prompt
stringlengths 19
879k
| completion
stringlengths 3
53.8k
| api
stringlengths 8
59
|
|---|---|---|
# -*- coding: utf-8 -*-
"""
Created on Thu Apr 7 10:17:56 2022
@author: <NAME>
"""
import time
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
import argparse
import numpy as np
import random
import scipy.sparse as sp
class GATLayer(nn.Module):
def __init__(self,input_feature,output_feature,dropout,alpha,concat=True):
super(GATLayer,self).__init__()
self.input_feature = input_feature
self.output_feature = output_feature
self.alpha = alpha
self.dropout = dropout
self.concat = concat
self.a = nn.Parameter(torch.empty(size=(2*output_feature,1)))
self.w = nn.Parameter(torch.empty(size=(input_feature,output_feature)))
self.leakyrelu = nn.LeakyReLU(self.alpha)
self.reset_parameters()
def reset_parameters(self):
nn.init.xavier_uniform_(self.w.data,gain=1.414)
nn.init.xavier_uniform_(self.a.data,gain=1.414)
def forward(self,h,adj):
Wh = torch.mm(h,self.w)
e = self._prepare_attentional_mechanism_input(Wh)
zero_vec = -9e15*torch.ones_like(e)
attention = torch.where(adj > 0, e, zero_vec) # adj>0的位置使用e对应位置的值替换，其余都为-9e15，这样设定经过Softmax后每个节点对应的行非邻居都会变为0。
attention = F.softmax(attention, dim=1) # 每行做Softmax，相当于每个节点做softmax
attention = F.dropout(attention, self.dropout, training=self.training)
h_prime = torch.mm(attention, Wh) # 得到下一层的输入
if self.concat:
return F.elu(h_prime) #激活
else:
return h_prime
def _prepare_attentional_mechanism_input(self,Wh):
Wh1 = torch.matmul(Wh,self.a[:self.output_feature,:]) # N*out_size @ out_size*1 = N*1
Wh2 = torch.matmul(Wh,self.a[self.output_feature:,:]) # N*1
e = Wh1+Wh2.T # Wh1的每个原始与Wh2的所有元素相加，生成N*N的矩阵
return self.leakyrelu(e)
class GAT(nn.Module):
def __init__(self,input_size,hidden_size,output_size,dropout,alpha,nheads,concat=True):
super(GAT,self).__init__()
self.dropout= dropout
self.attention = [GATLayer(input_size, hidden_size, dropout=dropout, alpha=alpha,concat=True) for _ in range(nheads)]
for i,attention in enumerate(self.attention):
self.add_module('attention_{}'.format(i),attention)
self.out_att = GATLayer(hidden_size*nheads, output_size, dropout=dropout, alpha=alpha,concat=False)
def forward(self,x,adj):
#x = F.dropout(x,self.dropout,training=self.training)
x = torch.cat([att(x,adj) for att in self.attention],dim=1)
#x = F.dropout(x,self.dropout,training=self.training)
x = F.elu(self.out_att(x,adj))
return F.log_softmax(x,dim=1)
def train(epoch):
t = time.time()
model.train()
optimizer.zero_grad()
output = model(features,adj)
loss_train = F.nll_loss(output[idx_train],labels[idx_train])
acc_train = accuracy(output[idx_train], labels[idx_train])
loss_train.backward()
optimizer.step()
model.eval()
output = model(features, adj)
acc_val = accuracy(output[idx_val],labels[idx_val])
loss_val = F.nll_loss(output[idx_val], labels[idx_val])
print('Epoch: {:04d}'.format(epoch+1),
'loss_train: {:.4f}'.format(loss_train.data.item()),
'acc_train: {:.4f}'.format(acc_train.data.item()),
'loss_val: {:.4f}'.format(loss_val.data.item()),
'acc_val: {:.4f}'.format(acc_val.data.item()),
'time: {:.4f}s'.format(time.time() - t))
return loss_val.data.item()
def compute_test():
model.eval()
output = model(features, adj)
loss_test = F.nll_loss(output[idx_test], labels[idx_test])
acc_test = accuracy(output[idx_test], labels[idx_test])
print("Test set results:",
"loss= {:.4f}".format(loss_test.data.item()),
"accuracy= {:.4f}".format(acc_test.data.item()))
def encode_onehot(labels):
classes = set(labels)
classes_dict = {c: np.identity(len(classes))[i, :] for i, c in
enumerate(classes)}
labels_onehot = np.array(list(map(classes_dict.get, labels)),
dtype=np.int32)
return labels_onehot
def normalize_adj(mx):
"""Row-normalize sparse matrix"""
rowsum = np.array(mx.sum(1))
r_inv_sqrt = | np.power(rowsum, -0.5) | numpy.power |
import numpy as np
import cv2 # OpenCV???C?u????
import matplotlib.pyplot as plt
import torch
import torch.utils.data as data
from itertools import product as product
import torch
import torch.nn as nn
import torch.nn.init as init
import torch.nn.functional as F
from torch.autograd import Function
# In[2]:
def group_annotation_by_class(dataset):
true_case_stat = {}
all_gt_boxes = {}
all_difficult_cases = {}
for i in range(len(dataset)):
image_id, annotation = dataset.get_annotation(i)
gt_boxes, classes, is_difficult = annotation
gt_boxes = torch.from_numpy(gt_boxes)
for i, difficult in enumerate(is_difficult):
class_index = int(classes[i])
gt_box = gt_boxes[i]
if not difficult:
true_case_stat[class_index] = true_case_stat.get(class_index, 0) + 1
if class_index not in all_gt_boxes:
all_gt_boxes[class_index] = {}
if image_id not in all_gt_boxes[class_index]:
all_gt_boxes[class_index][image_id] = []
all_gt_boxes[class_index][image_id].append(gt_box)
if class_index not in all_difficult_cases:
all_difficult_cases[class_index]={}
if image_id not in all_difficult_cases[class_index]:
all_difficult_cases[class_index][image_id] = []
all_difficult_cases[class_index][image_id].append(difficult)
for class_index in all_gt_boxes:
for image_id in all_gt_boxes[class_index]:
all_gt_boxes[class_index][image_id] = torch.stack(all_gt_boxes[class_index][image_id])
for class_index in all_difficult_cases:
for image_id in all_difficult_cases[class_index]:
all_gt_boxes[class_index][image_id] = torch.tensor(all_gt_boxes[class_index][image_id])
return true_case_stat, all_gt_boxes, all_difficult_cases
def compute_average_precision_per_class(num_true_cases, gt_boxes, difficult_cases,
prediction_file, iou_threshold, use_2007_metric):
with open(prediction_file) as f:
image_ids = []
boxes = []
scores = []
for line in f:
t = line.rstrip().split(" ")
image_ids.append(t[0])
scores.append(float(t[1]))
box = torch.tensor([float(v) for v in t[2:]]).unsqueeze(0)
box -= 1.0 # convert to python format where indexes start from 0
boxes.append(box)
scores = np.array(scores)
sorted_indexes = | np.argsort(-scores) | numpy.argsort |
#!/usr/bin/env python
# coding: utf-8
import skimage.io as io
import cv2
import matplotlib.pyplot as plt
import numpy as np
import face_recognition
from skimage.transform import PiecewiseAffineTransform, warp
from skimage import transform as tf
import warnings
warnings.filterwarnings('ignore')
def plot_landmarks(image,face_landmarks):
'''plot the landmarks on the image
INPUT:
face_landmarks - dict({"key1":(X1,Y1), "key2":(X2,Y2), ...})
OUTPUT:
the face landmarks plot of input image
'''
# image = face_recognition.load_image_file(filename)
plt.imshow(image)
for key, value in face_landmarks.items():
# print(key)
plt.scatter(value[0],value[1],s=1)
def get_boundary(face_landmarks,facial_feature,start,end):
'''
return the lower or upper boundary of face components
'''
X = np.array(face_landmarks[facial_feature]).T[0]
X = np.hstack((X,X))[start:end]
Y = | np.array(face_landmarks[facial_feature]) | numpy.array |
import sys, os
cur_file_path = os.path.dirname(os.path.realpath(__file__))
sys.path.append(os.path.join(cur_file_path, '..'))
import os.path as osp
import glob, time, copy, pickle, json
from torch.utils.data import Dataset, DataLoader
from fitting.fitting_utils import read_keypoints, load_planercnn_res
import numpy as np
import torch
import cv2
SPLIT = ['Scene04', 'Scene05', 'Scene07', 'Scene10', 'Scene11', 'Scene12', 'Scene13', 'Scene14']
SCENE_MAP = {'Scene04' : 'lobby19-3',
'Scene05' : 'lobby18-1',
'Scene07' : 'lobby15',
'Scene10' : 'lobby22-1-tog',
'Scene11' : 'livingroom00',
'Scene12' : 'office1-1-tog-lcrnet',
'Scene13' : 'library3-tog',
'Scene14' : 'garden1' }
# GT 3d joints do not align with images.
QUANT_BLACKLIST = ['Scene04', 'Scene12']
# for some reason 3d joint annotation is off by one frame
SHIFT_LIST = ['Scene05']
# which scene objects contact the ground, used for floor fit.
GROUND_CTC_PARTS = {'Scene05' : ['00_couch_seat'],
'Scene07' : ['00_couch_seat', '01_couch_seat'],
'Scene10' : ['00_couch_seat', '01_couch_seat', '03_couch_seat'],
'Scene11' : ['00_couch_seat', '01_couch_seat', '01_couch_seat-1', '02_couch_seat'],
'Scene13' : ['04_couch_seat', '05_chair_leg', '05_chair_leg-1', '05_chair_leg-2', '05_chair_leg-3',
'07_chair_leg', '07_chair_leg-1', '07_chair_leg-2', '07_chair_leg-3',
'08_chair_leg', '08_chair_leg-1', '08_chair_leg-2', '08_chair_leg-3',
'09_chair_leg', '09_chair_leg-1', '09_chair_leg-2', '09_chair_leg-3'],
'Scene14' : ['01_chair_leg', '01_chair_leg-1', '01_chair_leg-3', '01_chair_leg-4',
'02_chair_leg', '02_chair_leg-1', '02_chair_leg-3', '02_chair_leg-4',
'03_chair_leg', '03_chair_leg-1', '03_chair_leg-3', '03_chair_leg-4',
'04_table_leg', '04_table_leg-1', '04_table_leg-2', '04_table_leg-3',
'00_couch_leg', '00_couch_leg-1', '00_couch_leg-3', '00_couch_leg-4']}
IMG_WIDTH, IMG_HEIGHT = 1920, 1080
class iMapperDataset(Dataset):
def __init__(self, root_path,
seq_len=10, # split the data into sequences of this length
load_img=False,
load_floor_plane=False, # if true, loads the PlaneRCNN floor plane from the dataset and uses this
scene=None, # if given, loads only this scene
scene_subseq_idx=-1, # if given, loads only this single subsequence of a specified recording
load_gt_floor=False, # if true, uses object locations to get GT floor
load_scene_mesh=False,
mask_joints=False # if true, masks 2d joints based on person mask
):
super(iMapperDataset, self).__init__()
self.data_dir = root_path
self.seq_len = seq_len
self.load_img = load_img
self.load_floor_plane = load_floor_plane
self.load_gt_floor = load_gt_floor
self.load_scene_mesh = load_scene_mesh
self.scene = scene
self.scene_subseq_idx = scene_subseq_idx
self.mask_joints = mask_joints
if self.scene is None and self.scene_subseq_idx > 0:
print('Ignoring subseq_idx since scene is not specified...')
self.scene_subseq_idx = -1
self.split_scenes = SPLIT
# load (img) data paths
self.data_dict = self.load_data()
self.data_len = len(self.data_dict['img_paths'])
print('This split contains %d sub-sequences...' % (self.data_len))
def load_data(self):
'''
Loads in the full dataset, except for image frames which are loaded on the fly.
'''
# get the sequences we want
scene_list = []
if self.scene is not None:
scene_path = os.path.join(self.data_dir, self.scene)
if os.path.exists(scene_path):
scene_list = [scene_path]
else:
print('Could not find specified scene at %s!' % (scene_path))
else:
all_scene_dirs = [os.path.join(self.data_dir, scene_name) for scene_name in self.split_scenes]
scene_list = [f for f in all_scene_dirs if os.path.exists(f) and os.path.isdir(f)]
scene_names = [f.split('/')[-1] for f in scene_list]
print('Found %d scenes...' % (len(scene_names)))
print('Splitting into subsequences of length %d frames...' % (self.seq_len))
# split each scene into sequences and record information for loading data
data_out = {
'img_paths' : [],
'mask_paths' : [],
'cam_matx' : [],
'joints2d' : [],
'joints3d' : [],
'occlusions' : [],
'floor_plane' : [],
'gt_floor_plane' : [],
'scene_mesh' : [],
'names' : []
}
for scene_path, scene_name in zip(scene_list, scene_names):
# first load in data for full sequence
scene_data = dict()
#
# path to image frames
#
img_folder = osp.join(scene_path, 'raw_frames')
img_paths = [osp.join(img_folder, img_fn)
for img_fn in os.listdir(img_folder)
if img_fn.endswith('.png') or
img_fn.endswith('.jpg') and
not img_fn.startswith('.')]
img_paths = sorted(img_paths)
frame_names = ['.'.join(f.split('/')[-1].split('.')[:-1]) for f in img_paths]
mask_folder = osp.join(scene_path, 'masks')
mask_paths = [os.path.join(mask_folder, f + '.png') for f in frame_names]
cur_seq_len = len(img_paths)
if len(img_paths) < self.seq_len:
continue
if scene_name in QUANT_BLACKLIST:
continue
scene_data['img_paths'] = img_paths
scene_data['mask_paths'] = mask_paths
#
# intrinsics
#
intrins_path = osp.join(scene_path, 'intrinsics.json')
with open(intrins_path, 'r') as f:
intrins_data = json.load(f)
cam_mat = np.array(intrins_data)
#
# 2d observed keypoints (OpenPose)
#
keyp_folder = osp.join(scene_path, 'op_keypoints')
keyp_paths = [osp.join(keyp_folder, f + '_keypoints.json') for f in frame_names]
keyp_frames = [read_keypoints(f) for f in keyp_paths]
joint2d_data = np.stack(keyp_frames, axis=0) # T x J x 3 (x,y,conf)
nobs_frames = joint2d_data.shape[0]
scene_data['joints2d'] = joint2d_data
#
# scene GT info which gives 3d joints, occlusions for each joint, and ground plane
#
scene_info_path = osp.join(scene_path, 'gt/skel_%s_GT.json' % (SCENE_MAP[scene_name]))
with open(scene_info_path, 'r') as f:
scene_info = json.load(f)
# first joints 3d
joints3d = []
for k, v in sorted(scene_info['3d'].items()):
frame_id = int(k)
pose = np.zeros(shape=(len(v[list(v.keys())[0]]), len(v)),
dtype=np.float32)
for joint, pos in v.items():
pose[:, int(joint)] = pos
joints3d.append(pose.T)
joints3d = np.stack(joints3d, axis=0)
ngt_frames = joints3d.shape[0]
ngt_joints = joints3d.shape[1]
# confidence in 3d joint annotations (some are marked 0.0 and need to be thrown out)
conf3d = []
for frame_id, v in enumerate(scene_info['confidence']['values']):
cur_conf = np.zeros((ngt_joints, 1), dtype=np.float32)
for joint, jconf in v.items():
cur_conf[int(joint)] = float(jconf)
conf3d.append(cur_conf)
conf3d = np.stack(conf3d, axis=0)
# now use it to mask out 3d joints (inf means not observed)
conf3d[conf3d == 0.0] = float('inf')
joints3d = joints3d * conf3d
if scene_name in SHIFT_LIST:
joints3d_shift = np.ones_like(joints3d)*float('inf')
joints3d_shift[:-1] = joints3d[1:]
joints3d = joints3d_shift
occlusion_mask = np.zeros((ngt_frames, ngt_joints), dtype=np.int)
for k, v in scene_info['occluded'].items():
frame_id = int(k) - 1
occlusion_mask[frame_id] = v
floor_trans = np.array(scene_info['ground'])
floor_rot = np.array(scene_info['ground_rot'])
# align GT subsampled data to full 30 hz sampling rate observed data
joints3d_aligned = np.ones((nobs_frames, ngt_joints, 3), dtype=np.float)*float('inf')
occlusions_aligned = | np.ones((nobs_frames, ngt_joints), dtype=np.float) | numpy.ones |
#!/usr/bin/env python3
import numpy as np
from matplotlib import pyplot as plt
import torch
from torch import nn
from torch.autograd import Function
# import emd
class LaserScan:
"""Class that contains LaserScan with x,y,z,r"""
EXTENSIONS_SCAN = ['.bin']
def __init__(self, project=False, H=64, W=1024, fov_up=3.0, fov_down=-25.0):
self.project = project
self.proj_H = H
self.proj_W = W
self.proj_fov_up = fov_up
self.proj_fov_down = fov_down
self.reset()
def reset(self):
""" Reset scan members. """
self.points = np.zeros((0, 3), dtype=np.float32) # [m, 3]: x, y, z
self.remissions = np.zeros((0, 1), dtype=np.float32) # [m ,1]: remission
# projected range image - [H,W] range (-1 is no data)
self.proj_range = np.full((self.proj_H, self.proj_W), -1,
dtype=np.float32)
# unprojected range (list of depths for each point)
self.unproj_range = np.zeros((0, 1), dtype=np.float32)
# projected point cloud xyz - [H,W,3] xyz coord (-1 is no data)
self.proj_xyz = np.full((self.proj_H, self.proj_W, 3), -1,
dtype=np.float32)
# projected remission - [H,W] intensity (-1 is no data)
self.proj_remission = np.full((self.proj_H, self.proj_W), -1,
dtype=np.float32)
# projected index (for each pixel, what I am in the pointcloud)
# [H,W] index (-1 is no data)
self.proj_idx = np.full((self.proj_H, self.proj_W), -1,
dtype=np.int32)
# for each point, where it is in the range image
self.proj_x = np.zeros((0, 1), dtype=np.float32) # [m, 1]: x
self.proj_y = np.zeros((0, 1), dtype=np.float32) # [m, 1]: y
# mask containing for each pixel, if it contains a point or not
self.proj_mask = np.zeros((self.proj_H, self.proj_W),
dtype=np.int32) # [H,W] mask
def size(self):
""" Return the size of the point cloud. """
return self.points.shape[0]
def __len__(self):
return self.size()
def open_scan(self, filename):
""" Open raw scan and fill in attributes
"""
# reset just in case there was an open structure
self.reset()
# check filename is string
if not isinstance(filename, str):
raise TypeError("Filename should be string type, "
"but was {type}".format(type=str(type(filename))))
# check extension is a laserscan
if not any(filename.endswith(ext) for ext in self.EXTENSIONS_SCAN):
raise RuntimeError("Filename extension is not valid scan file.")
# if all goes well, open pointcloud
scan = np.fromfile(filename, dtype=np.float32, count=-1)
scan = scan.reshape((-1, 5))
# put in attribute
points = scan[:, 0:3] # get xyz
remissions = scan[:, 3] # get remission
self.set_points(points, remissions)
def set_points(self, points, remissions=None):
""" Set scan attributes (instead of opening from file)
"""
# reset just in case there was an open structure
self.reset()
# check scan makes sense
if not isinstance(points, np.ndarray):
raise TypeError("Scan should be numpy array")
# check remission makes sense
if remissions is not None and not isinstance(remissions, np.ndarray):
raise TypeError("Remissions should be numpy array")
# put in attribute
self.points = points # get xyz
if remissions is not None:
self.remissions = remissions # get remission
else:
self.remissions = np.zeros((points.shape[0]), dtype=np.float32)
# if projection is wanted, then do it and fill in the structure
if self.project:
self.do_range_projection()
def do_range_projection(self):
""" Project a pointcloud into a spherical projection image.projection.
Function takes no arguments because it can be also called externally
if the value of the constructor was not set (in case you change your
mind about wanting the projection)
"""
# laser parameters
fov_up = self.proj_fov_up / 180.0 * np.pi # field of view up in rad
fov_down = self.proj_fov_down / 180.0 * np.pi # field of view down in rad
fov = abs(fov_down) + abs(fov_up) # get field of view total in rad
# get depth of all points
depth = np.linalg.norm(self.points, 2, axis=1)
# get scan components
scan_x = self.points[:, 0]
scan_y = self.points[:, 1]
scan_z = self.points[:, 2]
# get angles of all points
yaw = -np.arctan2(scan_y, scan_x)
pitch = np.arcsin(scan_z / depth)
# get projections in image coords
proj_x = 0.5 * (yaw / np.pi + 1.0) # in [0.0, 1.0]
proj_y = 1.0 - (pitch + abs(fov_down)) / fov # in [0.0, 1.0]
# scale to image size using angular resolution
proj_x *= self.proj_W # in [0.0, W]
proj_y *= self.proj_H # in [0.0, H]
# round and clamp for use as index
proj_x = np.floor(proj_x)
proj_x = np.minimum(self.proj_W - 1, proj_x)
proj_x = np.maximum(0, proj_x).astype(np.int32) # in [0,W-1]
self.proj_x = np.copy(proj_x) # store a copy in orig order
proj_y = np.floor(proj_y)
proj_y = np.minimum(self.proj_H - 1, proj_y)
proj_y = np.maximum(0, proj_y).astype(np.int32) # in [0,H-1]
self.proj_y = np.copy(proj_y) # stope a copy in original order
# copy of depth in original order
self.unproj_range = np.copy(depth)
# order in decreasing depth
indices = np.arange(depth.shape[0])
order = np.argsort(depth)[::-1]
depth = depth[order]
indices = indices[order]
points = self.points[order]
remission = self.remissions[order]
proj_y = proj_y[order]
proj_x = proj_x[order]
# assing to images
self.proj_range[proj_y, proj_x] = depth
self.proj_xyz[proj_y, proj_x] = points
self.proj_remission[proj_y, proj_x] = remission
self.proj_idx[proj_y, proj_x] = indices
self.proj_mask = (self.proj_idx > 0).astype(np.float32)
class SemLaserScan(LaserScan):
"""Class that contains LaserScan with x,y,z,r,sem_label,sem_color_label,inst_label,inst_color_label"""
EXTENSIONS_LABEL = ['.label']
def __init__(self, nclasses, sem_color_dict=None, project=False, H=64, W=1024, fov_up=3.0, fov_down=-25.0):
super(SemLaserScan, self).__init__(project, H, W, fov_up, fov_down)
self.reset()
self.nclasses = nclasses # number of classes
# make semantic colors
max_sem_key = 0
for key, data in sem_color_dict.items():
if key + 1 > max_sem_key:
max_sem_key = key + 1
self.sem_color_lut = np.zeros((max_sem_key + 100, 3), dtype=np.float32)
for key, value in sem_color_dict.items():
self.sem_color_lut[key] = np.array(value, np.float32) / 255.0
# make instance colors
max_inst_id = 100000
self.inst_color_lut = np.random.uniform(low=0.0,
high=1.0,
size=(max_inst_id, 3))
# force zero to a gray-ish color
self.inst_color_lut[0] = np.full((3), 0.1)
def reset(self):
""" Reset scan members. """
super(SemLaserScan, self).reset()
# semantic labels
self.sem_label = np.zeros((0, 1), dtype=np.uint32) # [m, 1]: label
self.sem_label_color = | np.zeros((0, 3), dtype=np.float32) | numpy.zeros |
"""
Created on Thu Jan 26 17:04:11 2017
Preprocess Luna datasets and create nodule masks (and/or blank subsets)
NOTE that:
1. we do NOT segment the lungs at all -- we will use the raw images for training (DO_NOT_SEGMENT = True)
2. No corrections are made to the nodule radius in relation to the thickness of the layers (radius = (ca[4])/2, simply)
@author: <NAME>, <EMAIL>
Some functions have reused from the respective examples/kernels openly published at the https://www.kaggle.com/arnavkj95/data-science-bowl-2017/ , as referenced within the file
"""
#%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np # linear algebra
import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)
import scipy.ndimage as ndimage
import scipy.ndimage # added for scaling\
import cv2
import time
import glob
from skimage import measure, morphology, segmentation
import SimpleITK as sitk
DO_NOT_SEGMENT = True #### major difference with the initial/Feb version
RESIZE_SPACING = [2,2,2]
### z, y, x (x & y MUST be the same)
luna_subset = 0 # initial
LUNA_BASE_DIR = "../luna/data/original_lungs/subset%s/" # added on AWS; data as well
LUNA_DIR = LUNA_BASE_DIR % luna_subset
CSVFILES = "../luna/data/original_lungs/CSVFILES/%s"
LUNA_ANNOTATIONS = CSVFILES % "annotations.csv"
LUNA_CANDIDATES = CSVFILES % "candidates.csv"
MARKER_INTERNAL_THRESH = -400 # was -400; maybe use -320 ??
MARKER_FRAME_WIDTH = 9 # 9 seems OK for the half special case ...
def generate_markers(image):
#Creation of the internal Marker
useTestPlot = False
if useTestPlot:
timg = image
plt.imshow(timg, cmap='gray')
plt.show()
add_frame_vertical = True # NOT a good idea; no added value
if add_frame_vertical: # add frame for potentially closing the lungs that touch the edge, but only vertically
fw = MARKER_FRAME_WIDTH # frame width (it looks that 2 is the minimum width for the algorithms implemented here, namely the first 2 operations for the marker_internal)
xdim = image.shape[1]
#ydim = image.shape[0]
img2 = np.copy(image)
img2 [:, 0] = -1024
img2 [:, 1:fw] = 0
img2 [:, xdim-1:xdim] = -1024
img2 [:, xdim-fw:xdim-1] = 0
marker_internal = img2 < MARKER_INTERNAL_THRESH
else:
marker_internal = image < MARKER_INTERNAL_THRESH # was -400
useTestPlot = False
if useTestPlot:
timg = marker_internal
plt.imshow(timg, cmap='gray')
plt.show()
correct_edges2 = False ## NOT a good idea - no added value
if correct_edges2:
marker_internal[0,:] = 0
marker_internal[:,0] = 0
#marker_internal[:,1] = True
#marker_internal[:,2] = True
marker_internal[511,:] = 0
marker_internal[:,511] = 0
marker_internal = segmentation.clear_border(marker_internal, buffer_size=0)
marker_internal_labels = measure.label(marker_internal)
areas = [r.area for r in measure.regionprops(marker_internal_labels)]
areas.sort()
if len(areas) > 2:
for region in measure.regionprops(marker_internal_labels):
if region.area < areas[-2]:
for coordinates in region.coords:
marker_internal_labels[coordinates[0], coordinates[1]] = 0
marker_internal = marker_internal_labels > 0
#Creation of the external Marker
external_a = ndimage.binary_dilation(marker_internal, iterations=10) # was 10
external_b = ndimage.binary_dilation(marker_internal, iterations=55) # was 55
marker_external = external_b ^ external_a
#Creation of the Watershed Marker matrix
#marker_watershed = np.zeros((512, 512), dtype=np.int) # origi
marker_watershed = np.zeros((marker_external.shape), dtype=np.int)
marker_watershed += marker_internal * 255
marker_watershed += marker_external * 128
return marker_internal, marker_external, marker_watershed
def generate_markers_3d(image):
#Creation of the internal Marker
marker_internal = image < -400
marker_internal_labels = np.zeros(image.shape).astype(np.int16)
for i in range(marker_internal.shape[0]):
marker_internal[i] = segmentation.clear_border(marker_internal[i])
marker_internal_labels[i] = measure.label(marker_internal[i])
#areas = [r.area for r in measure.regionprops(marker_internal_labels)]
areas = [r.area for i in range(marker_internal.shape[0]) for r in measure.regionprops(marker_internal_labels[i])]
for i in range(marker_internal.shape[0]):
areas = [r.area for r in measure.regionprops(marker_internal_labels[i])]
areas.sort()
if len(areas) > 2:
for region in measure.regionprops(marker_internal_labels[i]):
if region.area < areas[-2]:
for coordinates in region.coords:
marker_internal_labels[i, coordinates[0], coordinates[1]] = 0
marker_internal = marker_internal_labels > 0
#Creation of the external Marker
# 3x3 structuring element with connectivity 1, used by default
struct1 = ndimage.generate_binary_structure(2, 1)
struct1 = struct1[np.newaxis,:,:] # expand by z axis .
external_a = ndimage.binary_dilation(marker_internal, structure=struct1, iterations=10)
external_b = ndimage.binary_dilation(marker_internal, structure=struct1, iterations=55)
marker_external = external_b ^ external_a
#Creation of the Watershed Marker matrix
#marker_watershed = np.zeros((512, 512), dtype=np.int) # origi
marker_watershed = np.zeros((marker_external.shape), dtype=np.int)
marker_watershed += marker_internal * 255
marker_watershed += marker_external * 128
return marker_internal, marker_external, marker_watershed
BINARY_CLOSING_SIZE = 7 ## added for tests; 5 for disk seems sufficient - fo safety let's go with 6 or even 7
def seperate_lungs(image):
#Creation of the markers as shown above:
marker_internal, marker_external, marker_watershed = generate_markers(image)
#Creation of the Sobel-Gradient
sobel_filtered_dx = ndimage.sobel(image, 1)
sobel_filtered_dy = ndimage.sobel(image, 0)
sobel_gradient = np.hypot(sobel_filtered_dx, sobel_filtered_dy)
sobel_gradient *= 255.0 / np.max(sobel_gradient)
#Watershed algorithm
watershed = morphology.watershed(sobel_gradient, marker_watershed)
#Reducing the image created by the Watershed algorithm to its outline
outline = ndimage.morphological_gradient(watershed, size=(3,3))
outline = outline.astype(bool)
#Performing Black-Tophat Morphology for reinclusion
#Creation of the disk-kernel and increasing its size a bit
blackhat_struct = [[0, 0, 1, 1, 1, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[1, 1, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1, 1],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 1, 1, 1, 0, 0]]
blackhat_struct = ndimage.iterate_structure(blackhat_struct, 8)
#Perform the Black-Hat
outline += ndimage.black_tophat(outline, structure=blackhat_struct)
#Use the internal marker and the Outline that was just created to generate the lungfilter
lungfilter = np.bitwise_or(marker_internal, outline)
#Close holes in the lungfilter
#fill_holes is not used here, since in some slices the heart would be reincluded by accident
##structure = np.ones((BINARY_CLOSING_SIZE,BINARY_CLOSING_SIZE)) # 5 is not enough, 7 is
structure = morphology.disk(BINARY_CLOSING_SIZE) # better , 5 seems sufficient, we use 7 for safety/just in case
lungfilter = ndimage.morphology.binary_closing(lungfilter, structure=structure, iterations=3) #, iterations=3) # was structure=np.ones((5,5))
### NOTE if no iterattions, i.e. default 1 we get holes within lungs for the disk(5) and perhaps more
#Apply the lungfilter (note the filtered areas being assigned -2000 HU)
segmented = np.where(lungfilter == 1, image, -2000*np.ones((512, 512))) ### was -2000
return segmented, lungfilter, outline, watershed, sobel_gradient, marker_internal, marker_external, marker_watershed
def rescale_n(n,reduce_factor):
return max( 1, int(round(n / reduce_factor)))
#image = image_slices[70]
def seperate_lungs_cv2(image):
#Creation of the markers as shown above:
marker_internal, marker_external, marker_watershed = generate_markers(image)
reduce_factor = 512 / image.shape[0]
#Creation of the Sobel-Gradient
sobel_filtered_dx = ndimage.sobel(image, 1)
sobel_filtered_dy = ndimage.sobel(image, 0)
sobel_gradient = np.hypot(sobel_filtered_dx, sobel_filtered_dy)
sobel_gradient *= 255.0 / np.max(sobel_gradient)
useTestPlot = False
if useTestPlot:
timg = sobel_gradient
plt.imshow(timg, cmap='gray')
plt.show()
#Watershed algorithm
watershed = morphology.watershed(sobel_gradient, marker_watershed)
if useTestPlot:
timg = marker_external
plt.imshow(timg, cmap='gray')
plt.show()
#Reducing the image created by the Watershed algorithm to its outline
#wsize = rescale_n(3,reduce_factor) # THIS IS TOO SMALL, dynamically adjusting the size for the watersehed algorithm
outline = ndimage.morphological_gradient(watershed, size=(3,3)) # original (3,3), (wsize, wsize) is too small to create an outline
outline = outline.astype(bool)
outline_u = outline.astype(np.uint8) #added
#Performing Black-Tophat Morphology for reinclusion
#Creation of the disk-kernel and increasing its size a bit
blackhat_struct = [[0, 0, 1, 1, 1, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[1, 1, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1, 1],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 1, 1, 1, 0, 0]]
blackhat_struct = ndimage.iterate_structure(blackhat_struct, rescale_n(8,reduce_factor)) # dyanmically adjust the number of iterattions; original was 8
blackhat_struct_cv2 = blackhat_struct.astype(np.uint8)
#Perform the Black-Hat
outline += (cv2.morphologyEx(outline_u, cv2.MORPH_BLACKHAT, kernel=blackhat_struct_cv2)).astype(np.bool) # fats
if useTestPlot:
timg = outline
plt.imshow(timg, cmap='gray')
plt.show()
#Use the internal marker and the Outline that was just created to generate the lungfilter
lungfilter = np.bitwise_or(marker_internal, outline)
if useTestPlot:
timg = lungfilter
plt.imshow(timg, cmap='gray')
plt.show()
#Close holes in the lungfilter
#fill_holes is not used here, since in some slices the heart would be reincluded by accident
##structure = np.ones((BINARY_CLOSING_SIZE,BINARY_CLOSING_SIZE)) # 5 is not enough, 7 is
structure2 = morphology.disk(2) # used to fill the gaos/holes close to the border (otherwise the large sttructure would create a gap by the edge)
structure3 = morphology.disk(rescale_n(BINARY_CLOSING_SIZE,reduce_factor)) # dynanically adjust; better , 5 seems sufficient, we use 7 for safety/just in case
##lungfilter = ndimage.morphology.binary_closing(lungfilter, structure=structure, iterations=3) #, ORIGINAL iterations=3) # was structure=np.ones((5,5))
lungfilter2 = ndimage.morphology.binary_closing(lungfilter, structure=structure2, iterations=3) # ADDED
lungfilter3 = ndimage.morphology.binary_closing(lungfilter, structure=structure3, iterations=3)
lungfilter = np.bitwise_or(lungfilter2, lungfilter3)
### NOTE if no iterattions, i.e. default 1 we get holes within lungs for the disk(5) and perhaps more
#Apply the lungfilter (note the filtered areas being assigned -2000 HU)
#image.shape
#segmented = np.where(lungfilter == 1, image, -2000*np.ones((512, 512)).astype(np.int16)) # was -2000 someone suggested 30
segmented = np.where(lungfilter == 1, image, -2000*np.ones(image.shape).astype(np.int16)) # was -2000 someone suggested 30
return segmented, lungfilter, outline, watershed, sobel_gradient, marker_internal, marker_external, marker_watershed
def seperate_lungs_3d(image):
#Creation of the markers as shown above:
marker_internal, marker_external, marker_watershed = generate_markers_3d(image)
#Creation of the Sobel-Gradient
sobel_filtered_dx = ndimage.sobel(image, axis=2)
sobel_filtered_dy = ndimage.sobel(image, axis=1)
sobel_gradient = np.hypot(sobel_filtered_dx, sobel_filtered_dy)
sobel_gradient *= 255.0 / np.max(sobel_gradient)
#Watershed algorithm
watershed = morphology.watershed(sobel_gradient, marker_watershed)
#Reducing the image created by the Watershed algorithm to its outline
outline = ndimage.morphological_gradient(watershed, size=(1,3,3))
outline = outline.astype(bool)
#Performing Black-Tophat Morphology for reinclusion
#Creation of the disk-kernel and increasing its size a bit
blackhat_struct = [[0, 0, 1, 1, 1, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[1, 1, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1, 1],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 1, 1, 1, 0, 0]]
blackhat_struct = ndimage.iterate_structure(blackhat_struct, 8)
blackhat_struct = blackhat_struct[np.newaxis,:,:]
#Perform the Black-Hat
outline += ndimage.black_tophat(outline, structure=blackhat_struct) # very long time
#Use the internal marker and the Outline that was just created to generate the lungfilter
lungfilter = | np.bitwise_or(marker_internal, outline) | numpy.bitwise_or |
################################################################################
# #
# This file is part of the Morphomatics library #
# see https://github.com/morphomatics/morphomatics #
# #
# Copyright (C) 2021 Zuse Institute Berlin #
# #
# Morphomatics is distributed under the terms of the ZIB Academic License. #
# see $MORPHOMATICS/LICENSE #
# #
################################################################################
import copy
import numpy as np
from . import Manifold, Connection, LieGroup, SO3, GLpn
class SE3(Manifold):
"""Returns the product manifold SE(3)^k, i.e., a product of k rigid body motions.
manifold = SE3(k)
Elements of SE(3)^k are represented as arrays of size kx4x4 where every 4x4 slice are homogeneous coordinates of an
element of SE(3), i.e., the upper-left 3x3 block is the rotational part, the upper-right 3x1 part is the
translational part, and the lower row is [0 0 0 1]. Tangent vectors, consequently, follow the same ‘layout‘.
To improve efficiency, tangent vectors are always represented in the Lie Algebra.
"""
def __init__(self, k=1, structure='AffineGroup'):
if k == 1:
name = 'Rigid motions'
elif k > 1:
name = 'Special Euclidean group SE(3)^{k}'.format(k=k)
else:
raise RuntimeError("k must be an integer no less than 1.")
self._k = k
self._SO = SO3(k)
dimension = 6 * self._k
point_shape = [self._k, 4, 4]
super().__init__(name, dimension, point_shape)
if structure:
getattr(self, f'init{structure}Structure')()
def initAffineGroupStructure(self):
"""
Instantiate SE(3)^k with standard Lie group structure and canonical Cartan-Shouten connection.
"""
structure = SE3.AffineGroupStructure(self)
self._connec = structure
self._group = structure
@property
def k(self):
return self._k
def rand(self):
P = np.zero(self.point_shape)
P[:, :3, :3] = self._SO.rand()
P[:, :3, 3] = np.random.rand((self._k, 3))
P[:, 3, 3] = 1
return P
def randvec(self, P):
X = | np.zero(self.point_shape) | numpy.zero |
# *****************************************************************************
# Copyright (c) 2019, Intel Corporation All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 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.
#
# 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
import sdc
import time
@sdc.jit
def logistic_regression(iterations):
t1 = time.time()
N = 10**8
D = 10
g = 2 * np.random.ranf(D) - 1
X = 2 * np.random.ranf((N, D)) - 1
Y = ((np.dot(X, g) > 0.0) == (np.random.ranf(N) > .90)) + .0
w = np.random.ranf(D) - .5
for i in range(iterations):
w -= np.dot(((1.0 / (1.0 + np.exp(-Y * np.dot(X, w))) - 1.0) * Y), X)
R = | np.dot(X, w) | numpy.dot |
import numpy as np
from scipy import integrate
from floris.utils.tools import valid_ops as vops
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #
# MISCELLANEOUS #
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #
# MAIN #
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #
def __Xie_Archer_wake(x, y, z, v_inflow, D_r, C_t, z_hub):
