self.fsmooth(I*np.abs(Y_l)**2) self.tilde_Sf[norm>0] = self.tilde_Sf[norm>0]/norm[norm>0] # Time smoothing self.tilde_S = self.alpha_s*self.tilde_S+(1-self.alpha_s)*self.tilde_Sf # [3,eq.27] # Update running minimum self.tilde_Smin = np.min(np.concatenate((self.tilde_Smin,self.tilde_S),1),1)[:,None] # [3,eq.26] self.tilde_Smin_sw = np.min(np.concatenate((self.tilde_Smin_sw,self.tilde_S),1),1)[:,None] # [3,eq.27] # A PRIORI SPEECH ABSENCE tilde_Gamma_min = (np.abs(Y_l)**2)/(self.Bmin*self.tilde_Smin) tilde_zeta = self.S/(self.Bmin*self.tilde_Smin) # [3,eq.28] # Speech absence self.q = np.zeros(Y_l.shape) self.q[(tilde_Gamma_min <= 1) & (tilde_zeta < self.zeta0)] = 1 # [3,eq.29] self.q[(1 < tilde_Gamma_min) & (tilde_Gamma_min < self.Gamma1) & (tilde_zeta < self.zeta0)] = (self.Gamma1 - tilde_Gamma_min[(1 < tilde_Gamma_min) & (tilde_Gamma_min < self.Gamma1) & (tilde_zeta < self.zeta0)])/(self.Gamma1-1) # [3,Eq.29] # self.q[:] = 1 # A POSTERIORI SPEECH PROBABILITY self.p = post_speech_prob(Y_l,self.q,Gamma,xi) self.p[self.p>self.p_upthr] = self.p_upthr # PROBABILITY DRIVEN RECURSIVE SMOOTHING # Smoothing parameter tilde_alpha_d = self.alpha_d+(1-self.alpha_d)*self.p # [3,eq.11] # UPDATE NOISE SPECTRUM ESTIMATE self.ov_Lambda_D = tilde_alpha_d*self.ov_Lambda_D + (1-tilde_alpha_d)*np.abs(Y_l)**2 # [3,eq.10] # Bias correction self.Lambda_D = self.beta*self.ov_Lambda_D # [3,eq.12] # UPDATE MINIMUM TRACKING self.j += 1 if self.j == self.V: # Minimum tracking for the first estimation if self.u < self.U: self.Storing[:,self.u:self.u+1] = self.Smin_sw else: self.Storing =

np.roll(self.Storing,-1,axis=1)

numpy.roll

from typing import Any, Set, Tuple, Union, Optional from pathlib import Path from collections import defaultdict from html.parser import HTMLParser import pytest from anndata import AnnData import numpy as np import xarray as xr from imageio import imread, imsave import tifffile from squidpy.im import ImageContainer from squidpy.im._utils import CropCoords, CropPadding, _NULL_COORDS from squidpy._constants._pkg_constants import Key class SimpleHTMLValidator(HTMLParser): # modified from CellRank def __init__(self, n_expected_rows: int, expected_tags: Set[str], **kwargs: Any): super().__init__(**kwargs) self._cnt = defaultdict(int) self._n_rows = 0 self._n_expected_rows = n_expected_rows self._expected_tags = expected_tags def handle_starttag(self, tag: str, attrs: Any) -> None: self._cnt[tag] += 1 self._n_rows += tag == "strong" def handle_endtag(self, tag: str) -> None: self._cnt[tag] -= 1 def validate(self) -> None: assert self._n_rows == self._n_expected_rows assert set(self._cnt.keys()) == self._expected_tags if len(self._cnt): assert set(self._cnt.values()) == {0} class TestContainerIO: def test_empty_initialization(self): img = ImageContainer() assert not len(img) assert isinstance(img.data, xr.Dataset) assert img.shape == (0, 0) assert str(img) assert repr(img) def _test_initialize_from_dataset(self): dataset = xr.Dataset({"foo": xr.DataArray(np.zeros((100, 100, 3)))}, attrs={"foo": "bar"}) img = ImageContainer._from_dataset(data=dataset) assert img.data is not dataset assert "foo" in img assert img.shape == (100, 100) np.testing.assert_array_equal(img.data.values(), dataset.values) assert img.data.attrs == dataset.attrs def test_save_load_zarr(self, tmpdir): img = ImageContainer(np.random.normal(size=(100, 100, 1))) img.data.attrs["scale"] = 42 img.save(Path(tmpdir) / "foo") img2 = ImageContainer.load(Path(tmpdir) / "foo") np.testing.assert_array_equal(img["image"].values, img2["image"].values) np.testing.assert_array_equal(img.data.dims, img2.data.dims) np.testing.assert_array_equal(sorted(img.data.attrs.keys()), sorted(img2.data.attrs.keys())) for k, v in img.data.attrs.items(): assert type(v) == type(img2.data.attrs[k]) # noqa: E721 assert v == img2.data.attrs[k] def test_load_zarr_2_objects_can_overwrite_store(self, tmpdir): img = ImageContainer(np.random.normal(size=(100, 100, 1))) img.data.attrs["scale"] = 42 img.save(Path(tmpdir) / "foo") img2 = ImageContainer.load(Path(tmpdir) / "foo") img2.data.attrs["sentinel"] = "foobar" img2["image"].values += 42 img2.save(Path(tmpdir) / "foo") img3 = ImageContainer.load(Path(tmpdir) / "foo") assert "sentinel" in img3.data.attrs assert img3.data.attrs["sentinel"] == "foobar" np.testing.assert_array_equal(img3["image"].values, img2["image"].values) np.testing.assert_allclose(img3["image"].values - 42, img["image"].values) @pytest.mark.parametrize( ("shape1", "shape2"), [ ((100, 200, 3), (100, 200, 1)), ((100, 200, 3), (100, 200)), ], ) def test_add_img(self, shape1: Tuple[int, ...], shape2: Tuple[int, ...]): img_orig = np.random.randint(low=0, high=255, size=shape1, dtype=np.uint8) cont = ImageContainer(img_orig, layer="img_orig") img_new = np.random.randint(low=0, high=255, size=shape2, dtype=np.uint8) cont.add_img(img_new, layer="img_new", channel_dim="mask") assert "img_orig" in cont assert "img_new" in cont np.testing.assert_array_equal(np.squeeze(cont.data["img_new"]), np.squeeze(img_new)) @pytest.mark.parametrize("shape", [(100, 200, 3), (100, 200, 1)]) def test_load_jpeg(self, shape: Tuple[int, ...], tmpdir): img_orig = np.random.randint(low=0, high=255, size=shape, dtype=np.uint8) fname = tmpdir / "tmp.jpeg" imsave(str(fname), img_orig) gt = imread(str(fname)) # because of compression, we load again cont = ImageContainer(str(fname)) np.testing.assert_array_equal(cont["image"].values.squeeze(), gt.squeeze()) @pytest.mark.parametrize("shape", [(100, 200, 3), (100, 200, 1), (10, 100, 200, 1)]) def test_load_tiff(self, shape: Tuple[int, ...], tmpdir): img_orig = np.random.randint(low=0, high=255, size=shape, dtype=np.uint8) fname = tmpdir / "tmp.tiff" tifffile.imsave(fname, img_orig) cont = ImageContainer(str(fname)) if len(shape) > 3: # multi-channel tiff np.testing.assert_array_equal(cont["image"], img_orig[..., 0].transpose(1, 2, 0)) else:

np.testing.assert_array_equal(cont["image"], img_orig)

numpy.testing.assert_array_equal