beta = (1. + | np.sqrt(1 - C_t) | numpy.sqrt |
import os
import unittest
import numpy as np
import config
from mos.dataset_reader import RawDatasetReader, MissingDataRawDatasetReader, \
SyntheticRawDatasetReader, CorruptSubjectRawDatasetReader
from mos.subjective_model import MosModel, DmosModel, \
MaximumLikelihoodEstimationModelReduced, MaximumLikelihoodEstimationModel, \
LiveDmosModel, MaximumLikelihoodEstimationDmosModel, LeastSquaresModel, \
SubjrejMosModel, ZscoringSubjrejMosModel, SubjrejDmosModel, \
ZscoringSubjrejDmosModel, PerSubjectModel
from tools.misc import import_python_file
__copyright__ = "Copyright 2016, Netflix, Inc."
__license__ = "Apache, Version 2.0"
class SubjectiveModelTest(unittest.TestCase):
def setUp(self):
self.dataset_filepath = config.ROOT + '/python/test/resource/NFLX_dataset_public_raw.py'
self.output_dataset_filepath = config.ROOT + '/workspace/workdir/NFLX_dataset_public_test.py'
self.output_dataset_pyc_filepath = config.ROOT + '/workspace/workdir/NFLX_dataset_public_test.pyc'
def tearDown(self):
if os.path.exists(self.output_dataset_filepath):
os.remove(self.output_dataset_filepath)
if os.path.exists(self.output_dataset_pyc_filepath):
os.remove(self.output_dataset_pyc_filepath)
def test_mos_subjective_model(self):
dataset = import_python_file(self.dataset_filepath)
dataset_reader = RawDatasetReader(dataset)
subjective_model = MosModel(dataset_reader)
result = subjective_model.run_modeling()
scores = result['quality_scores']
self.assertAlmostEquals(scores[0], 4.884615384615385, places=4)
self.assertAlmostEquals(scores[10], 2.0769230769230771, places=4)
self.assertAlmostEquals(np.mean(scores), 3.544790652385589, places=4)
def test_mos_subjective_model_output(self):
dataset = import_python_file(self.dataset_filepath)
dataset_reader = RawDatasetReader(dataset)
subjective_model = MosModel(dataset_reader)
subjective_model.run_modeling()
subjective_model.to_aggregated_dataset_file(self.output_dataset_filepath)
self.assertTrue(os.path.exists(self.output_dataset_filepath))
dataset2 = import_python_file(self.output_dataset_filepath)
dis_video = dataset2.dis_videos[0]
self.assertTrue('groundtruth' in dis_video)
self.assertTrue('os' not in dis_video)
self.assertAlmostEquals(dis_video['groundtruth'], 4.884615384615385, places=4)
def test_mos_subjective_model_output_custom_resampling(self):
dataset = import_python_file(self.dataset_filepath)
dataset_reader = RawDatasetReader(dataset)
subjective_model = MosModel(dataset_reader)
subjective_model.run_modeling()
subjective_model.to_aggregated_dataset_file(self.output_dataset_filepath, resampling_type='lanczos')
self.assertTrue(os.path.exists(self.output_dataset_filepath))
dataset2 = import_python_file(self.output_dataset_filepath)
self.assertFalse(hasattr(dataset2, 'quality_height'))
self.assertFalse(hasattr(dataset2, 'quality_width'))
self.assertEquals(dataset2.resampling_type, 'lanczos')
dis_video = dataset2.dis_videos[0]
self.assertTrue('groundtruth' in dis_video)
self.assertTrue('os' not in dis_video)
self.assertAlmostEquals(dis_video['groundtruth'], 4.884615384615385, places=4)
def test_mos_subjective_model_output2(self):
dataset = import_python_file(self.dataset_filepath)
dataset_reader = RawDatasetReader(dataset)
subjective_model = MosModel(dataset_reader)
subjective_model.run_modeling()
dataset2 = subjective_model.to_aggregated_dataset()
dis_video = dataset2.dis_videos[0]
self.assertTrue('groundtruth' in dis_video)
self.assertTrue('os' not in dis_video)
self.assertAlmostEquals(dis_video['groundtruth'], 4.884615384615385, places=4)
def test_mos_subjective_model_normalize_final(self):
dataset = import_python_file(self.dataset_filepath)
dataset_reader = RawDatasetReader(dataset)
subjective_model = MosModel(dataset_reader)
result = subjective_model.run_modeling(normalize_final=True)
scores = result['quality_scores']
self.assertAlmostEquals(scores[0], 1.1318646945818083, places=4)
self.assertAlmostEquals(scores[10], -1.2400334499143002, places=4)
self.assertAlmostEquals(np.mean(scores), 0.0, places=4)
def test_mos_subjective_model_transform_final(self):
dataset = import_python_file(self.dataset_filepath)
dataset_reader = RawDatasetReader(dataset)
subjective_model = MosModel(dataset_reader)
result = subjective_model.run_modeling(transform_final={'p1': 10, 'p0': 1})
scores = result['quality_scores']
self.assertAlmostEquals(scores[0], 49.84615384615385, places=4)
self.assertAlmostEquals(scores[10], 21.769230769230771, places=4)
self.assertAlmostEquals(np.mean(scores), 36.44790652385589, places=4)
def test_from_dataset_file(self):
subjective_model = MosModel.from_dataset_file(self.dataset_filepath)
result = subjective_model.run_modeling()
scores = result['quality_scores']
self.assertAlmostEquals(scores[0], 4.884615384615385, places=4)
self.assertAlmostEquals(scores[10], 2.0769230769230771, places=4)
self.assertAlmostEquals(np.mean(scores), 3.544790652385589, places=4)
def test_dmos_subjective_model(self):
subjective_model = DmosModel.from_dataset_file(self.dataset_filepath)
result = subjective_model.run_modeling()
scores = result['quality_scores']
self.assertAlmostEquals(scores[0], 5.0, places=4)
self.assertAlmostEquals(scores[10], 2.1923076923076921, places=4)
self.assertAlmostEquals(np.mean(scores), 3.7731256085686473, places=4)
def test_dmos_subjective_model_normalize_final(self):
subjective_model = DmosModel.from_dataset_file(self.dataset_filepath)
result = subjective_model.run_modeling(normalize_final=True)
scores = result['quality_scores']
self.assertAlmostEquals(scores[0], 1.0440613892053001, places=4)
self.assertAlmostEquals(scores[10], -1.3452648137895296, places=4)
self.assertAlmostEquals(np.mean(scores), 0.0, places=4)
def test_dmos_subjective_model_dscore_mode_same(self):
subjective_model = DmosModel.from_dataset_file(self.dataset_filepath)
result = subjective_model.run_modeling(normalize_final=True)
scores = result['quality_scores']
self.assertAlmostEquals(scores[0], 1.0440613892053001, places=4)
self.assertAlmostEquals(scores[10], -1.3452648137895296, places=4)
self.assertAlmostEquals(np.mean(scores), 0.0, places=4)
def test_observer_aware_subjective_model_with_dscoring(self):
subjective_model = MaximumLikelihoodEstimationModelReduced.from_dataset_file(
self.dataset_filepath)
result = subjective_model.run_modeling(dscore_mode=True)
self.assertAlmostEquals(np.sum(result['observer_bias']), -0.090840910829083799, places=4)
self.assertAlmostEquals(np.var(result['observer_bias']), 0.089032585621095089, places=4)
self.assertAlmostEquals(np.sum(result['observer_inconsistency']), 15.681766163430936, places=4)
self.assertAlmostEquals(np.var(result['observer_inconsistency']), 0.012565584832977776, places=4)
self.assertAlmostEquals(np.sum(result['quality_scores']), 298.35293969059796, places=4)
self.assertAlmostEquals(np.var(result['quality_scores']), 1.4163670233392607, places=4)
def test_observer_aware_subjective_model_with_zscoring(self):
subjective_model = MaximumLikelihoodEstimationModelReduced.from_dataset_file(
self.dataset_filepath)
result = subjective_model.run_modeling(zscore_mode=True)
self.assertAlmostEquals(np.sum(result['observer_bias']), 0.0, places=4)
self.assertAlmostEquals(np.var(result['observer_bias']), 0.0, places=4)
self.assertAlmostEquals(np.sum(result['observer_inconsistency']), 11.568205661696393, places=4)
self.assertAlmostEquals(np.var(result['observer_inconsistency']), 0.0079989301785523791, places=4)
self.assertAlmostEquals(np.sum(result['quality_scores']), 0.0, places=4)
self.assertAlmostEquals(np.var(result['quality_scores']), 0.80942484781493518, places=4)
def test_observer_aware_subjective_model_with_dscoring_and_zscoring(self):
subjective_model = MaximumLikelihoodEstimationModelReduced.from_dataset_file(
self.dataset_filepath)
result = subjective_model.run_modeling(dscore_mode=True, zscore_mode=True)
self.assertAlmostEquals(np.sum(result['observer_bias']), 0.0, places=4)
self.assertAlmostEquals(np.var(result['observer_bias']), 0.0, places=4)
self.assertAlmostEquals(np.sum(result['observer_inconsistency']), 11.628499078069273, places=4)
self.assertAlmostEquals(np.var(result['observer_inconsistency']), 0.0082089371266301642, places=4)
self.assertAlmostEquals(np.sum(result['quality_scores']), 0.0, places=4)
self.assertAlmostEquals(np.var(result['quality_scores']), 0.80806512456121071, places=4)
def test_observer_aware_subjective_model_use_log(self):
subjective_model = MaximumLikelihoodEstimationModelReduced.from_dataset_file(
self.dataset_filepath)
result = subjective_model.run_modeling(use_log=True)
self.assertAlmostEquals(np.sum(result['observer_bias']), -0.082429594509296211, places=4)
self.assertAlmostEquals(np.var(result['observer_bias']), 0.089032585621095089, places=4)
self.assertAlmostEquals(np.sum(result['observer_inconsistency']), 15.681766163430936, places=4)
self.assertAlmostEquals(np.var(result['observer_inconsistency']), 0.012565584832977776, places=4)
self.assertAlmostEquals(np.sum(result['quality_scores']), 280.2889206910113, places=4)
self.assertAlmostEquals(np.var(result['quality_scores']), 1.4355485462027884, places=4)
def test_observer_content_aware_subjective_model(self):
subjective_model = MaximumLikelihoodEstimationModel.from_dataset_file(
self.dataset_filepath)
result = subjective_model.run_modeling()
self.assertAlmostEquals(np.sum(result['content_bias']), 0, places=4)
self.assertAlmostEquals(np.var(result['content_bias']), 0, places=4)
self.assertAlmostEquals(np.sum(result['content_ambiguity']), 3.8972884776604402, places=4)
self.assertAlmostEquals(np.var(result['content_ambiguity']), 0.0041122094732031289, places=4)
self.assertAlmostEquals(np.sum(result['observer_bias']), -0.055712761348815837, places=4)
self.assertAlmostEquals(np.var(result['observer_bias']), 0.085842891905121704, places=4)
self.assertAlmostEquals(np.sum(result['observer_inconsistency']), 10.164665557559516, places=4)
self.assertAlmostEquals(np.var(result['observer_inconsistency']), 0.028749990587721687, places=4)
self.assertAlmostEquals(np.sum(result['quality_scores']), 280.20774261173619, places=4)
self.assertAlmostEquals(np.var(result['quality_scores']), 1.4351342153719635, places=4)
def test_observer_content_aware_subjective_model_missingdata(self):
dataset = import_python_file(self.dataset_filepath)
np.random.seed(0)
info_dict = {
'missing_probability': 0.1,
}
dataset_reader = MissingDataRawDatasetReader(dataset, input_dict=info_dict)
subjective_model = MaximumLikelihoodEstimationModel(dataset_reader)
result = subjective_model.run_modeling()
self.assertAlmostEquals(np.sum(result['content_bias']), 0, places=4)
self.assertAlmostEquals(np.var(result['content_bias']), 0, places=4)
self.assertAlmostEquals(np.sum(result['content_ambiguity']), 3.9104244772977128, places=4)
self.assertAlmostEquals(np.var(result['content_ambiguity']), 0.0037713583509767193, places=4)
self.assertAlmostEquals(np.sum(result['observer_bias']), -0.21903272050455846, places=4)
self.assertAlmostEquals(np.var(result['observer_bias']), 0.084353684687185043, places=4)
self.assertAlmostEquals(np.sum(result['observer_inconsistency']), 9.8168943054654481, places=4)
self.assertAlmostEquals(np.var(result['observer_inconsistency']), 0.028159236075789944, places=4)
self.assertAlmostEquals(np.sum(result['quality_scores']), 280.05548186797336, places=4)
self.assertAlmostEquals(np.var(result['quality_scores']), 1.4339487982797514, places=4)
np.random.seed(0)
info_dict = {
'missing_probability': 0.5,
}
dataset_reader = MissingDataRawDatasetReader(dataset, input_dict=info_dict)
subjective_model = MaximumLikelihoodEstimationModel(dataset_reader)
result = subjective_model.run_modeling()
self.assertAlmostEquals(np.sum(result['content_bias']), 0, places=4)
self.assertAlmostEquals(np.var(result['content_bias']), 0, places=4)
self.assertAlmostEquals(np.sum(result['content_ambiguity']), 2.63184284168883, places=4)
self.assertAlmostEquals(np.var(result['content_ambiguity']), 0.019164097909450246, places=4)
self.assertAlmostEquals(np.sum(result['observer_bias']), 0.2263148440748638, places=4)
self.assertAlmostEquals(np.var(result['observer_bias']), 0.070613033112114504, places=4)
self.assertAlmostEquals(np.sum(result['observer_inconsistency']), 12.317917502439435, places=4)
self.assertAlmostEquals(np.var(result['observer_inconsistency']), 0.029455722248727296, places=4)
self.assertAlmostEquals(np.sum(result['quality_scores']), 280.29962156788139, places=4)
self.assertAlmostEquals(np.var(result['quality_scores']), 1.4717366222424826, places=4)
def test_observer_content_aware_subjective_model_nocontent(self):
subjective_model = MaximumLikelihoodEstimationModel.from_dataset_file(
self.dataset_filepath)
result = subjective_model.run_modeling(mode='NO_CONTENT')
self.assertAlmostEquals(np.sum(result['observer_bias']), -0.090840910829083799, places=4)
self.assertAlmostEquals(np.var(result['observer_bias']), 0.089032585621095089, places=4)
self.assertAlmostEquals(np.sum(result['observer_inconsistency']), 15.681766163430936, places=4)
self.assertAlmostEquals(np.var(result['observer_inconsistency']), 0.012565584832977776, places=4)
self.assertAlmostEquals(np.sum(result['quality_scores']), 280.31447815213642, places=4)
self.assertAlmostEquals(np.var(result['quality_scores']), 1.4355485462027884, places=4)
self.assertAlmostEquals(np.sum(result['content_bias']), 0.0, places=4)
self.assertAlmostEquals(np.var(result['content_bias']), 0.0, places=4)
self.assertAlmostEquals(np.sum(result['content_ambiguity']), 0.0, places=4)
self.assertAlmostEquals(np.var(result['content_ambiguity']), 0.0, places=4)
def test_observer_content_aware_subjective_model_nosubject(self):
subjective_model = MaximumLikelihoodEstimationModel.from_dataset_file(
self.dataset_filepath)
result = subjective_model.run_modeling(mode='NO_SUBJECT')
self.assertAlmostEquals(np.sum(result['observer_bias']), 0.0, places=4)
self.assertAlmostEquals(np.var(result['observer_bias']), 0.0, places=4)
self.assertAlmostEquals(np.sum(result['observer_inconsistency']), 0.0, places=4)
self.assertAlmostEquals(np.var(result['observer_inconsistency']), 0.0, places=4)
self.assertAlmostEquals(np.sum(result['quality_scores']), 280.0384615384616, places=4)
self.assertAlmostEquals(np.var(result['quality_scores']), 1.4012220200639218, places=4)
self.assertAlmostEquals(np.sum(result['content_bias']), 0.0, places=4)
self.assertAlmostEquals(np.var(result['content_bias']), 0.0, places=4)
self.assertAlmostEquals( | np.sum(result['content_ambiguity']) | numpy.sum |
'''This class will log 1d array in Nd matrix from device and qualisys object'''
import numpy as np
from datetime import datetime as datetime
from time import time
from utils_mpc import quaternionToRPY
class LoggerControl():
def __init__(self, dt, N0_gait, joystick=None, estimator=None, loop=None, gait=None, statePlanner=None,
footstepPlanner=None, footTrajectoryGenerator=None, logSize=60e3, ringBuffer=False):
self.ringBuffer = ringBuffer
logSize = np.int(logSize)
self.logSize = logSize
self.i = 0
self.dt = dt
# Allocate the data:
# Joystick
self.joy_v_ref = np.zeros([logSize, 6]) # reference velocity of the joystick
# Estimator
self.esti_feet_status = np.zeros([logSize, 4]) # input feet status (contact or not)
self.esti_feet_goals = np.zeros([logSize, 3, 4]) # input feet goals (desired on the ground)
self.esti_q_filt = np.zeros([logSize, 19]) # output position
self.esti_v_filt = np.zeros([logSize, 18]) # output velocity
self.esti_v_secu = np.zeros([logSize, 12]) # filtered output velocity for security check
self.esti_FK_lin_vel = np.zeros([logSize, 3]) # estimated velocity of the base with FK
self.esti_FK_xyz = np.zeros([logSize, 3]) # estimated position of the base with FK
self.esti_xyz_mean_feet = np.zeros([logSize, 3]) # average of feet goals
self.esti_filt_lin_vel = np.zeros([logSize, 3]) # estimated velocity of the base before low pass filter
self.esti_HP_x = np.zeros([logSize, 3]) # x input of the velocity complementary filter
self.esti_HP_dx = np.zeros([logSize, 3]) # dx input of the velocity complementary filter
self.esti_HP_alpha = np.zeros([logSize, 3]) # alpha parameter of the velocity complementary filter
self.esti_HP_filt_x = np.zeros([logSize, 3]) # filtered output of the velocity complementary filter
self.esti_LP_x = np.zeros([logSize, 3]) # x input of the position complementary filter
self.esti_LP_dx = np.zeros([logSize, 3]) # dx input of the position complementary filter
self.esti_LP_alpha = np.zeros([logSize, 3]) # alpha parameter of the position complementary filter
self.esti_LP_filt_x = np.zeros([logSize, 3]) # filtered output of the position complementary filter
self.esti_kf_X = np.zeros([logSize, 18]) # state of the Kalman filter
self.esti_kf_Z = np.zeros([logSize, 16]) # measurement for the Kalman filter
# Loop
self.loop_o_q_int = np.zeros([logSize, 19]) # position in world frame (esti_q_filt + dt * loop_o_v)
self.loop_o_v = np.zeros([logSize, 18]) # estimated velocity in world frame
self.loop_h_v = np.zeros([logSize, 18]) # estimated velocity in horizontal frame
self.loop_pos_virtual_world = np.zeros([logSize, 3]) # x, y, yaw perfect position in world
# Gait
self.planner_gait = np.zeros([logSize, N0_gait, 4]) # Gait sequence
self.planner_is_static = np.zeros([logSize]) # if the planner is in static mode or not
self.planner_q_static = np.zeros([logSize, 19]) # position in static mode (4 stance phase)
self.planner_RPY_static = np.zeros([logSize, 3]) # RPY orientation in static mode (4 stance phase)
# State planner
if statePlanner is not None:
self.planner_xref = np.zeros([logSize, 12, 1+statePlanner.getNSteps()]) # Reference trajectory
# Footstep planner
if gait is not None:
self.planner_fsteps = np.zeros([logSize, gait.getCurrentGait().shape[0], 12]) # Reference footsteps position
self.planner_h_ref = np.zeros([logSize]) # reference height of the planner
# Foot Trajectory Generator
self.planner_goals = np.zeros([logSize, 3, 4]) # 3D target feet positions
self.planner_vgoals = np.zeros([logSize, 3, 4]) # 3D target feet velocities
self.planner_agoals = np.zeros([logSize, 3, 4]) # 3D target feet accelerations
# Model Predictive Control
# output vector of the MPC (next state + reference contact force)
if statePlanner is not None:
self.mpc_x_f = np.zeros([logSize, 24, statePlanner.getNSteps()])
# Whole body control
self.wbc_x_f = np.zeros([logSize, 24]) # input vector of the WBC (next state + reference contact force)
self.wbc_P = np.zeros([logSize, 12]) # proportionnal gains of the PD+
self.wbc_D = np.zeros([logSize, 12]) # derivative gains of the PD+
self.wbc_q_des = np.zeros([logSize, 12]) # desired position of actuators
self.wbc_v_des = np.zeros([logSize, 12]) # desired velocity of actuators
self.wbc_tau_ff = np.zeros([logSize, 12]) # feedforward torques computed by the WBC
self.wbc_f_ctc = np.zeros([logSize, 12]) # contact forces computed by the WBC
self.wbc_feet_pos = np.zeros([logSize, 3, 4]) # current feet positions according to WBC
self.wbc_feet_pos_target = np.zeros([logSize, 3, 4]) # current feet positions targets for WBC
self.wbc_feet_err = np.zeros([logSize, 3, 4]) # error between feet positions and their reference
self.wbc_feet_vel = np.zeros([logSize, 3, 4]) # current feet velocities according to WBC
self.wbc_feet_vel_target = np.zeros([logSize, 3, 4]) # current feet velocities targets for WBC
self.wbc_feet_acc_target = np.zeros([logSize, 3, 4]) # current feet accelerations targets for WBC
self.wbc_feet_pos_invkin = np.zeros([logSize, 3, 4]) # current feet positions according to InvKin
self.wbc_feet_vel_invkin = np.zeros([logSize, 3, 4]) # current feet velocities according to InvKin
# Timestamps
self.tstamps = np.zeros(logSize)
def sample(self, joystick, estimator, loop, gait, statePlanner, footstepPlanner, footTrajectoryGenerator, wbc):
if (self.i >= self.logSize):
if self.ringBuffer:
self.i = 0
else:
return
# Logging from joystick
self.joy_v_ref[self.i] = joystick.v_ref[:, 0]
# Logging from estimator
self.esti_feet_status[self.i] = estimator.feet_status[:]
self.esti_feet_goals[self.i] = estimator.feet_goals
self.esti_q_filt[self.i] = estimator.q_filt[:, 0]
self.esti_v_filt[self.i] = estimator.v_filt[:, 0]
self.esti_v_secu[self.i] = estimator.v_secu[:]
self.esti_FK_lin_vel[self.i] = estimator.FK_lin_vel[:]
self.esti_FK_xyz[self.i] = estimator.FK_xyz[:]
self.esti_xyz_mean_feet[self.i] = estimator.xyz_mean_feet[:]
self.esti_filt_lin_vel[self.i] = estimator.filt_lin_vel[:]
if not estimator.kf_enabled:
self.esti_HP_x[self.i] = estimator.filter_xyz_vel.x
self.esti_HP_dx[self.i] = estimator.filter_xyz_vel.dx
self.esti_HP_alpha[self.i] = estimator.filter_xyz_vel.alpha
self.esti_HP_filt_x[self.i] = estimator.filter_xyz_vel.filt_x
self.esti_LP_x[self.i] = estimator.filter_xyz_pos.x
self.esti_LP_dx[self.i] = estimator.filter_xyz_pos.dx
self.esti_LP_alpha[self.i] = estimator.filter_xyz_pos.alpha
self.esti_LP_filt_x[self.i] = estimator.filter_xyz_pos.filt_x
else:
self.esti_kf_X[self.i] = estimator.kf.X[:, 0]
self.esti_kf_Z[self.i] = estimator.Z[:, 0]
# Logging from the main loop
self.loop_o_q_int[self.i] = loop.q[:, 0]
self.loop_o_v[self.i] = loop.v[:, 0]
self.loop_h_v[self.i] = loop.h_v[:, 0]
self.loop_pos_virtual_world[self.i] = np.array([loop.q[0, 0], loop.q[1, 0], loop.yaw_estim])
# Logging from the planner
# self.planner_q_static[self.i] = planner.q_static[:]
# self.planner_RPY_static[self.i] = planner.RPY_static[:, 0]
self.planner_xref[self.i] = statePlanner.getReferenceStates()
self.planner_fsteps[self.i] = footstepPlanner.getFootsteps()
self.planner_gait[self.i] = gait.getCurrentGait()
self.planner_goals[self.i] = footTrajectoryGenerator.getFootPosition()
self.planner_vgoals[self.i] = footTrajectoryGenerator.getFootVelocity()
self.planner_agoals[self.i] = footTrajectoryGenerator.getFootAcceleration()
self.planner_is_static[self.i] = gait.getIsStatic()
self.planner_h_ref[self.i] = loop.h_ref
# Logging from model predictive control
self.mpc_x_f[self.i] = loop.x_f_mpc
# Logging from whole body control
self.wbc_x_f[self.i] = loop.x_f_wbc
self.wbc_P[self.i] = loop.result.P
self.wbc_D[self.i] = loop.result.D
self.wbc_q_des[self.i] = loop.result.q_des
self.wbc_v_des[self.i] = loop.result.v_des
self.wbc_tau_ff[self.i] = loop.result.tau_ff
self.wbc_f_ctc[self.i] = wbc.f_with_delta[:, 0]
self.wbc_feet_pos[self.i] = wbc.feet_pos
self.wbc_feet_pos_target[self.i] = wbc.log_feet_pos_target[:, :, self.i+1]
self.wbc_feet_err[self.i] = wbc.feet_err
self.wbc_feet_vel[self.i] = wbc.feet_vel
self.wbc_feet_vel_target[self.i] = wbc.log_feet_vel_target[:, :, self.i+1]
self.wbc_feet_acc_target[self.i] = wbc.log_feet_acc_target[:, :, self.i+1]
self.wbc_feet_pos_invkin[self.i] = wbc.invKin.cpp_posf.transpose()
self.wbc_feet_vel_invkin[self.i] = wbc.invKin.cpp_vf.transpose()
# Logging timestamp
self.tstamps[self.i] = time()
self.i += 1
def processMocap(self, N, loggerSensors):
self.mocap_b_v = np.zeros([N, 3])
self.mocap_b_w = np.zeros([N, 3])
self.mocap_RPY = np.zeros([N, 3])
for i in range(N):
oRb = loggerSensors.mocapOrientationMat9[i]
"""from IPython import embed
embed()"""
self.mocap_b_v[i] = (oRb.transpose() @ loggerSensors.mocapVelocity[i].reshape((3, 1))).ravel()
self.mocap_b_w[i] = (oRb.transpose() @ loggerSensors.mocapAngularVelocity[i].reshape((3, 1))).ravel()
self.mocap_RPY[i] = quaternionToRPY(loggerSensors.mocapOrientationQuat[i])[:, 0]
def plotAll(self, loggerSensors):
from matplotlib import pyplot as plt
N = self.tstamps.shape[0]
t_range = np.array([k*self.dt for k in range(N)])
self.processMocap(N, loggerSensors)
index6 = [1, 3, 5, 2, 4, 6]
index12 = [1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12]
"""plt.figure()
for i in range(4):
if i == 0:
ax0 = plt.subplot(2, 2, i+1)
else:
plt.subplot(2, 2, i+1, sharex=ax0)
switch = np.diff(self.esti_feet_status[:, i])
tmp = self.wbc_feet_pos[:-1, 2, i]
tmp_y = tmp[switch > 0]
tmp_x = t_range[:-1]
tmp_x = tmp_x[switch > 0]
plt.plot(tmp_x, tmp_y, linewidth=3)"""
lgd_X = ["FL", "FR", "HL", "HR"]
lgd_Y = ["Pos X", "Pos Y", "Pos Z"]
plt.figure()
for i in range(12):
if i == 0:
ax0 = plt.subplot(3, 4, index12[i])
else:
plt.subplot(3, 4, index12[i], sharex=ax0)
plt.plot(t_range, self.wbc_feet_pos[:, i % 3, np.int(i/3)], color='b', linewidth=3, marker='')
plt.plot(t_range, self.wbc_feet_err[:, i % 3, np.int(i/3)] + self.wbc_feet_pos[0, i % 3, np.int(i/3)], color='g', linewidth=3, marker='')
plt.plot(t_range, self.wbc_feet_pos_target[:, i % 3, np.int(i/3)], color='r', linewidth=3, marker='')
"""plt.plot(t_range, self.wbc_feet_pos_invkin[:, i % 3, np.int(i/3)],
color='darkviolet', linewidth=3, linestyle="--", marker='')"""
if (i % 3) == 2:
mini = np.min(self.wbc_feet_pos[:, i % 3, np.int(i/3)])
maxi = np.max(self.wbc_feet_pos[:, i % 3, np.int(i/3)])
plt.plot(t_range, self.planner_gait[:, 0, np.int(
i/3)] * (maxi - mini) + mini, color='k', linewidth=3, marker='')
plt.legend([lgd_Y[i % 3] + " " + lgd_X[np.int(i/3)]+"", "error",
lgd_Y[i % 3] + " " + lgd_X[np.int(i/3)]+" Ref", "Contact state"], prop={'size': 8})
plt.suptitle("Measured & Reference feet positions (base frame)")
lgd_X = ["FL", "FR", "HL", "HR"]
lgd_Y = ["Vel X", "Vel Y", "Vel Z"]
plt.figure()
for i in range(12):
if i == 0:
ax0 = plt.subplot(3, 4, index12[i])
else:
plt.subplot(3, 4, index12[i], sharex=ax0)
plt.plot(t_range, self.wbc_feet_vel[:, i % 3, np.int(i/3)], color='b', linewidth=3, marker='')
plt.plot(t_range, self.wbc_feet_vel_target[:, i % 3, np.int(i/3)], color='r', linewidth=3, marker='')
"""plt.plot(t_range, self.wbc_feet_vel_invkin[:, i % 3, np.int(i/3)],
color='darkviolet', linewidth=3, linestyle="--", marker='')"""
plt.legend([lgd_Y[i % 3] + " " + lgd_X[np.int(i/3)], lgd_Y[i %
3] + " " + lgd_X[np.int(i/3)]+" Ref"], prop={'size': 8})
plt.suptitle("Measured and Reference feet velocities (base frame)")
lgd_X = ["FL", "FR", "HL", "HR"]
lgd_Y = ["Acc X", "Acc Y", "Acc Z"]
plt.figure()
for i in range(12):
if i == 0:
ax0 = plt.subplot(3, 4, index12[i])
else:
plt.subplot(3, 4, index12[i], sharex=ax0)
plt.plot(t_range, self.wbc_feet_acc_target[:, i % 3, np.int(i/3)], color='r', linewidth=3, marker='')
plt.legend([lgd_Y[i % 3] + " " + lgd_X[np.int(i/3)]+" Ref"], prop={'size': 8})
plt.suptitle("Reference feet accelerations (base frame)")
# LOG_Q
lgd = ["Position X", "Position Y", "Position Z", "Position Roll", "Position Pitch", "Position Yaw"]
plt.figure()
for i in range(6):
if i == 0:
ax0 = plt.subplot(3, 2, index6[i])
else:
plt.subplot(3, 2, index6[i], sharex=ax0)
if i in [0, 1]:
plt.plot(t_range, self.loop_pos_virtual_world[:, i], "b", linewidth=3)
plt.plot(t_range, self.loop_pos_virtual_world[:, i], "r", linewidth=3)
elif i == 5:
plt.plot(t_range, self.loop_pos_virtual_world[:, 2], "b", linewidth=3)
plt.plot(t_range, self.loop_pos_virtual_world[:, 2], "r", linewidth=3)
else:
plt.plot(t_range, self.planner_xref[:, i, 0], "b", linewidth=2)
plt.plot(t_range, self.planner_xref[:, i, 1], "r", linewidth=3)
if i < 3:
plt.plot(t_range, loggerSensors.mocapPosition[:, i], "k", linewidth=3)
else:
plt.plot(t_range, self.mocap_RPY[:, i-3], "k", linewidth=3)
# plt.plot(t_range, self.log_q[i, :], "grey", linewidth=4)
# plt.plot(t_range[:-2], self.log_x_invkin[i, :-2], "g", linewidth=2)
# plt.plot(t_range[:-2], self.log_x_ref_invkin[i, :-2], "violet", linewidth=2, linestyle="--")
plt.legend(["Robot state", "Robot reference state", "Ground truth"], prop={'size': 8})
plt.ylabel(lgd[i])
plt.suptitle("Measured & Reference position and orientation")
# LOG_V
lgd = ["Linear vel X", "Linear vel Y", "Linear vel Z",
"Angular vel Roll", "Angular vel Pitch", "Angular vel Yaw"]
plt.figure()
for i in range(6):
if i == 0:
ax0 = plt.subplot(3, 2, index6[i])
else:
plt.subplot(3, 2, index6[i], sharex=ax0)
plt.plot(t_range, self.loop_h_v[:, i], "b", linewidth=2)
plt.plot(t_range, self.joy_v_ref[:, i], "r", linewidth=3)
if i < 3:
plt.plot(t_range, self.mocap_b_v[:, i], "k", linewidth=3)
# plt.plot(t_range, self.esti_FK_lin_vel[:, i], "violet", linewidth=3, linestyle="--")
plt.plot(t_range, self.esti_filt_lin_vel[:, i], "violet", linewidth=3, linestyle="--")
else:
plt.plot(t_range, self.mocap_b_w[:, i-3], "k", linewidth=3)
"""N = 2000
y = np.convolve(self.mocap_b_w[:, i-3], np.ones(N)/N, mode='valid')
plt.plot(t_range[int(N/2)-1:-int(N/2)], y, linewidth=3, linestyle="--")"""
# plt.plot(t_range, self.log_dq[i, :], "g", linewidth=2)
# plt.plot(t_range[:-2], self.log_dx_invkin[i, :-2], "g", linewidth=2)
# plt.plot(t_range[:-2], self.log_dx_ref_invkin[i, :-2], "violet", linewidth=2, linestyle="--")
plt.legend(["Robot state", "Robot reference state", "Ground truth"], prop={'size': 8})
plt.ylabel(lgd[i])
plt.suptitle("Measured & Reference linear and angular velocities")
"""plt.figure()
plt.plot(t_range[:-2], self.log_x[6, :-2], "b", linewidth=2)
plt.plot(t_range[:-2], self.log_x_cmd[6, :-2], "r", linewidth=2)
plt.plot(t_range[:-2], self.log_dx_invkin[0, :-2], "g", linewidth=2)
plt.plot(t_range[:-2], self.log_dx_ref_invkin[0, :-2], "violet", linewidth=2)
plt.legend(["WBC integrated output state", "Robot reference state",
"Task current state", "Task reference state"])"""
# Analysis of the footstep locations (current and future) with a slider to move along time
# self.slider_predicted_footholds()
# Analysis of the footholds locations during the whole experiment
"""import utils_mpc
import pinocchio as pin
f_c = ["r", "b", "forestgreen", "rebeccapurple"]
quat = np.zeros((4, 1))
steps = np.zeros((12, 1))
o_step = np.zeros((3, 1))
plt.figure()
plt.plot(self.loop_o_q_int[:, 0], self.loop_o_q_int[:, 1], linewidth=2, color="k")
for i in range(self.planner_fsteps.shape[0]):
fsteps = self.planner_fsteps[i]
RPY = utils_mpc.quaternionToRPY(self.loop_o_q_int[i, 3:7])
quat[:, 0] = utils_mpc.EulerToQuaternion([0.0, 0.0, RPY[2]])
oRh = pin.Quaternion(quat).toRotationMatrix()
for j in range(4):
#if np.any(fsteps[k, (j*3):((j+1)*3)]) and not np.array_equal(steps[(j*3):((j+1)*3), 0],
# fsteps[k, (j*3):((j+1)*3)]):
# steps[(j*3):((j+1)*3), 0] = fsteps[k, (j*3):((j+1)*3)]
# o_step[:, 0:1] = oRh @ steps[(j*3):((j+1)*3), 0:1] + self.loop_o_q_int[i:(i+1), 0:3].transpose()
o_step[:, 0:1] = oRh @ fsteps[0:1, (j*3):((j+1)*3)].transpose() + self.loop_o_q_int[i:(i+1), 0:3].transpose()
plt.plot(o_step[0, 0], o_step[1, 0], linestyle=None, linewidth=1, marker="o", color=f_c[j])
"""
lgd1 = ["HAA", "HFE", "Knee"]
lgd2 = ["FL", "FR", "HL", "HR"]
plt.figure()
for i in range(12):
if i == 0:
ax0 = plt.subplot(3, 4, index12[i])
else:
plt.subplot(3, 4, index12[i], sharex=ax0)
tau_fb = self.wbc_P[:, i] * (self.wbc_q_des[:, i] - self.esti_q_filt[:, 7+i]) + \
self.wbc_D[:, i] * (self.wbc_v_des[:, i] - self.esti_v_filt[:, 6+i])
h1, = plt.plot(t_range, self.wbc_tau_ff[:, i], "r", linewidth=3)
h2, = plt.plot(t_range, tau_fb, "b", linewidth=3)
h3, = plt.plot(t_range, self.wbc_tau_ff[:, i] + tau_fb, "g", linewidth=3)
h4, = plt.plot(t_range[:-1], loggerSensors.torquesFromCurrentMeasurment[1:, i],
"violet", linewidth=3, linestyle="--")
plt.xlabel("Time [s]")
plt.ylabel(lgd1[i % 3]+" "+lgd2[int(i/3)]+" [Nm]")
tmp = lgd1[i % 3]+" "+lgd2[int(i/3)]
plt.legend([h1, h2, h3, h4], ["FF "+tmp, "FB "+tmp, "PD+ "+tmp, "Meas "+tmp], prop={'size': 8})
plt.ylim([-8.0, 8.0])
plt.suptitle("FF torques & FB torques & Sent torques & Meas torques")
lgd1 = ["Ctct force X", "Ctct force Y", "Ctct force Z"]
lgd2 = ["FL", "FR", "HL", "HR"]
plt.figure()
for i in range(12):
if i == 0:
ax0 = plt.subplot(3, 4, index12[i])
else:
plt.subplot(3, 4, index12[i], sharex=ax0)
h1, = plt.plot(t_range, self.mpc_x_f[:, 12+i, 0], "r", linewidth=3)
h2, = plt.plot(t_range, self.wbc_f_ctc[:, i], "b", linewidth=3, linestyle="--")
plt.xlabel("Time [s]")
plt.ylabel(lgd1[i % 3]+" "+lgd2[int(i/3)]+" [N]")
plt.legend([h1, h2], ["MPC " + lgd1[i % 3]+" "+lgd2[int(i/3)],
"WBC " + lgd1[i % 3]+" "+lgd2[int(i/3)]], prop={'size': 8})
if (i % 3) == 2:
plt.ylim([-0.0, 26.0])
else:
plt.ylim([-26.0, 26.0])
plt.suptitle("Contact forces (MPC command) & WBC QP output")
lgd1 = ["HAA", "HFE", "Knee"]
lgd2 = ["FL", "FR", "HL", "HR"]
plt.figure()
for i in range(12):
if i == 0:
ax0 = plt.subplot(3, 4, index12[i])
else:
plt.subplot(3, 4, index12[i], sharex=ax0)
h1, = plt.plot(t_range, self.wbc_q_des[:, i], color='r', linewidth=3)
h2, = plt.plot(t_range, self.esti_q_filt[:, 7+i], color='b', linewidth=3)
plt.xlabel("Time [s]")
plt.ylabel(lgd1[i % 3]+" "+lgd2[int(i/3)]+" [rad]")
plt.legend([h1, h2], ["Ref "+lgd1[i % 3]+" "+lgd2[int(i/3)],
lgd1[i % 3]+" "+lgd2[int(i/3)]], prop={'size': 8})
plt.suptitle("Desired actuator positions & Measured actuator positions")
# Evolution of predicted trajectory along time
log_t_pred = np.array([k*self.dt*10 for k in range(self.mpc_x_f.shape[2])])
log_t_ref = np.array([k*self.dt*10 for k in range(self.planner_xref.shape[2])])
"""from IPython import embed
embed()"""
titles = ["X", "Y", "Z", "Roll", "Pitch", "Yaw"]
step = 1000
plt.figure()
for j in range(6):
plt.subplot(3, 2, index6[j])
c = [[i/(self.mpc_x_f.shape[0]+5), 0.0, i/(self.mpc_x_f.shape[0]+5)]
for i in range(0, self.mpc_x_f.shape[0], step)]
for i in range(0, self.mpc_x_f.shape[0], step):
h1, = plt.plot(log_t_pred+(i+10)*self.dt,
self.mpc_x_f[i, j, :], "b", linewidth=2, color=c[int(i/step)])
h2, = plt.plot(log_t_ref+i*self.dt,
self.planner_xref[i, j, :], linestyle="--", marker='x', color="g", linewidth=2)
#h3, = plt.plot(np.array([k*self.dt for k in range(self.mpc_x_f.shape[0])]),
# self.planner_xref[:, j, 0], linestyle=None, marker='x', color="r", linewidth=1)
plt.xlabel("Time [s]")
plt.legend([h1, h2, h3], ["Output trajectory of MPC",
"Input trajectory of planner"]) #, "Actual robot trajectory"])
plt.title("Predicted trajectory for " + titles[j])
plt.suptitle("Analysis of trajectories in position and orientation computed by the MPC")
plt.figure()
for j in range(6):
plt.subplot(3, 2, index6[j])
c = [[i/(self.mpc_x_f.shape[0]+5), 0.0, i/(self.mpc_x_f.shape[0]+5)]
for i in range(0, self.mpc_x_f.shape[0], step)]
for i in range(0, self.mpc_x_f.shape[0], step):
h1, = plt.plot(log_t_pred+(i+10)*self.dt,
self.mpc_x_f[i, j+6, :], "b", linewidth=2, color=c[int(i/step)])
h2, = plt.plot(log_t_ref+i*self.dt,
self.planner_xref[i, j+6, :], linestyle="--", marker='x', color="g", linewidth=2)
h3, = plt.plot(np.array([k*self.dt for k in range(self.mpc_x_f.shape[0])]),
self.planner_xref[:, j+6, 0], linestyle=None, marker='x', color="r", linewidth=1)
plt.xlabel("Time [s]")
plt.legend([h1, h2, h3], ["Output trajectory of MPC",
"Input trajectory of planner", "Actual robot trajectory"])
plt.title("Predicted trajectory for velocity in " + titles[j])
plt.suptitle("Analysis of trajectories of linear and angular velocities computed by the MPC")
step = 1000
lgd1 = ["Ctct force X", "Ctct force Y", "Ctct force Z"]
lgd2 = ["FL", "FR", "HL", "HR"]
plt.figure()
for i in range(12):
if i == 0:
ax0 = plt.subplot(3, 4, index12[i])
else:
plt.subplot(3, 4, index12[i], sharex=ax0)
h1, = plt.plot(t_range, self.mpc_x_f[:, 12+i, 0], "r", linewidth=3)
h2, = plt.plot(t_range, self.wbc_f_ctc[:, i], "b", linewidth=3, linestyle="--")
plt.xlabel("Time [s]")
plt.ylabel(lgd1[i % 3]+" "+lgd2[int(i/3)]+" [N]")
plt.legend([h1, h2], ["MPC " + lgd1[i % 3]+" "+lgd2[int(i/3)],
"WBC " + lgd1[i % 3]+" "+lgd2[int(i/3)]], prop={'size': 8})
if (i % 3) == 2:
plt.ylim([-0.0, 26.0])
else:
plt.ylim([-26.0, 26.0])
plt.suptitle("Contact forces (MPC command) & WBC QP output")
lgd1 = ["Ctct force X", "Ctct force Y", "Ctct force Z"]
lgd2 = ["FL", "FR", "HL", "HR"]
plt.figure()
for i in range(4):
if i == 0:
ax0 = plt.subplot(1, 4, i+1)
else:
plt.subplot(1, 4, i+1, sharex=ax0)
for k in range(0, self.mpc_x_f.shape[0], step):
h2, = plt.plot(log_t_pred+k*self.dt, self.mpc_x_f[k, 12+(3*i+2), :], linestyle="--", marker='x', linewidth=2)
h1, = plt.plot(t_range, self.mpc_x_f[:, 12+(3*i+2), 0], "r", linewidth=3)
# h3, = plt.plot(t_range, self.wbc_f_ctc[:, i], "b", linewidth=3, linestyle="--")
plt.plot(t_range, self.esti_feet_status[:, i], "k", linestyle="--")
plt.xlabel("Time [s]")
plt.ylabel(lgd2[i]+" [N]")
plt.legend([h1, h2], ["MPC "+lgd2[i],
"MPC "+lgd2[i]+" trajectory"])
plt.ylim([-1.0, 26.0])
plt.suptitle("Contact forces trajectories & Actual forces trajectories")
# Analysis of the complementary filter behaviour
clr = ["b", "darkred", "forestgreen"]
# Velocity complementary filter
lgd_Y = ["dx", "ddx", "alpha dx", "dx_out", "dy", "ddy", "alpha dy", "dy_out", "dz", "ddz", "alpha dz", "dz_out"]
plt.figure()
for i in range(12):
if i == 0:
ax0 = plt.subplot(3, 4, i+1)
else:
plt.subplot(3, 4, i+1, sharex=ax0)
if i % 4 == 0:
plt.plot(t_range, self.esti_HP_x[:, int(i/4)], color=clr[int(i/4)], linewidth=3, marker='') # x input of the velocity complementary filter
elif i % 4 == 1:
plt.plot(t_range, self.esti_HP_dx[:, int(i/4)], color=clr[int(i/4)], linewidth=3, marker='') # dx input of the velocity complementary filter
elif i % 4 == 2:
plt.plot(t_range, self.esti_HP_alpha[:, int(i/4)], color=clr[int(i/4)], linewidth=3, marker='') # alpha parameter of the velocity complementary filter
else:
plt.plot(t_range, self.esti_HP_filt_x[:, int(i/4)], color=clr[int(i/4)], linewidth=3, marker='') # filtered output of the velocity complementary filter
plt.legend([lgd_Y[i]], prop={'size': 8})
plt.suptitle("Evolution of the quantities of the velocity complementary filter")
# Position complementary filter
lgd_Y = ["x", "dx", "alpha x", "x_out", "y", "dy", "alpha y", "y_out", "z", "dz", "alpha z", "z_out"]
plt.figure()
for i in range(12):
if i == 0:
ax0 = plt.subplot(3, 4, i+1)
else:
plt.subplot(3, 4, i+1, sharex=ax0)
if i % 4 == 0:
plt.plot(t_range, self.esti_LP_x[:, int(i/4)], color=clr[int(i/4)], linewidth=3, marker='') # x input of the position complementary filter
elif i % 4 == 1:
plt.plot(t_range, self.esti_LP_dx[:, int(i/4)], color=clr[int(i/4)], linewidth=3, marker='') # dx input of the position complementary filter
elif i % 4 == 2:
plt.plot(t_range, self.esti_LP_alpha[:, int(i/4)], color=clr[int(i/4)], linewidth=3, marker='') # alpha parameter of the position complementary filter
else:
plt.plot(t_range, self.esti_LP_filt_x[:, int(i/4)], color=clr[int(i/4)], linewidth=3, marker='') # filtered output of the position complementary filter
plt.legend([lgd_Y[i]], prop={'size': 8})
plt.suptitle("Evolution of the quantities of the position complementary filter")
plt.show(block=True)
from IPython import embed
embed()
def saveAll(self, loggerSensors, fileName="data"):
date_str = datetime.now().strftime('_%Y_%m_%d_%H_%M')
np.savez(fileName + date_str + ".npz",
joy_v_ref=self.joy_v_ref,
esti_feet_status=self.esti_feet_status,
esti_feet_goals=self.esti_feet_goals,
esti_q_filt=self.esti_q_filt,
esti_v_filt=self.esti_v_filt,
esti_v_secu=self.esti_v_secu,
esti_FK_lin_vel=self.esti_FK_lin_vel,
esti_FK_xyz=self.esti_FK_xyz,
esti_xyz_mean_feet=self.esti_xyz_mean_feet,
esti_filt_lin_vel=self.esti_filt_lin_vel,
esti_HP_x=self.esti_HP_x,
esti_HP_dx=self.esti_HP_dx,
esti_HP_alpha=self.esti_HP_alpha,
esti_HP_filt_x=self.esti_HP_filt_x,
esti_LP_x=self.esti_LP_x,
esti_LP_dx=self.esti_LP_dx,
esti_LP_alpha=self.esti_LP_alpha,
esti_LP_filt_x=self.esti_LP_filt_x,
esti_kf_X=self.esti_kf_X,
esti_kf_Z=self.esti_kf_Z,
loop_o_q_int=self.loop_o_q_int,
loop_o_v=self.loop_o_v,
loop_h_v=self.loop_h_v,
loop_pos_virtual_world=self.loop_pos_virtual_world,
planner_q_static=self.planner_q_static,
planner_RPY_static=self.planner_RPY_static,
planner_xref=self.planner_xref,
planner_fsteps=self.planner_fsteps,
planner_gait=self.planner_gait,
planner_goals=self.planner_goals,
planner_vgoals=self.planner_vgoals,
planner_agoals=self.planner_agoals,
planner_is_static=self.planner_is_static,
planner_h_ref=self.planner_h_ref,
mpc_x_f=self.mpc_x_f,
wbc_x_f=self.wbc_x_f,
wbc_P=self.wbc_P,
wbc_D=self.wbc_D,
wbc_q_des=self.wbc_q_des,
wbc_v_des=self.wbc_v_des,
wbc_tau_ff=self.wbc_tau_ff,
wbc_f_ctc=self.wbc_f_ctc,
wbc_feet_pos=self.wbc_feet_pos,
wbc_feet_pos_target=self.wbc_feet_pos_target,
wbc_feet_err=self.wbc_feet_err,
wbc_feet_vel=self.wbc_feet_vel,
wbc_feet_vel_target=self.wbc_feet_vel_target,
wbc_feet_acc_target=self.wbc_feet_acc_target,
tstamps=self.tstamps,
q_mes=loggerSensors.q_mes,
v_mes=loggerSensors.v_mes,
baseOrientation=loggerSensors.baseOrientation,
baseAngularVelocity=loggerSensors.baseAngularVelocity,
baseLinearAcceleration=loggerSensors.baseLinearAcceleration,
baseAccelerometer=loggerSensors.baseAccelerometer,
torquesFromCurrentMeasurment=loggerSensors.torquesFromCurrentMeasurment,
mocapPosition=loggerSensors.mocapPosition,
mocapVelocity=loggerSensors.mocapVelocity,
mocapAngularVelocity=loggerSensors.mocapAngularVelocity,
mocapOrientationMat9=loggerSensors.mocapOrientationMat9,
mocapOrientationQuat=loggerSensors.mocapOrientationQuat,
)
def loadAll(self, loggerSensors, fileName=None):
if fileName is None:
import glob
fileName = np.sort(glob.glob('data_2021_*.npz'))[-1] # Most recent file
data = np.load(fileName)
# Load LoggerControl arrays
self.joy_v_ref = data["joy_v_ref"]
self.logSize = self.joy_v_ref.shape[0]
self.esti_feet_status = data["esti_feet_status"]
self.esti_feet_goals = data["esti_feet_goals"]
self.esti_q_filt = data["esti_q_filt"]
self.esti_v_filt = data["esti_v_filt"]
self.esti_v_secu = data["esti_v_secu"]
self.esti_FK_lin_vel = data["esti_FK_lin_vel"]
self.esti_FK_xyz = data["esti_FK_xyz"]
self.esti_xyz_mean_feet = data["esti_xyz_mean_feet"]
self.esti_filt_lin_vel = data["esti_filt_lin_vel"]
self.esti_HP_x = data["esti_HP_x"]
self.esti_HP_dx = data["esti_HP_dx"]
self.esti_HP_alpha = data["esti_HP_alpha"]
self.esti_HP_filt_x = data["esti_HP_filt_x"]
self.esti_LP_x = data["esti_LP_x"]
self.esti_LP_dx = data["esti_LP_dx"]
self.esti_LP_alpha = data["esti_LP_alpha"]
self.esti_LP_filt_x = data["esti_LP_filt_x"]
self.esti_kf_X = data["esti_kf_X"]
self.esti_kf_Z = data["esti_kf_Z"]
self.loop_o_q_int = data["loop_o_q_int"]
self.loop_o_v = data["loop_o_v"]
self.loop_h_v = data["loop_h_v"]
self.loop_pos_virtual_world = data["loop_pos_virtual_world"]
self.planner_q_static = data["planner_q_static"]
self.planner_RPY_static = data["planner_RPY_static"]
self.planner_xref = data["planner_xref"]
self.planner_fsteps = data["planner_fsteps"]
self.planner_gait = data["planner_gait"]
self.planner_goals = data["planner_goals"]
self.planner_vgoals = data["planner_vgoals"]
self.planner_agoals = data["planner_agoals"]
self.planner_is_static = data["planner_is_static"]
self.planner_h_ref = data["planner_h_ref"]
self.mpc_x_f = data["mpc_x_f"]
self.wbc_x_f = data["wbc_x_f"]
self.wbc_P = data["wbc_P"]
self.wbc_D = data["wbc_D"]
self.wbc_q_des = data["wbc_q_des"]
self.wbc_v_des = data["wbc_v_des"]
self.wbc_tau_ff = data["wbc_tau_ff"]
self.wbc_f_ctc = data["wbc_f_ctc"]
self.wbc_feet_pos = data["wbc_feet_pos"]
self.wbc_feet_pos_target = data["wbc_feet_pos_target"]
self.wbc_feet_err = data["wbc_feet_err"]
self.wbc_feet_vel = data["wbc_feet_vel"]
self.wbc_feet_vel_target = data["wbc_feet_vel_target"]
self.wbc_feet_acc_target = data["wbc_feet_acc_target"]
self.tstamps = data["tstamps"]
# Load LoggerSensors arrays
loggerSensors.q_mes = data["q_mes"]
loggerSensors.v_mes = data["v_mes"]
loggerSensors.baseOrientation = data["baseOrientation"]
loggerSensors.baseAngularVelocity = data["baseAngularVelocity"]
loggerSensors.baseLinearAcceleration = data["baseLinearAcceleration"]
loggerSensors.baseAccelerometer = data["baseAccelerometer"]
loggerSensors.torquesFromCurrentMeasurment = data["torquesFromCurrentMeasurment"]
loggerSensors.mocapPosition = data["mocapPosition"]
loggerSensors.mocapVelocity = data["mocapVelocity"]
loggerSensors.mocapAngularVelocity = data["mocapAngularVelocity"]
loggerSensors.mocapOrientationMat9 = data["mocapOrientationMat9"]
loggerSensors.mocapOrientationQuat = data["mocapOrientationQuat"]
loggerSensors.logSize = loggerSensors.q_mes.shape[0]
def slider_predicted_trajectory(self):
from matplotlib import pyplot as plt
from matplotlib.widgets import Slider, Button
# The parametrized function to be plotted
def f(t, time):
return np.sin(2 * np.pi * t) + time
index6 = [1, 3, 5, 2, 4, 6]
log_t_pred = np.array([(k+1)*self.dt*10 for k in range(self.mpc_x_f.shape[2])])
log_t_ref = np.array([k*self.dt*10 for k in range(self.planner_xref.shape[2])])
trange = np.max([np.max(log_t_pred), np.max(log_t_ref)])
h1s = []
h2s = []
axs = []
h1s_vel = []
h2s_vel = []
axs_vel = []
# Define initial parameters
init_time = 0.0
# Create the figure and the line that we will manipulate
fig = plt.figure()
ax = plt.gca()
for j in range(6):
ax = plt.subplot(3, 2, index6[j])
h1, = plt.plot(log_t_pred, self.mpc_x_f[0, j, :], "b", linewidth=2)
h2, = plt.plot(log_t_ref, self.planner_xref[0, j, :], linestyle="--", marker='x', color="g", linewidth=2)
h3, = plt.plot(np.array([k*self.dt for k in range(self.mpc_x_f.shape[0])]),
self.planner_xref[:, j, 0], linestyle=None, marker='x', color="r", linewidth=1)
axs.append(ax)
h1s.append(h1)
h2s.append(h2)
#ax.set_xlabel('Time [s]')
axcolor = 'lightgoldenrodyellow'
#ax.margins(x=0)
# Make a horizontal slider to control the time.
axtime = plt.axes([0.25, 0.03, 0.65, 0.03], facecolor=axcolor)
time_slider = Slider(
ax=axtime,
label='Time [s]',
valmin=0.0,
valmax=self.logSize*self.dt,
valinit=init_time,
)
# Create the figure and the line that we will manipulate (for velocities)
fig_vel = plt.figure()
ax = plt.gca()
for j in range(6):
ax = plt.subplot(3, 2, index6[j])
h1, = plt.plot(log_t_pred, self.mpc_x_f[0, j, :], "b", linewidth=2)
h2, = plt.plot(log_t_ref, self.planner_xref[0, j, :], linestyle="--", marker='x', color="g", linewidth=2)
h3, = plt.plot(np.array([k*self.dt for k in range(self.mpc_x_f.shape[0])]),
self.planner_xref[:, j+6, 0], linestyle=None, marker='x', color="r", linewidth=1)
axs_vel.append(ax)
h1s_vel.append(h1)
h2s_vel.append(h2)
#axcolor = 'lightgoldenrodyellow'
#ax.margins(x=0)
# Make a horizontal slider to control the time.
axtime_vel = plt.axes([0.25, 0.03, 0.65, 0.03], facecolor=axcolor)
time_slider_vel = Slider(
ax=axtime_vel,
label='Time [s]',
valmin=0.0,
valmax=self.logSize*self.dt,
valinit=init_time,
)
# The function to be called anytime a slider's value changes
def update(val, recursive=False):
time_slider.val = np.round(val / (self.dt*10), decimals=0) * (self.dt*10)
rounded = int(np.round(time_slider.val / self.dt, decimals=0))
for j in range(6):
h1s[j].set_xdata(log_t_pred + time_slider.val)
h2s[j].set_xdata(log_t_ref + time_slider.val)
y1 = self.mpc_x_f[rounded, j, :] - self.planner_xref[rounded, j, 1:]
y2 = self.planner_xref[rounded, j, :] - self.planner_xref[rounded, j, :]
h1s[j].set_ydata(y1)
h2s[j].set_ydata(y2)
axs[j].set_xlim([time_slider.val - self.dt * 3, time_slider.val+trange+self.dt * 3])
ymin = np.min([np.min(y1), np.min(y2)])
ymax = np.max([np.max(y1), np.max(y2)])
axs[j].set_ylim([ymin - 0.05 * (ymax - ymin), ymax + 0.05 * (ymax - ymin)])
fig.canvas.draw_idle()
if not recursive:
update_vel(time_slider.val, True)
def update_vel(val, recursive=False):
time_slider_vel.val = np.round(val / (self.dt*10), decimals=0) * (self.dt*10)
rounded = int(np.round(time_slider_vel.val / self.dt, decimals=0))
for j in range(6):
h1s_vel[j].set_xdata(log_t_pred + time_slider.val)
h2s_vel[j].set_xdata(log_t_ref + time_slider.val)
y1 = self.mpc_x_f[rounded, j+6, :]
y2 = self.planner_xref[rounded, j+6, :]
h1s_vel[j].set_ydata(y1)
h2s_vel[j].set_ydata(y2)
axs_vel[j].set_xlim([time_slider.val - self.dt * 3, time_slider.val+trange+self.dt * 3])
ymin = np.min([np.min(y1), np.min(y2)])
ymax = np.max([np.max(y1), | np.max(y2) | numpy.max |
"""
Code by <NAME>
Reference for the dataset:
https://www.aitex.es/afid/
AFID: a public fabric image database for defect detection.
<NAME>, <NAME>, <NAME>, <NAME>, <NAME>
AUTEX Research Journal, No. 4, 2019
Note: Mask_images/0044_019_04_mask1.png and
0044_019_04_mask2.png
... have been merged into
0044_019_04_mask.png
Mask_images/0097_030_03_mask1.png and
0097_030_03_mask2.png
... have been merged into
0097_030_03_mask.png
Mask_images/0100_025_08_mask.png was created manually since it was missing in the original dataset
"""
import logging
import argparse
import os
import cv2
import numpy as np
import sys
import PCA.ImagePCAModel
parser = argparse.ArgumentParser()
parser.add_argument('--imageFilepath', help="The filepath of the test image. Default: './data/Defect_images/0001_002_00.png'", default='./data/Defect_images/0001_002_00.png')
parser.add_argument('--outputDirectory', help="The output directory. Default: './outputs/'", default='./outputs/')
args = parser.parse_args()
file_handler = logging.FileHandler(filename=os.path.join(args.outputDirectory, 'texture_analysis.log'))
stdout_handler = logging.StreamHandler(sys.stdout)
handlers = [file_handler, stdout_handler]
logging.basicConfig(
level=logging.DEBUG,
format='[%(asctime)s] {%(filename)s:%(lineno)d} %(levelname)s - %(message)s',
handlers=handlers
)
def main():
logging.info("create_semseg_population.py main()")
# Create the output directory
if not os.path.exists(args.outputDirectory):
os.makedirs(args.outputDirectory)
# Load the test image
testImg = cv2.imread(args.imageFilepath, cv2.IMREAD_GRAYSCALE)
image_shapeHWC = testImg.shape
blurredImg = cv2.medianBlur(testImg, 3)
# Mask the saturated area at the left of the image, plus an additional band
_, saturation_mask = cv2.threshold(testImg, 254, 255, cv2.THRESH_BINARY)
saturation_mask = cv2.dilate(saturation_mask, kernel=np.ones((21, 21), dtype=np.uint8))
no_saturation_img = cv2.min(testImg, (255 - saturation_mask))
no_saturation_blurred_img = cv2.min(blurredImg, (255 - saturation_mask))
# Apply Sobel filter in the x and y directions
sobel_x_img = cv2.Sobel(no_saturation_blurred_img, ddepth=cv2.CV_32F, dx=1, dy=0, ksize=3)
sobel_x_img = (127 + sobel_x_img).astype(np.uint8)
sobel_y_img = cv2.Sobel(no_saturation_blurred_img, ddepth=cv2.CV_32F, dx=0, dy=1, ksize=3)
sobel_y_img = (127 + sobel_y_img).astype(np.uint8)
sobel_xy_img = cv2.Sobel(no_saturation_blurred_img, ddepth=cv2.CV_32F, dx=1, dy=1, ksize=3)
sobel_xy_img = (127 + sobel_xy_img).astype(np.uint8)
sobel_x2_img = cv2.Sobel(no_saturation_blurred_img, ddepth=cv2.CV_32F, dx=2, dy=0, ksize=3)
sobel_x2_img = (127 + sobel_x2_img).astype(np.uint8)
sobel_y2_img = cv2.Sobel(no_saturation_blurred_img, ddepth=cv2.CV_32F, dx=0, dy=2, ksize=3)
sobel_y2_img = (127 + sobel_y2_img).astype(np.uint8)
# Select surface samples
number_of_surface_samples = 300
sample_surface_sizeHW = (5, 5)
surface_sample_rect_list = []
surface_samples_img = cv2.cvtColor(testImg, cv2.COLOR_GRAY2BGR)
while len(surface_sample_rect_list) < number_of_surface_samples:
center = ( | np.random.randint(sample_surface_sizeHW[0]//2, image_shapeHWC[1] - 1 - sample_surface_sizeHW[0]//2) | numpy.random.randint |
import numpy as np
from quanser.hardware import HIL, HILError, PWMMode
saturate = lambda x, x_max, x_min: min(x_max, max(x_min, x))
class QCar():
#region: Buffers
# Throttle Write Only - PWM channel 0 is mtr cmd
write_pwm_channel_throttle = np.array([0], dtype=np.int32)
write_pwm_buffer_throttle = np.array([0], dtype=np.float64)
# Steering Write Only - Other channel 1000 is steering cmd
write_other_channel_steering = np.array([1000], dtype=np.int32)
write_other_buffer_steering = np.array([0], dtype=np.float64)
# LEDs Write Only - Other channel 11000:11003 + 11008:11011 are LEDs
write_other_channels_LEDs = np.array([11008, 11009, 11010, 11011, 11000, 11001, 11002, 11003], dtype=np.int32)
write_other_buffer_LEDs = np.zeros(8, dtype=np.float64)
# User LEDs Write Only - Other channel 11004:11007 are User LEDs
write_other_channels_usr_LEDs = np.array([11004, 11005, 11006, 11007], dtype=np.int32)
write_other_buffer_usr_LEDs = np.zeros(4, dtype=np.float64)
# Steering and LEDs Write - Other channel 1000 is steering cmd and 11000:11003 + 11008:11011 are LEDs
write_other_channels_str_LEDs = np.array([1000, 11008, 11009, 11010, 11011, 11000, 11001, 11002, 11003], dtype=np.int32)
write_other_buffer_str_LEDs = np.append(np.array([0], dtype=np.float64), np.zeros(8, dtype=np.float64))
# Initialize return arrays
mtr_current, bat_voltage = np.zeros(2, dtype=np.float64)
mtr_encoder = np.zeros(1, dtype=np.int32)
accelerometer = np.zeros(3, dtype=np.float64)
gyroscope = np.zeros(3, dtype=np.float64)
# Battery Read Only - Analog channel 6 is battery voltage
read_analog_channels_battery = np.array([6], dtype=np.int32)
read_analog_buffer_battery = np.zeros(1, dtype=np.float64)
# Encoder Read Only - Encoder channel 0 is throttle motor encoder
read_encoder_channels_throttle = np.array([0], dtype=np.int32)
read_encoder_buffer_throttle = np.zeros(1, dtype=np.int32)
# Gyroscope Read Only - Other channels 3000:3002 are for gyroscope
read_other_channels_gyroscope = np.array([3000, 3001, 3002], dtype=np.int32)
read_other_buffer_gyroscope = np.zeros(3, dtype=np.float64)
# Accelerometer Read Only - Other channels 4000:4002 are for accelerometer
read_other_channels_accelerometer = np.array([4000, 4001, 4002], dtype=np.int32)
read_other_buffer_accelerometer = np.zeros(3, dtype=np.float64)
# IMU Read - Other channels 3000:3002 + 4000:4002 are for IMU
read_other_channels_IMU = np.array([3000, 3001, 3002, 4000, 4001, 4002], dtype=np.int32)
read_other_buffer_IMU = np.zeros(6, dtype=np.float64)
# Power Read - Analog channels 5, 6 are motor current and battery voltage
read_analog_channels_power = np.array([5, 6], dtype=np.int32)
read_analog_buffer_power = np.zeros(2, dtype=np.float64)
#endregion
def __init__(self):
''' This function configures the QCar and returns a handle to the QCar card. Use the handle for other methods such as qcar_io or terminate_qcar.'''
self.card = HIL()
try:
# Open the Card
self.card.open("qcar", "0")
if self.card.is_valid():
# Set PWM mode (duty cycle) and frequency
self.card.set_pwm_mode( | np.array([0], dtype=np.uint32) | numpy.array |
"""
Version 1.01
Encodes fitting and interpolating using Gaussian processes following Rasmussen and Williams (2006).
The Gaussian process algorithms come from chapter 3 and the Jacobian of the negative log likelihood from chapter 5 of Rasmussen and Williams.
Covariance functions can either be linear, squared exponential, neural network-like, or squared exponential with a linear trend. Bounds for hyperparameters are specified in log10 space. Hyperparameters are given in log space.
A typical workflow is:
g= gp.maternGP({0: (-4, 4), 1: (-4, 4), 2: (-4, -2)}, x, y)
g.findhyperparameters()
g.results()
g.predict(x)
plt.figure()
g.sketch('.')
plt.show()
Prior functions can also be sampled. For example,
g= gp.sqexplinGP({0: (-2,2), 1: (-2,2), 2: (-2,2), 3: (-2,2), 4: (-2,2)}, x, y)
plot(x, g.sampleprior(3, th= [1.0, 0.1, 3.1, 1.3]))
will plot three samples of the prior latent functions with hyperparameters 1.0, 0.1, 3.1, and 1.3. There is no need to specify the hyperparameter for measurement error: it is not used to generate prior functions.
N.B. small (close to zero) values of the estimated measurement error can lead to instabilities in finding the hyperparameters.
"""
import numpy as np
from scipy import linalg
import matplotlib.pyplot as plt
class gaussianprocess:
def __init__(self, lthbounds, x, y, merrors= False):
'''
Creates a Gaussian process.
Arguments
--
lthbounds: a dictionary of pairs of the bounds on the hyperparameters in log10 space,
such as {0: [0,6], 1: [-3,4], 2: [-6,-4]}
x: a 1-d array of the abscissa data
y: a multi-dimensional array of the ordinate data
merrors: if specified, a 1-d array of the measurement errors (as variances)
v'''
self.b= [lthbounds[a] for a in lthbounds.keys()]
self.x, self.y, self.xnew= x, y, x
self.merrors= merrors
def covfn(self):
raise NotImplementedError(' No covariance function specified in class %s'
% self.__class__.__name__)
def d1covfn(self):
raise NotImplementedError(' No first derivative of the covariance function specified in class %s' % self.__class__.__name__)
def d1d2covfn(self):
raise NotImplementedError(' No second derivative of the covariance function specified in class %s' % self.__class__.__name__)
def kernelmatrix(self, lth, x):
"""
Returns kernel matrix K(X,X) supplemented with measurement noise and its Cholesky decomposition.
Arguments
--
lth: log of the hyperparameters
x: abscissa values
merrors: if specified, rescales the fitted measurement error
"""
k= np.empty((len(x), len(x)))
for i in range(len(x)):
k[i,:]= self.covfn(x[i], x, lth)[0]
if np.any(self.merrors):
kn= k + np.exp(lth[-1])*np.diag(self.merrors)
else:
kn= k + np.exp(lth[-1])*np.identity(len(x))
L= linalg.cho_factor(kn)
return k, L
def nlml(self, lth):
"""
Returns negative of log marginal likelihood.
Arguments
--
lth: log of the hyperparameters
"""
x, y= self.x, self.y
k, L= self.kernelmatrix(lth, x)
al= linalg.cho_solve(L, y)
halfdetK= np.sum(np.log(np.diagonal(L[0])))
return 0.5*np.dot(y, al) + halfdetK + 0.5*len(y)*np.log(2*np.pi)
def jacnlml(self, lth):
"""
Returns the Jacobian of negative log marginal likelihood with respect to the hyperparameters with deriviatives being taken assuming the hyperparmaters are in log space.
Arguments
--
lth: log of the hyperparameters
"""
x, y= self.x, self.y
k, L= self.kernelmatrix(lth, x)
# find derivatives of kernel matrix wrt hyperparameters
kjac= np.empty((len(x), len(x), len(lth)))
for i in range(len(x)):
kjac[i, :, :-1]= self.covfn(x[i], x, lth)[1]
if np.any(self.merrors):
kjac[:, :, -1]= np.diag(self.merrors)*np.exp(lth[-1])
else:
kjac[:, :, -1]= np.identity(len(x))*np.exp(lth[-1])
# calculate jacobian
al= linalg.cho_solve(L, y)
alal= np.outer(al, al)
Kinv= linalg.cho_solve(L, np.identity(len(x)))
return np.asarray([-0.5*np.trace(np.dot(alal - Kinv, kjac[:,:,i])) for i in range(len(lth))])
def findhyperparameters(self, noruns= 1, exitearly= False, stvals= False, optmethod= 'l_bfgs_b',
optmessages= False, quiet= True, linalgmax= 3):
"""
Finds the best fit hyperparameters (.lth_opt) and the optimum value of negative log marginal likelihood (.nlml_opt).
Arguments
--
noruns: number of attempts to find optimum hyperparameters (the best of all the runs is chosen)
exitearly: if True, fitting stops at the first successful attempt
stvals: an (optional) initial guess for the log hyperparameters
optmethod: the optimization routine to be used, either 'l_bfgs_b' (default) or 'tnc'
optmessages: if True, display messages from the optimization routine
quiet: if True, print warning that if an optimum hyperparameter is at a bound
linalgmax: number of attempts (default is 3) if a linear algebra (numerical) error is generated
"""
b= self.b
self.hparamerr= []
lmlml= np.empty(noruns)
lthf= np.empty((noruns, len(b)))
success= np.empty(noruns)
# convert b into exponential base
b= np.array(b)*np.log(10)
# run optimization
for i in range(noruns):
linalgerror= 0
while linalgerror < linalgmax:
try:
if np.any(stvals):
# initial values given for hyperparameters
lth= stvals
else:
# choose random initial values for hyperparameters
lth= [np.random.uniform(b[j][0], b[j][1]) for j in range(len(b))]
# run Gaussian process
if optmethod == 'tnc':
from scipy.optimize import fmin_tnc
lthf[i,:], nf, success[i]= fmin_tnc(self.nlml, lth, fprime= self.jacnlml,
bounds= b, maxfun= 1000, messages= optmessages)
linalgerror= linalgmax
lmlml[i]= self.nlml(lthf[i,:])
elif optmethod == 'l_bfgs_b':
from scipy.optimize import fmin_l_bfgs_b
lthf[i,:], lmlml[i], dout= fmin_l_bfgs_b(self.nlml, lth, fprime= self.jacnlml,
bounds= b, disp= optmessages)
linalgerror= linalgmax
success[i]= dout['warnflag'] + 1
else:
print(optmethod + ' unrecognized.')
except np.linalg.LinAlgError:
print(' Warning: linear algebra error - trying a different initial condition')
linalgerror += 1
if success[i] != 1 or np.any(np.isnan(lthf)):
print(' Warning: optimization failed at run ' + str(i+1))
else:
if exitearly: break
# only process runs that did not converge
if np.any(success == 1):
lmlml= lmlml[success == 1]
lthf= lthf[success == 1]
# find best choice
lthb= lthf[lmlml.argmin()]
self.nlml_opt= lmlml.min()
# print warning
for i in range(len(b)):
if (lthb[i] == b[i][1] or lthb[i] == b[i][0]):
if not quiet:
print( ' Warning: hparam[' + str(i) + '] is at a boundary')
print('\thparam[' + str(i) + ']= {:e}'.format(np.exp(lthb[i]))
+ ' [{:e}'.format(np.exp(b[i][0])) + ', {:e}]'.format(np.exp(b[i][1])))
if lthb[i] == b[i][1]:
self.hparamerr.append([i, 'u'])
else:
self.hparamerr.append([i, 'l'])
self.lth_opt= lthb
else:
raise gaussianprocessException('Optimization of hyperparameters failed')
def results(self, warning= True):
'''
Displays results from optimizing hyperparameters.
Arguments
--
warning: if True, warn when a hyperparameter hits a boundary
'''
print('log(max likelihood)= %e' % (-self.nlml_opt))
for j, pv in enumerate(np.exp(self.lth_opt)):
print('hparam[' + str(j) + ']= {:e}'.format(pv) + ' [{:e}'.format(10**(self.b[j][0]))
+ ', {:e}]'.format(10**(self.b[j][1])))
if warning:
for el in self.hparamerr:
if el[1] == 'l':
print('Warning: hyperparameter ' + str(el[0]) + ' is at a lower bound')
else:
print('Warning: hyperparameter ' + str(el[0]) + ' is at an upper bound')
def sample(self, size= 1):
'''
Generate samples from the Gaussian process as an array.
Arguments
--
size: number of samples
'''
try:
return np.transpose(np.random.multivariate_normal(self.mnp, self.covp, size))
except AttributeError:
print( ' Run gp.predict() first before sampling.')
def sampleprior(self, size= 1, lth= False):
'''
Generate samples from the prior of the Gaussian process as an array.
Arguments
--
size: number of samples
lth: log hyperparameters to use (if not specified, the hyperparameters are chosen at random)
'''
x, y, b= self.x, self.y, self.b
if np.any(lth):
# hyperparameters are given (measurement error is not necessary)
if len(lth) == self.noparams:
lth= np.concatenate((lth, [1.0]))
else:
# sample random hyperparameters
lth= np.log(np.power(10, [np.random.uniform(b[i][0], b[i][1]) for i in range(len(b))]))
cov= self.kernelmatrix(lth, x)[0]
return np.transpose(np.random.multivariate_normal(np.zeros(len(x)), cov, size))
def predict(self, xnew, merrorsnew= False, derivs= 0, addnoise= False):
"""
Determines the predicted mean latent function (.f) and its variance (.fvar) and potentially the predicted mean first derivative (.df) and its variance (.dfvar) and the predicted mean second derivative (.ddf) and its variance (.ddfvar) . Also .mnp is the predicted combined array of the mean latent function and its mean derivatives and .covp is the corresponding covariance matrix.
Arguments
--
xnew: abscissa values for which predicted ordinate values are desired
merrorsnew: if specified, the expected measurements errors at xnew (need not be specified if xnew= x)
derivs: if 0, only the latent function is inferred; if 1, the latent function and the first derivative are inferred; if 2, the latent function and the first and second derivatives are inferred
addnoise: if True, add measuremnet noise to the predicted variance
"""
if len(self.x) == len(xnew) and (self.x == xnew).all():
xold= True
else:
xold= False
if np.any(self.merrors) and not np.any(merrorsnew) and not xold:
print('Length of xnew is different from x.')
raise gaussianprocessException('Measurement errors were used to find the hyperparameters and measurement errors are therefore required for any predictions.')
elif not hasattr(self, 'lth_opt'):
raise gaussianprocessException(' Run gp.findhyperparameters() first before making predictions.')
else:
# set up
self.xnew= xnew
lth, x, y= self.lth_opt, self.x, self.y
# work with an array of length 3*N: the first N values being the function,
# the second N values being the first derivative, and the last N values being the second derivative
Knewold= np.empty((len(xnew), len(x)))
Knewnew= np.empty((len(xnew), len(xnew)))
if derivs > 0:
d1Knewold= np.empty((len(xnew), len(x)))
d1Knewnew= np.empty((len(xnew), len(xnew)))
d1d2Knewnew= np.empty((len(xnew), len(xnew)))
if derivs > 1:
d12Knewold= np.empty((len(xnew), len(x)))
d12Knewnew= np.empty((len(xnew), len(xnew)))
d12d2Knewnew= np.empty((len(xnew), len(xnew)))
d12d22Knewnew= np.empty((len(xnew), len(xnew)))
for i in range(len(xnew)):
Knewold[i,:]= self.covfn(xnew[i], x, lth)[0]
Knewnew[i,:]= self.covfn(xnew[i], xnew, lth)[0]
if derivs > 0:
d1Knewold[i,:]= self.d1covfn(xnew[i], x, lth)[0]
d1Knewnew[i,:]= self.d1covfn(xnew[i], xnew, lth)[0]
d1d2Knewnew[i,:]= self.d1d2covfn(xnew[i], xnew, lth)[0]
if derivs > 1:
d12Knewold[i,:]= self.d12covfn(xnew[i], x, lth)[0]
d12Knewnew[i,:]= self.d12covfn(xnew[i], xnew, lth)[0]
d12d2Knewnew[i,:]= self.d12d2covfn(xnew[i], xnew, lth)[0]
d12d22Knewnew[i,:]= self.d12d22covfn(xnew[i], xnew, lth)[0]
if derivs == 0:
kv= Knewold
km= Knewnew
elif derivs == 1:
kv= np.bmat([[Knewold], [d1Knewold]])
km= np.bmat([[Knewnew, np.transpose(d1Knewnew)],
[d1Knewnew, d1d2Knewnew]])
elif derivs == 2:
kv= np.bmat([[Knewold], [d1Knewold], [d12Knewold]])
km= np.bmat([[Knewnew, np.transpose(d1Knewnew), np.transpose(d12Knewnew)],
[d1Knewnew, d1d2Knewnew, np.transpose(d12d2Knewnew)],
[d12Knewnew, d12d2Knewnew, d12d22Knewnew]])
# find mean prediction
k, L= self.kernelmatrix(lth, x)
m= np.dot(kv, linalg.cho_solve(L, y))
mnp= np.reshape(np.array(m), np.size(m))
self.mnp= mnp
# find variance of prediction
covp= km - np.dot(kv, linalg.cho_solve(L, np.transpose(kv)))
self.covp= covp
varp= np.diag(covp)
# for user
self.f= mnp[:len(xnew)]
self.fvar= varp[:len(xnew)]
fvar= varp[:len(xnew)]
if addnoise:
# add measurement error to the variance of the latent function
if | np.any(self.merrors) | numpy.any |
"""TNQMetro: Tensor-network based package for efficient quantum metrology computations."""
# Table of Contents
#
# 1 Functions for finite size systems......................................29
# 1.1 High level functions...............................................37
# 1.2 Low level functions...............................................257
# 1.2.1 Problems with exact derivative.............................1207
# 1.2.2 Problems with discrete approximation of the derivative.....2411
# 2 Functions for infinite size systems..................................3808
# 2.1 High level functions.............................................3816
# 2.2 Low level functions..............................................4075
# 3 Auxiliary functions..................................................5048
import itertools
import math
import warnings
import numpy as np
from ncon import ncon
########################################
# #
# #
# 1 Functions for finite size systems. #
# #
# #
########################################
#############################
# #
# 1.1 High level functions. #
# #
#############################
def fin(N, so_before_list, h, so_after_list, BC='O', L_ini=None, psi0_ini=None, imprecision=10**-2, D_L_max=100, D_L_max_forced=False, L_herm=True, D_psi0_max=100, D_psi0_max_forced=False):
"""
Optimization of the QFI over operator L (in MPO representation) and wave function psi0 (in MPS representation) and check of convergence in their bond dimensions. Function for finite size systems.
User has to provide information about the dynamics by specifying the quantum channel. It is assumed that the quantum channel is translationally invariant and is built from layers of quantum operations.
User has to provide one defining operation for each layer as a local superoperator. These local superoperators have to be input in order of their action on the system.
Parameter encoding is a stand out quantum operation. It is assumed that the parameter encoding acts only once and is unitary so the user has to provide only its generator h.
Generator h has to be diagonal in computational basis, or in other words, it is assumed that local superoperators are expressed in the eigenbasis of h.
Parameters:
N: integer
Number of sites in the chain of tensors (usually number of particles).
so_before_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites a particular local superoperator acts
List of local superoperators (in order) which act before unitary parameter encoding.
h: ndarray of a shape (d,d)
Generator of unitary parameter encoding. Dimension d is the dimension of local Hilbert space (dimension of physical index).
Generator h has to be diagonal in the computational basis, or in other words, it is assumed that local superoperators are expressed in the eigenbasis of h.
so_after_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites particular local superoperator acts
List of local superoperators (in order) which act after unitary parameter encoding.
BC: 'O' or 'P', optional
Boundary conditions, 'O' for OBC, 'P' for PBC.
L_ini: list of length N of ndarrays of a shape (Dl_L,Dr_L,d,d) for OBC (Dl_L, Dr_L can vary between sites) or ndarray of a shape (D_L,D_L,d,d,N) for PBC, optional
Initial MPO for L.
psi0_ini: list of length N of ndarrays of a shape (Dl_psi0,Dr_psi0,d) for OBC (Dl_psi0, Dr_psi0 can vary between sites) or ndarray of a shape (D_psi0,D_psi0,d,N) for PBC, optional
Initial MPS for psi0.
imprecision: float, optional
Expected relative imprecision of the end results.
D_L_max: integer, optional
Maximal value of D_L (D_L is bond dimension for MPO representing L).
D_L_max_forced: bool, optional
True if D_L_max has to be reached, otherwise False.
L_herm: bool, optional
True if Hermitian gauge has to be imposed on MPO representing L, otherwise False.
D_psi0_max: integer, optional
Maximal value of D_psi0 (D_psi0 is bond dimension for MPS representing psi0).
D_psi0_max_forced: bool, optional
True if D_psi0_max has to be reached, otherwise False.
Returns:
result: float
Optimal value of figure of merit.
result_m: ndarray
Matrix describing the figure of merit as a function of bond dimensions of respectively L [rows] and psi0 [columns].
L: list of length N of ndarrays of a shape (Dl_L,Dr_L,d,d) for OBC (Dl_L, Dr_L can vary between sites) or ndarray of a shape (D_L,D_L,d,d,N) for PBC
Optimal L in MPO representation.
psi0: list of length N of ndarrays of a shape (Dl_psi0,Dr_psi0,d) for OBC (Dl_psi0, Dr_psi0 can vary between sites) or ndarray of a shape (D_psi0,D_psi0,d,N) for PBC
Optimal psi0 in MPS representation.
"""
if np.linalg.norm(h - np.diag(np.diag(h))) > 10**-10:
warnings.warn('Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.')
d = np.shape(h)[0]
ch = fin_create_channel(N, d, BC, so_before_list + so_after_list)
ch2 = fin_create_channel_derivative(N, d, BC, so_before_list, h, so_after_list)
result, result_m, L, psi0 = fin_gen(N, d, BC, ch, ch2, None, L_ini, psi0_ini, imprecision, D_L_max, D_L_max_forced, L_herm, D_psi0_max, D_psi0_max_forced)
return result, result_m, L, psi0
def fin_gen(N, d, BC, ch, ch2, epsilon=None, L_ini=None, psi0_ini=None, imprecision=10**-2, D_L_max=100, D_L_max_forced=False, L_herm=True, D_psi0_max=100, D_psi0_max_forced=False):
"""
Optimization of the figure of merit (usually interpreted as the QFI) over operator L (in MPO representation) and wave function psi0 (in MPS representation) and check of convergence when increasing their bond dimensions. Function for finite size systems.
User has to provide information about the dynamics by specifying a quantum channel ch and its derivative ch2 (or two channels separated by small parameter epsilon) as superoperators in MPO representation.
There are no constraints on the structure of the channel but the complexity of calculations highly depends on the channel's bond dimension.
Parameters:
N: integer
Number of sites in the chain of tensors (usually number of particles).
d: integer
Dimension of local Hilbert space (dimension of physical index).
BC: 'O' or 'P'
Boundary conditions, 'O' for OBC, 'P' for PBC.
ch: list of length N of ndarrays of a shape (Dl_ch,Dr_ch,d**2,d**2) for OBC (Dl_ch, Dr_ch can vary between sites) or ndarray of a shape (D_ch,D_ch,d**2,d**2,N) for PBC
Quantum channel as a superoperator in MPO representation.
ch2: list of length N of ndarrays of a shape (Dl_ch2,Dr_ch2,d**2,d**2) for OBC (Dl_ch2, Dr_ch2 can vary between sites) or ndarray of a shape (D_ch2,D_ch2,d**2,d**2,N) for PBC
Interpretiaon depends on whether epsilon is specifed (2) or not (1, default approach):
1) derivative of the quantum channel as a superoperator in the MPO representation,
2) the quantum channel as superoperator in the MPO representation for the value of estimated parameter shifted by epsilon in relation to ch.
epsilon: float, optional
If specified then interpeted as value of a separation between estimated parameters encoded in ch and ch2.
L_ini: list of length N of ndarrays of a shape (Dl_L,Dr_L,d,d) for OBC (Dl_L, Dr_L can vary between sites) or ndarray of a shape (D_L,D_L,d,d,N) for PBC, optional
Initial MPO for L.
psi0_ini: list of length N of ndarrays of a shape (Dl_psi0,Dr_psi0,d) for OBC (Dl_psi0, Dr_psi0 can vary between sites) or ndarray of a shape (D_psi0,D_psi0,d,N) for PBC, optional
Initial MPS for psi0.
imprecision: float, optional
Expected relative imprecision of the end results.
D_L_max: integer, optional
Maximal value of D_L (D_L is bond dimension for MPO representing L).
D_L_max_forced: bool, optional
True if D_L_max has to be reached, otherwise False.
L_herm: bool, optional
True if the Hermitian gauge has to be imposed on MPO representing L, otherwise False.
D_psi0_max: integer, optional
Maximal value of D_psi0 (D_psi0 is bond dimension for MPS representing psi0).
D_psi0_max_forced: bool, optional
True if D_psi0_max has to be reached, otherwise False.
Returns:
result: float
Optimal value of the figure of merit.
result_m: ndarray
Matrix describing the figure of merit as a function of bond dimensions of respectively L [rows] and psi0 [columns].
L: list of length N of ndarrays of a shape (Dl_L,Dr_L,d,d) for OBC (Dl_L, Dr_L can vary between sites) or ndarray of a shape (D_L,D_L,d,d,N) for PBC
Optimal L in MPO representation.
psi0: list of length N of ndarrays of a shape (Dl_psi0,Dr_psi0,d) for OBC (Dl_psi0, Dr_psi0 can vary between sites) or ndarray of a shape (D_psi0,D_psi0,d,N) for PBC
Optimal psi0 in MPS representation.
"""
if epsilon is None:
result, result_m, L, psi0 = fin_FoM_FoMD_optbd(N, d, BC, ch, ch2, L_ini, psi0_ini, imprecision, D_L_max, D_L_max_forced, L_herm, D_psi0_max, D_psi0_max_forced)
else:
result, result_m, L, psi0 = fin2_FoM_FoMD_optbd(N, d, BC, ch, ch2, epsilon, L_ini, psi0_ini, imprecision, D_L_max, D_L_max_forced, L_herm, D_psi0_max, D_psi0_max_forced)
return result, result_m, L, psi0
def fin_state(N, so_before_list, h, so_after_list, rho0, BC='O', L_ini=None, imprecision=10**-2, D_L_max=100, D_L_max_forced=False, L_herm=True):
"""
Optimization of the QFI over operator L (in MPO representation) and check of convergence when increasing its bond dimension. Function for finite size systems and fixed state of the system.
User has to provide information about the dynamics by specifying a quantum channel. It is assumed that the quantum channel is translationally invariant and is built from layers of quantum operations.
User has to provide one defining operation for each layer as a local superoperator. Those local superoperator have to be input in order of their action on the system.
Parameter encoding is a stand out quantum operation. It is assumed that parameter encoding acts only once and is unitary so the user has to provide only its generator h.
Generator h has to be diagonal in the computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.
Parameters:
N: integer
Number of sites in the chain of tensors (usually number of particles).
so_before_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites particular local superoperator acts
List of local superoperators (in order) which act before unitary parameter encoding.
h: ndarray of a shape (d,d)
Generator of unitary parameter encoding. Dimension d is the dimension of local Hilbert space (dimension of physical index).
Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.
so_after_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites particular local superoperator acts
List of local superoperators (in order) which act after unitary parameter encoding.
rho0: list of length N of ndarrays of a shape (Dl_rho0,Dr_rho0,d,d) for OBC (Dl_rho0, Dr_rho0 can vary between sites) or ndarray of a shape (D_rho0,D_rho0,d,d,N) for PBC
Density matrix describing initial state of the system in MPO representation.
BC: 'O' or 'P', optional
Boundary conditions, 'O' for OBC, 'P' for PBC.
L_ini: list of length N of ndarrays of shape (Dl_L,Dr_L,d,d) for OBC, (Dl_L, Dr_L can vary between sites) or ndarray of shape (D_L,D_L,d,d,N) for PBC, optional
Initial MPO for L.
imprecision: float, optional
Expected relative imprecision of the end results.
D_L_max: integer, optional
Maximal value of D_L (D_L is bond dimension for MPO representing L).
D_L_max_forced: bool, optional
True if D_L_max has to be reached, otherwise False.
L_herm: bool, optional
True if Hermitian gauge has to be imposed on MPO representing L, otherwise False.
Returns:
result: float
Optimal value of figure of merit.
result_v: ndarray
Vector describing figure of merit in function of bond dimensions of L.
L: list of length N of ndarrays of a shape (Dl_L,Dr_L,d,d) for OBC (Dl_L, Dr_L can vary between sites) or ndarray of a shape (D_L,D_L,d,d,N) for PBC
Optimal L in the MPO representation.
"""
if np.linalg.norm(h - np.diag(np.diag(h))) > 10**-10:
warnings.warn('Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.')
d = np.shape(h)[0]
ch = fin_create_channel(N, d, BC, so_before_list + so_after_list)
ch2 = fin_create_channel_derivative(N, d, BC, so_before_list, h, so_after_list)
rho = channel_acting_on_operator(ch, rho0)
rho2 = channel_acting_on_operator(ch2, rho0)
result, result_v, L = fin_state_gen(N, d, BC, rho, rho2, None, L_ini, imprecision, D_L_max, D_L_max_forced, L_herm)
return result, result_v, L
def fin_state_gen(N, d, BC, rho, rho2, epsilon=None, L_ini=None, imprecision=10**-2, D_L_max=100, D_L_max_forced=False, L_herm=True):
"""
Optimization of the the figure of merit (usually interpreted as the QFI) over operator L (in MPO representation) and check of convergence when increasing its bond dimension. Function for finite size systems and fixed state of the system.
User has to provide information about the dynamics by specifying a quantum channel ch and its derivative ch2 (or two channels separated by small parameter epsilon) as superoperators in the MPO representation.
There are no constraints on the structure of the channel but the complexity of calculations highly depends on channel's bond dimension.
Parameters:
N: integer
Number of sites in the chain of tensors (usually number of particles).
d: integer
Dimension of local Hilbert space (dimension of physical index).
BC: 'O' or 'P'
Boundary conditions, 'O' for OBC, 'P' for PBC.
rho: list of length N of ndarrays of a shape (Dl_rho,Dr_rho,d,d) for OBC (Dl_rho, Dr_rho can vary between sites) or ndarray of a shape (D_rho,D_rho,d,d,N) for PBC
Density matrix at the output of the quantum channel in the MPO representation.
rho2: list of length N of ndarrays of a shape (Dl_rho2,Dr_rho2,d,d) for OBC (Dl_rho2, Dr_rho2 can vary between sites) or ndarray of a shape (D_rho2,D_rho2,d,d,N) for PBC
Interpretaion depends on whether epsilon is specifed (2) or not (1, default approach):
1) derivative of density matrix at the output of quantum channel in MPO representation,
2) density matrix at the output of quantum channel in MPO representation for the value of estimated parameter shifted by epsilon in relation to rho.
epsilon: float, optional
If specified then it is interpeted as the value of separation between estimated parameters encoded in rho and rho2.
L_ini: list of length N of ndarrays of a shape (Dl_L,Dr_L,d,d) for OBC (Dl_L, Dr_L can vary between sites) or ndarray of a shape (D_L,D_L,d,d,N) for PBC, optional
Initial MPO for L.
imprecision: float, optional
Expected relative imprecision of the end results.
D_L_max: integer, optional
Maximal value of D_L (D_L is bond dimension for MPO representing L).
D_L_max_forced: bool, optional
True if D_L_max has to be reached, otherwise False.
L_herm: bool, optional
True if Hermitian gauge has to be imposed on MPO representing L, otherwise False.
Returns:
result: float
Optimal value of figure of merit.
result_v: ndarray
Vector describing figure of merit as a function of bond dimensions of L.
L: list of length N of ndarrays of a shape (Dl_L,Dr_L,d,d) for OBC (Dl_L, Dr_L can vary between sites) or ndarray of a shape (D_L,D_L,d,d,N) for PBC
Optimal L in MPO representation.
"""
if epsilon is None:
result, result_v, L = fin_FoM_optbd(N, d, BC, rho, rho2, L_ini, imprecision, D_L_max, D_L_max_forced, L_herm)
else:
result, result_v, L = fin2_FoM_optbd(N, d, BC, rho, rho2, epsilon, L_ini, imprecision, D_L_max, D_L_max_forced, L_herm)
return result, result_v, L
############################
# #
# 1.2 Low level functions. #
# #
############################
def fin_create_channel(N, d, BC, so_list, tol=10**-10):
"""
Creates MPO for a superoperator describing translationally invariant quantum channel from list of local superoperators. Function for finite size systems.
For OBC, tensor-network length N has to be at least 2k-1, where k is the correlation length (number of sites on which acts the biggest local superoperator).
Local superoperators acting on more then 4 neighbouring sites are not currently supported.
Parameters:
N: integer
Number of sites in the chain of tensors (usually number of particles).
For OBC tensor-network length N has to be at least 2k-1 where k is the correlation length (number of sites on which acts the biggest local superoperator).
d: integer
Dimension of local Hilbert space (dimension of physical index).
BC: 'O' or 'P'
Boundary conditions, 'O' for OBC, 'P' for PBC.
so_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites a particular local superoperator acts
List of local superoperators in order of their action on the system.
Local superoperators acting on more then 4 neighbour sites are not currently supported.
tol: float, optional
Factor which after multiplication by the highest singular value gives a cutoff on singular values that are treated as nonzero.
Returns:
ch: list of length N of ndarrays of shape (Dl_ch,Dr_ch,d**2,d**2) for OBC (Dl_ch, Dr_ch can vary between sites) or ndarray of shape (D_ch,D_ch,d**2,d**2,N) for PBC
Quantum channel as a superoperator in the MPO representation.
"""
if so_list == []:
if BC == 'O':
ch = np.eye(d**2,dtype=complex)
ch = ch[np.newaxis,np.newaxis,:,:]
ch = [ch]*N
elif BC == 'P':
ch = np.eye(d**2,dtype=complex)
ch = ch[np.newaxis,np.newaxis,:,:,np.newaxis]
ch = np.tile(ch,(1,1,1,1,N))
return ch
if BC == 'O':
ch = [0]*N
kmax = max([int(math.log(np.shape(so_list[i])[0],d**2)) for i in range(len(so_list))])
if N < 2*kmax-1:
warnings.warn('For OBC tensor-network length N have to be at least 2k-1 where k is correlation length (number of sites on which acts the biggest local superoperator).')
for x in range(N):
if x >= kmax and N-x >= kmax:
ch[x] = ch[x-1]
continue
for i in range(len(so_list)):
so = so_list[i]
k = int(math.log(np.shape(so)[0],d**2))
if np.linalg.norm(so-np.diag(np.diag(so))) < 10**-10:
so = np.diag(so)
if k == 1:
bdchil = 1
bdchir = 1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
chi[:,:,nx,nx] = so[nx]
elif k == 2:
so = np.reshape(so,(d**2,d**2),order='F')
u,s,vh = np.linalg.svd(so)
s = s[s > s[0]*tol]
bdchi = np.shape(s)[0]
u = u[:,:bdchi]
vh = vh[:bdchi,:]
us = u @ np.diag(np.sqrt(s))
sv = np.diag(np.sqrt(s)) @ vh
if x == 0:
bdchil = 1
bdchir = bdchi
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [us[nx,:]]
legs = [[-1]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x > 0 and x < N-1:
bdchil = bdchi
bdchir = bdchi
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv[:,nx],us[nx,:]]
legs = [[-1],[-2]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x == N-1:
bdchil = bdchi
bdchir = 1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv[:,nx]]
legs = [[-1]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif k == 3:
so = np.reshape(so,(d**2,d**4),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
sv1 = np.reshape(sv1,(bdchi1*d**2,d**2),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
if x == 0:
bdchil = 1
bdchir = bdchi1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [us1[nx,:]]
legs = [[-1]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x == 1:
bdchil = bdchi1
bdchir = bdchi2*bdchi1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [us2[:,nx,:],us1[nx,:]]
legs = [[-1,-2],[-3]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x > 1 and x < N-2:
bdchil = bdchi2*bdchi1
bdchir = bdchi2*bdchi1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv2[:,nx],us2[:,nx,:],us1[nx,:]]
legs = [[-1],[-2,-3],[-4]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x == N-2:
bdchil = bdchi2*bdchi1
bdchir = bdchi2
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv2[:,nx],us2[:,nx,:]]
legs = [[-1],[-2,-3]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x == N-1:
bdchil = bdchi2
bdchir = 1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv2[:,nx]]
legs = [[-1]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif k == 4:
so = np.reshape(so,(d**2,d**6),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
sv1 = np.reshape(sv1,(bdchi1*d**2,d**4),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
sv2 = np.reshape(sv2,(bdchi2*d**2,d**2),order='F')
u3,s3,vh3 = np.linalg.svd(sv2,full_matrices=False)
s3 = s3[s3 > s3[0]*tol]
bdchi3 = np.shape(s3)[0]
u3 = u3[:,:bdchi3]
vh3 = vh3[:bdchi3,:]
us3 = u3 @ np.diag(np.sqrt(s3))
us3 = np.reshape(us3,(bdchi2,d**2,bdchi3),order='F')
sv3 = np.diag(np.sqrt(s3)) @ vh3
if x == 0:
bdchil = 1
bdchir = bdchi1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [us1[nx,:]]
legs = [[-1]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x == 1:
bdchil = bdchi1
bdchir = bdchi2*bdchi1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [us2[:,nx,:],us1[nx,:]]
legs = [[-1,-2],[-3]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x == 2:
bdchil = bdchi2*bdchi1
bdchir = bdchi3*bdchi2*bdchi1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [us3[:,nx,:],us2[:,nx,:],us1[nx,:]]
legs = [[-1,-3],[-2,-4],[-5]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x > 2 and x < N-3:
bdchil = bdchi3*bdchi2*bdchi1
bdchir = bdchi3*bdchi2*bdchi1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv3[:,nx],us3[:,nx,:],us2[:,nx,:],us1[nx,:]]
legs = [[-1],[-2,-4],[-3,-5],[-6]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x == N-3:
bdchil = bdchi3*bdchi2*bdchi1
bdchir = bdchi3*bdchi2
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv3[:,nx],us3[:,nx,:],us2[:,nx,:]]
legs = [[-1],[-2,-4],[-3,-5]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x == N-2:
bdchil = bdchi3*bdchi2
bdchir = bdchi3
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv3[:,nx],us3[:,nx,:]]
legs = [[-1],[-2,-3]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
elif x == N-1:
bdchil = bdchi3
bdchir = 1
chi = np.zeros((bdchil,bdchir,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv3[:,nx]]
legs = [[-1]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchil,bdchir),order='F')
else:
warnings.warn('Local superoperators acting on more then 4 neighbour sites are not currently supported.')
else:
if k == 1:
bdchil = 1
bdchir = 1
chi = so[np.newaxis,np.newaxis,:,:]
elif k == 2:
u,s,vh = np.linalg.svd(so)
s = s[s > s[0]*tol]
bdchi = np.shape(s)[0]
u = u[:,:bdchi]
vh = vh[:bdchi,:]
us = u @ np.diag(np.sqrt(s))
sv = np.diag(np.sqrt(s)) @ vh
us = np.reshape(us,(d**2,d**2,bdchi),order='F')
sv = np.reshape(sv,(bdchi,d**2,d**2),order='F')
tensors = [sv,us]
legs = [[-1,-3,1],[1,-4,-2]]
chi = ncon(tensors,legs)
if x == 0:
tensors = [us]
legs = [[-2,-3,-1]]
chi = ncon(tensors,legs)
bdchil = 1
bdchir = bdchi
elif x > 0 and x < N-1:
tensors = [sv,us]
legs = [[-1,-3,1],[1,-4,-2]]
chi = ncon(tensors,legs)
bdchil = bdchi
bdchir = bdchi
elif x == N-1:
tensors = [sv]
legs = [[-1,-2,-3]]
chi = ncon(tensors,legs)
bdchil = bdchi
bdchir = 1
chi = np.reshape(chi,(bdchil,bdchir,d**2,d**2),order='F')
elif k == 3:
so = np.reshape(so,(d**4,d**8),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
us1 = np.reshape(us1,(d**2,d**2,bdchi1),order='F')
sv1 = np.reshape(sv1,(bdchi1*d**4,d**4),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
sv2 = np.reshape(sv2,(bdchi2,d**2,d**2),order='F')
if x == 0:
tensors = [us1]
legs = [[-2,-3,-1]]
chi = ncon(tensors,legs)
bdchil = 1
bdchir = bdchi1
elif x == 1:
tensors = [us2,us1]
legs = [[-1,-5,1,-2],[1,-6,-3]]
chi = ncon(tensors,legs)
bdchil = bdchi1
bdchir = bdchi2*bdchi1
elif x > 1 and x < N-2:
tensors = [sv2,us2,us1]
legs = [[-1,-5,1],[-2,1,2,-3],[2,-6,-4]]
chi = ncon(tensors,legs)
bdchil = bdchi2*bdchi1
bdchir = bdchi2*bdchi1
elif x == N-2:
tensors = [sv2,us2]
legs = [[-1,-4,1],[-2,1,-5,-3]]
chi = ncon(tensors,legs)
bdchil = bdchi2*bdchi1
bdchir = bdchi2
elif x == N-1:
tensors = [sv2]
legs = [[-1,-2,-3]]
chi = ncon(tensors,legs)
bdchil = bdchi2
bdchir = 1
chi = np.reshape(chi,(bdchil,bdchir,d**2,d**2),order='F')
elif k == 4:
so = np.reshape(so,(d**4,d**12),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
us1 = np.reshape(us1,(d**2,d**2,bdchi1),order='F')
sv1 = np.reshape(sv1,(bdchi1*d**4,d**8),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
sv2 = np.reshape(sv2,(bdchi2*d**4,d**4),order='F')
u3,s3,vh3 = np.linalg.svd(sv2,full_matrices=False)
s3 = s3[s3 > s3[0]*tol]
bdchi3 = np.shape(s3)[0]
u3 = u3[:,:bdchi3]
vh3 = vh3[:bdchi3,:]
us3 = u3 @ np.diag(np.sqrt(s3))
us3 = np.reshape(us3,(bdchi2,d**2,d**2,bdchi3),order='F')
sv3 = np.diag(np.sqrt(s3)) @ vh3
sv3 = np.reshape(sv3,(bdchi3,d**2,d**2),order='F')
if x == 0:
tensors = [us1]
legs = [[-2,-3,-1]]
chi = ncon(tensors,legs)
bdchil = 1
bdchir = bdchi1
elif x == 1:
tensors = [us2,us1]
legs = [[-1,-4,1,-2],[1,-5,-3]]
chi = ncon(tensors,legs)
bdchil = bdchi1
bdchir = bdchi2*bdchi1
elif x == 2:
tensors = [us3,us2,us1]
legs = [[-1,-6,1,-3],[-2,1,2,-4],[2,-7,-5]]
chi = ncon(tensors,legs)
bdchil = bdchi2*bdchi1
bdchir = bdchi3*bdchi2*bdchi1
elif x > 2 and x < N-3:
tensors = [sv3,us3,us2,us1]
legs = [[-1,-7,1],[-2,1,2,-4],[-3,2,3,-5],[3,-8,-6]]
chi = ncon(tensors,legs)
bdchil = bdchi3*bdchi2*bdchi1
bdchir = bdchi3*bdchi2*bdchi1
elif x == N-3:
tensors = [sv3,us3,us2]
legs = [[-1,-6,1],[-2,1,2,-4],[-3,2,-7,-5]]
chi = ncon(tensors,legs)
bdchil = bdchi3*bdchi2*bdchi1
bdchir = bdchi3*bdchi2
elif x == N-2:
tensors = [sv3,us3]
legs = [[-1,-4,1],[-2,1,-5,-3]]
chi = ncon(tensors,legs)
bdchil = bdchi3*bdchi2
bdchir = bdchi3
elif x == N-1:
tensors = [sv3]
legs = [[-1,-2,-3]]
chi = ncon(tensors,legs)
bdchil = bdchi3
bdchir = 1
chi = np.reshape(chi,(bdchi,bdchi,d**2,d**2),order='F')
else:
warnings.warn('Local superoperators acting on more then 4 neighbour sites are not currently supported.')
if i == 0:
bdchl = bdchil
bdchr = bdchir
ch[x] = chi
else:
bdchl = bdchil*bdchl
bdchr = bdchir*bdchr
tensors = [chi,ch[x]]
legs = [[-1,-3,-5,1],[-2,-4,1,-6]]
ch[x] = ncon(tensors,legs)
ch[x] = np.reshape(ch[x],(bdchl,bdchr,d**2,d**2),order='F')
elif BC == 'P':
for i in range(len(so_list)):
so = so_list[i]
k = int(math.log(np.shape(so)[0],d**2))
if np.linalg.norm(so-np.diag(np.diag(so))) < 10**-10:
so = np.diag(so)
if k == 1:
bdchi = 1
chi = np.zeros((bdchi,bdchi,d**2,d**2),dtype=complex)
for nx in range(d**2):
chi[:,:,nx,nx] = so[nx]
elif k == 2:
so = np.reshape(so,(d**2,d**2),order='F')
u,s,vh = np.linalg.svd(so)
s = s[s > s[0]*tol]
bdchi = np.shape(s)[0]
u = u[:,:bdchi]
vh = vh[:bdchi,:]
us = u @ np.diag(np.sqrt(s))
sv = np.diag(np.sqrt(s)) @ vh
chi = np.zeros((bdchi,bdchi,d**2,d**2),dtype=complex)
for nx in range(d**2):
chi[:,:,nx,nx] = np.outer(sv[:,nx],us[nx,:])
elif k == 3:
so = np.reshape(so,(d**2,d**4),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
sv1 = np.reshape(sv1,(bdchi1*d**2,d**2),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
bdchi = bdchi2*bdchi1
chi = np.zeros((bdchi,bdchi,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv2[:,nx],us2[:,nx,:],us1[nx,:]]
legs = [[-1],[-2,-3],[-4]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchi,bdchi),order='F')
elif k == 4:
so = np.reshape(so,(d**2,d**6),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
sv1 = np.reshape(sv1,(bdchi1*d**2,d**4),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
sv2 = np.reshape(sv2,(bdchi2*d**2,d**2),order='F')
u3,s3,vh3 = np.linalg.svd(sv2,full_matrices=False)
s3 = s3[s3 > s3[0]*tol]
bdchi3 = np.shape(s3)[0]
u3 = u3[:,:bdchi3]
vh3 = vh3[:bdchi3,:]
us3 = u3 @ np.diag(np.sqrt(s3))
us3 = np.reshape(us3,(bdchi2,d**2,bdchi3),order='F')
sv3 = np.diag(np.sqrt(s3)) @ vh3
bdchi = bdchi3*bdchi2*bdchi1
chi = np.zeros((bdchi,bdchi,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv3[:,nx],us3[:,nx,:],us2[:,nx,:],us1[nx,:]]
legs = [[-1],[-2,-4],[-3,-5],[-6]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchi,bdchi),order='F')
else:
warnings.warn('Local superoperators acting on more then 4 neighbour sites are not currently supported.')
else:
if k == 1:
bdchi = 1
chi = so[np.newaxis,np.newaxis,:,:]
elif k == 2:
u,s,vh = np.linalg.svd(so)
s = s[s > s[0]*tol]
bdchi = np.shape(s)[0]
u = u[:,:bdchi]
vh = vh[:bdchi,:]
us = u @ np.diag(np.sqrt(s))
sv = np.diag(np.sqrt(s)) @ vh
us = np.reshape(us,(d**2,d**2,bdchi),order='F')
sv = np.reshape(sv,(bdchi,d**2,d**2),order='F')
tensors = [sv,us]
legs = [[-1,-3,1],[1,-4,-2]]
chi = ncon(tensors,legs)
elif k == 3:
so = np.reshape(so,(d**4,d**8),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
us1 = np.reshape(us1,(d**2,d**2,bdchi1),order='F')
sv1 = np.reshape(sv1,(bdchi1*d**4,d**4),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
sv2 = np.reshape(sv2,(bdchi2,d**2,d**2),order='F')
tensors = [sv2,us2,us1]
legs = [[-1,-5,1],[-2,1,2,-3],[2,-6,-4]]
chi = ncon(tensors,legs)
bdchi = bdchi2*bdchi1
chi = np.reshape(chi,(bdchi,bdchi,d**2,d**2),order='F')
elif k == 4:
so = np.reshape(so,(d**4,d**12),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
us1 = np.reshape(us1,(d**2,d**2,bdchi1),order='F')
sv1 = np.reshape(sv1,(bdchi1*d**4,d**8),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
sv2 = np.reshape(sv2,(bdchi2*d**4,d**4),order='F')
u3,s3,vh3 = np.linalg.svd(sv2,full_matrices=False)
s3 = s3[s3 > s3[0]*tol]
bdchi3 = np.shape(s3)[0]
u3 = u3[:,:bdchi3]
vh3 = vh3[:bdchi3,:]
us3 = u3 @ np.diag(np.sqrt(s3))
us3 = np.reshape(us3,(bdchi2,d**2,d**2,bdchi3),order='F')
sv3 = np.diag(np.sqrt(s3)) @ vh3
sv3 = np.reshape(sv3,(bdchi3,d**2,d**2),order='F')
tensors = [sv3,us3,us2,us1]
legs = [[-1,-7,1],[-2,1,2,-4],[-3,2,3,-5],[3,-8,-6]]
chi = ncon(tensors,legs)
bdchi = bdchi3*bdchi2*bdchi1
chi = np.reshape(chi,(bdchi,bdchi,d**2,d**2),order='F')
else:
warnings.warn('Local superoperators acting on more then 4 neighbour sites are not currently supported.')
if i == 0:
bdch = bdchi
ch = chi
else:
bdch = bdchi*bdch
tensors = [chi,ch]
legs = [[-1,-3,-5,1],[-2,-4,1,-6]]
ch = ncon(tensors,legs)
ch = np.reshape(ch,(bdch,bdch,d**2,d**2),order='F')
ch = ch[:,:,:,:,np.newaxis]
ch = np.tile(ch,(1,1,1,1,N))
return ch
def fin_create_channel_derivative(N, d, BC, so_before_list, h, so_after_list):
"""
Creates a MPO for the derivative (over estimated parameter) of the superoperator describing the quantum channel. Function for finite size systems.
Function for translationally invariant channels with unitary parameter encoding generated by h.
Generator h has to be diagonal in the computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.
Parameters:
N: integer
Number of sites in the chain of tensors (usually number of particles).
d: integer
Dimension of local Hilbert space (dimension of physical index).
BC: 'O' or 'P'
Boundary conditions, 'O' for OBC, 'P' for PBC.
so_before_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites particular local superoperator acts
List of local superoperators (in order) which act before unitary parameter encoding.
h: ndarray of a shape (d,d)
Generator of unitary parameter encoding.
Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.
so_after_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites particular local superoperator acts
List of local superoperators (in order) which act after unitary parameter encoding.
Returns:
chd: list of length N of ndarrays of a shape (Dl_chd,Dr_chd,d**2,d**2) for OBC (Dl_chd, Dr_chd can vary between sites) or ndarray of a shape (D_chd,D_chd,d**2,d**2,N) for PBC
Derivative of superoperator describing quantum channel in MPO representation.
"""
if np.linalg.norm(h-np.diag(np.diag(h))) > 10**-10:
warnings.warn('Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.')
if len(so_before_list) == 0:
if BC == 'O':
ch1 = np.eye(d**2,dtype=complex)
ch1 = ch1[np.newaxis,np.newaxis,:,:]
ch1 = [ch1]*N
elif BC == 'P':
ch1 = np.eye(d**2,dtype=complex)
ch1 = ch1[np.newaxis,np.newaxis,:,:,np.newaxis]
ch1 = np.tile(ch1,(1,1,1,1,N))
ch1d = fin_commutator(N,d,BC,ch1,h,1j)
ch2 = fin_create_channel(N,d,BC,so_after_list)
if BC == 'O':
chd = [0]*N
for x in range(N):
bdch1dl = np.shape(ch1d[x])[0]
bdch1dr = np.shape(ch1d[x])[1]
bdch2l = np.shape(ch2[x])[0]
bdch2r = np.shape(ch2[x])[1]
tensors = [ch2[x],ch1d[x]]
legs = [[-1,-3,-5,1],[-2,-4,1,-6]]
chd[x] = np.reshape(ncon(tensors,legs),(bdch1dl*bdch2l,bdch1dr*bdch2r,d**2,d**2),order='F')
elif BC == 'P':
bdch1d = np.shape(ch1d)[0]
bdch2 = np.shape(ch2)[0]
chd = np.zeros((bdch1d*bdch2,bdch1d*bdch2,d**2,d**2,N),dtype=complex)
for x in range(N):
tensors = [ch2[:,:,:,:,x],ch1d[:,:,:,:,x]]
legs = [[-1,-3,-5,1],[-2,-4,1,-6]]
chd[:,:,:,:,x] = np.reshape(ncon(tensors,legs),(bdch1d*bdch2,bdch1d*bdch2,d**2,d**2),order='F')
elif len(so_after_list) == 0:
ch1 = fin_create_channel(N,d,BC,so_before_list)
chd = fin_commutator(N,d,BC,ch1,h,1j)
else:
ch1 = fin_create_channel(N,d,BC,so_before_list)
ch1d = fin_commutator(N,d,BC,ch1,h,1j)
ch2 = fin_create_channel(N,d,BC,so_after_list)
if BC == 'O':
chd = [0]*N
for x in range(N):
bdch1dl = np.shape(ch1d[x])[0]
bdch1dr = np.shape(ch1d[x])[1]
bdch2l = np.shape(ch2[x])[0]
bdch2r = np.shape(ch2[x])[1]
tensors = [ch2[x],ch1d[x]]
legs = [[-1,-3,-5,1],[-2,-4,1,-6]]
chd[x] = np.reshape(ncon(tensors,legs),(bdch1dl*bdch2l,bdch1dr*bdch2r,d**2,d**2),order='F')
elif BC == 'P':
bdch1d = np.shape(ch1d)[0]
bdch2 = np.shape(ch2)[0]
chd = np.zeros((bdch1d*bdch2,bdch1d*bdch2,d**2,d**2,N),dtype=complex)
for x in range(N):
tensors = [ch2[:,:,:,:,x],ch1d[:,:,:,:,x]]
legs = [[-1,-3,-5,1],[-2,-4,1,-6]]
chd[:,:,:,:,x] = np.reshape(ncon(tensors,legs),(bdch1d*bdch2,bdch1d*bdch2,d**2,d**2),order='F')
return chd
def fin_commutator(N, d, BC, a, h, c):
"""
Calculate MPO for commutator b = [a, c*sum{h}] of MPO a with sum of local generators h and with arbitrary multiplicative scalar factor c.
Generator h have to be diagonal in computational basis, or in other words it is assumed that a is expressed in the eigenbasis of h.
Parameters:
N: integer
Number of sites in the chain of tensors (usually number of particles).
d: integer
Dimension of local Hilbert space (dimension of physical index).
BC: 'O' or 'P'
Boundary conditions, 'O' for OBC, 'P' for PBC.
a: list of length N of ndarrays of a shape (Dl_a,Dr_a,d,d) for OBC (Dl_a, Dr_a can vary between sites) or ndarray of a shape (D_a,D_a,d,d,N) for PBC
MPO.
h: ndarray of a shape (d,d)
Generator of unitary parameter encoding.
Generator h have to be diagonal in computational basis, or in other words it is assumed that a is expressed in the eigenbasis of h.
c: complex
Scalar factor which multiplies sum of local generators.
Returns:
b: list of length N of ndarrays of a shape (Dl_b,Dr_b,d,d) for OBC (Dl_b, Dr_b can vary between sites) or ndarray of a shape (D_b,D_b,d,d,N) for PBC
Commutator [a, c*sum{h}] in MPO representation.
"""
if np.linalg.norm(h-np.diag(np.diag(h))) > 10**-10:
warnings.warn('Generator h have to be diagonal in computational basis, or in other words it is assumed that a is expressed in the eigenbasis of h.')
if BC == 'O':
bh = [0]*N
b = [0]*N
for x in range(N):
da = np.shape(a[x])[2]
bda1 = np.shape(a[x])[0]
bda2 = np.shape(a[x])[1]
if x == 0:
bdbh1 = 1
bdbh2 = 2
bh[x] = np.zeros((bdbh1,bdbh2,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
bh[x][:,:,nx,nxp] = np.array([[c*(h[nxp,nxp]-h[nx,nx]),1]])
elif x > 0 and x < N-1:
bdbh1 = 2
bdbh2 = 2
bh[x] = np.zeros((bdbh1,bdbh2,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
bh[x][:,:,nx,nxp] = np.array([[1,0],[c*(h[nxp,nxp]-h[nx,nx]),1]])
elif x == N-1:
bdbh1 = 2
bdbh2 = 1
bh[x] = np.zeros((bdbh1,bdbh2,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
bh[x][:,:,nx,nxp] = np.array([[1],[c*(h[nxp,nxp]-h[nx,nx])]])
if da == d:
# a is operator
b[x] = np.zeros((bdbh1*bda1,bdbh2*bda2,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
b[x][:,:,nx,nxp] = np.kron(bh[x][:,:,nx,nxp],a[x][:,:,nx,nxp])
elif da == d**2:
# a is superoperator (vectorized channel)
bh[x] = np.reshape(bh[x],(bdbh1,bdbh2,d**2),order='F')
b[x] = np.zeros((bdbh1*bda1,bdbh2*bda2,d**2,d**2),dtype=complex)
for nx in range(d**2):
for nxp in range(d**2):
b[x][:,:,nx,nxp] = np.kron(bh[x][:,:,nx],a[x][:,:,nx,nxp])
elif BC == 'P':
da = np.shape(a)[2]
bda = np.shape(a)[0]
if N == 1:
bdbh = 1
else:
bdbh = 2
bh = np.zeros((bdbh,bdbh,d,d,N),dtype=complex)
for nx in range(d):
for nxp in range(d):
if N == 1:
bh[:,:,nx,nxp,0] = c*(h[nxp,nxp]-h[nx,nx])
else:
bh[:,:,nx,nxp,0] = np.array([[c*(h[nxp,nxp]-h[nx,nx]),1],[0,0]])
for x in range(1,N-1):
bh[:,:,nx,nxp,x] = np.array([[1,0],[c*(h[nxp,nxp]-h[nx,nx]),1]])
bh[:,:,nx,nxp,N-1] = np.array([[1,0],[c*(h[nxp,nxp]-h[nx,nx]),0]])
if da == d:
# a is operator
b = np.zeros((bdbh*bda,bdbh*bda,d,d,N),dtype=complex)
for nx in range(d):
for nxp in range(d):
for x in range(N):
b[:,:,nx,nxp,x] = np.kron(bh[:,:,nx,nxp,x],a[:,:,nx,nxp,x])
elif da == d**2:
# a is superoperator (vectorized channel)
bh = np.reshape(bh,(bdbh,bdbh,d**2,N),order='F')
b = np.zeros((bdbh*bda,bdbh*bda,d**2,d**2,N),dtype=complex)
for nx in range(d**2):
for nxp in range(d**2):
for x in range(N):
b[:,:,nx,nxp,x] = np.kron(bh[:,:,nx,x],a[:,:,nx,nxp,x])
return b
def fin_enlarge_bdl(cold,factor):
"""
Enlarge bond dimension of SLD MPO. Function for finite size systems.
Parameters:
cold: SLD MPO, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
factor: factor which determine on average relation between old and newly added values of SLD MPO
Returns:
c: SLD MPO with bd += 1
"""
rng = np.random.default_rng()
if type(cold) is list:
n = len(cold)
if n == 1:
warnings.warn('Tensor networks with OBC and length one have to have bond dimension equal to one.')
else:
c = [0]*n
x = 0
d = np.shape(cold[x])[2]
bdl1 = 1
bdl2 = np.shape(cold[x])[1]+1
c[x] = np.zeros((bdl1,bdl2,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
meanrecold = np.sum(np.abs(np.real(cold[x][:,:,nx,nxp])))/(bdl2-1)
meanimcold = np.sum(np.abs(np.imag(cold[x][:,:,nx,nxp])))/(bdl2-1)
c[x][:,:,nx,nxp] = (meanrecold*rng.random((bdl1,bdl2))+1j*meanimcold*rng.random((bdl1,bdl2)))*factor
c[x] = (c[x] + np.conj(np.moveaxis(c[x],2,3)))/2
c[x][0:bdl1-1,0:bdl2-1,:,:] = cold[x]
for x in range(1,n-1):
d = np.shape(cold[x])[2]
bdl1 = np.shape(cold[x])[0]+1
bdl2 = np.shape(cold[x])[1]+1
c[x] = np.zeros((bdl1,bdl2,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
meanrecold = np.sum(np.abs(np.real(cold[x][:,:,nx,nxp])))/((bdl1-1)*(bdl2-1))
meanimcold = np.sum(np.abs(np.imag(cold[x][:,:,nx,nxp])))/((bdl1-1)*(bdl2-1))
c[x][:,:,nx,nxp] = (meanrecold*rng.random((bdl1,bdl2))+1j*meanimcold*rng.random((bdl1,bdl2)))*factor
c[x] = (c[x] + np.conj(np.moveaxis(c[x],2,3)))/2
c[x][0:bdl1-1,0:bdl2-1,:,:] = cold[x]
x = n-1
d = np.shape(cold[x])[2]
bdl1 = np.shape(cold[x])[0]+1
bdl2 = 1
c[x] = np.zeros((bdl1,bdl2,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
meanrecold = np.sum(np.abs(np.real(cold[x][:,:,nx,nxp])))/(bdl1-1)
meanimcold = np.sum(np.abs(np.imag(cold[x][:,:,nx,nxp])))/(bdl1-1)
c[x][:,:,nx,nxp] = (meanrecold*rng.random((bdl1,bdl2))+1j*meanimcold*rng.random((bdl1,bdl2)))*factor
c[x] = (c[x] + np.conj(np.moveaxis(c[x],2,3)))/2
c[x][0:bdl1-1,0:bdl2-1,:,:] = cold[x]
elif type(cold) is np.ndarray:
n = np.shape(cold)[4]
d = np.shape(cold)[2]
bdl = np.shape(cold)[0]+1
c = np.zeros((bdl,bdl,d,d,n),dtype=complex)
for nx in range(d):
for nxp in range(d):
for x in range(n):
meanrecold = np.sum(np.abs(np.real(cold[:,:,nx,nxp,x])))/(bdl-1)**2
meanimcold = np.sum(np.abs(np.imag(cold[:,:,nx,nxp,x])))/(bdl-1)**2
c[:,:,nx,nxp,x] = (meanrecold*rng.random((bdl,bdl))+1j*meanimcold*rng.random((bdl,bdl)))*factor
c = (c + np.conj(np.moveaxis(c,2,3)))/2
c[0:bdl-1,0:bdl-1,:,:,:] = cold
return c
def fin_enlarge_bdpsi(a0old,factor):
"""
Enlarge bond dimension of wave function MPS. Function for finite size systems.
Parameters:
a0old: wave function MPS, expected list of length n of ndarrays of a shape (bd,bd,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,n) for PBC
ratio: factor which determine on average relation between last and next to last values of diagonals of wave function MPS
Returns:
a0: wave function MPS with bd += 1
"""
rng = np.random.default_rng()
if type(a0old) is list:
n = len(a0old)
if n == 1:
warnings.warn('Tensor networks with OBC and length one have to have bond dimension equal to one.')
else:
a0 = [0]*n
x = 0
d = np.shape(a0old[x])[2]
bdpsi1 = 1
bdpsi2 = np.shape(a0old[x])[1]+1
a0[x] = np.zeros((bdpsi1,bdpsi2,d),dtype=complex)
for nx in range(d):
meanrea0old = np.sum(np.abs(np.real(a0old[x][:,:,nx])))/(bdpsi2-1)
meanima0old = np.sum(np.abs(np.imag(a0old[x][:,:,nx])))/(bdpsi2-1)
a0[x][:,:,nx] = (meanrea0old*rng.random((bdpsi1,bdpsi2))+1j*meanima0old*rng.random((bdpsi1,bdpsi2)))*factor
a0[x][0:bdpsi1-1,0:bdpsi2-1,:] = a0old[x]
for x in range(1,n-1):
d = np.shape(a0old[x])[2]
bdpsi1 = np.shape(a0old[x])[0]+1
bdpsi2 = np.shape(a0old[x])[1]+1
a0[x] = np.zeros((bdpsi1,bdpsi2,d),dtype=complex)
for nx in range(d):
meanrea0old = np.sum(np.abs(np.real(a0old[x][:,:,nx])))/((bdpsi1-1)*(bdpsi2-1))
meanima0old = np.sum(np.abs(np.imag(a0old[x][:,:,nx])))/((bdpsi1-1)*(bdpsi2-1))
a0[x][:,:,nx] = (meanrea0old*rng.random((bdpsi1,bdpsi2))+1j*meanima0old*rng.random((bdpsi1,bdpsi2)))*factor
a0[x][0:bdpsi1-1,0:bdpsi2-1,:] = a0old[x]
x = n-1
d = np.shape(a0old[x])[2]
bdpsi1 = np.shape(a0old[x])[0]+1
bdpsi2 = 1
a0[x] = np.zeros((bdpsi1,bdpsi2,d),dtype=complex)
for nx in range(d):
meanrea0old = np.sum(np.abs(np.real(a0old[x][:,:,nx])))/(bdpsi1-1)
meanima0old = np.sum(np.abs(np.imag(a0old[x][:,:,nx])))/(bdpsi1-1)
a0[x][:,:,nx] = (meanrea0old*rng.random((bdpsi1,bdpsi2))+1j*meanima0old*rng.random((bdpsi1,bdpsi2)))*factor
a0[x][0:bdpsi1-1,0:bdpsi2-1,:] = a0old[x]
tensors = [np.conj(a0[n-1]),a0[n-1]]
legs = [[-1,-3,1],[-2,-4,1]]
r1 = ncon(tensors,legs)
a0[n-1] = a0[n-1]/np.sqrt(np.linalg.norm(np.reshape(r1,-1,order='F')))
tensors = [np.conj(a0[n-1]),a0[n-1]]
legs = [[-1,-3,1],[-2,-4,1]]
r2 = ncon(tensors,legs)
for x in range(n-2,0,-1):
tensors = [np.conj(a0[x]),a0[x],r2]
legs = [[-1,2,1],[-2,3,1],[2,3,-3,-4]]
r1 = ncon(tensors,legs)
a0[x] = a0[x]/np.sqrt(np.linalg.norm(np.reshape(r1,-1,order='F')))
tensors = [np.conj(a0[x]),a0[x],r2]
legs = [[-1,2,1],[-2,3,1],[2,3,-3,-4]]
r2 = ncon(tensors,legs)
tensors = [np.conj(a0[0]),a0[0],r2]
legs = [[4,2,1],[5,3,1],[2,3,4,5]]
r1 = ncon(tensors,legs)
a0[0] = a0[0]/np.sqrt(np.abs(r1))
elif type(a0old) is np.ndarray:
n = np.shape(a0old)[3]
d = np.shape(a0old)[2]
bdpsi = np.shape(a0old)[0]+1
a0 = np.zeros((bdpsi,bdpsi,d,n),dtype=complex)
for nx in range(d):
for x in range(n):
meanrea0old = np.sum(np.abs(np.real(a0old[:,:,nx,x])))/(bdpsi-1)**2
meanima0old = np.sum(np.abs(np.imag(a0old[:,:,nx,x])))/(bdpsi-1)**2
a0[:,:,nx,x] = (meanrea0old*rng.random((bdpsi,bdpsi))+1j*meanima0old*rng.random((bdpsi,bdpsi)))*factor
a0[0:bdpsi-1,0:bdpsi-1,:,:] = a0old
if n == 1:
tensors = [np.conj(a0[:,:,:,0]),a0[:,:,:,0]]
legs = [[2,2,1],[3,3,1]]
r1 = ncon(tensors,legs)
a0[:,:,:,0] = a0[:,:,:,0]/np.sqrt(np.abs(r1))
else:
tensors = [np.conj(a0[:,:,:,n-1]),a0[:,:,:,n-1]]
legs = [[-1,-3,1],[-2,-4,1]]
r1 = ncon(tensors,legs)
a0[:,:,:,n-1] = a0[:,:,:,n-1]/np.sqrt(np.linalg.norm(np.reshape(r1,-1,order='F')))
tensors = [np.conj(a0[:,:,:,n-1]),a0[:,:,:,n-1]]
legs = [[-1,-3,1],[-2,-4,1]]
r2 = ncon(tensors,legs)
for x in range(n-2,0,-1):
tensors = [np.conj(a0[:,:,:,x]),a0[:,:,:,x],r2]
legs = [[-1,2,1],[-2,3,1],[2,3,-3,-4]]
r1 = ncon(tensors,legs)
a0[:,:,:,x] = a0[:,:,:,x]/np.sqrt(np.linalg.norm(np.reshape(r1,-1,order='F')))
tensors = [np.conj(a0[:,:,:,x]),a0[:,:,:,x],r2]
legs = [[-1,2,1],[-2,3,1],[2,3,-3,-4]]
r2 = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),a0[:,:,:,0],r2]
legs = [[4,2,1],[5,3,1],[2,3,4,5]]
r1 = ncon(tensors,legs)
a0[:,:,:,0] = a0[:,:,:,0]/np.sqrt(np.abs(r1))
return a0
#########################################
# 1.2.1 Problems with exact derivative. #
#########################################
def fin_FoM_FoMD_optbd(n,d,bc,ch,chp,cini=None,a0ini=None,imprecision=10**-2,bdlmax=100,alwaysbdlmax=False,lherm=True,bdpsimax=100,alwaysbdpsimax=False):
"""
Iterative optimization of FoM/FoMD over SLD MPO and initial wave function MPS and also check of convergence in bond dimensions. Function for finite size systems.
Parameters:
n: number of sites in TN
d: dimension of local Hilbert space (dimension of physical index)
bc: boundary conditions, 'O' for OBC, 'P' for PBC
ch: MPO for quantum channel, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC
chp: MPO for generalized derivative of quantum channel, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC
cini: initial MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
a0ini: initial MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,n) for PBC
imprecision: expected imprecision of the end results, default value is 10**-2
bdlmax: maximal value of bd for SLD MPO, default value is 100
alwaysbdlmax: boolean value, True if maximal value of bd for SLD MPO have to be reached, otherwise False (default value)
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
bdpsimax: maximal value of bd for initial wave function MPS, default value is 100
alwaysbdpsimax: boolean value, True if maximal value of bd for initial wave function MPS have to be reached, otherwise False (default value)
Returns:
result: optimal value of FoM/FoMD
resultm: matrix describing FoM/FoMD in function of bd of respectively SLD MPO [rows] and initial wave function MPS [columns]
c: optimal MPO for SLD
a0: optimal MPS for initial wave function
"""
while True:
if a0ini is None:
bdpsi = 1
a0 = np.zeros(d,dtype=complex)
for i in range(d):
a0[i] = np.sqrt(math.comb(d-1,i))*2**(-(d-1)/2) # prod
# a0[i] = np.sqrt(2/(d+1))*np.sin((1+i)*np.pi/(d+1)) # sine
if bc == 'O':
a0 = a0[np.newaxis,np.newaxis,:]
a0 = [a0]*n
elif bc == 'P':
a0 = a0[np.newaxis,np.newaxis,:,np.newaxis]
a0 = np.tile(a0,(1,1,1,n))
else:
a0 = a0ini
if bc == 'O':
bdpsi = max([np.shape(a0[i])[0] for i in range(n)])
a0 = [a0[i].astype(complex) for i in range(n)]
elif bc == 'P':
bdpsi = np.shape(a0)[0]
a0 = a0.astype(complex)
if cini is None:
bdl = 1
rng = np.random.default_rng()
if bc == 'O':
c = [0]*n
c[0] = (rng.random((1,bdl,d,d)) + 1j*rng.random((1,bdl,d,d)))/bdl
c[0] = (c[0] + np.conj(np.moveaxis(c[0],2,3)))/2
for x in range(1,n-1):
c[x] = (rng.random((bdl,bdl,d,d)) + 1j*rng.random((bdl,bdl,d,d)))/bdl
c[x] = (c[x] + np.conj(np.moveaxis(c[x],2,3)))/2
c[n-1] = (rng.random((bdl,1,d,d)) + 1j*rng.random((bdl,1,d,d)))/bdl
c[n-1] = (c[n-1] + np.conj(np.moveaxis(c[n-1],2,3)))/2
elif bc == 'P':
c = (rng.random((bdl,bdl,d,d,n)) + 1j*rng.random((bdl,bdl,d,d,n)))/bdl
c = (c + np.conj(np.moveaxis(c,2,3)))/2
else:
c = cini
if bc == 'O':
bdl = max([np.shape(c[i])[0] for i in range(n)])
c = [c[i].astype(complex) for i in range(n)]
elif bc == 'P':
bdl = np.shape(c)[0]
c = c.astype(complex)
resultm = np.zeros((bdlmax,bdpsimax),dtype=float)
resultm[bdl-1,bdpsi-1],c,a0 = fin_FoM_FoMD_optm(n,d,bc,c,a0,ch,chp,imprecision,lherm)
if bc == 'O' and n == 1:
resultm = resultm[0:bdl,0:bdpsi]
result = resultm[bdl-1,bdpsi-1]
return result,resultm,c,a0
factorv = np.array([0.5,0.25,0.1,1,0.01])
problem = False
while True:
while True:
if bdpsi == bdpsimax:
break
else:
a0old = a0
bdpsi += 1
i = 0
while True:
a0 = fin_enlarge_bdpsi(a0,factorv[i])
resultm[bdl-1,bdpsi-1],cnew,a0new = fin_FoM_FoMD_optm(n,d,bc,c,a0,ch,chp,imprecision,lherm)
if resultm[bdl-1,bdpsi-1] >= resultm[bdl-1,bdpsi-2]:
break
i += 1
if i == np.size(factorv):
problem = True
break
if problem:
break
if not(alwaysbdpsimax) and resultm[bdl-1,bdpsi-1] < (1+imprecision)*resultm[bdl-1,bdpsi-2]:
bdpsi += -1
a0 = a0old
a0copy = a0new
ccopy = cnew
break
else:
a0 = a0new
c = cnew
if problem:
break
if bdl == bdlmax:
if bdpsi == bdpsimax:
resultm = resultm[0:bdl,0:bdpsi]
result = resultm[bdl-1,bdpsi-1]
else:
a0 = a0copy
c = ccopy
resultm = resultm[0:bdl,0:bdpsi+1]
result = resultm[bdl-1,bdpsi]
break
else:
bdl += 1
i = 0
while True:
c = fin_enlarge_bdl(c,factorv[i])
resultm[bdl-1,bdpsi-1],cnew,a0new = fin_FoM_FoMD_optm(n,d,bc,c,a0,ch,chp,imprecision,lherm)
if resultm[bdl-1,bdpsi-1] >= resultm[bdl-2,bdpsi-1]:
a0 = a0new
c = cnew
break
i += 1
if i == np.size(factorv):
problem = True
break
if problem:
break
if not(alwaysbdlmax) and resultm[bdl-1,bdpsi-1] < (1+imprecision)*resultm[bdl-2,bdpsi-1]:
if bdpsi == bdpsimax:
resultm = resultm[0:bdl,0:bdpsi]
result = resultm[bdl-1,bdpsi-1]
else:
if resultm[bdl-1,bdpsi-1] < resultm[bdl-2,bdpsi]:
a0 = a0copy
c = ccopy
resultm = resultm[0:bdl,0:bdpsi+1]
bdl += -1
bdpsi += 1
result = resultm[bdl-1,bdpsi-1]
else:
resultm = resultm[0:bdl,0:bdpsi+1]
result = resultm[bdl-1,bdpsi-1]
break
if not(problem):
break
return result,resultm,c,a0
def fin_FoM_optbd(n,d,bc,a,b,cini=None,imprecision=10**-2,bdlmax=100,alwaysbdlmax=False,lherm=True):
"""
Optimization of FoM over SLD MPO and also check of convergence in bond dimension. Function for finite size systems.
Parameters:
n: number of sites in TN
d: dimension of local Hilbert space (dimension of physical index)
bc: boundary conditions, 'O' for OBC, 'P' for PBC
a: MPO for density matrix, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
b: MPO for generalized derivative of density matrix, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
cini: initial MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
imprecision: expected imprecision of the end results, default value is 10**-2
bdlmax: maximal value of bd for SLD MPO, default value is 100
alwaysbdlmax: boolean value, True if maximal value of bd for SLD MPO have to be reached, otherwise False (default value)
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
result: optimal value of FoM
resultv: vector describing FoM in function of bd of SLD MPO
c: optimal MPO for SLD
"""
while True:
if cini is None:
bdl = 1
rng = np.random.default_rng()
if bc == 'O':
c = [0]*n
c[0] = (rng.random((1,bdl,d,d)) + 1j*rng.random((1,bdl,d,d)))/bdl
c[0] = (c[0] + np.conj(np.moveaxis(c[0],2,3)))/2
for x in range(1,n-1):
c[x] = (rng.random((bdl,bdl,d,d)) + 1j*rng.random((bdl,bdl,d,d)))/bdl
c[x] = (c[x] + np.conj(np.moveaxis(c[x],2,3)))/2
c[n-1] = (rng.random((bdl,1,d,d)) + 1j*rng.random((bdl,1,d,d)))/bdl
c[n-1] = (c[n-1] + np.conj(np.moveaxis(c[n-1],2,3)))/2
elif bc == 'P':
c = (rng.random((bdl,bdl,d,d,n)) + 1j*rng.random((bdl,bdl,d,d,n)))/bdl
c = (c + np.conj(np.moveaxis(c,2,3)))/2
else:
c = cini
if bc == 'O':
bdl = max([np.shape(c[i])[0] for i in range(n)])
c = [c[i].astype(complex) for i in range(n)]
elif bc == 'P':
bdl = np.shape(c)[0]
c = c.astype(complex)
resultv = np.zeros(bdlmax,dtype=float)
if bc == 'O':
resultv[bdl-1],c = fin_FoM_OBC_optm(a,b,c,imprecision,lherm)
if n == 1:
resultv = resultv[0:bdl]
result = resultv[bdl-1]
return result,resultv,c
elif bc == 'P':
resultv[bdl-1],c = fin_FoM_PBC_optm(a,b,c,imprecision,lherm)
factorv = np.array([0.5,0.25,0.1,1,0.01])
problem = False
while True:
if bdl == bdlmax:
resultv = resultv[0:bdl]
result = resultv[bdl-1]
break
else:
bdl += 1
i = 0
while True:
c = fin_enlarge_bdl(c,factorv[i])
if bc == 'O':
resultv[bdl-1],cnew = fin_FoM_OBC_optm(a,b,c,imprecision,lherm)
elif bc == 'P':
resultv[bdl-1],cnew = fin_FoM_PBC_optm(a,b,c,imprecision,lherm)
if resultv[bdl-1] >= resultv[bdl-2]:
c = cnew
break
i += 1
if i == np.size(factorv):
problem = True
break
if problem:
break
if not(alwaysbdlmax) and resultv[bdl-1] < (1+imprecision)*resultv[bdl-2]:
resultv = resultv[0:bdl]
result = resultv[bdl-1]
break
if not(problem):
break
return result,resultv,c
def fin_FoMD_optbd(n,d,bc,c2d,cpd,a0ini=None,imprecision=10**-2,bdpsimax=100,alwaysbdpsimax=False):
"""
Optimization of FoMD over initial wave function MPS and also check of convergence in bond dimension. Function for finite size systems.
Parameters:
n: number of sites in TN
d: dimension of local Hilbert space (dimension of physical index)
bc: boundary conditions, 'O' for OBC, 'P' for PBC
c2d: MPO for square of dual of SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
cpd: MPO for dual of generalized derivative of SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
a0ini: initial MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,n) for PBC
imprecision: expected imprecision of the end results, default value is 10**-2
bdpsimax: maximal value of bd for initial wave function MPS, default value is 100
alwaysbdpsimax: boolean value, True if maximal value of bd for initial wave function MPS have to be reached, otherwise False (default value)
Returns:
result: optimal value of FoMD
resultv: vector describing FoMD in function of bd of initial wave function MPS
a0: optimal MPS for initial wave function
"""
while True:
if a0ini is None:
bdpsi = 1
a0 = np.zeros(d,dtype=complex)
for i in range(d):
a0[i] = np.sqrt(math.comb(d-1,i))*2**(-(d-1)/2) # prod
# a0[i] = np.sqrt(2/(d+1))*np.sin((1+i)*np.pi/(d+1)) # sine
if bc == 'O':
a0 = a0[np.newaxis,np.newaxis,:]
a0 = [a0]*n
elif bc == 'P':
a0 = a0[np.newaxis,np.newaxis,:,np.newaxis]
a0 = np.tile(a0,(1,1,1,n))
else:
a0 = a0ini
if bc == 'O':
bdpsi = max([np.shape(a0[i])[0] for i in range(n)])
a0 = [a0[i].astype(complex) for i in range(n)]
elif bc == 'P':
bdpsi = np.shape(a0)[0]
a0 = a0.astype(complex)
resultv = np.zeros(bdpsimax,dtype=float)
if bc == 'O':
resultv[bdpsi-1],a0 = fin_FoMD_OBC_optm(c2d,cpd,a0,imprecision)
if n == 1:
resultv = resultv[0:bdpsi]
result = resultv[bdpsi-1]
return result,resultv,a0
elif bc == 'P':
resultv[bdpsi-1],a0 = fin_FoMD_PBC_optm(c2d,cpd,a0,imprecision)
factorv = np.array([0.5,0.25,0.1,1,0.01])
problem = False
while True:
if bdpsi == bdpsimax:
resultv = resultv[0:bdpsi]
result = resultv[bdpsi-1]
break
else:
bdpsi += 1
i = 0
while True:
a0 = fin_enlarge_bdpsi(a0,factorv[i])
if bc == 'O':
resultv[bdpsi-1],a0new = fin_FoMD_OBC_optm(c2d,cpd,a0,imprecision)
elif bc == 'P':
resultv[bdpsi-1],a0new = fin_FoMD_PBC_optm(c2d,cpd,a0,imprecision)
if resultv[bdpsi-1] >= resultv[bdpsi-2]:
a0 = a0new
break
i += 1
if i == np.size(factorv):
problem = True
break
if problem:
break
if not(alwaysbdpsimax) and resultv[bdpsi-1] < (1+imprecision)*resultv[bdpsi-2]:
resultv = resultv[0:bdpsi]
result = resultv[bdpsi-1]
break
if not(problem):
break
return result,resultv,a0
def fin_FoM_FoMD_optm(n,d,bc,c,a0,ch,chp,imprecision=10**-2,lherm=True):
"""
Iterative optimization of FoM/FoMD over SLD MPO and initial wave function MPS. Function for finite size systems.
Parameters:
n: number of sites in TN
d: dimension of local Hilbert space (dimension of physical index)
bc: boundary conditions, 'O' for OBC, 'P' for PBC
c: MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
a0: MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,n) for PBC
ch: MPO for quantum channel, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC
chp: MPO for generalized derivative of quantum channel, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC
imprecision: expected imprecision of the end results, default value is 10**-2
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
fval: optimal value of FoM/FoMD
c: optimal MPO for SLD
a0: optimal MPS for initial wave function
"""
relunc_f = 0.1*imprecision
if bc == 'O':
chd = [0]*n
chpd = [0]*n
for x in range(n):
chd[x] = np.conj(np.moveaxis(ch[x],2,3))
chpd[x] = np.conj(np.moveaxis(chp[x],2,3))
elif bc == 'P':
chd = np.conj(np.moveaxis(ch,2,3))
chpd = np.conj(np.moveaxis(chp,2,3))
f = np.array([])
iter_f = 0
while True:
a0_dm = wave_function_to_density_matrix(a0)
a = channel_acting_on_operator(ch,a0_dm)
b = channel_acting_on_operator(chp,a0_dm)
if bc == 'O':
fom,c = fin_FoM_OBC_optm(a,b,c,imprecision,lherm)
elif bc == 'P':
fom,c = fin_FoM_PBC_optm(a,b,c,imprecision,lherm)
f = np.append(f,fom)
if iter_f >= 2 and np.std(f[-4:])/np.mean(f[-4:]) <= relunc_f:
break
if bc == 'O':
c2 = [0]*n
for x in range(n):
bdl1 = np.shape(c[x])[0]
bdl2 = np.shape(c[x])[1]
c2[x] = np.zeros((bdl1**2,bdl2**2,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
for nxpp in range(d):
c2[x][:,:,nx,nxp] = c2[x][:,:,nx,nxp]+np.kron(c[x][:,:,nx,nxpp],c[x][:,:,nxpp,nxp])
elif bc == 'P':
bdl = np.shape(c)[0]
c2 = np.zeros((bdl**2,bdl**2,d,d,n),dtype=complex)
for nx in range(d):
for nxp in range(d):
for nxpp in range(d):
for x in range(n):
c2[:,:,nx,nxp,x] = c2[:,:,nx,nxp,x]+np.kron(c[:,:,nx,nxpp,x],c[:,:,nxpp,nxp,x])
c2d = channel_acting_on_operator(chd,c2)
cpd = channel_acting_on_operator(chpd,c)
if bc == 'O':
fomd,a0 = fin_FoMD_OBC_optm(c2d,cpd,a0,imprecision)
elif bc == 'P':
fomd,a0 = fin_FoMD_PBC_optm(c2d,cpd,a0,imprecision)
f = np.append(f,fomd)
iter_f += 1
fval = f[-1]
return fval,c,a0
def fin_FoM_OBC_optm(a,b,c,imprecision=10**-2,lherm=True):
"""
Optimization of FoM over MPO for SLD. Function for finite size systems with OBC.
Parameters:
a: MPO for density matrix, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
b: MPO for generalized derivative of density matrix, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
c: MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
imprecision: expected imprecision of the end results, default value is 10**-2
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
fomval: optimal value of FoM
c: optimal MPO for SLD
"""
n = len(c)
tol_fom = 0.1*imprecision/n**2
if n == 1:
if np.shape(a[0])[0] == 1 and np.shape(b[0])[0] == 1 and np.shape(c[0])[0] == 1:
d = np.shape(c[0])[2]
tensors = [b[0][0,0,:,:]]
legs = [[-2,-1]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [a[0][0,0,:,:],np.eye(d)]
legs = [[-2,-3],[-4,-1]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(d*d,d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*l1
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[0][0,0,:,:] = np.reshape(cv,(d,d),order='F')
if lherm:
c[0] = (c[0]+np.conj(np.moveaxis(c[0],2,3)))/2
cv = np.reshape(c[0],-1,order='F')
fomval = np.real(2*cv @ l1 - cv @ l2 @ cv)
else:
warnings.warn('Tensor networks with OBC and length one have to have bond dimension equal to one.')
else:
relunc_fom = 0.1*imprecision
l1f = [0]*n
l2f = [0]*n
fom = np.array([])
iter_fom = 0
while True:
tensors = [c[n-1],b[n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1f[n-2] = ncon(tensors,legs)
l1f[n-2] = l1f[n-2][:,:,0,0]
tensors = [c[n-1],a[n-1],c[n-1]]
legs = [[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]]
l2f[n-2] = ncon(tensors,legs)
l2f[n-2] = l2f[n-2][:,:,:,0,0,0]
for x in range(n-2,0,-1):
tensors = [c[x],b[x],l1f[x]]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4]]
l1f[x-1] = ncon(tensors,legs)
tensors = [c[x],a[x],c[x],l2f[x]]
legs = [[-1,4,1,2],[-2,5,2,3],[-3,6,3,1],[4,5,6]]
l2f[x-1] = ncon(tensors,legs)
bdl1,bdl2,d,d = np.shape(c[0])
tensors = [b[0],l1f[0]]
legs = [[-5,1,-4,-3],[-2,1]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [a[0],np.eye(d),l2f[0]]
legs = [[-9,1,-4,-7],[-8,-3],[-2,1,-6]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl1*bdl2*d*d,bdl1*bdl2*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*l1
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[0] = np.reshape(cv,(bdl1,bdl2,d,d),order='F')
if lherm:
c[0] = (c[0]+np.conj(np.moveaxis(c[0],2,3)))/2
cv = np.reshape(c[0],-1,order='F')
fom = np.append(fom,np.real(2*cv @ l1 - cv @ l2 @ cv))
tensors = [c[0],b[0]]
legs = [[-3,-1,1,2],[-4,-2,2,1]]
l1c = ncon(tensors,legs)
l1c = l1c[:,:,0,0]
tensors = [c[0],a[0],c[0]]
legs = [[-4,-1,1,2],[-5,-2,2,3],[-6,-3,3,1]]
l2c = ncon(tensors,legs)
l2c = l2c[:,:,:,0,0,0]
for x in range(1,n-1):
bdl1,bdl2,d,d = np.shape(c[x])
tensors = [l1c,b[x],l1f[x]]
legs = [[-1,1],[1,2,-4,-3],[-2,2]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [l2c,a[x],np.eye(d),l2f[x]]
legs = [[-1,1,-5],[1,2,-4,-7],[-8,-3],[-2,2,-6]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl1*bdl2*d*d,bdl1*bdl2*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*l1
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[x] = np.reshape(cv,(bdl1,bdl2,d,d),order='F')
if lherm:
c[x] = (c[x]+np.conj(np.moveaxis(c[x],2,3)))/2
cv = np.reshape(c[x],-1,order='F')
fom = np.append(fom,np.real(2*cv @ l1 - cv @ l2 @ cv))
tensors = [l1c,c[x],b[x]]
legs = [[3,4],[3,-1,1,2],[4,-2,2,1]]
l1c = ncon(tensors,legs)
tensors = [l2c,c[x],a[x],c[x]]
legs = [[4,5,6],[4,-1,1,2],[5,-2,2,3],[6,-3,3,1]]
l2c = ncon(tensors,legs)
bdl1,bdl2,d,d = np.shape(c[n-1])
tensors = [l1c,b[n-1]]
legs = [[-1,1],[1,-5,-4,-3]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [l2c,a[n-1],np.eye(d)]
legs = [[-1,1,-5],[1,-9,-4,-7],[-8,-3]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl1*bdl2*d*d,bdl1*bdl2*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*l1
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[n-1] = np.reshape(cv,(bdl1,bdl2,d,d),order='F')
if lherm:
c[n-1] = (c[n-1]+np.conj(np.moveaxis(c[n-1],2,3)))/2
cv = np.reshape(c[n-1],-1,order='F')
fom = np.append(fom,np.real(2*cv @ l1 - cv @ l2 @ cv))
iter_fom += 1
if iter_fom >= 2 and all(fom[-2*n:] > 0) and np.std(fom[-2*n:])/np.mean(fom[-2*n:]) <= relunc_fom:
break
fomval = fom[-1]
return fomval,c
def fin_FoM_PBC_optm(a,b,c,imprecision=10**-2,lherm=True):
"""
Optimization of FoM over MPO for SLD. Function for finite size systems with PBC.
Parameters:
a: MPO for density matrix, expected ndarray of a shape (bd,bd,d,d,n)
b: MPO for generalized derivative of density matrix, expected ndarray of a shape (bd,bd,d,d,n)
c: MPO for SLD, expected ndarray of a shape (bd,bd,d,d,n)
imprecision: expected imprecision of the end results, default value is 10**-2
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
fomval: optimal value of FoM
c: optimal MPO for SLD
"""
n = np.shape(a)[4]
d = np.shape(a)[2]
bdr = np.shape(a)[0]
bdrp = np.shape(b)[0]
bdl = np.shape(c)[0]
tol_fom = 0.1*imprecision/n**2
if n == 1:
tensors = [b[:,:,:,:,0],np.eye(bdl)]
legs = [[1,1,-4,-3],[-2,-1]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [a[:,:,:,:,0],np.eye(d),np.eye(bdl),np.eye(bdl)]
legs = [[1,1,-4,-7],[-8,-3],[-2,-1],[-6,-5]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl*bdl*d*d,bdl*bdl*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*l1
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[:,:,:,:,0] = np.reshape(cv,(bdl,bdl,d,d),order='F')
if lherm:
c[:,:,:,:,0] = (c[:,:,:,:,0]+np.conj(np.moveaxis(c[:,:,:,:,0],2,3)))/2
cv = np.reshape(c[:,:,:,:,0],-1,order='F')
fomval = np.real(2*cv @ l1 - cv @ l2 @ cv)
else:
relunc_fom = 0.1*imprecision
l1f = np.zeros((bdl,bdrp,bdl,bdrp,n-1),dtype=complex)
l2f = np.zeros((bdl,bdr,bdl,bdl,bdr,bdl,n-1),dtype=complex)
fom = np.array([])
iter_fom = 0
while True:
tensors = [c[:,:,:,:,n-1],b[:,:,:,:,n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1f[:,:,:,:,n-2] = ncon(tensors,legs)
tensors = [c[:,:,:,:,n-1],a[:,:,:,:,n-1],c[:,:,:,:,n-1]]
legs = [[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]]
l2f[:,:,:,:,:,:,n-2] = ncon(tensors,legs)
for x in range(n-2,0,-1):
tensors = [c[:,:,:,:,x],b[:,:,:,:,x],l1f[:,:,:,:,x]]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4,-3,-4]]
l1f[:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [c[:,:,:,:,x],a[:,:,:,:,x],c[:,:,:,:,x],l2f[:,:,:,:,:,:,x]]
legs = [[-1,4,1,2],[-2,5,2,3],[-3,6,3,1],[4,5,6,-4,-5,-6]]
l2f[:,:,:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [b[:,:,:,:,0],l1f[:,:,:,:,0]]
legs = [[2,1,-4,-3],[-2,1,-1,2]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [a[:,:,:,:,0],np.eye(d),l2f[:,:,:,:,:,:,0]]
legs = [[2,1,-4,-7],[-8,-3],[-2,1,-6,-1,2,-5]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl*bdl*d*d,bdl*bdl*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*l1
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[:,:,:,:,0] = np.reshape(cv,(bdl,bdl,d,d),order='F')
if lherm:
c[:,:,:,:,0] = (c[:,:,:,:,0]+np.conj(np.moveaxis(c[:,:,:,:,0],2,3)))/2
cv = np.reshape(c[:,:,:,:,0],-1,order='F')
fom = np.append(fom,np.real(2*cv @ l1 - cv @ l2 @ cv))
tensors = [c[:,:,:,:,0],b[:,:,:,:,0]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1c = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],a[:,:,:,:,0],c[:,:,:,:,0]]
legs = [[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]]
l2c = ncon(tensors,legs)
for x in range(1,n-1):
tensors = [l1c,b[:,:,:,:,x],l1f[:,:,:,:,x]]
legs = [[3,4,-1,1],[1,2,-4,-3],[-2,2,3,4]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [l2c,a[:,:,:,:,x],np.eye(d),l2f[:,:,:,:,:,:,x]]
legs = [[3,4,5,-1,1,-5],[1,2,-4,-7],[-8,-3],[-2,2,-6,3,4,5]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl*bdl*d*d,bdl*bdl*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*l1
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[:,:,:,:,x] = np.reshape(cv,(bdl,bdl,d,d),order='F')
if lherm:
c[:,:,:,:,x] = (c[:,:,:,:,x]+np.conj(np.moveaxis(c[:,:,:,:,x],2,3)))/2
cv = np.reshape(c[:,:,:,:,x],-1,order='F')
fom = np.append(fom,np.real(2*cv @ l1 - cv @ l2 @ cv))
tensors = [l1c,c[:,:,:,:,x],b[:,:,:,:,x]]
legs = [[-1,-2,3,4],[3,-3,1,2],[4,-4,2,1]]
l1c = ncon(tensors,legs)
tensors = [l2c,c[:,:,:,:,x],a[:,:,:,:,x],c[:,:,:,:,x]]
legs = [[-1,-2,-3,4,5,6],[4,-4,1,2],[5,-5,2,3],[6,-6,3,1]]
l2c = ncon(tensors,legs)
tensors = [l1c,b[:,:,:,:,n-1]]
legs = [[-2,2,-1,1],[1,2,-4,-3]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [l2c,a[:,:,:,:,n-1],np.eye(d)]
legs = [[-2,2,-6,-1,1,-5],[1,2,-4,-7],[-8,-3]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl*bdl*d*d,bdl*bdl*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*l1
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[:,:,:,:,n-1] = np.reshape(cv,(bdl,bdl,d,d),order='F')
if lherm:
c[:,:,:,:,n-1] = (c[:,:,:,:,n-1]+np.conj(np.moveaxis(c[:,:,:,:,n-1],2,3)))/2
cv = np.reshape(c[:,:,:,:,n-1],-1,order='F')
fom = np.append(fom,np.real(2*cv @ l1 - cv @ l2 @ cv))
iter_fom += 1
if iter_fom >= 2 and all(fom[-2*n:] > 0) and np.std(fom[-2*n:])/np.mean(fom[-2*n:]) <= relunc_fom:
break
fomval = fom[-1]
return fomval,c
def fin_FoMD_OBC_optm(c2d,cpd,a0,imprecision=10**-2):
"""
Optimization of FoMD over MPS for initial wave function. Function for finite size systems with OBC.
Parameters:
c2d: MPO for square of dual of SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
cpd: MPO for dual of generalized derivative of SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
a0: MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
imprecision: expected imprecision of the end results, default value is 10**-2
Returns:
fomdval: optimal value of FoMD
a0: optimal MPS for initial wave function
"""
n = len(a0)
if n == 1:
if np.shape(c2d[0])[0] == 1 and np.shape(cpd[0])[0] == 1 and np.shape(a0[0])[0] == 1:
d = np.shape(a0[0])[2]
tensors = [c2d[0][0,0,:,:]]
legs = [[-1,-2]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(d,d),order='F')
tensors = [cpd[0][0,0,:,:]]
legs = [[-1,-2]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(d,d),order='F')
eiginput = 2*lpd-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ a0v))
a0[0][0,0,:] = np.reshape(a0v,(d),order='F')
fomdval = np.real(fomdval[position])
else:
warnings.warn('Tensor networks with OBC and length one have to have bond dimension equal to one.')
else:
relunc_fomd = 0.1*imprecision
l2df = [0]*n
lpdf = [0]*n
fomd = np.array([])
iter_fomd = 0
while True:
tensors = [np.conj(a0[n-1]),c2d[n-1],a0[n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
l2df[n-2] = ncon(tensors,legs)
l2df[n-2] = l2df[n-2][:,:,:,0,0,0]
tensors = [np.conj(a0[n-1]),cpd[n-1],a0[n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
lpdf[n-2] = ncon(tensors,legs)
lpdf[n-2] = lpdf[n-2][:,:,:,0,0,0]
for x in range(n-2,0,-1):
tensors = [np.conj(a0[x]),c2d[x],a0[x],l2df[x]]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
l2df[x-1] = ncon(tensors,legs)
tensors = [np.conj(a0[x]),cpd[x],a0[x],lpdf[x]]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
lpdf[x-1] = ncon(tensors,legs)
bdpsi1,bdpsi2,d = np.shape(a0[0])
tensors = [c2d[0],l2df[0]]
legs = [[-7,1,-3,-6],[-2,1,-5]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
tensors = [cpd[0],lpdf[0]]
legs = [[-7,1,-3,-6],[-2,1,-5]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
eiginput = 2*lpd-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ a0v))
a0[0] = np.reshape(a0v,(bdpsi1,bdpsi2,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
a0[0] = np.moveaxis(a0[0],2,0)
a0[0] = np.reshape(a0[0],(d*bdpsi1,bdpsi2),order='F')
u,s,vh = np.linalg.svd(a0[0],full_matrices=False)
a0[0] = np.reshape(u,(d,bdpsi1,np.shape(s)[0]),order='F')
a0[0] = np.moveaxis(a0[0],0,2)
tensors = [np.diag(s) @ vh,a0[1]]
legs = [[-1,1],[1,-2,-3]]
a0[1] = ncon(tensors,legs)
tensors = [np.conj(a0[0]),c2d[0],a0[0]]
legs = [[-4,-1,1],[-5,-2,1,2],[-6,-3,2]]
l2dc = ncon(tensors,legs)
l2dc = l2dc[:,:,:,0,0,0]
tensors = [np.conj(a0[0]),cpd[0],a0[0]]
legs = [[-4,-1,1],[-5,-2,1,2],[-6,-3,2]]
lpdc = ncon(tensors,legs)
lpdc = lpdc[:,:,:,0,0,0]
for x in range(1,n-1):
bdpsi1,bdpsi2,d = np.shape(a0[x])
tensors = [l2dc,c2d[x],l2df[x]]
legs = [[-1,1,-4],[1,2,-3,-6],[-2,2,-5]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
tensors = [lpdc,cpd[x],lpdf[x]]
legs = [[-1,1,-4],[1,2,-3,-6],[-2,2,-5]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
eiginput = 2*lpd-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ a0v))
a0[x] = np.reshape(a0v,(bdpsi1,bdpsi2,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
a0[x] = np.moveaxis(a0[x],2,0)
a0[x] = np.reshape(a0[x],(d*bdpsi1,bdpsi2),order='F')
u,s,vh = np.linalg.svd(a0[x],full_matrices=False)
a0[x] = np.reshape(u,(d,bdpsi1,np.shape(s)[0]),order='F')
a0[x] = np.moveaxis(a0[x],0,2)
tensors = [np.diag(s) @ vh,a0[x+1]]
legs = [[-1,1],[1,-2,-3]]
a0[x+1] = ncon(tensors,legs)
tensors = [l2dc,np.conj(a0[x]),c2d[x],a0[x]]
legs = [[3,4,5],[3,-1,1],[4,-2,1,2],[5,-3,2]]
l2dc = ncon(tensors,legs)
tensors = [lpdc,np.conj(a0[x]),cpd[x],a0[x]]
legs = [[3,4,5],[3,-1,1],[4,-2,1,2],[5,-3,2]]
lpdc = ncon(tensors,legs)
bdpsi1,bdpsi2,d = np.shape(a0[n-1])
tensors = [l2dc,c2d[n-1]]
legs = [[-1,1,-4],[1,-7,-3,-6]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
tensors = [lpdc,cpd[n-1]]
legs = [[-1,1,-4],[1,-7,-3,-6]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
eiginput = 2*lpd-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ a0v))
a0[n-1] = np.reshape(a0v,(bdpsi1,bdpsi2,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
iter_fomd += 1
for x in range(n-1,0,-1):
bdpsi1,bdpsi2,d = np.shape(a0[x])
a0[x] = np.moveaxis(a0[x],2,1)
a0[x] = np.reshape(a0[x],(bdpsi1,d*bdpsi2),order='F')
u,s,vh = np.linalg.svd(a0[x],full_matrices=False)
a0[x] = np.reshape(vh,(np.shape(s)[0],d,bdpsi2),order='F')
a0[x] = np.moveaxis(a0[x],1,2)
tensors = [a0[x-1],u @ np.diag(s)]
legs = [[-1,1,-3],[1,-2]]
a0[x-1] = ncon(tensors,legs)
if iter_fomd >= 2 and all(fomd[-2*n:] > 0) and np.std(fomd[-2*n:])/np.mean(fomd[-2*n:]) <= relunc_fomd:
break
fomdval = fomd[-1]
return fomdval,a0
def fin_FoMD_PBC_optm(c2d,cpd,a0,imprecision=10**-2):
"""
Optimization of FoMD over MPS for initial wave function. Function for finite size systems with PBC.
Parameters:
c2d: MPO for square of dual of SLD, expected ndarray of a shape (bd,bd,d,d,n)
cpd: MPO for dual of generalized derivative of SLD, expected ndarray of a shape (bd,bd,d,d,n)
a0: MPS for initial wave function, expected ndarray of a shape (bd,bd,d,n)
imprecision: expected imprecision of the end results, default value is 10**-2
Returns:
fomdval: optimal value of FoMD
a0: optimal MPS for initial wave function
"""
n = np.shape(c2d)[4]
d = np.shape(c2d)[2]
bdl2d = np.shape(c2d)[0]
bdlpd = np.shape(cpd)[0]
bdpsi = np.shape(a0)[0]
tol_fomd = 0.1*imprecision/n**2
if n == 1:
tensors = [c2d[:,:,:,:,0],np.eye(bdpsi),np.eye(bdpsi)]
legs = [[1,1,-3,-6],[-2,-1],[-5,-4]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [cpd[:,:,:,:,0],np.eye(bdpsi),np.eye(bdpsi)]
legs = [[1,1,-3,-6],[-2,-1],[-5,-4]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [np.eye(bdpsi),np.eye(bdpsi)]
legs = [[-2,-1],[-4,-3]]
psinorm = ncon(tensors,legs)
psinorm = np.reshape(psinorm,(bdpsi*bdpsi,bdpsi*bdpsi),order='F')
psinorm = (psinorm+np.conj(psinorm).T)/2
psinormpinv = np.linalg.pinv(psinorm,tol_fomd,hermitian=True)
psinormpinv = (psinormpinv+np.conj(psinormpinv).T)/2
psinormpinv = np.kron(np.eye(d),psinormpinv)
eiginput = 2*lpd-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
eiginput = psinormpinv @ eiginput
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ np.kron(np.eye(d),psinorm) @ a0v))
a0[:,:,:,0] = np.reshape(a0v,(bdpsi,bdpsi,d),order='F')
fomdval = np.real(fomdval[position])
else:
relunc_fomd = 0.1*imprecision
l2df = np.zeros((bdpsi,bdl2d,bdpsi,bdpsi,bdl2d,bdpsi,n-1),dtype=complex)
lpdf = np.zeros((bdpsi,bdlpd,bdpsi,bdpsi,bdlpd,bdpsi,n-1),dtype=complex)
psinormf = np.zeros((bdpsi,bdpsi,bdpsi,bdpsi,n-1),dtype=complex)
fomd = np.array([])
iter_fomd = 0
while True:
tensors = [np.conj(a0[:,:,:,n-1]),c2d[:,:,:,:,n-1],a0[:,:,:,n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
l2df[:,:,:,:,:,:,n-2] = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,n-1]),cpd[:,:,:,:,n-1],a0[:,:,:,n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
lpdf[:,:,:,:,:,:,n-2] = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,n-1]),a0[:,:,:,n-1]]
legs = [[-1,-3,1],[-2,-4,1]]
psinormf[:,:,:,:,n-2] = ncon(tensors,legs)
for x in range(n-2,0,-1):
tensors = [np.conj(a0[:,:,:,x]),c2d[:,:,:,:,x],a0[:,:,:,x],l2df[:,:,:,:,:,:,x]]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5,-4,-5,-6]]
l2df[:,:,:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,x]),cpd[:,:,:,:,x],a0[:,:,:,x],lpdf[:,:,:,:,:,:,x]]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5,-4,-5,-6]]
lpdf[:,:,:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,x]),a0[:,:,:,x],psinormf[:,:,:,:,x]]
legs = [[-1,2,1],[-2,3,1],[2,3,-3,-4]]
psinormf[:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [c2d[:,:,:,:,0],l2df[:,:,:,:,:,:,0]]
legs = [[2,1,-3,-6],[-2,1,-5,-1,2,-4]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [cpd[:,:,:,:,0],lpdf[:,:,:,:,:,:,0]]
legs = [[2,1,-3,-6],[-2,1,-5,-1,2,-4]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [psinormf[:,:,:,:,0]]
legs = [[-2,-4,-1,-3]]
psinorm = ncon(tensors,legs)
psinorm = np.reshape(psinorm,(bdpsi*bdpsi,bdpsi*bdpsi),order='F')
psinorm = (psinorm+np.conj(psinorm).T)/2
psinormpinv = np.linalg.pinv(psinorm,tol_fomd,hermitian=True)
psinormpinv = (psinormpinv+np.conj(psinormpinv).T)/2
psinormpinv = np.kron(np.eye(d),psinormpinv)
eiginput = 2*lpd-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
eiginput = psinormpinv @ eiginput
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ np.kron(np.eye(d),psinorm) @ a0v))
a0[:,:,:,0] = np.reshape(a0v,(bdpsi,bdpsi,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
tensors = [np.conj(a0[:,:,:,0]),c2d[:,:,:,:,0],a0[:,:,:,0]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
l2dc = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),cpd[:,:,:,:,0],a0[:,:,:,0]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
lpdc = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),a0[:,:,:,0]]
legs = [[-1,-3,1],[-2,-4,1]]
psinormc = ncon(tensors,legs)
for x in range(1,n-1):
tensors = [l2dc,c2d[:,:,:,:,x],l2df[:,:,:,:,:,:,x]]
legs = [[3,4,5,-1,1,-4],[1,2,-3,-6],[-2,2,-5,3,4,5]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [lpdc,cpd[:,:,:,:,x],lpdf[:,:,:,:,:,:,x]]
legs = [[3,4,5,-1,1,-4],[1,2,-3,-6],[-2,2,-5,3,4,5]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [psinormc,psinormf[:,:,:,:,x]]
legs = [[1,2,-1,-3],[-2,-4,1,2]]
psinorm = ncon(tensors,legs)
psinorm = np.reshape(psinorm,(bdpsi*bdpsi,bdpsi*bdpsi),order='F')
psinorm = (psinorm+np.conj(psinorm).T)/2
psinormpinv = np.linalg.pinv(psinorm,tol_fomd,hermitian=True)
psinormpinv = (psinormpinv+np.conj(psinormpinv).T)/2
psinormpinv = np.kron(np.eye(d),psinormpinv)
eiginput = 2*lpd-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
eiginput = psinormpinv @ eiginput
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ np.kron(np.eye(d),psinorm) @ a0v))
a0[:,:,:,x] = np.reshape(a0v,(bdpsi,bdpsi,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
tensors = [l2dc,np.conj(a0[:,:,:,x]),c2d[:,:,:,:,x],a0[:,:,:,x]]
legs = [[-1,-2,-3,3,4,5],[3,-4,1],[4,-5,1,2],[5,-6,2]]
l2dc = ncon(tensors,legs)
tensors = [lpdc,np.conj(a0[:,:,:,x]),cpd[:,:,:,:,x],a0[:,:,:,x]]
legs = [[-1,-2,-3,3,4,5],[3,-4,1],[4,-5,1,2],[5,-6,2]]
lpdc = ncon(tensors,legs)
tensors = [psinormc,np.conj(a0[:,:,:,x]),a0[:,:,:,x]]
legs = [[-1,-2,2,3],[2,-3,1],[3,-4,1]]
psinormc = ncon(tensors,legs)
tensors = [l2dc,c2d[:,:,:,:,n-1]]
legs = [[-2,2,-5,-1,1,-4],[1,2,-3,-6]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [lpdc,cpd[:,:,:,:,n-1]]
legs = [[-2,2,-5,-1,1,-4],[1,2,-3,-6]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [psinormc]
legs = [[-2,-4,-1,-3]]
psinorm = ncon(tensors,legs)
psinorm = np.reshape(psinorm,(bdpsi*bdpsi,bdpsi*bdpsi),order='F')
psinorm = (psinorm+np.conj(psinorm).T)/2
psinormpinv = np.linalg.pinv(psinorm,tol_fomd,hermitian=True)
psinormpinv = (psinormpinv+np.conj(psinormpinv).T)/2
psinormpinv = np.kron(np.eye(d),psinormpinv)
eiginput = 2*lpd-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
eiginput = psinormpinv @ eiginput
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ np.kron(np.eye(d),psinorm) @ a0v))
a0[:,:,:,n-1] = np.reshape(a0v,(bdpsi,bdpsi,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
iter_fomd += 1
if iter_fomd >= 2 and all(fomd[-2*n:] > 0) and np.std(fomd[-2*n:])/np.mean(fomd[-2*n:]) <= relunc_fomd:
break
fomdval = fomd[-1]
return fomdval,a0
def fin_FoM_OBC_val(a,b,c):
"""
Calculate the value of FoM. Function for finite size systems with OBC.
Parameters:
a: MPO for density matrix, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
b: MPO for generalized derivative of density matrix, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
c: MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
Returns:
fomval: value of FoM
"""
n = len(c)
if n == 1:
if np.shape(a[0])[0] == 1 and np.shape(b[0])[0] == 1 and np.shape(c[0])[0] == 1:
tensors = [c[0][0,0,:,:],b[0][0:,0,:,:]]
legs = [[1,2],[2,1]]
l1 = ncon(tensors,legs)
tensors = [c[0][0,0,:,:],[0][0,0,:,:],[0][0,0,:,:]]
legs = [[1,2],[2,3],[3,1]]
l2 = ncon(tensors,legs)
fomval = 2*l1-l2
else:
warnings.warn('Tensor networks with OBC and length one have to have bond dimension equal to one.')
else:
tensors = [c[n-1],b[n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1 = ncon(tensors,legs)
l1 = l1[:,:,0,0]
tensors = [c[n-1],a[n-1],c[n-1]]
legs = [[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]]
l2 = ncon(tensors,legs)
l2 = l2[:,:,:,0,0,0]
for x in range(n-2,0,-1):
tensors = [c[x],b[x],l1]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4]]
l1 = ncon(tensors,legs)
tensors = [c[x],a[x],c[x],l2]
legs = [[-1,4,1,2],[-2,5,2,3],[-3,6,3,1],[4,5,6]]
l2 = ncon(tensors,legs)
tensors = [c[0],b[0],l1]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4]]
l1 = ncon(tensors,legs)
l1 = float(l1)
tensors = [c[0],a[0],c[0],l2]
legs = [[-1,4,1,2],[-2,5,2,3],[-3,6,3,1],[4,5,6]]
l2 = ncon(tensors,legs)
l2 = float(l2)
fomval = 2*l1-l2
return fomval
def fin_FoM_PBC_val(a,b,c):
"""
Calculate the value of FoM. Function for finite size systems with PBC.
Parameters:
a: MPO for a density matrix, expected ndarray of a shape (bd,bd,d,d,n)
b: MPO for generalized derivative of a density matrix, expected ndarray of a shape (bd,bd,d,d,n)
c: MPO for the SLD, expected ndarray of a shape (bd,bd,d,d,n)
Returns:
fomval: value of FoM
"""
n = np.shape(a)[4]
if n == 1:
tensors = [c[:,:,:,:,0],b[:,:,:,:,0]]
legs = [[3,3,1,2],[4,4,2,1]]
l1 = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],a[:,:,:,:,0],c[:,:,:,:,0]]
legs = [[4,4,1,2],[5,5,2,3],[6,6,3,1]]
l2 = ncon(tensors,legs)
fomval = 2*l1-l2
else:
tensors = [c[:,:,:,:,n-1],b[:,:,:,:,n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1 = ncon(tensors,legs)
tensors = [c[:,:,:,:,n-1],a[:,:,:,:,n-1],c[:,:,:,:,n-1]]
legs = [[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]]
l2 = ncon(tensors,legs)
for x in range(n-2,0,-1):
tensors = [c[:,:,:,:,x],b[:,:,:,:,x],l1]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4,-3,-4]]
l1 = ncon(tensors,legs)
tensors = [c[:,:,:,:,x],a[:,:,:,:,x],c[:,:,:,:,x],l2]
legs = [[-1,4,1,2],[-2,5,2,3],[-3,6,3,1],[4,5,6,-4,-5,-6]]
l2 = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],b[:,:,:,:,0],l1]
legs = [[5,3,1,2],[6,4,2,1],[3,4,5,6]]
l1 = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],a[:,:,:,:,0],c[:,:,:,:,0],l2]
legs = [[7,4,1,2],[8,5,2,3],[9,6,3,1],[4,5,6,7,8,9]]
l2 = ncon(tensors,legs)
fomval = 2*l1-l2
return fomval
def fin_FoMD_OBC_val(c2d,cpd,a0):
"""
Calculate value of FoMD. Function for finite size systems with OBC.
Parameters:
c2d: MPO for square of dual of SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
cpd: MPO for dual of generalized derivative of SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
a0: MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
Returns:
fomdval: value of FoMD
"""
n = len(a0)
if n == 1:
if np.shape(c2d[0])[0] == 1 and np.shape(cpd[0])[0] == 1 and np.shape(a0[0])[0] == 1:
tensors = [np.conj(a0[0][0,0,:]),c2d[0][0,0,:,:],a0[0][0,0,:]]
legs = [[1],[1,2],[2]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[0][0,0,:]),cpd[0][0,0,:,:],a0[0][0,0,:]]
legs = [[1],[1,2],[2]]
lpd = ncon(tensors,legs)
fomdval = 2*lpd-l2d
else:
warnings.warn('Tensor networks with OBC and length one have to have bond dimension equal to one.')
else:
tensors = [np.conj(a0[n-1]),c2d[n-1],a0[n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
l2d = ncon(tensors,legs)
l2d = l2d[:,:,:,0,0,0]
tensors = [np.conj(a0[n-1]),cpd[n-1],a0[n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
lpd = ncon(tensors,legs)
lpd = lpd[:,:,:,0,0,0]
for x in range(n-2,0,-1):
tensors = [np.conj(a0[x]),c2d[x],a0[x],l2d]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[x]),cpd[x],a0[x],lpd]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
lpd = ncon(tensors,legs)
tensors = [np.conj(a0[0]),c2d[0],a0[0],l2d]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
l2d = ncon(tensors,legs)
l2d = float(l2d)
tensors = [np.conj(a0[0]),cpd[0],a0[0],lpd]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
lpd = ncon(tensors,legs)
lpd = float(lpd)
fomdval = 2*lpd-l2d
return fomdval
def fin_FoMD_PBC_val(c2d,cpd,a0):
"""
Calculate the value of FoMD. Function for finite size systems with PBC.
Parameters:
c2d: MPO for square of dual of the SLD, expected ndarray of a shape (bd,bd,d,d,n)
cpd: MPO for dual of generalized derivative of the SLD, expected ndarray of a shape (bd,bd,d,d,n)
a0: MPS for the initial wave function, expected ndarray of a shape (bd,bd,d,n)
Returns:
fomdval: value of FoMD
"""
n = np.shape(c2d)[4]
if n == 1:
tensors = [np.conj(a0[:,:,:,0]),c2d[:,:,:,:,0],a0[:,:,:,0]]
legs = [[3,3,1],[4,4,1,2],[5,5,2]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),cpd[:,:,:,:,0],a0[:,:,:,0]]
legs = [[3,3,1],[4,4,1,2],[5,5,2]]
lpd = ncon(tensors,legs)
fomdval = 2*lpd-l2d
else:
tensors = [np.conj(a0[:,:,:,n-1]),c2d[:,:,:,:,n-1],a0[:,:,:,n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,n-1]),cpd[:,:,:,:,n-1],a0[:,:,:,n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
lpd = ncon(tensors,legs)
for x in range(n-2,0,-1):
tensors = [np.conj(a0[:,:,:,x]),c2d[:,:,:,:,x],a0[:,:,:,x],l2d]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5,-4,-5,-6]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,x]),cpd[:,:,:,:,x],a0[:,:,:,x],lpd]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5,-4,-5,-6]]
lpd = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),c2d[:,:,:,:,0],a0[:,:,:,0],l2d]
legs = [[6,3,1],[7,4,1,2],[8,5,2],[3,4,5,6,7,8]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),cpd[:,:,:,:,0],a0[:,:,:,0],lpd]
legs = [[6,3,1],[7,4,1,2],[8,5,2],[3,4,5,6,7,8]]
lpd = ncon(tensors,legs)
fomdval = 2*lpd-l2d
return fomdval
#################################################################
# 1.2.2 Problems with discrete approximation of the derivative. #
#################################################################
def fin2_FoM_FoMD_optbd(n,d,bc,ch,chp,epsilon,cini=None,a0ini=None,imprecision=10**-2,bdlmax=100,alwaysbdlmax=False,lherm=True,bdpsimax=100,alwaysbdpsimax=False):
"""
Iterative optimization of FoM/FoMD over SLD MPO and initial wave function MPS and also a check of convergence with increasing bond dimensions. Function for finite size systems. Version with two channels separated by epsilon.
Parameters:
n: number of sites in TN
d: dimension of the local Hilbert space (dimension of the physical index)
bc: boundary conditions, 'O' for OBC, 'P' for PBC
ch: MPO for a quantum channel at the value of estimated parameter phi=phi_0, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC
chp: MPO for a quantum channel at the value of estimated parameter phi=phi_0+epsilon, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC
epsilon: value of a separation between estimated parameters encoded in ch and chp, float
cini: initial MPO for the SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
a0ini: initial MPS for the initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,n) for PBC
imprecision: expected imprecision of the end results, default value is 10**-2
bdlmax: maximal value of bd for SLD MPO, default value is 100
alwaysbdlmax: boolean value, True if the maximal value of bd for SLD MPO has to be reached, otherwise False (default value)
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
bdpsimax: maximal value of bd for the initial wave function MPS, default value is 100
alwaysbdpsimax: boolean value, True if the maximal value of bd for initial wave function MPS has to be reached, otherwise False (default value)
Returns:
result: optimal value of FoM/FoMD
resultm: matrix describing FoM/FoMD as a function of bd of respectively SLD MPO [rows] and the initial wave function MPS [columns]
c: optimal MPO for SLD
a0: optimal MPS for initial wave function
"""
while True:
if a0ini is None:
bdpsi = 1
a0 = np.zeros(d,dtype=complex)
for i in range(d):
a0[i] = np.sqrt(math.comb(d-1,i))*2**(-(d-1)/2) # prod
# a0[i] = np.sqrt(2/(d+1))*np.sin((1+i)*np.pi/(d+1)) # sine
if bc == 'O':
a0 = a0[np.newaxis,np.newaxis,:]
a0 = [a0]*n
elif bc == 'P':
a0 = a0[np.newaxis,np.newaxis,:,np.newaxis]
a0 = np.tile(a0,(1,1,1,n))
else:
a0 = a0ini
if bc == 'O':
bdpsi = max([np.shape(a0[i])[0] for i in range(n)])
a0 = [a0[i].astype(complex) for i in range(n)]
elif bc == 'P':
bdpsi = np.shape(a0)[0]
a0 = a0.astype(complex)
if cini is None:
bdl = 1
rng = np.random.default_rng()
if bc == 'O':
c = [0]*n
c[0] = (rng.random((1,bdl,d,d)) + 1j*rng.random((1,bdl,d,d)))/bdl
c[0] = (c[0] + np.conj(np.moveaxis(c[0],2,3)))/2
for x in range(1,n-1):
c[x] = (rng.random((bdl,bdl,d,d)) + 1j*rng.random((bdl,bdl,d,d)))/bdl
c[x] = (c[x] + np.conj(np.moveaxis(c[x],2,3)))/2
c[n-1] = (rng.random((bdl,1,d,d)) + 1j*rng.random((bdl,1,d,d)))/bdl
c[n-1] = (c[n-1] + np.conj(np.moveaxis(c[n-1],2,3)))/2
elif bc == 'P':
c = (rng.random((bdl,bdl,d,d,n)) + 1j*rng.random((bdl,bdl,d,d,n)))/bdl
c = (c + np.conj(np.moveaxis(c,2,3)))/2
else:
c = cini
if bc == 'O':
bdl = max([np.shape(c[i])[0] for i in range(n)])
c = [c[i].astype(complex) for i in range(n)]
elif bc == 'P':
bdl = np.shape(c)[0]
c = c.astype(complex)
resultm = np.zeros((bdlmax,bdpsimax),dtype=float)
resultm[bdl-1,bdpsi-1],c,a0 = fin2_FoM_FoMD_optm(n,d,bc,c,a0,ch,chp,epsilon,imprecision,lherm)
if bc == 'O' and n == 1:
resultm = resultm[0:bdl,0:bdpsi]
result = resultm[bdl-1,bdpsi-1]
return result,resultm,c,a0
factorv = np.array([0.5,0.25,0.1,1,0.01])
problem = False
while True:
while True:
if bdpsi == bdpsimax:
break
else:
a0old = a0
bdpsi += 1
i = 0
while True:
a0 = fin_enlarge_bdpsi(a0,factorv[i])
resultm[bdl-1,bdpsi-1],cnew,a0new = fin2_FoM_FoMD_optm(n,d,bc,c,a0,ch,chp,epsilon,imprecision,lherm)
if resultm[bdl-1,bdpsi-1] >= resultm[bdl-1,bdpsi-2]:
break
i += 1
if i == np.size(factorv):
problem = True
break
if problem:
break
if not(alwaysbdpsimax) and resultm[bdl-1,bdpsi-1] < (1+imprecision)*resultm[bdl-1,bdpsi-2]:
bdpsi += -1
a0 = a0old
a0copy = a0new
ccopy = cnew
break
else:
a0 = a0new
c = cnew
if problem:
break
if bdl == bdlmax:
if bdpsi == bdpsimax:
resultm = resultm[0:bdl,0:bdpsi]
result = resultm[bdl-1,bdpsi-1]
else:
a0 = a0copy
c = ccopy
resultm = resultm[0:bdl,0:bdpsi+1]
result = resultm[bdl-1,bdpsi]
break
else:
bdl += 1
i = 0
while True:
c = fin_enlarge_bdl(c,factorv[i])
resultm[bdl-1,bdpsi-1],cnew,a0new = fin2_FoM_FoMD_optm(n,d,bc,c,a0,ch,chp,epsilon,imprecision,lherm)
if resultm[bdl-1,bdpsi-1] >= resultm[bdl-2,bdpsi-1]:
a0 = a0new
c = cnew
break
i += 1
if i == np.size(factorv):
problem = True
break
if problem:
break
if not(alwaysbdlmax) and resultm[bdl-1,bdpsi-1] < (1+imprecision)*resultm[bdl-2,bdpsi-1]:
if bdpsi == bdpsimax:
resultm = resultm[0:bdl,0:bdpsi]
result = resultm[bdl-1,bdpsi-1]
else:
if resultm[bdl-1,bdpsi-1] < resultm[bdl-2,bdpsi]:
a0 = a0copy
c = ccopy
resultm = resultm[0:bdl,0:bdpsi+1]
bdl += -1
bdpsi += 1
result = resultm[bdl-1,bdpsi-1]
else:
resultm = resultm[0:bdl,0:bdpsi+1]
result = resultm[bdl-1,bdpsi-1]
break
if not(problem):
break
return result,resultm,c,a0
def fin2_FoM_optbd(n,d,bc,a,b,epsilon,cini=None,imprecision=10**-2,bdlmax=100,alwaysbdlmax=False,lherm=True):
"""
Optimization of FoM over SLD MPO and also check of convergence in bond dimension. Function for finite size systems. Version with two states separated by epsilon.
Parameters:
n: number of sites in TN
d: dimension of local Hilbert space (dimension of physical index)
bc: boundary conditions, 'O' for OBC, 'P' for PBC
a: MPO for the density matrix at the value of estimated parameter phi=phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
b: MPO for the density matrix at the value of estimated parameter phi=phi_0+epsilon, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
epsilon: value of a separation between estimated parameters encoded in a and b, float
cini: initial MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
imprecision: expected imprecision of the end results, default value is 10**-2
bdlmax: maximal value of bd for SLD MPO, default value is 100
alwaysbdlmax: boolean value, True if maximal value of bd for SLD MPO have to be reached, otherwise False (default value)
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
result: optimal value of FoM
resultv: vector describing FoM as a function of bd of the SLD MPO
c: optimal MPO for SLD
"""
while True:
if cini is None:
bdl = 1
rng = np.random.default_rng()
if bc == 'O':
c = [0]*n
c[0] = (rng.random((1,bdl,d,d)) + 1j*rng.random((1,bdl,d,d)))/bdl
c[0] = (c[0] + np.conj(np.moveaxis(c[0],2,3)))/2
for x in range(1,n-1):
c[x] = (rng.random((bdl,bdl,d,d)) + 1j*rng.random((bdl,bdl,d,d)))/bdl
c[x] = (c[x] + np.conj(np.moveaxis(c[x],2,3)))/2
c[n-1] = (rng.random((bdl,1,d,d)) + 1j*rng.random((bdl,1,d,d)))/bdl
c[n-1] = (c[n-1] + np.conj(np.moveaxis(c[n-1],2,3)))/2
elif bc == 'P':
c = (rng.random((bdl,bdl,d,d,n)) + 1j*rng.random((bdl,bdl,d,d,n)))/bdl
c = (c + np.conj(np.moveaxis(c,2,3)))/2
else:
c = cini
if bc == 'O':
bdl = max([np.shape(c[i])[0] for i in range(n)])
c = [c[i].astype(complex) for i in range(n)]
elif bc == 'P':
bdl = np.shape(c)[0]
c = c.astype(complex)
resultv = np.zeros(bdlmax,dtype=float)
if bc == 'O':
resultv[bdl-1],c = fin2_FoM_OBC_optm(a,b,epsilon,c,imprecision,lherm)
if n == 1:
resultv = resultv[0:bdl]
result = resultv[bdl-1]
return result,resultv,c
elif bc == 'P':
resultv[bdl-1],c = fin2_FoM_PBC_optm(a,b,epsilon,c,imprecision,lherm)
factorv = np.array([0.5,0.25,0.1,1,0.01])
problem = False
while True:
if bdl == bdlmax:
resultv = resultv[0:bdl]
result = resultv[bdl-1]
break
else:
bdl += 1
i = 0
while True:
c = fin_enlarge_bdl(c,factorv[i])
if bc == 'O':
resultv[bdl-1],cnew = fin2_FoM_OBC_optm(a,b,epsilon,c,imprecision,lherm)
elif bc == 'P':
resultv[bdl-1],cnew = fin2_FoM_PBC_optm(a,b,epsilon,c,imprecision,lherm)
if resultv[bdl-1] >= resultv[bdl-2]:
c = cnew
break
i += 1
if i == np.size(factorv):
problem = True
break
if problem:
break
if not(alwaysbdlmax) and resultv[bdl-1] < (1+imprecision)*resultv[bdl-2]:
resultv = resultv[0:bdl]
result = resultv[bdl-1]
break
if not(problem):
break
return result,resultv,c
def fin2_FoMD_optbd(n,d,bc,c2d,cd,cpd,epsilon,a0ini=None,imprecision=10**-2,bdpsimax=100,alwaysbdpsimax=False):
"""
Optimization of FoMD over initial wave function MPS and also check of convergence when increasing the bond dimension. Function for finite size systems. Version with two dual SLDs separated by epsilon.
Parameters:
n: number of sites in TN
d: dimension of local Hilbert space (dimension of physical index)
bc: boundary conditions, 'O' for OBC, 'P' for PBC
c2d: MPO for square of dual of SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
cd: MPO for dual of SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
cpd: MPO for dual of SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
epsilon: value of a separation between estimated parameters encoded in cd and cpd, float
a0ini: initial MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,n) for PBC
imprecision: expected imprecision of the end results, default value is 10**-2
bdpsimax: maximal value of bd for initial wave function MPS, default value is 100
alwaysbdpsimax: boolean value, True if maximal value of bd for initial wave function MPS have to be reached, otherwise False (default value)
Returns:
result: optimal value of FoMD
resultv: vector describing FoMD in function of bd of initial wave function MPS
a0: optimal MPS for initial wave function
"""
while True:
if a0ini is None:
bdpsi = 1
a0 = np.zeros(d,dtype=complex)
for i in range(d):
a0[i] = np.sqrt(math.comb(d-1,i))*2**(-(d-1)/2) # prod
# a0[i] = np.sqrt(2/(d+1))*np.sin((1+i)*np.pi/(d+1)) # sine
if bc == 'O':
a0 = a0[np.newaxis,np.newaxis,:]
a0 = [a0]*n
elif bc == 'P':
a0 = a0[np.newaxis,np.newaxis,:,np.newaxis]
a0 = np.tile(a0,(1,1,1,n))
else:
a0 = a0ini
if bc == 'O':
bdpsi = max([np.shape(a0[i])[0] for i in range(n)])
a0 = [a0[i].astype(complex) for i in range(n)]
elif bc == 'P':
bdpsi = np.shape(a0)[0]
a0 = a0.astype(complex)
resultv = np.zeros(bdpsimax,dtype=float)
if bc == 'O':
resultv[bdpsi-1],a0 = fin2_FoMD_OBC_optm(c2d,cd,cpd,epsilon,a0,imprecision)
if n == 1:
resultv = resultv[0:bdpsi]
result = resultv[bdpsi-1]
return result,resultv,a0
elif bc == 'P':
resultv[bdpsi-1],a0 = fin2_FoMD_PBC_optm(c2d,cd,cpd,epsilon,a0,imprecision)
factorv = np.array([0.5,0.25,0.1,1,0.01])
problem = False
while True:
if bdpsi == bdpsimax:
resultv = resultv[0:bdpsi]
result = resultv[bdpsi-1]
break
else:
bdpsi += 1
i = 0
while True:
a0 = fin_enlarge_bdpsi(a0,factorv[i])
if bc == 'O':
resultv[bdpsi-1],a0new = fin2_FoMD_OBC_optm(c2d,cd,cpd,epsilon,a0,imprecision)
elif bc == 'P':
resultv[bdpsi-1],a0new = fin2_FoMD_PBC_optm(c2d,cd,cpd,epsilon,a0,imprecision)
if resultv[bdpsi-1] >= resultv[bdpsi-2]:
a0 = a0new
break
i += 1
if i == np.size(factorv):
problem = True
break
if problem:
break
if not(alwaysbdpsimax) and resultv[bdpsi-1] < (1+imprecision)*resultv[bdpsi-2]:
resultv = resultv[0:bdpsi]
result = resultv[bdpsi-1]
break
if not(problem):
break
return result,resultv,a0
def fin2_FoM_FoMD_optm(n,d,bc,c,a0,ch,chp,epsilon,imprecision=10**-2,lherm=True):
"""
Iterative optimization of FoM/FoMD over SLD MPO and initial wave function MPS. Function for finite size systems. Version with two channels separated by epsilon.
Parameters:
n: number of sites in TN
d: dimension of local Hilbert space (dimension of physical index)
bc: boundary conditions, 'O' for OBC, 'P' for PBC
c: MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC
a0: MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,n) for PBC
ch: MPO for quantum channel at the value of estimated parameter phi=phi_0, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC
chp: MPO for quantum channel at the value of estimated parameter phi=phi_0+epsilon, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC
epsilon: value of a separation between estimated parameters encoded in ch and chp, float
imprecision: expected imprecision of the end results, default value is 10**-2
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
fval: optimal value of FoM/FoMD
c: optimal MPO for SLD
a0: optimal MPS for initial wave function
"""
relunc_f = 0.1*imprecision
if bc == 'O':
chd = [0]*n
chpd = [0]*n
for x in range(n):
chd[x] = np.conj(np.moveaxis(ch[x],2,3))
chpd[x] = np.conj(np.moveaxis(chp[x],2,3))
elif bc == 'P':
chd = np.conj(np.moveaxis(ch,2,3))
chpd = np.conj(np.moveaxis(chp,2,3))
f = np.array([])
iter_f = 0
while True:
a0_dm = wave_function_to_density_matrix(a0)
a = channel_acting_on_operator(ch,a0_dm)
b = channel_acting_on_operator(chp,a0_dm)
if bc == 'O':
fom,c = fin2_FoM_OBC_optm(a,b,epsilon,c,imprecision,lherm)
elif bc == 'P':
fom,c = fin2_FoM_PBC_optm(a,b,epsilon,c,imprecision,lherm)
f = np.append(f,fom)
if iter_f >= 2 and np.std(f[-4:])/np.mean(f[-4:]) <= relunc_f:
break
if bc == 'O':
c2 = [0]*n
for x in range(n):
bdl1 = np.shape(c[x])[0]
bdl2 = np.shape(c[x])[1]
c2[x] = np.zeros((bdl1**2,bdl2**2,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
for nxpp in range(d):
c2[x][:,:,nx,nxp] = c2[x][:,:,nx,nxp]+np.kron(c[x][:,:,nx,nxpp],c[x][:,:,nxpp,nxp])
elif bc == 'P':
bdl = np.shape(c)[0]
c2 = np.zeros((bdl**2,bdl**2,d,d,n),dtype=complex)
for nx in range(d):
for nxp in range(d):
for nxpp in range(d):
for x in range(n):
c2[:,:,nx,nxp,x] = c2[:,:,nx,nxp,x]+np.kron(c[:,:,nx,nxpp,x],c[:,:,nxpp,nxp,x])
c2d = channel_acting_on_operator(chd,c2)
cd = channel_acting_on_operator(chd,c)
cpd = channel_acting_on_operator(chpd,c)
if bc == 'O':
fomd,a0 = fin2_FoMD_OBC_optm(c2d,cd,cpd,epsilon,a0,imprecision)
elif bc == 'P':
fomd,a0 = fin2_FoMD_PBC_optm(c2d,cd,cpd,epsilon,a0,imprecision)
f = np.append(f,fomd)
iter_f += 1
fval = f[-1]
return fval,c,a0
def fin2_FoM_OBC_optm(a,b,epsilon,c,imprecision=10**-2,lherm=True):
"""
Optimization of FoM over MPO for SLD. Function for finite size systems with OBC. Version with two states separated by epsilon.
Parameters:
a: MPO for the density matrix at the value of estimated parameter phi=phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
b: MPO for the density matrix at the value of estimated parameter phi=phi_0+epsilon, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
epsilon: value of a separation between estimated parameters encoded in a and b, float
c: MPO for the SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
imprecision: expected imprecision of the end results, default value is 10**-2
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
fomval: optimal value of FoM
c: optimal MPO for SLD
"""
n = len(c)
tol_fom = 0.1*imprecision/n**2
if n == 1:
if np.shape(a[0])[0] == 1 and np.shape(b[0])[0] == 1 and np.shape(c[0])[0] == 1:
d = np.shape(c[0])[2]
tensors = [b[0][0,0,:,:]]
legs = [[-2,-1]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [a[0][0,0,:,:]]
legs = [[-2,-1]]
l1_0 = ncon(tensors,legs)
l1_0 = np.reshape(l1_0,-1,order='F')
tensors = [a[0][0,0,:,:],np.eye(d)]
legs = [[-2,-3],[-4,-1]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(d*d,d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*(l1-l1_0)/epsilon
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[0][0,0,:,:] = np.reshape(cv,(d,d),order='F')
if lherm:
c[0] = (c[0]+np.conj(np.moveaxis(c[0],2,3)))/2
cv = np.reshape(c[0],-1,order='F')
fomval = np.real(2*cv @ (l1-l1_0)/epsilon - cv @ l2 @ cv)
else:
warnings.warn('Tensor networks with OBC and length one have to have bond dimension equal to one.')
else:
relunc_fom = 0.1*imprecision
l1f = [0]*n
l1_0f = [0]*n
l2f = [0]*n
fom = np.array([])
iter_fom = 0
while True:
tensors = [c[n-1],b[n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1f[n-2] = ncon(tensors,legs)
l1f[n-2] = l1f[n-2][:,:,0,0]
tensors = [c[n-1],a[n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1_0f[n-2] = ncon(tensors,legs)
l1_0f[n-2] = l1_0f[n-2][:,:,0,0]
tensors = [c[n-1],a[n-1],c[n-1]]
legs = [[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]]
l2f[n-2] = ncon(tensors,legs)
l2f[n-2] = l2f[n-2][:,:,:,0,0,0]
for x in range(n-2,0,-1):
tensors = [c[x],b[x],l1f[x]]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4]]
l1f[x-1] = ncon(tensors,legs)
tensors = [c[x],a[x],l1_0f[x]]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4]]
l1_0f[x-1] = ncon(tensors,legs)
tensors = [c[x],a[x],c[x],l2f[x]]
legs = [[-1,4,1,2],[-2,5,2,3],[-3,6,3,1],[4,5,6]]
l2f[x-1] = ncon(tensors,legs)
bdl1,bdl2,d,d = np.shape(c[0])
tensors = [b[0],l1f[0]]
legs = [[-5,1,-4,-3],[-2,1]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [a[0],l1_0f[0]]
legs = [[-5,1,-4,-3],[-2,1]]
l1_0 = ncon(tensors,legs)
l1_0 = np.reshape(l1_0,-1,order='F')
tensors = [a[0],np.eye(d),l2f[0]]
legs = [[-9,1,-4,-7],[-8,-3],[-2,1,-6]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl1*bdl2*d*d,bdl1*bdl2*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*(l1-l1_0)/epsilon
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[0] = np.reshape(cv,(bdl1,bdl2,d,d),order='F')
if lherm:
c[0] = (c[0]+np.conj(np.moveaxis(c[0],2,3)))/2
cv = np.reshape(c[0],-1,order='F')
fom = np.append(fom,np.real(2*cv @ (l1-l1_0)/epsilon - cv @ l2 @ cv))
tensors = [c[0],b[0]]
legs = [[-3,-1,1,2],[-4,-2,2,1]]
l1c = ncon(tensors,legs)
l1c = l1c[:,:,0,0]
tensors = [c[0],a[0]]
legs = [[-3,-1,1,2],[-4,-2,2,1]]
l1_0c = ncon(tensors,legs)
l1_0c = l1_0c[:,:,0,0]
tensors = [c[0],a[0],c[0]]
legs = [[-4,-1,1,2],[-5,-2,2,3],[-6,-3,3,1]]
l2c = ncon(tensors,legs)
l2c = l2c[:,:,:,0,0,0]
for x in range(1,n-1):
bdl1,bdl2,d,d = np.shape(c[x])
tensors = [l1c,b[x],l1f[x]]
legs = [[-1,1],[1,2,-4,-3],[-2,2]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [l1_0c,a[x],l1_0f[x]]
legs = [[-1,1],[1,2,-4,-3],[-2,2]]
l1_0 = ncon(tensors,legs)
l1_0 = np.reshape(l1_0,-1,order='F')
tensors = [l2c,a[x],np.eye(d),l2f[x]]
legs = [[-1,1,-5],[1,2,-4,-7],[-8,-3],[-2,2,-6]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl1*bdl2*d*d,bdl1*bdl2*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*(l1-l1_0)/epsilon
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[x] = np.reshape(cv,(bdl1,bdl2,d,d),order='F')
if lherm:
c[x] = (c[x]+np.conj(np.moveaxis(c[x],2,3)))/2
cv = np.reshape(c[x],-1,order='F')
fom = np.append(fom,np.real(2*cv @ (l1-l1_0)/epsilon - cv @ l2 @ cv))
tensors = [l1c,c[x],b[x]]
legs = [[3,4],[3,-1,1,2],[4,-2,2,1]]
l1c = ncon(tensors,legs)
tensors = [l1_0c,c[x],a[x]]
legs = [[3,4],[3,-1,1,2],[4,-2,2,1]]
l1_0c = ncon(tensors,legs)
tensors = [l2c,c[x],a[x],c[x]]
legs = [[4,5,6],[4,-1,1,2],[5,-2,2,3],[6,-3,3,1]]
l2c = ncon(tensors,legs)
bdl1,bdl2,d,d = np.shape(c[n-1])
tensors = [l1c,b[n-1]]
legs = [[-1,1],[1,-5,-4,-3]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [l1_0c,a[n-1]]
legs = [[-1,1],[1,-5,-4,-3]]
l1_0 = ncon(tensors,legs)
l1_0 = np.reshape(l1_0,-1,order='F')
tensors = [l2c,a[n-1],np.eye(d)]
legs = [[-1,1,-5],[1,-9,-4,-7],[-8,-3]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl1*bdl2*d*d,bdl1*bdl2*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*(l1-l1_0)/epsilon
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[n-1] = np.reshape(cv,(bdl1,bdl2,d,d),order='F')
if lherm:
c[n-1] = (c[n-1]+np.conj(np.moveaxis(c[n-1],2,3)))/2
cv = np.reshape(c[n-1],-1,order='F')
fom = np.append(fom,np.real(2*cv @ (l1-l1_0)/epsilon - cv @ l2 @ cv))
iter_fom += 1
if iter_fom >= 2 and all(fom[-2*n:] > 0) and np.std(fom[-2*n:])/np.mean(fom[-2*n:]) <= relunc_fom:
break
fomval = fom[-1]
return fomval,c
def fin2_FoM_PBC_optm(a,b,epsilon,c,imprecision=10**-2,lherm=True):
"""
Optimization of FoM over MPO for SLD. Function for finite size systems with PBC. Version with two states separated by epsilon.
Parameters:
a: MPO for the density matrix at the value of estimated parameter phi=phi_0, expected ndarray of a shape (bd,bd,d,d,n)
b: MPO for the density matrix at the value of estimated parameter phi=phi_0+epsilon, expected ndarray of a shape (bd,bd,d,d,n)
epsilon: value of a separation between estimated parameters encoded in a and b, float
c: MPO for the SLD, expected ndarray of a shape (bd,bd,d,d,n)
imprecision: expected imprecision of the end results, default value is 10**-2
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
fomval: optimal value of FoM
c: optimal MPO for SLD
"""
n = np.shape(a)[4]
d = np.shape(a)[2]
bdr = np.shape(a)[0]
bdrp = np.shape(b)[0]
bdl = np.shape(c)[0]
tol_fom = 0.1*imprecision/n**2
if n == 1:
tensors = [b[:,:,:,:,0],np.eye(bdl)]
legs = [[1,1,-4,-3],[-2,-1]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [a[:,:,:,:,0],np.eye(bdl)]
legs = [[1,1,-4,-3],[-2,-1]]
l1_0 = ncon(tensors,legs)
l1_0 = np.reshape(l1_0,-1,order='F')
tensors = [a[:,:,:,:,0],np.eye(d),np.eye(bdl),np.eye(bdl)]
legs = [[1,1,-4,-7],[-8,-3],[-2,-1],[-6,-5]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl*bdl*d*d,bdl*bdl*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*(l1-l1_0)/epsilon
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[:,:,:,:,0] = np.reshape(cv,(bdl,bdl,d,d),order='F')
if lherm:
c[:,:,:,:,0] = (c[:,:,:,:,0]+np.conj(np.moveaxis(c[:,:,:,:,0],2,3)))/2
cv = np.reshape(c[:,:,:,:,0],-1,order='F')
fomval = np.real(2*cv @ (l1-l1_0)/epsilon - cv @ l2 @ cv)
else:
relunc_fom = 0.1*imprecision
l1f = np.zeros((bdl,bdrp,bdl,bdrp,n-1),dtype=complex)
l1_0f = np.zeros((bdl,bdrp,bdl,bdrp,n-1),dtype=complex)
l2f = np.zeros((bdl,bdr,bdl,bdl,bdr,bdl,n-1),dtype=complex)
fom = np.array([])
iter_fom = 0
while True:
tensors = [c[:,:,:,:,n-1],b[:,:,:,:,n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1f[:,:,:,:,n-2] = ncon(tensors,legs)
tensors = [c[:,:,:,:,n-1],a[:,:,:,:,n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1_0f[:,:,:,:,n-2] = ncon(tensors,legs)
tensors = [c[:,:,:,:,n-1],a[:,:,:,:,n-1],c[:,:,:,:,n-1]]
legs = [[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]]
l2f[:,:,:,:,:,:,n-2] = ncon(tensors,legs)
for x in range(n-2,0,-1):
tensors = [c[:,:,:,:,x],b[:,:,:,:,x],l1f[:,:,:,:,x]]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4,-3,-4]]
l1f[:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [c[:,:,:,:,x],a[:,:,:,:,x],l1_0f[:,:,:,:,x]]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4,-3,-4]]
l1_0f[:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [c[:,:,:,:,x],a[:,:,:,:,x],c[:,:,:,:,x],l2f[:,:,:,:,:,:,x]]
legs = [[-1,4,1,2],[-2,5,2,3],[-3,6,3,1],[4,5,6,-4,-5,-6]]
l2f[:,:,:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [b[:,:,:,:,0],l1f[:,:,:,:,0]]
legs = [[2,1,-4,-3],[-2,1,-1,2]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [a[:,:,:,:,0],l1_0f[:,:,:,:,0]]
legs = [[2,1,-4,-3],[-2,1,-1,2]]
l1_0 = ncon(tensors,legs)
l1_0 = np.reshape(l1_0,-1,order='F')
tensors = [a[:,:,:,:,0],np.eye(d),l2f[:,:,:,:,:,:,0]]
legs = [[2,1,-4,-7],[-8,-3],[-2,1,-6,-1,2,-5]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl*bdl*d*d,bdl*bdl*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*(l1-l1_0)/epsilon
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[:,:,:,:,0] = np.reshape(cv,(bdl,bdl,d,d),order='F')
if lherm:
c[:,:,:,:,0] = (c[:,:,:,:,0]+np.conj(np.moveaxis(c[:,:,:,:,0],2,3)))/2
cv = np.reshape(c[:,:,:,:,0],-1,order='F')
fom = np.append(fom,np.real(2*cv @ (l1-l1_0)/epsilon - cv @ l2 @ cv))
tensors = [c[:,:,:,:,0],b[:,:,:,:,0]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1c = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],a[:,:,:,:,0]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1_0c = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],a[:,:,:,:,0],c[:,:,:,:,0]]
legs = [[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]]
l2c = ncon(tensors,legs)
for x in range(1,n-1):
tensors = [l1c,b[:,:,:,:,x],l1f[:,:,:,:,x]]
legs = [[3,4,-1,1],[1,2,-4,-3],[-2,2,3,4]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [l1_0c,a[:,:,:,:,x],l1_0f[:,:,:,:,x]]
legs = [[3,4,-1,1],[1,2,-4,-3],[-2,2,3,4]]
l1_0 = ncon(tensors,legs)
l1_0 = np.reshape(l1_0,-1,order='F')
tensors = [l2c,a[:,:,:,:,x],np.eye(d),l2f[:,:,:,:,:,:,x]]
legs = [[3,4,5,-1,1,-5],[1,2,-4,-7],[-8,-3],[-2,2,-6,3,4,5]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl*bdl*d*d,bdl*bdl*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*(l1-l1_0)/epsilon
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[:,:,:,:,x] = np.reshape(cv,(bdl,bdl,d,d),order='F')
if lherm:
c[:,:,:,:,x] = (c[:,:,:,:,x]+np.conj(np.moveaxis(c[:,:,:,:,x],2,3)))/2
cv = np.reshape(c[:,:,:,:,x],-1,order='F')
fom = np.append(fom,np.real(2*cv @ (l1-l1_0)/epsilon - cv @ l2 @ cv))
tensors = [l1c,c[:,:,:,:,x],b[:,:,:,:,x]]
legs = [[-1,-2,3,4],[3,-3,1,2],[4,-4,2,1]]
l1c = ncon(tensors,legs)
tensors = [l1_0c,c[:,:,:,:,x],a[:,:,:,:,x]]
legs = [[-1,-2,3,4],[3,-3,1,2],[4,-4,2,1]]
l1_0c = ncon(tensors,legs)
tensors = [l2c,c[:,:,:,:,x],a[:,:,:,:,x],c[:,:,:,:,x]]
legs = [[-1,-2,-3,4,5,6],[4,-4,1,2],[5,-5,2,3],[6,-6,3,1]]
l2c = ncon(tensors,legs)
tensors = [l1c,b[:,:,:,:,n-1]]
legs = [[-2,2,-1,1],[1,2,-4,-3]]
l1 = ncon(tensors,legs)
l1 = np.reshape(l1,-1,order='F')
tensors = [l1_0c,a[:,:,:,:,n-1]]
legs = [[-2,2,-1,1],[1,2,-4,-3]]
l1_0 = ncon(tensors,legs)
l1_0 = np.reshape(l1_0,-1,order='F')
tensors = [l2c,a[:,:,:,:,n-1],np.eye(d)]
legs = [[-2,2,-6,-1,1,-5],[1,2,-4,-7],[-8,-3]]
l2 = ncon(tensors,legs)
l2 = np.reshape(l2,(bdl*bdl*d*d,bdl*bdl*d*d),order='F')
dl2 = l2+l2.T
dl1 = 2*(l1-l1_0)/epsilon
dl2pinv = np.linalg.pinv(dl2,tol_fom)
dl2pinv = (dl2pinv+dl2pinv.T)/2
cv = dl2pinv @ dl1
c[:,:,:,:,n-1] = np.reshape(cv,(bdl,bdl,d,d),order='F')
if lherm:
c[:,:,:,:,n-1] = (c[:,:,:,:,n-1]+np.conj(np.moveaxis(c[:,:,:,:,n-1],2,3)))/2
cv = np.reshape(c[:,:,:,:,n-1],-1,order='F')
fom = np.append(fom,np.real(2*cv @ (l1-l1_0)/epsilon - cv @ l2 @ cv))
iter_fom += 1
if iter_fom >= 2 and all(fom[-2*n:] > 0) and np.std(fom[-2*n:])/np.mean(fom[-2*n:]) <= relunc_fom:
break
fomval = fom[-1]
return fomval,c
def fin2_FoMD_OBC_optm(c2d,cd,cpd,epsilon,a0,imprecision=10**-2):
"""
Optimization of FoMD over MPS for initial wave function. Function for finite size systems with OBC. Version with two dual SLDs separated by epsilon.
Parameters:
c2d: MPO for the square of the dual of the SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
cd: MPO for the dual of the SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
cpd: MPO for the dual of the SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
epsilon: value of a separation between estimated parameters encoded in cd and cpd, float
a0: MPS for the initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
imprecision: expected imprecision of the end results, default value is 10**-2
Returns:
fomdval: optimal value of FoMD
a0: optimal MPS for the initial wave function
"""
n = len(a0)
if n == 1:
if np.shape(c2d[0])[0] == 1 and np.shape(cpd[0])[0] == 1 and np.shape(a0[0])[0] == 1:
d = np.shape(a0[0])[2]
tensors = [c2d[0][0,0,:,:]]
legs = [[-1,-2]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(d,d),order='F')
tensors = [cpd[0][0,0,:,:]]
legs = [[-1,-2]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(d,d),order='F')
tensors = [cd[0][0,0,:,:]]
legs = [[-1,-2]]
ld = ncon(tensors,legs)
ld = np.reshape(ld,(d,d),order='F')
eiginput = 2*(lpd-ld)/epsilon-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ a0v))
a0[0][0,0,:] = np.reshape(a0v,(d),order='F')
fomdval = np.real(fomdval[position])
else:
warnings.warn('Tensor networks with OBC and length one have to have bond dimension equal to one.')
else:
relunc_fomd = 0.1*imprecision
l2df = [0]*n
lpdf = [0]*n
ldf = [0]*n
fomd = np.array([])
iter_fomd = 0
while True:
tensors = [np.conj(a0[n-1]),c2d[n-1],a0[n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
l2df[n-2] = ncon(tensors,legs)
l2df[n-2] = l2df[n-2][:,:,:,0,0,0]
tensors = [np.conj(a0[n-1]),cpd[n-1],a0[n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
lpdf[n-2] = ncon(tensors,legs)
lpdf[n-2] = lpdf[n-2][:,:,:,0,0,0]
tensors = [np.conj(a0[n-1]),cd[n-1],a0[n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
ldf[n-2] = ncon(tensors,legs)
ldf[n-2] = ldf[n-2][:,:,:,0,0,0]
for x in range(n-2,0,-1):
tensors = [np.conj(a0[x]),c2d[x],a0[x],l2df[x]]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
l2df[x-1] = ncon(tensors,legs)
tensors = [np.conj(a0[x]),cpd[x],a0[x],lpdf[x]]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
lpdf[x-1] = ncon(tensors,legs)
tensors = [np.conj(a0[x]),cd[x],a0[x],ldf[x]]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
ldf[x-1] = ncon(tensors,legs)
bdpsi1,bdpsi2,d = np.shape(a0[0])
tensors = [c2d[0],l2df[0]]
legs = [[-7,1,-3,-6],[-2,1,-5]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
tensors = [cpd[0],lpdf[0]]
legs = [[-7,1,-3,-6],[-2,1,-5]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
tensors = [cd[0],ldf[0]]
legs = [[-7,1,-3,-6],[-2,1,-5]]
ld = ncon(tensors,legs)
ld = np.reshape(ld,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
eiginput = 2*(lpd-ld)/epsilon-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ a0v))
a0[0] = np.reshape(a0v,(bdpsi1,bdpsi2,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
a0[0] = np.moveaxis(a0[0],2,0)
a0[0] = np.reshape(a0[0],(d*bdpsi1,bdpsi2),order='F')
u,s,vh = np.linalg.svd(a0[0],full_matrices=False)
a0[0] = np.reshape(u,(d,bdpsi1,np.shape(s)[0]),order='F')
a0[0] = np.moveaxis(a0[0],0,2)
tensors = [np.diag(s) @ vh,a0[1]]
legs = [[-1,1],[1,-2,-3]]
a0[1] = ncon(tensors,legs)
tensors = [np.conj(a0[0]),c2d[0],a0[0]]
legs = [[-4,-1,1],[-5,-2,1,2],[-6,-3,2]]
l2dc = ncon(tensors,legs)
l2dc = l2dc[:,:,:,0,0,0]
tensors = [np.conj(a0[0]),cpd[0],a0[0]]
legs = [[-4,-1,1],[-5,-2,1,2],[-6,-3,2]]
lpdc = ncon(tensors,legs)
lpdc = lpdc[:,:,:,0,0,0]
tensors = [np.conj(a0[0]),cd[0],a0[0]]
legs = [[-4,-1,1],[-5,-2,1,2],[-6,-3,2]]
ldc = ncon(tensors,legs)
ldc = ldc[:,:,:,0,0,0]
for x in range(1,n-1):
bdpsi1,bdpsi2,d = np.shape(a0[x])
tensors = [l2dc,c2d[x],l2df[x]]
legs = [[-1,1,-4],[1,2,-3,-6],[-2,2,-5]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
tensors = [lpdc,cpd[x],lpdf[x]]
legs = [[-1,1,-4],[1,2,-3,-6],[-2,2,-5]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
tensors = [ldc,cd[x],ldf[x]]
legs = [[-1,1,-4],[1,2,-3,-6],[-2,2,-5]]
ld = ncon(tensors,legs)
ld = np.reshape(ld,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
eiginput = 2*(lpd-ld)/epsilon-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ a0v))
a0[x] = np.reshape(a0v,(bdpsi1,bdpsi2,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
a0[x] = np.moveaxis(a0[x],2,0)
a0[x] = np.reshape(a0[x],(d*bdpsi1,bdpsi2),order='F')
u,s,vh = np.linalg.svd(a0[x],full_matrices=False)
a0[x] = np.reshape(u,(d,bdpsi1,np.shape(s)[0]),order='F')
a0[x] = np.moveaxis(a0[x],0,2)
tensors = [np.diag(s) @ vh,a0[x+1]]
legs = [[-1,1],[1,-2,-3]]
a0[x+1] = ncon(tensors,legs)
tensors = [l2dc,np.conj(a0[x]),c2d[x],a0[x]]
legs = [[3,4,5],[3,-1,1],[4,-2,1,2],[5,-3,2]]
l2dc = ncon(tensors,legs)
tensors = [lpdc,np.conj(a0[x]),cpd[x],a0[x]]
legs = [[3,4,5],[3,-1,1],[4,-2,1,2],[5,-3,2]]
lpdc = ncon(tensors,legs)
tensors = [ldc,np.conj(a0[x]),cd[x],a0[x]]
legs = [[3,4,5],[3,-1,1],[4,-2,1,2],[5,-3,2]]
ldc = ncon(tensors,legs)
bdpsi1,bdpsi2,d = np.shape(a0[n-1])
tensors = [l2dc,c2d[n-1]]
legs = [[-1,1,-4],[1,-7,-3,-6]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
tensors = [lpdc,cpd[n-1]]
legs = [[-1,1,-4],[1,-7,-3,-6]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
tensors = [ldc,cd[n-1]]
legs = [[-1,1,-4],[1,-7,-3,-6]]
ld = ncon(tensors,legs)
ld = np.reshape(ld,(bdpsi1*bdpsi2*d,bdpsi1*bdpsi2*d),order='F')
eiginput = 2*(lpd-ld)/epsilon-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ a0v))
a0[n-1] = np.reshape(a0v,(bdpsi1,bdpsi2,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
iter_fomd += 1
for x in range(n-1,0,-1):
bdpsi1,bdpsi2,d = np.shape(a0[x])
a0[x] = np.moveaxis(a0[x],2,1)
a0[x] = np.reshape(a0[x],(bdpsi1,d*bdpsi2),order='F')
u,s,vh = np.linalg.svd(a0[x],full_matrices=False)
a0[x] = np.reshape(vh,(np.shape(s)[0],d,bdpsi2),order='F')
a0[x] = np.moveaxis(a0[x],1,2)
tensors = [a0[x-1],u @ np.diag(s)]
legs = [[-1,1,-3],[1,-2]]
a0[x-1] = ncon(tensors,legs)
if iter_fomd >= 2 and all(fomd[-2*n:] > 0) and np.std(fomd[-2*n:])/np.mean(fomd[-2*n:]) <= relunc_fomd:
break
fomdval = fomd[-1]
return fomdval,a0
def fin2_FoMD_PBC_optm(c2d,cd,cpd,epsilon,a0,imprecision=10**-2):
"""
Optimization of FoMD over MPS for initial wave function. Function for finite size systems with PBC. Version with two dual SLDs separated by epsilon.
Parameters:
c2d: MPO for square of dual of SLD at the value of estimated parameter phi=-phi_0, expected ndarray of a shape (bd,bd,d,d,n)
cd: MPO for dual of SLD at the value of estimated parameter phi=-phi_0, expected ndarray of a shape (bd,bd,d,d,n)
cpd: MPO for dual of SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected ndarray of a shape (bd,bd,d,d,n)
epsilon: value of a separation between estimated parameters encoded in cd and cpd, float
a0: MPS for initial wave function, expected ndarray of a shape (bd,bd,d,n)
imprecision: expected imprecision of the end results, default value is 10**-2
Returns:
fomdval: optimal value of FoMD
a0: optimal MPS for initial wave function
"""
n = np.shape(c2d)[4]
d = np.shape(c2d)[2]
bdl2d = np.shape(c2d)[0]
bdlpd = np.shape(cpd)[0]
bdld = np.shape(cd)[0]
bdpsi = np.shape(a0)[0]
tol_fomd = 0.1*imprecision/n**2
if n == 1:
tensors = [c2d[:,:,:,:,0],np.eye(bdpsi),np.eye(bdpsi)]
legs = [[1,1,-3,-6],[-2,-1],[-5,-4]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [cpd[:,:,:,:,0],np.eye(bdpsi),np.eye(bdpsi)]
legs = [[1,1,-3,-6],[-2,-1],[-5,-4]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [cd[:,:,:,:,0],np.eye(bdpsi),np.eye(bdpsi)]
legs = [[1,1,-3,-6],[-2,-1],[-5,-4]]
ld = ncon(tensors,legs)
ld = np.reshape(ld,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [np.eye(bdpsi),np.eye(bdpsi)]
legs = [[-2,-1],[-4,-3]]
psinorm = ncon(tensors,legs)
psinorm = np.reshape(psinorm,(bdpsi*bdpsi,bdpsi*bdpsi),order='F')
psinorm = (psinorm+np.conj(psinorm).T)/2
psinormpinv = np.linalg.pinv(psinorm,tol_fomd,hermitian=True)
psinormpinv = (psinormpinv+np.conj(psinormpinv).T)/2
psinormpinv = np.kron(np.eye(d),psinormpinv)
eiginput = 2*(lpd-ld)/epsilon-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
eiginput = psinormpinv @ eiginput
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ np.kron(np.eye(d),psinorm) @ a0v))
a0[:,:,:,0] = np.reshape(a0v,(bdpsi,bdpsi,d),order='F')
fomdval = np.real(fomdval[position])
else:
relunc_fomd = 0.1*imprecision
l2df = np.zeros((bdpsi,bdl2d,bdpsi,bdpsi,bdl2d,bdpsi,n-1),dtype=complex)
lpdf = np.zeros((bdpsi,bdlpd,bdpsi,bdpsi,bdlpd,bdpsi,n-1),dtype=complex)
ldf = np.zeros((bdpsi,bdld,bdpsi,bdpsi,bdld,bdpsi,n-1),dtype=complex)
psinormf = np.zeros((bdpsi,bdpsi,bdpsi,bdpsi,n-1),dtype=complex)
fomd = np.array([])
iter_fomd = 0
while True:
tensors = [np.conj(a0[:,:,:,n-1]),c2d[:,:,:,:,n-1],a0[:,:,:,n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
l2df[:,:,:,:,:,:,n-2] = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,n-1]),cpd[:,:,:,:,n-1],a0[:,:,:,n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
lpdf[:,:,:,:,:,:,n-2] = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,n-1]),cd[:,:,:,:,n-1],a0[:,:,:,n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
ldf[:,:,:,:,:,:,n-2] = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,n-1]),a0[:,:,:,n-1]]
legs = [[-1,-3,1],[-2,-4,1]]
psinormf[:,:,:,:,n-2] = ncon(tensors,legs)
for x in range(n-2,0,-1):
tensors = [np.conj(a0[:,:,:,x]),c2d[:,:,:,:,x],a0[:,:,:,x],l2df[:,:,:,:,:,:,x]]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5,-4,-5,-6]]
l2df[:,:,:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,x]),cpd[:,:,:,:,x],a0[:,:,:,x],lpdf[:,:,:,:,:,:,x]]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5,-4,-5,-6]]
lpdf[:,:,:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,x]),cd[:,:,:,:,x],a0[:,:,:,x],ldf[:,:,:,:,:,:,x]]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5,-4,-5,-6]]
ldf[:,:,:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,x]),a0[:,:,:,x],psinormf[:,:,:,:,x]]
legs = [[-1,2,1],[-2,3,1],[2,3,-3,-4]]
psinormf[:,:,:,:,x-1] = ncon(tensors,legs)
tensors = [c2d[:,:,:,:,0],l2df[:,:,:,:,:,:,0]]
legs = [[2,1,-3,-6],[-2,1,-5,-1,2,-4]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [cpd[:,:,:,:,0],lpdf[:,:,:,:,:,:,0]]
legs = [[2,1,-3,-6],[-2,1,-5,-1,2,-4]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [cd[:,:,:,:,0],ldf[:,:,:,:,:,:,0]]
legs = [[2,1,-3,-6],[-2,1,-5,-1,2,-4]]
ld = ncon(tensors,legs)
ld = np.reshape(ld,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [psinormf[:,:,:,:,0]]
legs = [[-2,-4,-1,-3]]
psinorm = ncon(tensors,legs)
psinorm = np.reshape(psinorm,(bdpsi*bdpsi,bdpsi*bdpsi),order='F')
psinorm = (psinorm+np.conj(psinorm).T)/2
psinormpinv = np.linalg.pinv(psinorm,tol_fomd,hermitian=True)
psinormpinv = (psinormpinv+np.conj(psinormpinv).T)/2
psinormpinv = np.kron(np.eye(d),psinormpinv)
eiginput = 2*(lpd-ld)/epsilon-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
eiginput = psinormpinv @ eiginput
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ np.kron(np.eye(d),psinorm) @ a0v))
a0[:,:,:,0] = np.reshape(a0v,(bdpsi,bdpsi,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
tensors = [np.conj(a0[:,:,:,0]),c2d[:,:,:,:,0],a0[:,:,:,0]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
l2dc = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),cpd[:,:,:,:,0],a0[:,:,:,0]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
lpdc = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),cd[:,:,:,:,0],a0[:,:,:,0]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
ldc = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),a0[:,:,:,0]]
legs = [[-1,-3,1],[-2,-4,1]]
psinormc = ncon(tensors,legs)
for x in range(1,n-1):
tensors = [l2dc,c2d[:,:,:,:,x],l2df[:,:,:,:,:,:,x]]
legs = [[3,4,5,-1,1,-4],[1,2,-3,-6],[-2,2,-5,3,4,5]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [lpdc,cpd[:,:,:,:,x],lpdf[:,:,:,:,:,:,x]]
legs = [[3,4,5,-1,1,-4],[1,2,-3,-6],[-2,2,-5,3,4,5]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [ldc,cd[:,:,:,:,x],ldf[:,:,:,:,:,:,x]]
legs = [[3,4,5,-1,1,-4],[1,2,-3,-6],[-2,2,-5,3,4,5]]
ld = ncon(tensors,legs)
ld = np.reshape(ld,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [psinormc,psinormf[:,:,:,:,x]]
legs = [[1,2,-1,-3],[-2,-4,1,2]]
psinorm = ncon(tensors,legs)
psinorm = np.reshape(psinorm,(bdpsi*bdpsi,bdpsi*bdpsi),order='F')
psinorm = (psinorm+np.conj(psinorm).T)/2
psinormpinv = np.linalg.pinv(psinorm,tol_fomd,hermitian=True)
psinormpinv = (psinormpinv+np.conj(psinormpinv).T)/2
psinormpinv = np.kron(np.eye(d),psinormpinv)
eiginput = 2*(lpd-ld)/epsilon-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
eiginput = psinormpinv @ eiginput
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ np.kron(np.eye(d),psinorm) @ a0v))
a0[:,:,:,x] = np.reshape(a0v,(bdpsi,bdpsi,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
tensors = [l2dc,np.conj(a0[:,:,:,x]),c2d[:,:,:,:,x],a0[:,:,:,x]]
legs = [[-1,-2,-3,3,4,5],[3,-4,1],[4,-5,1,2],[5,-6,2]]
l2dc = ncon(tensors,legs)
tensors = [lpdc,np.conj(a0[:,:,:,x]),cpd[:,:,:,:,x],a0[:,:,:,x]]
legs = [[-1,-2,-3,3,4,5],[3,-4,1],[4,-5,1,2],[5,-6,2]]
lpdc = ncon(tensors,legs)
tensors = [ldc,np.conj(a0[:,:,:,x]),cd[:,:,:,:,x],a0[:,:,:,x]]
legs = [[-1,-2,-3,3,4,5],[3,-4,1],[4,-5,1,2],[5,-6,2]]
ldc = ncon(tensors,legs)
tensors = [psinormc,np.conj(a0[:,:,:,x]),a0[:,:,:,x]]
legs = [[-1,-2,2,3],[2,-3,1],[3,-4,1]]
psinormc = ncon(tensors,legs)
tensors = [l2dc,c2d[:,:,:,:,n-1]]
legs = [[-2,2,-5,-1,1,-4],[1,2,-3,-6]]
l2d = ncon(tensors,legs)
l2d = np.reshape(l2d,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [lpdc,cpd[:,:,:,:,n-1]]
legs = [[-2,2,-5,-1,1,-4],[1,2,-3,-6]]
lpd = ncon(tensors,legs)
lpd = np.reshape(lpd,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [ldc,cd[:,:,:,:,n-1]]
legs = [[-2,2,-5,-1,1,-4],[1,2,-3,-6]]
ld = ncon(tensors,legs)
ld = np.reshape(ld,(bdpsi*bdpsi*d,bdpsi*bdpsi*d),order='F')
tensors = [psinormc]
legs = [[-2,-4,-1,-3]]
psinorm = ncon(tensors,legs)
psinorm = np.reshape(psinorm,(bdpsi*bdpsi,bdpsi*bdpsi),order='F')
psinorm = (psinorm+np.conj(psinorm).T)/2
psinormpinv = np.linalg.pinv(psinorm,tol_fomd,hermitian=True)
psinormpinv = (psinormpinv+np.conj(psinormpinv).T)/2
psinormpinv = np.kron(np.eye(d),psinormpinv)
eiginput = 2*(lpd-ld)/epsilon-l2d
eiginput = (eiginput+np.conj(eiginput).T)/2
eiginput = psinormpinv @ eiginput
fomdval,a0v = np.linalg.eig(eiginput)
position = np.argmax(np.real(fomdval))
a0v = np.reshape(a0v[:,position],-1,order='F')
a0v = a0v/np.sqrt(np.abs(np.conj(a0v) @ np.kron(np.eye(d),psinorm) @ a0v))
a0[:,:,:,n-1] = np.reshape(a0v,(bdpsi,bdpsi,d),order='F')
fomd = np.append(fomd,np.real(fomdval[position]))
iter_fomd += 1
if iter_fomd >= 2 and all(fomd[-2*n:] > 0) and np.std(fomd[-2*n:])/np.mean(fomd[-2*n:]) <= relunc_fomd:
break
fomdval = fomd[-1]
return fomdval,a0
def fin2_FoM_OBC_val(a,b,epsilon,c):
"""
Calculate value of FoM. Function for finite size systems with OBC. Version with two states separated by epsilon.
Parameters:
a: MPO for density matrix at the value of estimated parameter phi=phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
b: MPO for density matrix at the value of estimated parameter phi=phi_0+epsilon, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
epsilon: value of a separation between estimated parameters encoded in a and b, float
c: MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
Returns:
fomval: value of FoM
"""
n = len(c)
if n == 1:
if np.shape(a[0])[0] == 1 and np.shape(b[0])[0] == 1 and np.shape(c[0])[0] == 1:
tensors = [c[0][0,0,:,:],b[0][0,0,:,:]]
legs = [[1,2],[2,1]]
l1 = ncon(tensors,legs)
tensors = [c[0][0,0,:,:],a[0][0,0,:,:]]
legs = [[1,2],[2,1]]
l1_0 = ncon(tensors,legs)
tensors = [c[0][0,0,:,:],a[0][0,0,:,:],c[0][0,0,:,:]]
legs = [[1,2],[2,3],[3,1]]
l2 = ncon(tensors,legs)
fomval = 2*(l1-l1_0)/epsilon-l2
else:
warnings.warn('Tensor networks with OBC and length one have to have bond dimension equal to one.')
else:
tensors = [c[n-1],b[n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1 = ncon(tensors,legs)
l1 = l1[:,:,0,0]
tensors = [c[n-1],a[n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1_0 = ncon(tensors,legs)
l1_0 = l1_0[:,:,0,0]
tensors = [c[n-1],a[n-1],c[n-1]]
legs = [[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]]
l2 = ncon(tensors,legs)
l2 = l2[:,:,:,0,0,0]
for x in range(n-2,0,-1):
tensors = [c[x],b[x],l1]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4]]
l1 = ncon(tensors,legs)
tensors = [c[x],a[x],l1_0]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4]]
l1_0 = ncon(tensors,legs)
tensors = [c[x],a[x],c[x],l2]
legs = [[-1,4,1,2],[-2,5,2,3],[-3,6,3,1],[4,5,6]]
l2 = ncon(tensors,legs)
tensors = [c[0],b[0],l1]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4]]
l1 = ncon(tensors,legs)
l1 = float(l1)
tensors = [c[0],a[0],l1_0]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4]]
l1_0 = ncon(tensors,legs)
l1_0 = float(l1_0)
tensors = [c[0],a[0],c[0],l2]
legs = [[-1,4,1,2],[-2,5,2,3],[-3,6,3,1],[4,5,6]]
l2 = ncon(tensors,legs)
l2 = float(l2)
fomval = 2*(l1-l1_0)/epsilon-l2
return fomval
def fin2_FoM_PBC_val(a,b,epsilon,c):
"""
Calculate value of FoM. Function for finite size systems with PBC. Version with two states separated by epsilon.
Parameters:
a: MPO for density matrix at the value of estimated parameter phi=phi_0, expected ndarray of a shape (bd,bd,d,d,n)
b: MPO for density matrix at the value of estimated parameter phi=phi_0+epsilon, expected ndarray of a shape (bd,bd,d,d,n)
epsilon: value of a separation between estimated parameters encoded in a and b, float
c: MPO for SLD, expected ndarray of a shape (bd,bd,d,d,n)
Returns:
fomval: value of FoM
"""
n = np.shape(a)[4]
if n == 1:
tensors = [c[:,:,:,:,0],b[:,:,:,:,0]]
legs = [[3,3,1,2],[4,4,2,1]]
l1 = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],a[:,:,:,:,0]]
legs = [[3,3,1,2],[4,4,2,1]]
l1_0 = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],a[:,:,:,:,0],c[:,:,:,:,0]]
legs = [[4,4,1,2],[5,5,2,3],[6,6,3,1]]
l2 = ncon(tensors,legs)
fomval = 2*(l1-l1_0)/epsilon-l2
else:
tensors = [c[:,:,:,:,n-1],b[:,:,:,:,n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1 = ncon(tensors,legs)
tensors = [c[:,:,:,:,n-1],a[:,:,:,:,n-1]]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
l1_0 = ncon(tensors,legs)
tensors = [c[:,:,:,:,n-1],a[:,:,:,:,n-1],c[:,:,:,:,n-1]]
legs = [[-1,-4,1,2],[-2,-5,2,3],[-3,-6,3,1]]
l2 = ncon(tensors,legs)
for x in range(n-2,0,-1):
tensors = [c[:,:,:,:,x],b[:,:,:,:,x],l1]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4,-3,-4]]
l1 = ncon(tensors,legs)
tensors = [c[:,:,:,:,x],a[:,:,:,:,x],l1_0]
legs = [[-1,3,1,2],[-2,4,2,1],[3,4,-3,-4]]
l1_0 = ncon(tensors,legs)
tensors = [c[:,:,:,:,x],a[:,:,:,:,x],c[:,:,:,:,x],l2]
legs = [[-1,4,1,2],[-2,5,2,3],[-3,6,3,1],[4,5,6,-4,-5,-6]]
l2 = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],b[:,:,:,:,0],l1]
legs = [[5,3,1,2],[6,4,2,1],[3,4,5,6]]
l1 = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],a[:,:,:,:,0],l1_0]
legs = [[5,3,1,2],[6,4,2,1],[3,4,5,6]]
l1_0 = ncon(tensors,legs)
tensors = [c[:,:,:,:,0],a[:,:,:,:,0],c[:,:,:,:,0],l2]
legs = [[7,4,1,2],[8,5,2,3],[9,6,3,1],[4,5,6,7,8,9]]
l2 = ncon(tensors,legs)
fomval = 2*(l1-l1_0)/epsilon-l2
return fomval
def fin2_FoMD_OBC_val(c2d,cd,cpd,epsilon,a0):
"""
Calculate value of FoMD. Function for finite size systems with OBC. Version with two dual SLDs separated by epsilon.
Parameters:
c2d: MPO for square of dual of SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
cd: MPO for dual of SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
cpd: MPO for dual of SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
epsilon: value of a separation between estimated parameters encoded in cd and cpd, float
a0: MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
Returns:
fomdval: value of FoMD
"""
n = len(a0)
if n == 1:
if np.shape(c2d[0])[0] == 1 and np.shape(cpd[0])[0] == 1 and np.shape(a0[0])[0] == 1:
tensors = [np.conj(a0[0][0,0,:]),c2d[0][0,0,:,:],a0[0][0,0,:]]
legs = [[1],[1,2],[2]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[0][0,0,:]),cpd[0][0,0,:,:],a0[0][0,0,:]]
legs = [[1],[1,2],[2]]
lpd = ncon(tensors,legs)
tensors = [np.conj(a0[0][0,0,:]),cd[0][0,0,:,:],a0[0][0,0,:]]
legs = [[1],[1,2],[2]]
ld = ncon(tensors,legs)
fomdval = 2*(lpd-ld)/epsilon-l2d
else:
warnings.warn('Tensor networks with OBC and length one have to have bond dimension equal to one.')
else:
tensors = [np.conj(a0[n-1]),c2d[n-1],a0[n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
l2d = ncon(tensors,legs)
l2d = l2d[:,:,:,0,0,0]
tensors = [np.conj(a0[n-1]),cpd[n-1],a0[n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
lpd = ncon(tensors,legs)
lpd = lpd[:,:,:,0,0,0]
tensors = [np.conj(a0[n-1]),cd[n-1],a0[n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
ld = ncon(tensors,legs)
ld = ld[:,:,:,0,0,0]
for x in range(n-2,0,-1):
tensors = [np.conj(a0[x]),c2d[x],a0[x],l2d]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[x]),cpd[x],a0[x],lpd]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
lpd = ncon(tensors,legs)
tensors = [np.conj(a0[x]),cd[x],a0[x],ld]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
ld = ncon(tensors,legs)
tensors = [np.conj(a0[0]),c2d[0],a0[0],l2d]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
l2d = ncon(tensors,legs)
l2d = float(l2d)
tensors = [np.conj(a0[0]),cpd[0],a0[0],lpd]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
lpd = ncon(tensors,legs)
lpd = float(lpd)
tensors = [np.conj(a0[0]),cd[0],a0[0],ld]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5]]
ld = ncon(tensors,legs)
ld = float(ld)
fomdval = 2*(lpd-ld)/epsilon-l2d
return fomdval
def fin2_FoMD_PBC_val(c2d,cd,cpd,epsilon,a0):
"""
Calculate value of FoMD. Function for finite size systems with PBC. Version with two dual SLDs separated by epsilon.
Parameters:
c2d: MPO for square of dual of SLD at the value of estimated parameter phi=-phi_0, expected ndarray of a shape (bd,bd,d,d,n)
cd: MPO for dual of SLD at the value of estimated parameter phi=-phi_0, expected ndarray of a shape (bd,bd,d,d,n)
cpd: MPO for dual of SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected ndarray of a shape (bd,bd,d,d,n)
epsilon: value of a separation between estimated parameters encoded in cd and cpd, float
a0: MPS for initial wave function, expected ndarray of a shape (bd,bd,d,n)
Returns:
fomdval: value of FoMD
"""
n = np.shape(c2d)[4]
if n == 1:
tensors = [np.conj(a0[:,:,:,0]),c2d[:,:,:,:,0],a0[:,:,:,0]]
legs = [[3,3,1],[4,4,1,2],[5,5,2]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),cpd[:,:,:,:,0],a0[:,:,:,0]]
legs = [[3,3,1],[4,4,1,2],[5,5,2]]
lpd = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),cd[:,:,:,:,0],a0[:,:,:,0]]
legs = [[3,3,1],[4,4,1,2],[5,5,2]]
ld = ncon(tensors,legs)
fomdval = 2*(lpd-ld)/epsilon-l2d
else:
tensors = [np.conj(a0[:,:,:,n-1]),c2d[:,:,:,:,n-1],a0[:,:,:,n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,n-1]),cpd[:,:,:,:,n-1],a0[:,:,:,n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
lpd = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,n-1]),cd[:,:,:,:,n-1],a0[:,:,:,n-1]]
legs = [[-1,-4,1],[-2,-5,1,2],[-3,-6,2]]
ld = ncon(tensors,legs)
for x in range(n-2,0,-1):
tensors = [np.conj(a0[:,:,:,x]),c2d[:,:,:,:,x],a0[:,:,:,x],l2d]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5,-4,-5,-6]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,x]),cpd[:,:,:,:,x],a0[:,:,:,x],lpd]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5,-4,-5,-6]]
lpd = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,x]),cd[:,:,:,:,x],a0[:,:,:,x],ld]
legs = [[-1,3,1],[-2,4,1,2],[-3,5,2],[3,4,5,-4,-5,-6]]
ld = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),c2d[:,:,:,:,0],a0[:,:,:,0],l2d]
legs = [[6,3,1],[7,4,1,2],[8,5,2],[3,4,5,6,7,8]]
l2d = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),cpd[:,:,:,:,0],a0[:,:,:,0],lpd]
legs = [[6,3,1],[7,4,1,2],[8,5,2],[3,4,5,6,7,8]]
lpd = ncon(tensors,legs)
tensors = [np.conj(a0[:,:,:,0]),cd[:,:,:,:,0],a0[:,:,:,0],ld]
legs = [[6,3,1],[7,4,1,2],[8,5,2],[3,4,5,6,7,8]]
ld = ncon(tensors,legs)
fomdval = 2*(lpd-ld)/epsilon-l2d
return fomdval
##########################################
# #
# #
# 2 Functions for infinite size systems. #
# #
# #
##########################################
#############################
# #
# 2.1 High level functions. #
# #
#############################
def inf(so_before_list, h, so_after_list, L_ini=None, psi0_ini=None, imprecision=10**-2, D_L_max=100, D_L_max_forced=False, L_herm=True, D_psi0_max=100, D_psi0_max_forced=False):
"""
Optimization of the lim_{N --> infinity} QFI/N over operator tilde{L} (in iMPO representation) and wave function psi0 (in iMPS representation) and check of convergence in their bond dimensions. Function for infinite size systems.
User has to provide information about the dynamics by specifying quantum channel. It is assumed that quantum channel is translationally invariant and is build from layers of quantum operations.
User has to provide one defining for each layer operation as a local superoperator. Those local superoperator have to be input in order of their action on the system.
Parameter encoding is a stand out quantum operation. It is assumed that parameter encoding acts only once and is unitary so the user have to provide only its generator h.
Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.
Parameters:
so_before_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites particular local superoperator acts
List of local superoperators (in order) which act before unitary parameter encoding.
h: ndarray of a shape (d,d)
Generator of unitary parameter encoding. Dimension d is the dimension of local Hilbert space (dimension of physical index).
Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.
so_after_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites particular local superoperator acts
List of local superoperators (in order) which act after unitary parameter encoding.
L_ini: ndarray of a shape (D_L,D_L,d,d), optional
Initial iMPO for tilde{L}.
psi0_ini: ndarray of a shape (D_psi0,D_psi0,d), optional
Initial iMPS for psi0.
imprecision: float, optional
Expected relative imprecision of the end results.
D_L_max: integer, optional
Maximal value of D_L (D_L is bond dimension for iMPO representing tilde{L}).
D_L_max_forced: bool, optional
True if D_L_max have to be reached, otherwise False.
L_herm: bool, optional
True if Hermitian gauge have to be imposed on iMPO representing tilde{L}, otherwise False.
D_psi0_max: integer, optional
Maximal value of D_psi0 (D_psi0 is bond dimension for iMPS representing psi0).
D_psi0_max_forced: bool, optional
True if D_psi0_max have to be reached, otherwise False.
Returns:
result: float
Optimal value of figure of merit.
result_m: ndarray
Matrix describing figure of merit in function of bond dimensions of respectively tilde{L} [rows] and psi0 [columns].
L: ndarray of a shape (D_L,D_L,d,d)
Optimal tilde{L} in iMPO representation.
psi0: ndarray of a shape (D_psi0,D_psi0,d)
Optimal psi0 in iMPS representation.
"""
if np.linalg.norm(h - np.diag(np.diag(h))) > 10**-10:
warnings.warn('Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.')
d = np.shape(h)[0]
epsilon = 10**-4
aux = np.kron(h, np.eye(d)) - np.kron(np.eye(d), h)
z = np.diag(np.exp(-1j * np.diag(aux) * epsilon))
ch = inf_create_channel(d, so_before_list + so_after_list)
ch2 = inf_create_channel(d, so_before_list + [z] + so_after_list)
result, result_m, L, psi0 = inf_gen(d, ch, ch2, epsilon, inf_L_symfun, inf_psi0_symfun, L_ini, psi0_ini, imprecision, D_L_max, D_L_max_forced, L_herm, D_psi0_max, D_psi0_max_forced)
return result, result_m, L, psi0
def inf_gen(d, ch, ch2, epsilon, symfun_L, symfun_psi0, L_ini=None, psi0_ini=None, imprecision=10**-2, D_L_max=100, D_L_max_forced=False, L_herm=True, D_psi0_max=100, D_psi0_max_forced=False):
"""
Optimization of the figure of merit (usually interpreted as lim_{N --> infinity} QFI/N) over operator tilde{L} (in iMPO representation) and wave function psi0 (in iMPS representation) and check of convergence in their bond dimensions. Function for infinite size systems.
User has to provide information about the dynamics by specifying two channels separated by small parameter epsilon as superoperators in iMPO representation.
By definition this infinite approach assumes translation invariance of the problem, other than that there are no constraints on the structure of the channel but the complexity of calculations highly depends on channel's bond dimension.
Parameters:
d: integer
Dimension of local Hilbert space (dimension of physical index).
ch: ndarray of a shape (D_ch,D_ch,d**2,d**2)
Quantum channel as superoperator in iMPO representation.
ch2: ndarray of a shape (D_ch2,D_ch2,d**2,d**2)
Quantum channel as superoperator in iMPO representation for the value of estimated parameter shifted by epsilon in relation to ch.
epsilon: float
Value of a separation between estimated parameters encoded in ch and ch2.
symfun_L: function
Function which symmetrize iMPO for tilde{L} after each step of otimization (the most simple one would be lambda x: x).
Choosing good function is key factor for successful optimization in infinite approach.
TNQMetro package features inf_L_symfun function which performs well in dephasing type problems.
symfun_psi0: function
Function which symmetrize iMPS for psi0 after each step of otimization (the most simple one would be lambda x: x).
Choosing good function is key factor for successful optimization in infinite approach.
TNQMetro package features inf_psi0_symfun function which performs well in dephasing type problems.
L_ini: ndarray of a shape (D_L,D_L,d,d), optional
Initial iMPO for tilde{L}.
psi0_ini: ndarray of a shape (D_psi0,D_psi0,d), optional
Initial iMPS for psi0.
imprecision: float, optional
Expected relative imprecision of the end results.
D_L_max: integer, optional
Maximal value of D_L (D_L is bond dimension for iMPO representing tilde{L}).
D_L_max_forced: bool, optional
True if D_L_max have to be reached, otherwise False.
L_herm: bool, optional
True if Hermitian gauge have to be imposed on iMPO representing tilde{L}, otherwise False.
D_psi0_max: integer, optional
Maximal value of D_psi0 (D_psi0 is bond dimension for iMPS representing psi0).
D_psi0_max_forced: bool, optional
True if D_psi0_max have to be reached, otherwise False.
Returns:
result: float
Optimal value of figure of merit.
result_m: ndarray
Matrix describing figure of merit in function of bond dimensions of respectively tilde{L} [rows] and psi0 [columns].
L: ndarray of a shape (D_L,D_L,d,d)
Optimal tilde{L} in iMPO representation.
psi0: ndarray of a shape (D_psi0,D_psi0,d)
Optimal psi0 in iMPS representation.
"""
result, result_m, L, psi0 = inf_FoM_FoMD_optbd(d, ch, ch2, epsilon, symfun_L, symfun_psi0, L_ini, psi0_ini, imprecision, D_L_max, D_L_max_forced, L_herm, D_psi0_max, D_psi0_max_forced)
return result, result_m, L, psi0
def inf_state(so_before_list, h, so_after_list, rho0, L_ini=None, imprecision=10**-2, D_L_max=100, D_L_max_forced=False, L_herm=True):
"""
Optimization of the lim_{N --> infinity} QFI/N over operator tilde{L} (in iMPO representation) and check of convergence in its bond dimension. Function for infinite size systems and fixed state of the system.
User has to provide information about the dynamics by specifying quantum channel. It is assumed that quantum channel is translationally invariant and is build from layers of quantum operations.
User has to provide one defining for each layer operation as a local superoperator. Those local superoperator have to be input in order of their action on the system.
Parameter encoding is a stand out quantum operation. It is assumed that parameter encoding acts only once and is unitary so the user have to provide only its generator h.
Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.
Parameters:
so_before_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites particular local superoperator acts
List of local superoperators (in order) which act before unitary parameter encoding.
h: ndarray of a shape (d,d)
Generator of unitary parameter encoding. Dimension d is the dimension of local Hilbert space (dimension of physical index).
Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.
so_after_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites particular local superoperator acts
List of local superoperators (in order) which act after unitary parameter encoding.
rho0: ndarray of a shape (D_rho0,D_rho0,d,d)
Density matrix describing initial state of the system in iMPO representation.
L_ini: ndarray of a shape (D_L,D_L,d,d), optional
Initial iMPO for tilde{L}.
imprecision: float, optional
Expected relative imprecision of the end results.
D_L_max: integer, optional
Maximal value of D_L (D_L is bond dimension for iMPO representing tilde{L}).
D_L_max_forced: bool, optional
True if D_L_max have to be reached, otherwise False.
L_herm: bool, optional
True if Hermitian gauge have to be imposed on iMPO representing tilde{L}, otherwise False.
Returns:
result: float
Optimal value of figure of merit.
result_v: ndarray
Vector describing figure of merit in function of bond dimensions of tilde{L}.
L: ndarray of a shape (D_L,D_L,d,d)
Optimal tilde{L} in iMPO representation.
"""
if np.linalg.norm(h - np.diag(np.diag(h))) > 10**-10:
warnings.warn('Generator h have to be diagonal in computational basis, or in other words it is assumed that local superoperators are expressed in the eigenbasis of h.')
d = np.shape(h)[0]
epsilon = 10**-4
aux = np.kron(h, np.eye(d)) - np.kron(np.eye(d), h)
z = np.diag(np.exp(-1j * np.diag(aux) * epsilon))
ch = inf_create_channel(d, so_before_list + so_after_list)
ch2 = inf_create_channel(d, so_before_list + [z] + so_after_list)
rho = channel_acting_on_operator(ch, rho0)
rho2 = channel_acting_on_operator(ch2, rho0)
result, result_v, L = inf_state_gen(d, rho, rho2, epsilon, inf_L_symfun, L_ini, imprecision, D_L_max, D_L_max_forced, L_herm)
return result, result_v, L
def inf_state_gen(d, rho, rho2, epsilon, symfun_L, L_ini=None, imprecision=10**-2, D_L_max=100, D_L_max_forced=False, L_herm=True):
"""
Optimization of the figure of merit (usually interpreted as lim_{N --> infinity} QFI/N) over operator tilde{L} (in iMPO representation) and check of convergence in its bond dimension. Function for infinite size systems and fixed state of the system.
User has to provide information about the dynamics by specifying two channels separated by small parameter epsilon as superoperators in iMPO representation.
By definition this infinite approach assumes translation invariance of the problem, other than that there are no constraints on the structure of the channel but the complexity of calculations highly depends on channel's bond dimension.
Parameters:
d: integer
Dimension of local Hilbert space (dimension of physical index).
rho: ndarray of a shape (D_rho,D_rho,d,d)
Density matrix at the output of quantum channel in iMPO representation.
rho2: ndarray of a shape (D_rho2,D_rho2,d,d)
Density matrix at the output of quantum channel in iMPO representation for the value of estimated parameter shifted by epsilon in relation to rho.
epsilon: float
Value of a separation between estimated parameters encoded in rho and rho2.
symfun_L: function
Function which symmetrize iMPO for tilde{L} after each step of otimization (the most simple one would be lambda x: x).
Choosing good function is key factor for successful optimization in infinite approach.
TNQMetro package features inf_L_symfun function which performs well in dephasing type problems.
L_ini: ndarray of a shape (D_L,D_L,d,d), optional
Initial iMPO for tilde{L}.
imprecision: float, optional
Expected relative imprecision of the end results.
D_L_max: integer, optional
Maximal value of D_L (D_L is bond dimension for iMPO representing tilde{L}).
D_L_max_forced: bool, optional
True if D_L_max have to be reached, otherwise False.
L_herm: bool, optional
True if Hermitian gauge have to be imposed on iMPO representing tilde{L}, otherwise False.
Returns:
result: float
Optimal value of figure of merit.
result_v: ndarray
Vector describing figure of merit in function of bond dimensions of tilde{L}.
L: ndarray of a shape (D_L,D_L,d,d)
Optimal tilde{L} in iMPO representation.
"""
result, result_v, L = inf_FoM_optbd(d, rho, rho2, epsilon, symfun_L, L_ini, imprecision, D_L_max, D_L_max_forced, L_herm)
return result, result_v, L
def inf_L_symfun(l):
"""
Symmetrize function for iMPO representing tilde{L} which performs well in dephasing type problems.
Parameters:
l: ndarray of a shape (D_L,D_L,d,d)
iMPO for tilde{L}.
Returns:
l: ndarray of a shape (D_L,D_L,d,d)
Symmetrize iMPO for tilde{L}.
"""
bdl = np.shape(l)[0]
d = np.shape(l)[2]
if bdl == 1:
l = np.reshape(l,(d,d),order='F')
lmd = np.mean(np.diag(l))
l = np.imag(l)
l = (l+np.rot90(l,2).T)/2
l = lmd*np.eye(d)+1j*l
l = np.reshape(l,(bdl,bdl,d,d),order='F')
else:
for nx in range(d):
l[:,:,nx,nx] = np.zeros((bdl,bdl),dtype=complex)
l[0,0,nx,nx] = 1
return l
def inf_psi0_symfun(p):
"""
Symmetrize function for iMPS representing psi0 which performs well in dephasing type problems.
Parameters:
p: ndarray of a shape (D_psi0,D_psi0,d)
iMPS for psi0.
Returns:
p: ndarray of a shape (D_psi0,D_psi0,d)
Symmetrize iMPS for psi0.
"""
p = (p+np.conj(np.moveaxis(p,0,1)))/2
p = (p+np.moveaxis(np.flip(p,2),0,1))/2
p = (p+np.moveaxis(np.rot90(p,2),0,1))/2
return p
############################
# #
# 2.2 Low level functions. #
# #
############################
def inf_create_channel(d, so_list, tol=10**-10):
"""
Creates iMPO for superoperator describing translationally invariant quantum channel from list of local superoperators. Function for infinite size systems.
Local superoperators acting on more then 4 neighbour sites are not currently supported.
Parameters:
d: integer
Dimension of local Hilbert space (dimension of physical index).
so_list: list of ndarrays of a shape (d**(2*k),d**(2*k)) where k describes on how many sites particular local superoperator acts
List of local superoperators in order of their action on the system.
Local superoperators acting on more then 4 neighbour sites are not currently supported.
tol: float, optional
Factor which after multiplication by the highest singular value give cutoff on singular values.
Returns:
ch: ndarray of a shape (D_ch,D_ch,d**2,d**2)
Quantum channel as superoperator in iMPO representation.
"""
if so_list == []:
ch = np.eye(d**2,dtype=complex)
ch = ch[np.newaxis,np.newaxis,:,:]
return ch
for i in range(len(so_list)):
so = so_list[i]
k = int(math.log(np.shape(so)[0],d**2))
if np.linalg.norm(so-np.diag(np.diag(so))) < 10**-10:
so = np.diag(so)
if k == 1:
bdchi = 1
chi = np.zeros((bdchi,bdchi,d**2,d**2),dtype=complex)
for nx in range(d**2):
chi[:,:,nx,nx] = so[nx]
elif k == 2:
so = np.reshape(so,(d**2,d**2),order='F')
u,s,vh = np.linalg.svd(so)
s = s[s > s[0]*tol]
bdchi = np.shape(s)[0]
u = u[:,:bdchi]
vh = vh[:bdchi,:]
us = u @ np.diag(np.sqrt(s))
sv = np.diag(np.sqrt(s)) @ vh
chi = np.zeros((bdchi,bdchi,d**2,d**2),dtype=complex)
for nx in range(d**2):
chi[:,:,nx,nx] = np.outer(sv[:,nx],us[nx,:])
elif k == 3:
so = np.reshape(so,(d**2,d**4),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
sv1 = np.reshape(sv1,(bdchi1*d**2,d**2),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
bdchi = bdchi2*bdchi1
chi = np.zeros((bdchi,bdchi,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv2[:,nx],us2[:,nx,:],us1[nx,:]]
legs = [[-1],[-2,-3],[-4]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchi,bdchi),order='F')
elif k == 4:
so = np.reshape(so,(d**2,d**6),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
sv1 = np.reshape(sv1,(bdchi1*d**2,d**4),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
sv2 = np.reshape(sv2,(bdchi2*d**2,d**2),order='F')
u3,s3,vh3 = np.linalg.svd(sv2,full_matrices=False)
s3 = s3[s3 > s3[0]*tol]
bdchi3 = np.shape(s3)[0]
u3 = u3[:,:bdchi3]
vh3 = vh3[:bdchi3,:]
us3 = u3 @ np.diag(np.sqrt(s3))
us3 = np.reshape(us3,(bdchi2,d**2,bdchi3),order='F')
sv3 = np.diag(np.sqrt(s3)) @ vh3
bdchi = bdchi3*bdchi2*bdchi1
chi = np.zeros((bdchi,bdchi,d**2,d**2),dtype=complex)
for nx in range(d**2):
tensors = [sv3[:,nx],us3[:,nx,:],us2[:,nx,:],us1[nx,:]]
legs = [[-1],[-2,-4],[-3,-5],[-6]]
chi[:,:,nx,nx] = np.reshape(ncon(tensors,legs),(bdchi,bdchi),order='F')
else:
warnings.warn('Local noise superoperators acting on more then 4 neighbour sites are not currently supported.')
else:
if k == 1:
bdchi = 1
chi = so[np.newaxis,np.newaxis,:,:]
elif k == 2:
u,s,vh = np.linalg.svd(so)
s = s[s > s[0]*tol]
bdchi = np.shape(s)[0]
u = u[:,:bdchi]
vh = vh[:bdchi,:]
us = u @ np.diag(np.sqrt(s))
sv = np.diag(np.sqrt(s)) @ vh
us = np.reshape(us,(d**2,d**2,bdchi),order='F')
sv = np.reshape(sv,(bdchi,d**2,d**2),order='F')
tensors = [sv,us]
legs = [[-1,-3,1],[1,-4,-2]]
chi = ncon(tensors,legs)
elif k == 3:
so = np.reshape(so,(d**4,d**8),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
us1 = np.reshape(us1,(d**2,d**2,bdchi1),order='F')
sv1 = np.reshape(sv1,(bdchi1*d**4,d**4),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
sv2 = np.reshape(sv2,(bdchi2,d**2,d**2),order='F')
tensors = [sv2,us2,us1]
legs = [[-1,-5,1],[-2,1,2,-3],[2,-6,-4]]
chi = ncon(tensors,legs)
bdchi = bdchi2*bdchi1
chi = np.reshape(chi,(bdchi,bdchi,d**2,d**2),order='F')
elif k == 4:
so = np.reshape(so,(d**4,d**12),order='F')
u1,s1,vh1 = np.linalg.svd(so,full_matrices=False)
s1 = s1[s1 > s1[0]*tol]
bdchi1 = np.shape(s1)[0]
u1 = u1[:,:bdchi1]
vh1 = vh1[:bdchi1,:]
us1 = u1 @ np.diag(np.sqrt(s1))
sv1 = np.diag(np.sqrt(s1)) @ vh1
us1 = np.reshape(us1,(d**2,d**2,bdchi1),order='F')
sv1 = np.reshape(sv1,(bdchi1*d**4,d**8),order='F')
u2,s2,vh2 = np.linalg.svd(sv1,full_matrices=False)
s2 = s2[s2 > s2[0]*tol]
bdchi2 = np.shape(s2)[0]
u2 = u2[:,:bdchi2]
vh2 = vh2[:bdchi2,:]
us2 = u2 @ np.diag(np.sqrt(s2))
us2 = np.reshape(us2,(bdchi1,d**2,d**2,bdchi2),order='F')
sv2 = np.diag(np.sqrt(s2)) @ vh2
sv2 = np.reshape(sv2,(bdchi2*d**4,d**4),order='F')
u3,s3,vh3 = np.linalg.svd(sv2,full_matrices=False)
s3 = s3[s3 > s3[0]*tol]
bdchi3 = np.shape(s3)[0]
u3 = u3[:,:bdchi3]
vh3 = vh3[:bdchi3,:]
us3 = u3 @ np.diag(np.sqrt(s3))
us3 = np.reshape(us3,(bdchi2,d**2,d**2,bdchi3),order='F')
sv3 = np.diag(np.sqrt(s3)) @ vh3
sv3 = np.reshape(sv3,(bdchi3,d**2,d**2),order='F')
tensors = [sv3,us3,us2,us1]
legs = [[-1,-7,1],[-2,1,2,-4],[-3,2,3,-5],[3,-8,-6]]
chi = ncon(tensors,legs)
bdchi = bdchi3*bdchi2*bdchi1
chi = np.reshape(chi,(bdchi,bdchi,d**2,d**2),order='F')
else:
warnings.warn('Local noise superoperators acting on more then 4 neighbour sites are not currently supported.')
if i == 0:
bdch = bdchi
ch = chi
else:
bdch = bdchi*bdch
tensors = [chi,ch]
legs = [[-1,-3,-5,1],[-2,-4,1,-6]]
ch = ncon(tensors,legs)
ch = np.reshape(ch,(bdch,bdch,d**2,d**2),order='F')
return ch
def inf_L_normalization(l):
"""
Normalize (shifted) SLD iMPO.
Parameters:
l: (shifted) SLD iMPO, expected ndarray of a shape (bd,bd,d,d)
Returns:
l: normalized (shifted) SLD iMPO
"""
d = np.shape(l)[2]
tensors = [l]
legs = [[-1,-2,1,1]]
tm = ncon(tensors,legs)
ltr = np.linalg.eigvals(tm)
ltr = ltr[np.argmax(np.abs(ltr))]
ltr = np.real(ltr)
l = d*l/ltr
return l
def inf_psi0_normalization(p):
"""
Normalize wave function iMPS.
Parameters:
p: wave function iMPS, expected ndarray of a shape (bd,bd,d)
Returns:
p: normalized wave function iMPS
"""
bdp = np.shape(p)[0]
tensors = [np.conj(p),p]
legs = [[-1,-3,1],[-2,-4,1]]
tm = ncon(tensors,legs)
tm = np.reshape(tm,(bdp*bdp,bdp*bdp),order='F')
tm = (tm+np.conj(tm).T)/2
tmval = np.linalg.eigvalsh(tm)
pnorm = np.sqrt(tmval[-1])
p = p/pnorm
return p
def inf_enlarge_bdl(cold,factor,symfun):
"""
Enlarge bond dimension of (shifted) SLD iMPO. Function for infinite size systems.
Parameters:
cold: (shifted) SLD iMPO, expected ndarray of a shape (bd,bd,d,d)
factor: factor which determine on average relation between old and newly added values of (shifted) SLD iMPO
symfun: symmetrize function
Returns:
c: (shifted) SLD iMPO with bd += 1
"""
d = np.shape(cold)[2]
bdl = np.shape(cold)[0]+1
rng = np.random.default_rng()
c = np.zeros((bdl,bdl,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
meanrecold = np.sum(np.abs(np.real(cold[:,:,nx,nxp])))/(bdl-1)**2
meanimcold = np.sum(np.abs(np.imag(cold[:,:,nx,nxp])))/(bdl-1)**2
c[:,:,nx,nxp] = (meanrecold*rng.random((bdl,bdl))+1j*meanimcold*rng.random((bdl,bdl)))*factor
c = (c + np.conj(np.moveaxis(c,2,3)))/2
c[0:bdl-1,0:bdl-1,:,:] = cold
c = symfun(c)
c = inf_L_normalization(c)
return c
def inf_enlarge_bdpsi(a0old,ratio,symfund):
"""
Enlarge bond dimension of wave function iMPS. Function for infinite size systems.
Parameters:
a0old: wave function iMPS, expected ndarray of a shape (bd,bd,d)
ratio: factor which determine on average relation between last and next to last values of diagonals of wave function iMPS
symfund: symmetrize function
Returns:
a0: wave function iMPS with bd += 1
"""
d = np.shape(a0old)[2]
bdpsi = np.shape(a0old)[0]+1
a0 = np.zeros((bdpsi,bdpsi,d),dtype=complex)
for i in range(d):
if i <= np.ceil(d/2)-1:
a0oldihalf = np.triu(np.rot90(a0old[:,:,i],-1))
a0[0:bdpsi-1,1:bdpsi,i] = a0oldihalf
a0[:,:,i] = a0[:,:,i]+a0[:,:,i].T
a0[:,:,i] = a0[:,:,i]+np.diag(np.concatenate(([0],np.diag(a0[:,:,i],2),[0])))
a0[:,:,i] = np.rot90(a0[:,:,i],1)
a0[0,-1,i] = ratio*(1+1j)*np.abs(a0[0,-2,i])
a0[-1,0,i] = np.conj(a0[0,-1,i])
if i == np.ceil(d/2)-1 and np.mod(d,2) == 1:
a0[:,:,i] = (a0[:,:,i]+a0[:,:,i].T)/2
else:
a0[:,:,i] = a0[:,:,d-1-i].T
a0 = symfund(a0)
a0 = inf_psi0_normalization(a0)
return a0
def inf_FoM_FoMD_optbd(d,ch,chp,epsilon,symfun,symfund,cini=None,a0ini=None,imprecision=10**-2,bdlmax=100,alwaysbdlmax=False,lherm=True,bdpsimax=100,alwaysbdpsimax=False):
"""
Iterative optimization of FoM/FoMD over (shifted) SLD iMPO and initial wave function iMPS and also check of convergence in bond dimensions. Function for infinite size systems.
Parameters:
d: dimension of local Hilbert space (dimension of physical index)
ch: iMPO for quantum channel at the value of estimated parameter phi=phi_0, expected ndarray of a shape (bd,bd,d**2,d**2)
chp: iMPO for quantum channel at the value of estimated parameter phi=phi_0+epsilon, expected ndarray of a shape (bd,bd,d**2,d**2)
epsilon: value of a separation between estimated parameters encoded in ch and chp, float
symfun: symmetrize function for iMPO for (shifted) SLD
symfund: symmetrize function for iMPS for initial wave function
cini: initial iMPO for (shifted) SLD, expected TN of a shape (bd,bd,d,d)
a0ini: initial iMPS for initial wave function, expected TN of a shape (bd,bd,d)
imprecision: expected imprecision of the end results, default value is 10**-2
bdlmax: maximal value of bd for (shifted) SLD iMPO, default value is 100
alwaysbdlmax: boolean value, True if maximal value of bd for (shifted) SLD iMPO have to be reached, otherwise False (default value)
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD iMPO, otherwise False
bdpsimax: maximal value of bd for iMPS for initial wave function, default value is 100
alwaysbdpsimax: boolean value, True if maximal value of bd for iMPS for initial wave function have to be reached, otherwise False (default value)
Returns:
result: optimal value of FoM/FoMD
resultm: matrix describing FoM/FoMD in function of bd of respectively (shifted) SLD iMPO [rows] and initial wave function iMPS [columns]
c: optimal iMPO for (shifted) SLD
a0: optimal iMPS for initial wave function
"""
while True:
if a0ini is None:
bdpsi = 1
a0 = np.zeros(d,dtype=complex)
for i in range(d):
a0[i] = np.sqrt(math.comb(d-1,i))*2**(-(d-1)/2) # prod
# a0[i] = np.sqrt(2/(d+1))*np.sin((1+i)*np.pi/(d+1)) # sine
a0 = a0[np.newaxis,np.newaxis,:]
else:
a0 = a0ini
bdpsi = np.shape(a0)[0]
a0 = a0.astype(complex)
if cini is None:
bdl = 1
c = np.triu(np.ones((d,d))-np.eye(d))
c = 1j*epsilon*c
c = c+np.conj(c).T
c = np.eye(d)+c
c = np.reshape(c,(bdl,bdl,d,d),order='F')
else:
c = cini
bdl = np.shape(c)[0]
c = c.astype(complex)
resultm = np.zeros((bdlmax,bdpsimax),dtype=float)
resultm[bdl-1,bdpsi-1],c,a0 = inf_FoM_FoMD_optm(c,a0,ch,chp,epsilon,symfun,symfund,imprecision,lherm)
ratiov = np.array([10**-3,10**-2.5,10**-2])
factorv = np.array([0.5,0.25,0.1,1,0.01])
problem = False
while True:
while True:
if bdpsi == bdpsimax:
break
else:
a0old = a0
bdpsi += 1
i = 0
while True:
a0 = inf_enlarge_bdpsi(a0,ratiov[i],symfund)
resultm[bdl-1,bdpsi-1],cnew,a0new = inf_FoM_FoMD_optm(c,a0,ch,chp,epsilon,symfun,symfund,imprecision,lherm)
if resultm[bdl-1,bdpsi-1] >= resultm[bdl-1,bdpsi-2]:
break
i += 1
if i == np.size(ratiov):
problem = True
break
if problem:
break
if not(alwaysbdpsimax) and resultm[bdl-1,bdpsi-1] < (1+imprecision)*resultm[bdl-1,bdpsi-2]:
bdpsi += -1
a0 = a0old
a0copy = a0new
ccopy = cnew
break
else:
a0 = a0new
c = cnew
if problem:
break
if bdl == bdlmax:
if bdpsi == bdpsimax:
resultm = resultm[0:bdl,0:bdpsi]
result = resultm[bdl-1,bdpsi-1]
else:
a0 = a0copy
c = ccopy
resultm = resultm[0:bdl,0:bdpsi+1]
result = resultm[bdl-1,bdpsi]
break
else:
bdl += 1
i = 0
while True:
c = inf_enlarge_bdl(c,factorv[i],symfun)
resultm[bdl-1,bdpsi-1],cnew,a0new = inf_FoM_FoMD_optm(c,a0,ch,chp,epsilon,symfun,symfund,imprecision,lherm)
if resultm[bdl-1,bdpsi-1] >= resultm[bdl-2,bdpsi-1]:
a0 = a0new
c = cnew
break
i += 1
if i == np.size(factorv):
problem = True
break
if problem:
break
if not(alwaysbdlmax) and resultm[bdl-1,bdpsi-1] < (1+imprecision)*resultm[bdl-2,bdpsi-1]:
if bdpsi == bdpsimax:
resultm = resultm[0:bdl,0:bdpsi]
result = resultm[bdl-1,bdpsi-1]
else:
if resultm[bdl-1,bdpsi-1] < resultm[bdl-2,bdpsi]:
a0 = a0copy
c = ccopy
resultm = resultm[0:bdl,0:bdpsi+1]
bdl += -1
bdpsi += 1
result = resultm[bdl-1,bdpsi-1]
else:
resultm = resultm[0:bdl,0:bdpsi+1]
result = resultm[bdl-1,bdpsi-1]
break
if not(problem):
break
return result,resultm,c,a0
def inf_FoM_optbd(d,a,b,epsilon,symfun,cini=None,imprecision=10**-2,bdlmax=100,alwaysbdlmax=False,lherm=True):
"""
Optimization of FoM over (shifted) SLD iMPO and also check of convergence in bond dimension. Function for infinite size systems.
Parameters:
d: dimension of local Hilbert space (dimension of physical index)
a: iMPO for density matrix at the value of estimated parameter phi=phi_0, expected ndarray of a shape (bd,bd,d,d)
b: iMPO for density matrix at the value of estimated parameter phi=phi_0+epsilon, expected ndarray of a shape (bd,bd,d,d)
epsilon: value of a separation between estimated parameters encoded in a and b, float
symfun: symmetrize function for iMPO for (shifted) SLD
cini: initial iMPO for (shifted) SLD, expected TN of a shape (bd,bd,d,d)
imprecision: expected imprecision of the end results, default value is 10**-2
bdlmax: maximal value of bd for (shifted) SLD iMPO, default value is 100
alwaysbdlmax: boolean value, True if maximal value of bd for (shifted) SLD iMPO have to be reached, otherwise False (default value)
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD iMPO, otherwise False
Returns:
result: optimal value of FoM
resultv: matrix describing FoM in function of bd of (shifted) SLD iMPO
c: optimal iMPO for (shifted) SLD
"""
while True:
if cini is None:
bdl = 1
c = np.triu(np.ones((d,d))-np.eye(d))
c = 1j*epsilon*c
c = c+np.conj(c).T
c = np.eye(d)+c
c = np.reshape(c,(bdl,bdl,d,d),order='F')
else:
c = cini
bdl = np.shape(c)[0]
c = c.astype(complex)
resultv = np.zeros(bdlmax,dtype=float)
resultv[bdl-1],c = inf_FoM_optm_glob(a,b,c,epsilon,symfun,imprecision,lherm)
factorv = np.array([0.5,0.25,0.1,1,0.01])
problem = False
while True:
if bdl == bdlmax:
resultv = resultv[0:bdl]
result = resultv[bdl-1]
break
else:
bdl += 1
i = 0
while True:
c = inf_enlarge_bdl(c,factorv[i],symfun)
resultv[bdl-1],cnew = inf_FoM_optm_glob(a,b,c,epsilon,symfun,imprecision,lherm)
if resultv[bdl-1] >= resultv[bdl-2]:
c = cnew
break
i += 1
if i == np.size(factorv):
problem = True
break
if problem:
break
if not(alwaysbdlmax) and resultv[bdl-1] < (1+imprecision)*resultv[bdl-2]:
resultv = resultv[0:bdl]
result = resultv[bdl-1]
break
if not(problem):
break
return result,resultv,c
def inf_FoMD_optbd(d,c2d,cpd,epsilon,symfund,a0ini=None,imprecision=10**-2,bdpsimax=100,alwaysbdpsimax=False):
"""
Optimization of FoMD over initial wave function iMPS and also check of convergence in bond dimension. Function for infinite size systems.
Parameters:
d: dimension of local Hilbert space (dimension of physical index)
c2d: iMPO for square of dual of (shifted) SLD at the value of estimated parameter phi=-phi_0, expected ndarray of a shape (bd,bd,d,d)
cpd: iMPO for dual of (shifted) SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected ndarray of a shape (bd,bd,d,d)
epsilon: value of a separation between estimated parameters encoded in c2d and cpd, float
symfund: symmetrize function for iMPS for initial wave function
a0ini: initial iMPS for initial wave function, expected TN of a shape (bd,bd,d)
imprecision: expected imprecision of the end results, default value is 10**-2
bdpsimax: maximal value of bd for iMPS for initial wave function, default value is 100
alwaysbdpsimax: boolean value, True if maximal value of bd for iMPS for initial wave function have to be reached, otherwise False (default value)
Returns:
result: optimal value of FoMD
resultv: matrix describing FoMD in function of bd of initial wave function iMPS
a0: optimal iMPS for initial wave function
"""
while True:
if a0ini is None:
bdpsi = 1
a0 = np.zeros(d,dtype=complex)
for i in range(d):
a0[i] = np.sqrt(math.comb(d-1,i))*2**(-(d-1)/2) # prod
# a0[i] = np.sqrt(2/(d+1))*np.sin((1+i)*np.pi/(d+1)) # sine
a0 = a0[np.newaxis,np.newaxis,:]
else:
a0 = a0ini
bdpsi = np.shape(a0)[0]
a0 = a0.astype(complex)
resultv = np.zeros(bdpsimax,dtype=float)
resultv[bdpsi-1],a0 = inf_FoMD_optm_glob(c2d,cpd,a0,epsilon,symfund,imprecision)
ratiov = np.array([10**-3,10**-2.5,10**-2])
problem = False
while True:
if bdpsi == bdpsimax:
resultv = resultv[0:bdpsi]
result = resultv[bdpsi-1]
break
else:
bdpsi += 1
i = 0
while True:
a0 = inf_enlarge_bdpsi(a0,ratiov[i],symfund)
resultv[bdpsi-1],a0new = inf_FoMD_optm_glob(c2d,cpd,a0,epsilon,symfund,imprecision)
if resultv[bdpsi-1] >= resultv[bdpsi-2]:
a0 = a0new
break
i += 1
if i == np.size(ratiov):
problem = True
break
if problem:
break
if not(alwaysbdpsimax) and resultv[bdpsi-1] < (1+imprecision)*resultv[bdpsi-2]:
resultv = resultv[0:bdpsi]
result = resultv[bdpsi-1]
break
if not(problem):
break
return result,resultv,a0
def inf_FoM_FoMD_optm(c,a0,ch,chp,epsilon,symfun,symfund,imprecision=10**-2,lherm=True):
"""
Iterative optimization of FoM/FoMD over (shifted) SLD iMPO and initial wave function iMPS. Function for infinite size systems.
Parameters:
c: iMPO for (shifted) SLD, expected ndarray of a shape (bd,bd,d,d)
a0: iMPS for initial wave function, expected ndarray of a shape (bd,bd,d)
ch: iMPO for quantum channel at the value of estimated parameter phi=phi_0, expected ndarray of a shape (bd,bd,d**2,d**2)
chp: iMPO for quantum channel at the value of estimated parameter phi=phi_0+epsilon, expected ndarray of a shape (bd,bd,d**2,d**2)
epsilon: value of a separation between estimated parameters encoded in ch and chp, float
symfun: symmetrize function for iMPO for (shifted) SLD
symfund: symmetrize function for iMPS for initial wave function
imprecision: expected imprecision of the end results, default value is 10**-2
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD iMPO, otherwise False
Returns:
fval: optimal value of FoM/FoMD
c: optimal iMPO for (shifted) SLD
a0: optimal iMPS for initial wave function
"""
d = np.shape(c)[2]
bdl = np.shape(c)[0]
relunc_f = 0.1*imprecision
chd = np.conj(np.moveaxis(ch,2,3))
chpd = np.conj(np.moveaxis(chp,2,3))
f = np.array([])
iter_f = 0
while True:
a0_dm = wave_function_to_density_matrix(a0)
a = channel_acting_on_operator(ch,a0_dm)
b = channel_acting_on_operator(chp,a0_dm)
fom,c = inf_FoM_optm_glob(a,b,c,epsilon,symfun,imprecision,lherm)
f = np.append(f,fom)
if iter_f >= 2 and np.std(f[-4:])/np.mean(f[-4:]) <= relunc_f:
break
c2 = np.zeros((bdl**2,bdl**2,d,d),dtype=complex)
for nx in range(d):
for nxp in range(d):
for nxpp in range(d):
c2[:,:,nx,nxp] = c2[:,:,nx,nxp]+np.kron(c[:,:,nx,nxpp],c[:,:,nxpp,nxp])
c2d = channel_acting_on_operator(chd,c2)
cpd = channel_acting_on_operator(chpd,c)
fomd,a0 = inf_FoMD_optm_glob(c2d,cpd,a0,epsilon,symfund,imprecision)
f = np.append(f,fomd)
iter_f += 1
fval = f[-1]
return fval,c,a0
def inf_FoM_optm_glob(a,b,c,epsilon,symfun,imprecision=10**-2,lherm=True):
"""
Optimization of FoM over iMPO for (shifted) SLD. Function for infinite size systems.
Parameters:
a: iMPO for density matrix at the value of estimated parameter phi=phi_0, expected ndarray of a shape (bd,bd,d,d)
b: iMPO for density matrix at the value of estimated parameter phi=phi_0+epsilon, expected ndarray of a shape (bd,bd,d,d)
c: iMPO for (shifted) SLD, expected ndarray of a shape (bd,bd,d,d)
epsilon: value of a separation between estimated parameters encoded in a and b, float
symfun: symmetrize function for iMPO for (shifted) SLD
imprecision: expected imprecision of the end results, default value is 10**-2
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD iMPO, otherwise False
Returns:
fomval: optimal value of FoM
c: optimal iMPO for (shifted) SLD
"""
def inf_FoM_optm_glob_mix(m,c_old,opt_flag=True,c_old_locopt=None):
"""
Nested function for mixing localy optimal iMPO for (shifted) SLD with its initial form according to parameter m.
Parameters:
m: mixing parameter
c_old: initial iMPO for (shifted) SLD, expected ndarray of a shape (bd,bd,d,d)
opt_flag: boolean value, True (default value) if calculating localy optimal iMPO is necessary, otherwise False
c_old_locopt: localy optimal iMPO for (shifted) SLD used when opt_flag=False, default value is None
Returns:
fomvalf: value of FoM
c_newf: iMPO for (shifted) SLD after mixing
c_locoptf: localy optimal iMPO for (shifted) SLD before mixing
"""
if opt_flag:
c_locoptf = inf_FoM_optm_loc(a,b,c_old,epsilon,imprecision,lherm)
c_locoptf = symfun(c_locoptf)
c_locoptf = inf_L_normalization(c_locoptf)
else:
c_locoptf = c_old_locopt
c_newf = c_locoptf*np.sin(m*np.pi)-c_old*np.cos(m*np.pi)
c_newf = symfun(c_newf)
c_newf = inf_L_normalization(c_newf)
fomvalf = inf_FoM_val(a,b,c_newf,epsilon)
return fomvalf,c_newf,c_locoptf
step_ini = 10**-1
step_tiny = 10**-10
relunc_fom = 0.1*imprecision
fom = np.array([])
fom_1 = inf_FoM_val(a,b,c,epsilon)
fom_05,c_05 = inf_FoM_optm_glob_mix(1/2,c)[:2]
if fom_05 > fom_1:
c = c_05
fom = np.append(fom,fom_05)
else:
fom = np.append(fom,fom_1)
del c_05
fom_tinylean = inf_FoM_optm_glob_mix(1+step_tiny,c)[0]
if fom_tinylean > fom[0]:
step = step_ini
else:
step = -step_ini
opt_flag = True
c_locopt = None
iter_fom = 1
while True:
fomval,c_new,c_locopt = inf_FoM_optm_glob_mix(1+step,c,opt_flag,c_locopt)
if fomval > fom[-1]:
c = c_new
fom = np.append(fom,fomval)
opt_flag = True
iter_fom += 1
else:
step = step/2
opt_flag = False
if np.abs(step) < step_tiny or (iter_fom >= 4 and all(fom[-4:] > 0) and np.std(fom[-4:])/np.mean(fom[-4:]) <= relunc_fom):
break
fomval = fom[-1]
return fomval,c
def inf_FoMD_optm_glob(c2d,cpd,a0,epsilon,symfund,imprecision=10**-2):
"""
Optimization of FoMD over iMPS for initial wave function. Function for infinite size systems.
Parameters:
c2d: iMPO for square of dual of (shifted) SLD at the value of estimated parameter phi=-phi_0, expected ndarray of a shape (bd,bd,d,d)
cpd: iMPO for dual of (shifted) SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected ndarray of a shape (bd,bd,d,d)
a0: iMPS for initial wave function, expected ndarray of a shape (bd,bd,d)
epsilon: value of a separation between estimated parameters encoded in c2d and cpd, float
symfund: symmetrize function for iMPS for initial wave function
imprecision: expected imprecision of the end results, default value is 10**-2
Returns:
fomdval: optimal value of FoMD
a0: optimal iMPS for initial wave function
"""
def inf_FoMD_optm_glob_mix(m,a0_old,opt_flag=True,a0_old_locopt=None):
"""
Nested function for mixing localy optimal iMPS for initial wave function with its initial form according to parameter m.
Parameters:
m: mixing parameter
a0_old: initial iMPS for initial wave function, expected ndarray of a shape (bd,bd,d)
opt_flag: boolean value, True (default value) if calculating localy optimal iMPS is necessary, otherwise False
a0_old_locopt: localy optimal iMPS for initial wave function used when opt_flag=False, default value is None
Returns:
fomdvalf: value of FoMD
a0_newf: iMPS for initial wave function after mixing
a0_locoptf: localy optimal iMPS for initial wave function before mixing
"""
if opt_flag:
a0_locoptf = inf_FoMD_optm_loc(c2d,cpd,a0_old,epsilon,imprecision)
a0_locoptf = symfund(a0_locoptf)
a0_locoptf = inf_psi0_normalization(a0_locoptf)
else:
a0_locoptf = a0_old_locopt
a0_newf = a0_locoptf*np.sin(m*np.pi)-a0_old*np.cos(m*np.pi)
a0_newf = symfund(a0_newf)
a0_newf = inf_psi0_normalization(a0_newf)
fomdvalf = inf_FoMD_val(c2d,cpd,a0_newf,epsilon)
return fomdvalf,a0_newf,a0_locoptf
step_ini = 10**-1
step_tiny = 10**-10
relunc_fomd = 0.1*imprecision
fomd = np.array([])
fomd_1 = inf_FoMD_val(c2d,cpd,a0,epsilon)
fomd_05,a0_05 = inf_FoMD_optm_glob_mix(1/2,a0)[:2]
if fomd_05 > fomd_1:
a0 = a0_05
fomd = np.append(fomd,fomd_05)
else:
fomd = np.append(fomd,fomd_1)
del a0_05
fomd_tinylean = inf_FoMD_optm_glob_mix(1+step_tiny,a0)[0]
if fomd_tinylean > fomd[0]:
step = step_ini
else:
step = -step_ini
opt_flag = True
a0_locopt = None
iter_fomd = 1
while True:
fomdval,a0_new,a0_locopt = inf_FoMD_optm_glob_mix(1+step,a0,opt_flag,a0_locopt)
if fomdval > fomd[-1]:
a0 = a0_new
fomd = np.append(fomd,fomdval)
opt_flag = True
iter_fomd += 1
else:
step = step/2
opt_flag = False
if np.abs(step) < step_tiny or (iter_fomd >= 4 and all(fomd[-4:] > 0) and np.std(fomd[-4:])/np.mean(fomd[-4:]) <= relunc_fomd):
break
fomdval = fomd[-1]
return fomdval,a0
def inf_FoM_optm_loc(a,b,c,epsilon,imprecision=10**-2,lherm=True):
"""
Calculate localy optimal iMPO for (shifted) SLD. Function for infinite size systems.
Parameters:
a: iMPO for density matrix at the value of estimated parameter phi=phi_0, expected ndarray of a shape (bd,bd,d,d)
b: iMPO for density matrix at the value of estimated parameter phi=phi_0+epsilon, expected ndarray of a shape (bd,bd,d,d)
c: iMPO for (shifted) SLD, expected ndarray of a shape (bd,bd,d,d)
epsilon: value of a separation between estimated parameters encoded in a and b, float
imprecision: expected imprecision of the end results, default value is 10**-2
lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD iMPO, otherwise False
Returns:
c: localy optimal iMPO for (shifted) SLD
"""
d = np.shape(a)[2]
bdr = np.shape(a)[0]
bdrp = np.shape(b)[0]
bdl = np.shape(c)[0]
tol_fom = imprecision*epsilon**2
tensors = [c,b]
legs = [[-1,-3,1,2],[-2,-4,2,1]]
tm = ncon(tensors,legs)
tm = np.reshape(tm,(bdl*bdrp,bdl*bdrp),order='F')
tmval,tmvr = | np.linalg.eig(tm) | numpy.linalg.eig |
"""
This module contains code for data retrieval and sampling.
Preprocess of data took place in advance of this file.
"""
from solardataretrieval import utilities
import boto3
from solardatatools.clear_day_detection import filter_for_sparsity
from solardatatools import find_clear_days
from io import BytesIO
import pandas as pd
import numpy as np
import sys
from sys import path
path.append('..')
from functools import partial
def get_summary_file():
"""
This function gets the summary file (.csv) for sunpower data that was generated by preprossing.
param: not applicable
return: summary file as a dataframe
"""
key, secret_key = utilities.get_credentials()
s3 = boto3.client('s3', aws_access_key_id=key, aws_secret_access_key=secret_key)
summary_df = pd.read_csv('s3://pv.insight.sunpower.preprocessed/summary_file.csv', index_col=0)
return summary_df
class Retrieval():
""" This class includes three functions for data sampling pipeline. Initially, the data are filtered_indexes
based on the user filter threshold parameters. The data are randmoly retrieved from the filtered data based on user input of
number of sites and days per site. The selected data are uploaded in AWS S3 bucket including power output values and metadata.
Parameters
----------
Data sampling: number_of_sites, number_of_days, quantile_percent
Returns
----------
Random selection of sites and days per site, uploaded data on AWS S3 Bucket.
"""
def __init__(self):
self.number_of_sites = None
self.number_of_days = None
self.quantile_percent = None
self.site_filter_list = []
self.daily_filter_list = []
self.summary_df = get_summary_file()
def add_site_filter(self, site_filter_expression):
self.site_filter_list.append(site_filter_expression)
return self.site_filter_list
def construct_standard_site_filters(self):
self.add_site_filter(self.summary_df['overall_sparsity'] <0.3)
self.add_site_filter(self.summary_df['overall_quality'] >0.7)
self.add_site_filter(self.summary_df['time_sample'] ==288)
def add_daily_filter(self, daily_filter):
self.daily_filter_list.append(daily_filter)
return self.daily_filter_list
def data_retrieval(self, number_of_sites, number_of_days, quantile_percent):
df_site_filter = pd.DataFrame(data=self.site_filter_list).T
filtered_indexes = np.alltrue(df_site_filter, axis=1)
df_meta_data = pd.DataFrame(columns=['site_ID', 'sensor_ID', 'start_timestamp', 'end_timestamp', 'duration_days', 'time_sample', 'quantile_95', 'overall_sparsity', "overall_quality", "days_selected"])
summary_file_filtered = self.summary_df[filtered_indexes]
all_sites = summary_file_filtered.site_ID.unique()
site_IDs_selected = np.random.choice(all_sites, number_of_sites)
index_to_download = [] #from original summary file!
sensor_IDs_selected = []
for site_id in site_IDs_selected:
site1 = summary_file_filtered.loc[summary_file_filtered['site_ID'] == site_id]
sensor_IDs = site1.sensor_ID.unique()
selected_sensor = | np.random.choice(sensor_IDs, 1) | 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]) | numpy.array |
import numpy as np
import _pickle as pickle
import gpflow
import os
from Dataset import getDemonstrationDataset
from Sliding_Block import *
import sys
sys.path.insert(0,'./../Task_Agnostic_Online_Multitask_Imitation_Learning/')
from Housekeeping import *
def validate_GP_controller(context_code, window_size, partial_observability, drift_per_time_step, moving_windows_x_size, behavior_controller, mean_x, deviation_x, mean_y, deviation_y):
if not os.path.exists(LOGS_DIRECTORY):
os.makedirs(LOGS_DIRECTORY)
file_to_save_logs = LOGS_DIRECTORY + str(context_code) + '_' + str(window_size) + '_' + str(partial_observability) + '_' + 'GP.pkl'
logs_for_all_blocks = {}
for block_mass in ALL_BLOCK_MASSES_TO_VALIDATE:
logs_for_a_block_and_initial_state = {}
for initial_state in INITIALIZATION_STATES_TO_VALIDATE:
all_observations = []
all_behavior_control_means = []
all_behavior_control_deviations = []
all_behavior_costs = []
all_target_control_means, all_target_control_deviations = [], []
env = Sliding_Block(mass=block_mass, initial_state=initial_state)
total_cost = total_variance = 0.
observation = env.state
from LQR import dlqr
K, X, eigVals = dlqr(env.A, env.B, env.Q, env.R)
target_mean_control, target_var_control = -1. * np.dot(K, observation), np.array([[0.]])
if not partial_observability:
observation = np.append(observation.T, np.array([[block_mass]]), axis=1)
else:
observation = observation.T
moving_window_x = np.zeros((1, moving_windows_x_size))
moving_window_x[0, -observation.shape[1]:] = observation[0]
behavior_mean_control, behavior_var_control = behavior_controller.predict_y(NORMALIZE(moving_window_x, mean_x, deviation_x))
behavior_mean_control = REVERSE_NORMALIZE(behavior_mean_control, mean_y, deviation_y)
behavior_var_control = behavior_var_control * deviation_y
step_limit = 0
while (step_limit < MAXIMUM_NUMBER_OF_STEPS):
step_limit += 1
all_observations.append(observation)
all_behavior_control_means.append(behavior_mean_control)
all_behavior_control_deviations.append(np.sqrt(behavior_var_control))
all_target_control_means.append(target_mean_control)
all_target_control_deviations.append(target_var_control)
observation, cost, finish = env.step(behavior_mean_control)
all_behavior_costs.append(cost)
target_mean_control, target_var_control = -1. * np.dot(K, observation), np.array([[0.]])
if not window_size == 1:
moving_window_x[0, :-drift_per_time_step] = moving_window_x[0, drift_per_time_step:]
moving_window_x[0, -drift_per_time_step:-(drift_per_time_step-behavior_mean_control.shape[1])] = behavior_mean_control[0]
moving_window_x[0, -(drift_per_time_step-behavior_mean_control.shape[0])] = -cost
if not partial_observability:
observation = np.append(observation.T, np.array([[block_mass]]), axis=1)
else:
observation = observation.T
moving_window_x[0, -observation.shape[1]:] = observation[0]
behavior_mean_control, behavior_var_control = behavior_controller.predict_y(NORMALIZE(moving_window_x, mean_x, deviation_x))
behavior_mean_control = REVERSE_NORMALIZE(behavior_mean_control, mean_y, deviation_y)
behavior_var_control = behavior_var_control * deviation_y
logs_for_a_block_and_initial_state[str(initial_state)] = {OBSERVATIONS_LOG_KEY: | np.concatenate(all_observations) | numpy.concatenate |
# 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]) | numpy.array |
import numpy as np
from scipy.io.wavfile import read
import librosa
import torch
import os
import csv
max_wav_value=32768.0
def get_mask_from_lengths(lengths):
max_len = torch.max(lengths).item()
ids = torch.arange(0, max_len, out=torch.cuda.LongTensor(max_len))
#mask = (ids < lengths.unsqueeze(1)).byte() #deprecated
mask = (ids < lengths.unsqueeze(1)).bool()
return mask
def load_wav_to_torch(full_path):
sampling_rate, data = read(full_path)
return torch.FloatTensor(data.astype(np.float32)), sampling_rate
def load_filepaths_and_text(filename, split="|"):
with open(filename, encoding='utf-8') as f:
filepaths_and_text = [line.strip().split(split) for line in f]
return filepaths_and_text
def to_gpu(x):
x = x.contiguous()
if torch.cuda.is_available():
x = x.cuda(non_blocking=True)
return torch.autograd.Variable(x)
def flatten_list(l):
return [item for sublist in l for item in sublist]
def str2bool(v):
return v.lower() in ('true', '1')
def makedirs(path):
if not os.path.exists(path):
print(" [*] Make directories : {}".format(path))
os.makedirs(path)
def add_postfix(path, postfix):
path_without_ext, ext = path.rsplit('.', 1)
return "{}.{}.{}".format(path_without_ext, postfix, ext)
def get_kl_weight(af, lag, k, x0, upper, constant, nsteps=250000):
kl_weights = [0 for _ in range(nsteps)]
steps = list(range(nsteps))
for i, step in enumerate(steps):
if step >= lag:
if af == 'logistic':
kl_weights[i] = float(upper/(1+np.exp(-k*(step-x0))))
elif af == 'linear':
#kl_weights[i] = min(upper, step/x0)
kl_weights[i] = min(upper, (step-lag)/x0)
elif af == 'constant':
kl_weights[i] = constant
else:
kl_weights[i] = 0
return kl_weights
def get_text_padding_rate(input_lengths, top_n=3):
batch_size = input_lengths.size(0)
max_len = int(max(input_lengths))
mean_len = float(sum(input_lengths)) / len(input_lengths)
padding_rate = 1 - mean_len / max_len
top_len = input_lengths[:min(batch_size, top_n)]
top_len = '-'.join([str(int(l)) for l in top_len])
return padding_rate, max_len, top_len
def get_mel_padding_rate(gate_padded, top_n=3):
batch_size, max_len = gate_padded.shape
padded_zeros = torch.sum(gate_padded, 1) - 1
padding_rate = float(sum(padded_zeros) / gate_padded.numel())
min_padded_zeros = sorted(padded_zeros)[:min(batch_size, top_n)]
top_len = [max_len-i for i in min_padded_zeros]
top_len = '-'.join([str(int(l)) for l in top_len])
return padding_rate, max_len, top_len
def add_rand_noise(key_values, noise_range=(-0.5,0.5), seed=0):
n = len(key_values)
np.random.seed(seed)
values = np.random.rand(n)
lower, upper = noise_range
noises = [v * (upper-lower) + lower for v in values]
key_values_with_noise = [d+n for (d,n) in zip(key_values, noises)]
return key_values_with_noise
def sort_with_noise(key_values, key_values_noisy, reverse=True):
"""order clean key values with the order sorted by noisy key values"""
idx = [i[0] for i in sorted(enumerate(key_values_noisy),
key=lambda x:x[1], reverse=reverse)]
key_values_resorted = [key_values[i] for i in idx]
return key_values_resorted
def get_key_values(filelist, filelist_cols):
if 'dur' in filelist_cols:
key = 'dur'
key_idx = filelist_cols.index(key)
key_values = [float(line[key_idx]) for line in filelist]
else:
key = 'text'
key_idx = filelist_cols.index(key)
key_values = [len(line[key_idx]) for line in filelist]
return key_values, key
def get_batch_sizes(filelist, filelist_cols, batch_size):
key_values, key = get_key_values(filelist, filelist_cols)
values_sorted = sorted(key_values, reverse=True)
batch_len_max_mean = np.mean(values_sorted[:batch_size])
batch_capacity = batch_size * batch_len_max_mean
# get batches where each batch gets full capacity
batch_sizes = []
remaining = key_values[:]
while len(remaining) > 0:
bs = 1
while np.max(remaining[:min(bs, len(remaining))]) * bs <= batch_capacity:
bs += 1
batch_size_current = min(bs-1, len(remaining))
batch_sizes.append(batch_size_current)
remaining = remaining[batch_size_current:]
return batch_sizes
def permute_filelist(filelist, filelist_cols, seed=0, permute_opt='rand',
local_rand_factor=0.1):
if permute_opt == 'rand':
filelist_permuted = filelist[:]
| np.random.seed(seed) | numpy.random.seed |
from __future__ import absolute_import, division, print_function
import logging
import sys
logging.basicConfig(
stream=sys.stdout,
format='%(asctime)s %(name)s-%(levelname)s: %(message)s',
datefmt='%Y-%m-%d %H:%M:%S')
import os
import numpy as np
from operator import itemgetter
from biopandas.pdb import PandasPdb
from . import utils
from . import filtering
from . import data_projection as dp
logger = logging.getLogger("postprocessing")
class PostProcessor(object):
def __init__(self,
extractor=None,
working_dir=None,
rescale_results=True,
filter_results=False,
feature_to_resids=None,
pdb_file=None,
accuracy_method='mse',
predefined_relevant_residues=None,
use_GMM_estimator=True):
"""
Class which computes all the necessary averages and saves them as fields
TODO move some functionality from class feature_extractor here
:param extractor:
:param feature_importance:
:param std_feature_importance:
:param cluster_indices:
:param working_dir:
:param feature_to_resids: an array of dimension nfeatures*2 which tells which two residues are involved in a feature
"""
self.extractor = extractor
self.name = extractor.name
self.feature_importances = extractor.feature_importance
self.std_feature_importances = extractor.std_feature_importance
self.supervised = extractor.supervised
self.cluster_indices = extractor.cluster_indices
self.nclusters = 1 if extractor.labels is None else extractor.labels.shape[1]
self.working_dir = working_dir
if self.working_dir is None:
self.working_dir = os.getcwd()
self.pdb_file = pdb_file
self.predefined_relevant_residues = predefined_relevant_residues
self.use_GMM_estimator = use_GMM_estimator
# Rescale and filter results if needed
self.rescale_results = rescale_results
if self.feature_importances is not None:
if rescale_results:
self.feature_importances, self.std_feature_importances = utils.rescale_feature_importance(
self.feature_importances, self.std_feature_importances)
if filter_results:
self.feature_importances, self.std_feature_importances = filtering.filter_feature_importance(
self.feature_importances, self.std_feature_importances)
# Put importance and std to 0 for residues pairs which were filtered out during features filtering (they are set as -1 in self.feature_importances and self.std_feature_importances)
self.indices_filtered = np.where(self.feature_importances[:, 0] == -1)[0]
self.feature_importances[self.indices_filtered, :] = 0
self.std_feature_importances[self.indices_filtered, :] = 0
# Set mapping from features to residues
self.nfeatures = self.feature_importances.shape[0]
else:
self.indices_filtered = np.empty((0, 0))
self.nfeatures = self.extractor.samples.shape[1]
if feature_to_resids is None and self.pdb_file is None:
feature_to_resids = utils.get_default_feature_to_resids(self.nfeatures)
elif feature_to_resids is None and self.pdb_file is not None:
feature_to_resids = utils.get_feature_to_resids_from_pdb(self.nfeatures, self.pdb_file)
self.feature_to_resids = feature_to_resids
self.accuracy_method = accuracy_method
# Set average feature importances to None
self.importance_per_residue_and_cluster = None
self.std_importance_per_residue_and_cluster = None
self.importance_per_residue = None
self.std_importance_per_residue = None
# Performance metrics
self.predefined_relevant_residues = predefined_relevant_residues
self.average_std = None
if extractor.test_set_errors is not None:
self.test_set_errors = extractor.test_set_errors.mean()
else:
self.test_set_errors = None
self.data_projector = None
self.separation_score = None
self.accuracy = None
self.accuracy_per_cluster = None
self._importance_mapped_to_resids = None
self._std_importance_mapped_to_resids = None
def average(self):
"""
Computes average importance per cluster and residue and residue etc.
Sets the fields importance_per_residue_and_cluster, importance_per_residue
:return: itself
"""
self._map_feature_to_resids()
self._compute_importance_per_residue()
if self.supervised:
self._compute_importance_per_residue_and_cluster()
return self
def evaluate_performance(self):
"""
Computes -average of standard deviation (per residue)
-projection classification entropy
-classification score (for toy model only)
"""
self._compute_average_std()
self._compute_projection_classification_entropy()
if self.predefined_relevant_residues is not None:
self.compute_accuracy()
return self
def get_important_features(self, states=None, sort=True):
"""
:param states: (optional) the indices of the states
:param sort: (optional) sort the features by their importance
:return: np.array of shape (n_features, 2) with entries (feature_index, importance)
"""
fi = self.feature_importances
if states is not None and self.supervised:
fi = fi[:, states]
fi = fi.sum(axis=1)
fi, _ = utils.rescale_feature_importance(fi)
fi = fi.squeeze()
fi = [(e, i) for (e, i) in enumerate(fi)]
if sort:
fi = [(e, i) for (e, i) in sorted(fi, key=itemgetter(1), reverse=True)]
return np.array(fi)
def persist(self):
"""
Save .npy files of the different averages and pdb files with the beta column set to importance
:return: itself
"""
directory = self.get_output_dir()
if not os.path.exists(directory):
os.makedirs(directory)
np.save(directory + "importance_per_residue", self.importance_per_residue)
np.save(directory + "std_importance_per_residue", self.std_importance_per_residue)
np.save(directory + "feature_importance", self.feature_importances)
np.save(directory + "std_feature_importance", self.std_feature_importances)
if self.importance_per_residue_and_cluster is not None and self.std_importance_per_residue_and_cluster is not None:
np.save(directory + "importance_per_residue_and_cluster", self.importance_per_residue_and_cluster)
np.save(directory + "std_importance_per_residue_and_cluster", self.std_importance_per_residue_and_cluster)
if self.separation_score is not None:
np.save(directory + 'separation_score', self.separation_score)
if self.predefined_relevant_residues is not None:
np.save(directory + "predefined_relevant_residues", self.predefined_relevant_residues)
if self.accuracy is not None:
np.save(directory + 'accuracy', self.accuracy)
if self.accuracy_per_cluster is not None:
np.save(directory + 'accuracy_per_cluster', self.accuracy_per_cluster)
if self.test_set_errors is not None:
np.save(directory + 'test_set_errors', self.test_set_errors)
if self.feature_to_resids is not None:
np.save(directory + 'feature_to_resids', self.feature_to_resids)
if self.pdb_file is not None:
pdb = PandasPdb()
pdb.read_pdb(self.pdb_file)
self._save_to_pdb(pdb, directory + "importance.pdb",
self._map_to_correct_residues(self.importance_per_residue))
if self.importance_per_residue_and_cluster is not None:
for cluster_idx, importance in enumerate(self.importance_per_residue_and_cluster.T):
cluster_name = "cluster_{}".format(cluster_idx) \
if self.extractor.label_names is None else \
self.extractor.label_names[cluster_idx]
self._save_to_pdb(pdb, directory + "{}_importance.pdb".format(cluster_name),
self._map_to_correct_residues(importance))
return self
def _load_if_exists(self, filepath):
if os.path.exists(filepath):
return np.load(filepath)
else:
return None
def get_output_dir(self):
return self.working_dir + "/{}/".format(self.extractor.name)
def load(self):
"""
Loads files dumped by the 'persist' method
:return: itself
"""
directory = self.get_output_dir()
if not os.path.exists(directory):
return self
self.importance_per_residue = np.load(directory + "importance_per_residue.npy")
self.std_importance_per_residue = np.load(directory + "std_importance_per_residue.npy")
self.feature_importances = np.load(directory + "feature_importance.npy")
self.std_feature_importances = np.load(directory + "std_feature_importance.npy")
self.importance_per_residue_and_cluster = self._load_if_exists(
directory + "importance_per_residue_and_cluster.npy")
self.std_importance_per_residue_and_cluster = self._load_if_exists(
directory + "std_importance_per_residue_and_cluster.npy")
self.separation_score = self._load_if_exists(directory + "separation_score.npy")
self.predefined_relevant_residues = self._load_if_exists(directory + "predefined_relevant_residues.npy")
self.accuracy = self._load_if_exists(directory + "accuracy.npy")
self.accuracy_per_cluster = self._load_if_exists(directory + "accuracy_per_cluster.npy")
self.test_set_errors = self._load_if_exists(directory + "test_set_errors.npy")
if self.feature_to_resids is None: # Can be useful to override this in postprocesseing
self.feature_to_resids = self._load_if_exists(directory + "feature_to_resids.npy")
#np.unique(np.asarray(self.feature_to_resids.flatten()))
return self
def _map_feature_to_resids(self):
# Create array of all unique reside numbers
index_to_resid = self.get_index_to_resid()
self.nresidues = len(index_to_resid)
res_id_to_index = {} # a map pointing back to the index in the array index_to_resid
for idx, resid in enumerate(index_to_resid):
res_id_to_index[resid] = idx # Now we now which residue points to which feature
_importance_mapped_to_resids = | np.zeros((self.nresidues, self.feature_importances.shape[1])) | numpy.zeros |
import unittest
import pickle
import numpy as np
import numpy.testing as npt
from sigpy import nufft, util
if __name__ == '__main__':
unittest.main()
class TestNufft(unittest.TestCase):
def test_nufft(self):
# Check deltas
ishape = [3]
input = np.array([0, 1, 0], np.complex) # delta
coord = np.array([[-1], [0], [1]], np.float)
npt.assert_allclose(nufft.nufft(input, coord),
np.array([1.0, 1.0, 1.0]) / (3**0.5),
atol=0.01, rtol=0.01)
ishape = [4]
input = np.array([0, 0, 1, 0], np.complex) # delta
coord = np.array([[-2], [-1], [0], [1]], np.float)
npt.assert_allclose(nufft.nufft(input, coord),
np.array([1.0, 1.0, 1.0, 1.0]) / (4**0.5),
atol=0.01, rtol=0.01)
ishape = [5]
input = np.array([0, 0, 1, 0, 0], np.complex) # delta
coord = | np.array([[-2], [-1], [0], [1], [2]], np.float) | numpy.array |
from __future__ import division
import sys
import os
import random
import argparse
from pathlib import Path
import torch
from torch.utils import data
import numpy as np
from tqdm import tqdm
from models import get_model
from datasets import get_dataset
from loss import *
from utils import *
from buffer import createBuffer
import time
def train(args):
# prepare datasets
if args.dataset == 'i19S':
datasetSs = get_dataset('7S')
datasetTs = get_dataset('12S')
else:
if args.dataset in ['7S', 'i7S']:
dataset_get = get_dataset('7S')
if args.dataset in ['12S', 'i12S']:
dataset_get = get_dataset('12S')
# loss
reg_loss = EuclideanLoss()
if args.model == 'hscnet':
cls_loss = CELoss()
if args.dataset in ['i7S', 'i12S', 'i19S']:
w1, w2, w3 = 1, 1, 100000
else:
w1, w2, w3 = 1, 1, 10
# prepare model and optimizer
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
model = get_model(args.model, args.dataset)
model.init_weights()
model.to(device)
optimizer = torch.optim.Adam(model.parameters(), lr=args.init_lr, eps=1e-8,
betas=(0.9, 0.999))
# resume from existing or start a new session
if args.resume is not None:
if os.path.isfile(args.resume):
print("Loading model and optimizer from checkpoint '{}'".format\
(args.resume))
checkpoint = torch.load(args.resume, map_location=device)
model.load_state_dict(checkpoint['model_state'])
optimizer.load_state_dict(checkpoint['optimizer_state'])
print("Loaded checkpoint '{}' (epoch{})".format(args.resume,
checkpoint['epoch']))
save_path = Path(args.resume)
args.save_path = save_path.parent
#start_epoch = checkpoint['epoch'] + 1
else:
print("No checkpoint found at '{}'".format(args.resume))
sys.exit()
else:
if args.dataset in ['i7S', 'i12S', 'i19S']:
model_id = "{}-{}-{}-initlr{}-iters{}-bsize{}-aug{}-{}".format(\
args.exp_name, args.dataset, args.model, args.init_lr, args.n_iter,
args.batch_size, int(args.aug), args.train_id)
else:
model_id = "{}-{}-{}-initlr{}-iters{}-bsize{}-aug{}-{}".format(\
args.exp_name, args.dataset, args.scene.replace('/','.'),
args.model, args.init_lr, args.n_iter, args.batch_size,
int(args.aug), args.train_id)
save_path = Path(model_id)
args.save_path = 'checkpoints'/save_path
args.save_path.mkdir(parents=True, exist_ok=True)
start_epoch = 1
# Continual learning over scenes
buffer = createBuffer(data_path=args.data_path, exp=args.exp_name, buffer_size=args.buffer_size, dataset= args.dataset)
if args.dataset == 'i7S':
scenes = ['chess', 'fire', 'heads', 'office', 'pumpkin', 'redkitchen', 'stairs']
if args.dataset == 'i12S':
scenes = ['apt1/kitchen','apt1/living','apt2/bed',
'apt2/kitchen','apt2/living','apt2/luke','office1/gates362',
'office1/gates381','office1/lounge','office1/manolis',
'office2/5a','office2/5b']
if args.dataset == 'i19S':
scenes = ['chess', 'fire', 'heads', 'office', 'pumpkin', 'redkitchen', 'stairs', 'apt1/kitchen','apt1/living','apt2/bed',
'apt2/kitchen','apt2/living','apt2/luke','office1/gates362',
'office1/gates381','office1/lounge','office1/manolis',
'office2/5a','office2/5b']
for i,scene in enumerate(scenes):
# if not first scene
if args.dataset in ['i7S', 'i12S']:
if i > 0:
dataset = dataset_get(args.data_path, args.dataset, args.scene, split='train_{}'.format(scene),
model=args.model, aug=args.aug, Buffer=True, dense_pred_flag=args.dense_pred, exp=args.exp_name)
else:
dataset = dataset_get(args.data_path, args.dataset, args.scene, split='train_{}'.format(scene),
model=args.model, aug=args.aug, Buffer=False, exp=args.exp_name)
trainloader = data.DataLoader(dataset, batch_size=args.batch_size,
num_workers=4, shuffle=True)
buffer_dataset = dataset_get(args.data_path, args.dataset, args.scene, split='train_{}'.format(scene),
model=args.model, aug=False, Buffer=False, dense_pred_flag=args.dense_pred, exp=args.exp_name)
buffer_trainloader = data.DataLoader(buffer_dataset, batch_size=args.batch_size, num_workers=4, shuffle=True)
if args.dataset == 'i19S':
if i == 0:
dataset = datasetSs(args.data_path, args.dataset, args.scene, split='train_{}'.format(scene),
model=args.model, aug=args.aug, Buffer=False, exp=args.exp_name)
buffer_dataset = datasetSs(args.data_path, args.dataset, args.scene, split='train_{}'.format(scene),
model=args.model, aug=False, Buffer=False, dense_pred_flag=args.dense_pred, exp=args.exp_name)
if i >0 and i < 7:
dataset = datasetSs(args.data_path, args.dataset, args.scene, split='train_{}'.format(scene),
model=args.model, aug=args.aug, Buffer=True, dense_pred_flag=args.dense_pred, exp=args.exp_name)
buffer_dataset = datasetSs(args.data_path, args.dataset, args.scene, split='train_{}'.format(scene),
model=args.model, aug=False, Buffer=False, dense_pred_flag=args.dense_pred, exp=args.exp_name)
if i >= 7:
dataset = datasetTs(args.data_path, args.dataset, args.scene, split='train_{}'.format(scene),
model=args.model, aug=args.aug, Buffer=True, dense_pred_flag=args.dense_pred, exp=args.exp_name)
buffer_dataset = datasetTs(args.data_path, args.dataset, args.scene, split='train_{}'.format(scene),
model=args.model, aug=False, Buffer=False, dense_pred_flag=args.dense_pred, exp=args.exp_name)
trainloader = data.DataLoader(dataset, batch_size=args.batch_size, num_workers=4, shuffle=True)
buffer_trainloader = data.DataLoader(buffer_dataset, batch_size=args.batch_size, num_workers=4, shuffle=True)
# start training
args.n_epoch = int(np.ceil(args.n_iter * args.batch_size / len(dataset)))
#for epoch in range(start_epoch, start_epoch + args.n_epoch+1):
for epoch in range(1, args.n_epoch+1):
lr = args.init_lr
model.train()
train_loss_list = []
coord_loss_list = []
if args.model == 'hscnet':
lbl_1_loss_list = []
lbl_2_loss_list = []
for _, (data_ori, data_buffer) in enumerate(tqdm(trainloader)):
img, coord, mask, lbl_1, lbl_2, lbl_1_oh, lbl_2_oh, _ = data_ori
if mask.sum() == 0:
continue
optimizer.zero_grad()
img = img.to(device)
coord = coord.to(device)
mask = mask.to(device)
train_loss, coord_loss, lbl_1_loss, lbl_2_loss = loss(img, coord, mask, lbl_1, lbl_2, lbl_1_oh,
lbl_2_oh, model, reg_loss, cls_loss, device, w1, w2, w3)
# compute loss for buffer if not first scene
if i > 0 :
# sample a random minibatch from buffer dataloader
img_buff, coord_buff, mask_buff, lbl_1_buff, lbl_2_buff, lbl_1_oh_buff, lbl_2_oh_buff, _, dense_pred = data_buffer
if mask_buff.sum() == 0:
continue
img_buff = img_buff.to(device)
coord_buff = coord_buff.to(device)
mask_buff = mask_buff.to(device)
buff_loss = loss_buff_DK(img_buff, coord_buff, mask_buff, lbl_1_buff, lbl_2_buff, lbl_1_oh_buff,
lbl_2_oh_buff, model, reg_loss, cls_loss, device, w1, w2, w3, dense_pred=dense_pred)
train_loss+= 1 * buff_loss
coord_loss_list.append(coord_loss.item())
if args.model == 'hscnet':
lbl_1_loss_list.append(lbl_1_loss.item())
lbl_2_loss_list.append(lbl_2_loss.item())
train_loss_list.append(train_loss.item())
train_loss.backward()
optimizer.step()
with open(args.save_path/args.log_summary, 'a') as logfile:
if args.model == 'hscnet':
logtt = 'task {}:Epoch {}/{} - lr: {} - reg_loss: {} - cls_loss_1: {}' \
' - cls_loss_2: {} - train_loss: {} '.format(scene,
epoch, args.n_epoch, lr, np.mean(coord_loss_list),
| np.mean(lbl_1_loss_list) | numpy.mean |
import numpy as np
import gym
from gym import spaces
from numpy.random import default_rng
import pickle
import os
import math
import matplotlib.pyplot as plt
from PIL import Image
from gym_flp import rewards
from IPython.display import display, clear_output
import anytree
from anytree import Node, RenderTree, PreOrderIter, LevelOrderIter, LevelOrderGroupIter
'''
v0.0.3
Significant changes:
08.09.2020:
- Dicrete option removed from spaces; only Box allowed
- Classes for quadtratic set covering and mixed integer programming (-ish) added
- Episodic tasks: no more terminal states (exception: max. no. of trials reached)
12.10.2020:
- mip added
- fbs added
'''
class qapEnv(gym.Env):
metadata = {'render.modes': ['rgb_array', 'human']}
def __init__(self, mode=None, instance=None):
__location__ = os.path.realpath(os.path.join(os.getcwd(), os.path.dirname(__file__)))
self.DistanceMatrices, self.FlowMatrices = pickle.load(open(os.path.join(__location__,'discrete', 'qap_matrices.pkl'), 'rb'))
self.transport_intensity = None
self.instance = instance
self.mode = mode
while not (self.instance in self.DistanceMatrices.keys() or self.instance in self.FlowMatrices.keys() or self.instance in ['Neos-n6', 'Neos-n7', 'Brewery']):
print('Available Problem Sets:', self.DistanceMatrices.keys())
self.instance = input('Pick a problem:').strip()
self.D = self.DistanceMatrices[self.instance]
self.F = self.FlowMatrices[self.instance]
# Determine problem size relevant for much stuff in here:
self.n = len(self.D[0])
# Action space has two option:
# 1) Define as Box with shape (1, 2) and allow values to range from 1 through self.n
# 2) Define as Discrete with x = 1+((n^2-n)/2) actions (one half of matrix + 1 value from diagonal) --> Omit "+1" to obtain range from 0 to x!
# self.action_space = spaces.Box(low=-1, high=6, shape=(1,2), dtype=np.int) # Doubles complexity of the problem as it allows the identical action (1,2) and (2,1)
self.action_space = spaces.Discrete(int((self.n**2-self.n)*0.5)+1)
# If you are using images as input, the input values must be in [0, 255] as the observation is normalized (dividing by 255 to have values in [0, 1]) when using CNN policies.
if self.mode == "rgb_array":
self.observation_space = spaces.Box(low = 0, high = 255, shape=(1, self.n, 3), dtype = np.uint8) # Image representation
elif self.mode == 'human':
self.observation_space = spaces.Box(low=1, high = self.n, shape=(self.n,), dtype=np.float32)
self.states = {} # Create an empty dictonary where states and their respective reward will be stored for future reference
self.actions = self.pairwiseExchange(self.n)
# Initialize Environment with empty state and action
self.action = None
self.state = None
self.internal_state = None
#Initialize moving target to incredibly high value. To be updated if reward obtained is smaller.
self.movingTargetReward = np.inf
self.MHC = rewards.mhc.MHC() # Create an instance of class MHC in module mhc.py from package rewards
def reset(self):
state = default_rng().choice(range(1,self.n+1), size=self.n, replace=False)
#MHC, self.TM = self.MHC.compute(self.D, self.F, state)
self.internal_state = state.copy()
return state
def step(self, action):
# Create new State based on action
fromState = self.internal_state.copy()
swap = self.actions[action]
fromState[swap[0]-1], fromState[swap[1]-1] = fromState[swap[1]-1], fromState[swap[0]-1]
newState = fromState.copy()
#MHC, self.TM = self.MHC.compute(self.D, self.F, current_permutation)
MHC, self.TM = self.MHC.compute(self.D, self.F, newState)
if self.mode == 'human':
self.states[tuple(fromState)] = MHC
if self.movingTargetReward == np.inf:
self.movingTargetReward = MHC
#reward = self.movingTargetReward - MHC
reward = -1 if MHC > self.movingTargetReward else 10
self.movingTargetReward = MHC if MHC < self.movingTargetReward else self.movingTargetReward
if self.mode == "rgb_array":
rgb = np.zeros((1,self.n,3), dtype=np.uint8)
sources = np.sum(self.TM, axis = 1)
sinks = np.sum(self.TM, axis = 0)
R = np.array((fromState-np.min(fromState))/(np.max(fromState)-np.min(fromState))*255).astype(int)
G = np.array((sources-np.min(sources))/(np.max(sources)-np.min(sources))*255).astype(int)
B = np.array((sinks-np.min(sinks))/(np.max(sinks)-np.min(sinks))*255).astype(int)
for i, s in enumerate(fromState):
rgb[0:1, i] = [R[s-1], G[s-1], B[s-1]]
newState = np.array(rgb)
self.state = newState.copy()
self.internal_state = fromState.copy()
return newState, reward, False, {}
def render(self, mode=None):
if self.mode == "human":
SCALE = 1 # Scale size of pixels for displayability
img_h, img_w = SCALE, (len(self.internal_state))*SCALE
data = np.zeros((img_h, img_w, 3), dtype=np.uint8)
sources = np.sum(self.TM, axis = 1)
sinks = np.sum(self.TM, axis = 0)
R = np.array((self.internal_state-np.min(self.internal_state))/(np.max(self.internal_state)-np.min(self.internal_state))*255).astype(int)
G = np.array((sources-np.min(sources))/(np.max(sources)-np.min(sources))*255).astype(int)
B = np.array((sinks-np.min(sinks))/(np.max(sinks)-np.min(sinks))*255).astype(int)
for i, s in enumerate(self.internal_state):
data[0*SCALE:1*SCALE, i*SCALE:(i+1)*SCALE] = [R[s-1], G[s-1], B[s-1]]
img = Image.fromarray(data, 'RGB')
if self.mode == 'rgb_array':
img = Image.fromarray(self.state, 'RGB')
plt.imshow(img)
plt.axis('off')
plt.show()
return img
def close(self):
pass
def pairwiseExchange(self, x):
actions = [(i,j) for i in range(1,x) for j in range(i+1,x+1) if not i==j]
actions.append((1,1))
return actions
class fbsEnv(gym.Env):
metadata = {'render.modes': ['rgb_array', 'human']}
def __init__(self, mode=None, instance = None):
__location__ = os.path.realpath(os.path.join(os.getcwd(), os.path.dirname(__file__)))
self.problems, self.FlowMatrices, self.sizes, self.LayoutWidths, self.LayoutLengths = pickle.load(open(os.path.join(__location__,'continual', 'cont_instances.pkl'), 'rb'))
self.mode = mode
self.instance = instance
while not (self.instance in self.FlowMatrices.keys() or self.instance in ['Brewery']):
print('Available Problem Sets:', self.FlowMatrices.keys())
self.instance = input('Pick a problem:').strip()
self.F = self.FlowMatrices[self.instance]
self.n = self.problems[self.instance]
self.AreaData = self.sizes[self.instance]
# Obtain size data: FBS needs a length and area
self.beta, self.l, self.w, self.a, self.min_side_length = getAreaData(self.AreaData) #Investigate available area data and compute missing values if needed
'''
Nomenclature:
W --> Width of Plant (y coordinate)
L --> Length of Plant (x coordinate)
w --> Width of facility/bay (x coordinate)
l --> Length of facility/bay (y coordinate)
A --> Area of Plant
a --> Area of facility
Point of origin analoguous to numpy indexing (top left corner of plant)
beta --> aspect ratios (as alpha is reserved for learning rate)
'''
#if self.l is None or self.w is None:
# self.l = np.random.randint(max(self.min_side_length, np.min(self.a)/self.min_side_length), max(self.min_side_length, np.min(self.a)/self.min_side_length), size=(self.n,))
# self.l = np.sqrt(self.A/self.aspect_ratio)
# self.w = np.round(self.a/self.l)
# Check if there are Layout Dimensions available, if not provide enough (sqrt(a)*1.5)
if self.instance in self.LayoutWidths.keys() and self.instance in self.LayoutLengths.keys():
self.L = int(self.LayoutLengths[self.instance]) # We need both values to be integers for converting into image
self.W = int(self.LayoutWidths[self.instance])
else:
self.A = np.sum(self.a)
# Design a squared plant layout
self.L = int(round(math.sqrt(self.A),0)) # We want the plant dimensions to be integers to fit them into an image
self.W = self.L
# Design a layout with l = 1,5 * w
#self.L = divisor(int(self.A))
#self.W = self.A/self.L
# These values need to be set manually, e.g. acc. to data from literature. Following Eq. 1 in Ulutas & Kulturel-Konak (2012), the minimum side length can be determined by assuming the smallest facility will occupy alone.
self.aspect_ratio = int(max(self.beta)) if not self.beta is None else 1
self.min_length = np.min(self.a) / self.L
self.min_width = np.min(self.a) / self.W
# We define minimum side lengths to be 1 in order to be displayable in array
self.min_length = 1
self.min_width = 1
self.action_space = spaces.Discrete(5) #Taken from doi:10.1016/j.engappai.2020.103697
self.actions = {0: 'Randomize', 1: 'Bit Swap', 2: 'Bay Exchange', 3: 'Inverse', 4: 'Idle'}
#self.state_space = spaces.Box(low=1, high = self.n, shape=(self.n,), dtype=np.int)
self.bay_space = spaces.Box(low=0, high = 1, shape=(self.n,), dtype=np.int) # binary vector indicating bay breaks (i = 1 means last facility in bay)
self.state = None
self.permutation = None # Permutation of all n facilities, read from top to bottom
self.bay = None
self.done = False
self.MHC = rewards.mhc.MHC()
if self.mode == "rgb_array":
self.observation_space = spaces.Box(low = 0, high = 255, shape= (self.W, self.L,3), dtype = np.uint8) # Image representation
elif self.mode == "human":
observation_low = np.tile(np.array([0,0,self.min_length,self.min_width],dtype=int), self.n)
observation_high = np.tile(np.array([self.W, self.L, self.W, self.L], dtype=int), self.n)
self.observation_space = spaces.Box(low=observation_low, high=observation_high, dtype = int) # Vector representation of coordinates
else:
print("Nothing correct selected")
def reset(self):
# 1. Get a random permutation and bays
self.permutation, self.bay = self.sampler()
# 2. Last position in bay break vector has to be 1 by default.
self.bay[-1] = 1
self.fac_x, self.fac_y, self.fac_b, self.fac_h = self.getCoordinates()
self.D = getDistances(self.fac_x, self.fac_y)
reward, self.TM = self.MHC.compute(self.D, self.F, self.permutation[:])
self.state = self.constructState(self.fac_x, self.fac_y, self.fac_b, self.fac_h, self.n)
return self.state
def constructState(self, x, y, l, w, n):
# Construct state
state_prelim = np.zeros((4*n,), dtype=float)
state_prelim[0::4] = y
state_prelim[1::4] = x
state_prelim[2::4] = w
state_prelim[3::4] = l
if self.mode == "human":
self.state = np.array(state_prelim)
elif self.mode == "rgb_array":
self.state = self.ConvertCoordinatesToState(state_prelim)
return self.state[:]
def ConvertCoordinatesToState(self, state_prelim):
data = np.zeros((self.observation_space.shape)) if self.mode == 'rgb_array' else np.zeros((self.W, self.L, 3),dtype=np.uint8)
sources = np.sum(self.TM, axis = 1)
sinks = np.sum(self.TM, axis = 0)
R = np.array((self.permutation-np.min(self.permutation))/(np.max(self.permutation)-np.min(self.permutation))*255).astype(int)
G = np.array((sources-np.min(sources))/(np.max(sources)-np.min(sources))*255).astype(int)
B = np.array((sinks-np.min(sinks))/(np.max(sinks)-np.min(sinks))*255).astype(int)
for x, p in enumerate(self.permutation):
x_from = state_prelim[4*x+1] -0.5 * state_prelim[4*x+3]
y_from = state_prelim[4*x+0] -0.5 * state_prelim[4*x+2]
x_to = state_prelim[4*x+1] + 0.5 * state_prelim[4*x+3]
y_to = state_prelim[4*x+0] + 0.5 * state_prelim[4*x+2]
data[int(y_from):int(y_to), int(x_from):int(x_to)] = [R[p-1], G[p-1], B[p-1]]
return np.array(data, dtype=np.uint8)
def sampler(self):
return default_rng().choice(range(1,self.n+1), size=self.n, replace=False), self.bay_space.sample()
def getCoordinates(self):
facilities = np.where(self.bay==1)[0] #Read all positions with a bay break
bays = np.split(self.permutation, facilities[:-1]+1)
lengths = np.zeros((len(self.permutation,)))
widths = np.zeros((len(self.permutation,)))
fac_x = np.zeros((len(self.permutation,)))
fac_y = np.zeros((len(self.permutation,)))
x = 0
start = 0
for b in bays: #Get the facilities that are located in the bay
areas = self.a[b-1] #Get the area associated with the facilities
end = start + len(areas)
lengths[start:end] = np.sum(areas)/self.W #Calculate all facility widhts in bay acc. to Eq. (1) in https://doi.org/10.1016/j.eswa.2011.11.046
widths[start:end] = areas/lengths[start:end]
fac_x[start:end] = lengths[start:end] * 0.5 + x
x += np.sum(areas)/self.W
y = np.ones(len(b))
ll = 0
for idx, l in enumerate(widths[start:end]):
y[idx] = ll + 0.5*l
ll += l
fac_y[start:end] = y
start = end
return fac_x, fac_y, lengths, widths
def step(self, action):
a = self.actions[action]
#k = np.count_nonzero(self.bay)
fromState = np.array(self.permutation)
# Get lists with a bay positions and facilities in each bay
facilities = np.where(self.bay==1)[0]
bay_breaks = np.split(self.bay, facilities[:-1]+1)
# Load indiv. facilities into bay acc. to breaks; omit break on last position to avoid empty array in list.
bays = np.split(self.permutation, facilities[:-1]+1)
if a == 'Randomize':
# Two vector elements randomly chosen are exchanged. Bay vector remains untouched.
k = default_rng().choice(range(len(self.permutation-1)), size=1, replace=False)
l = default_rng().choice(range(len(self.permutation-1)), size=1, replace=False)
fromState[k], fromState[l] = fromState[l], fromState[k]
self.permutation = np.array(fromState)
elif a == 'Bit Swap':
#One element randomly selected flips its value (1 to 0 or 0 to 1)
j = default_rng().choice(range(len(self.bay-1)), size=1, replace=False)
temp_bay = np.array(self.bay) # Make a copy of bay
temp_bay[j] = 1 if temp_bay[j] == 0 else 0
self.bay = np.array(temp_bay)
elif a == 'Bay Exchange':
#Two bays are randomly selected and exchange facilities contained in them
o = int(default_rng().choice(range(len(bays)), size=1, replace=False))
p = int(default_rng().choice(range(len(bays)), size=1, replace=False))
while p==o: # Make sure bays are not the same
p = int(default_rng().choice(range(len(bays)), size=1, replace=False))
# Swap bays and break points accordingly:
bays[o], bays[p] = bays[p], bays[o]
bay_breaks[o], bay_breaks[p] = bay_breaks[p], bay_breaks[o]
new_bay = np.concatenate(bay_breaks)
new_state = np.concatenate(bays)
# Make sure state is saved as copy
self.permutation = np.array(new_state)
self.bay = np.array(new_bay)
elif a == 'Inverse':
#Facilities present in a certain bay randomly chosen are inverted.
q = default_rng().choice(range(len(bays)))
bays[q] = np.flip(bays[q])
new_bay = np.concatenate(bay_breaks)
new_state = np.concatenate(bays)
# Make sure state is saved as copy
self.permutation = np.array(new_state)
self.bay = np.array(new_bay)
elif a == 'Idle':
pass # Keep old state
self.fac_x, self.fac_y, self.fac_b, self.fac_h = self.getCoordinates()
self.D = getDistances(self.fac_x, self.fac_y)
reward, self.TM = self.MHC.compute(self.D, self.F, fromState)
self.state = self.constructState(self.fac_x, self.fac_y, self.fac_b, self.fac_h, self.n)
self.done = False #Always false for continuous task
return self.state[:], reward, self.done, {}
def render(self, mode= None):
if self.mode== "human":
# Mode 'human' needs intermediate step to convert state vector into image array
data = self.ConvertCoordinatesToState(self.state[:])
img = Image.fromarray(data, 'RGB')
if self.mode == "rgb_array":
data = self.state[:]
img = Image.fromarray(self.state, 'RGB')
plt.imshow(img)
plt.axis('off')
plt.show()
#23.02.21: Switched to data instead of img for testing video
return img
def close(self):
pass
#self.close()
class ofpEnv(gym.Env):
metadata = {'render.modes': ['rgb_array', 'human']}
def __init__(self, mode = None, instance = None, distance = None, aspect_ratio = None, step_size = None, greenfield = None):
__location__ = os.path.realpath(os.path.join(os.getcwd(), os.path.dirname(__file__)))
self.problems, self.FlowMatrices, self.sizes, self.LayoutWidths, self.LayoutLengths = pickle.load(open(os.path.join(__location__,'continual', 'cont_instances.pkl'), 'rb'))
self.mode = mode
self.aspect_ratio = 2 if aspect_ratio is None else aspect_ratio
self.step_size = 2 if step_size is None else step_size
self.greenfield = greenfield
self.instance = instance
while not (self.instance in self.FlowMatrices.keys() or self.instance in ['Brewery']):
print('Available Problem Sets:', self.FlowMatrices.keys())
self.instance = input('Pick a problem:').strip()
self.F = self.FlowMatrices[self.instance]
self.n = self.problems[self.instance]
self.AreaData = self.sizes[self.instance]
self.counter = 0
self.done = False
self.pseudo_stability = 0 #If the reward has not improved in the last 200 steps, terminate the episode
self.best_reward = None
# Obtain size data: FBS needs a length and area
self.beta, self.l, self.w, self.a, self.min_side_length = getAreaData(self.AreaData) #Investigate available area data and compute missing values if needed
'''
Nomenclature:
W --> Width of Plant (x coordinate)
L --> Length of Plant (y coordinate)
w --> Width of facility/bay (x coordinate)
l --> Length of facility/bay (y coordinate)
A --> Area of Plant
a --> Area of facility
Point of origin analoguous to numpy indexing (top left corner of plant)
beta --> aspect ratios (as alpha is reserved for learning rate)
'''
#if self.l is None or self.w is None:
# self.l = np.random.randint(max(self.min_side_length, np.min(self.a)/self.min_side_length), max(self.min_side_length, np.min(self.a)/self.min_side_length), size=(self.n,))
# self.l = np.sqrt(self.A/self.aspect_ratio)
# self.w = np.round(self.a/self.l)
# Check if there are Layout Dimensions available, if not provide enough (sqrt(a)*1.5)
if self.instance in self.LayoutWidths.keys() and self.instance in self.LayoutLengths.keys():
self.L = int(self.LayoutLengths[self.instance]) # We need both values to be integers for converting into image
self.W = int(self.LayoutWidths[self.instance])
else:
self.A = np.sum(self.a)
# Design a squared plant layout
self.L = int(round(math.sqrt(self.A),0)) # We want the plant dimensions to be integers to fit them into an image
self.W = self.L
if self.greenfield:
self.L = 2*self.L
self.W = 2*self.W
# Design a layout with l = 1,5 * w
#self.L = divisor(int(self.A))
#self.W = self.A/self.L
# These values need to be set manually, e.g. acc. to data from literature. Following Eq. 1 in Ulutas & Kulturel-Konak (2012), the minimum side length can be determined by assuming the smallest facility will occupy alone.
self.aspect_ratio = int(max(self.beta)) if not self.beta is None else self.aspect_ratio
self.min_length = 1
self.min_width = 1
# 3. Define the possible actions: 5 for each box [toDo: plus 2 to manipulate sizes] + 1 idle action for all
self.actions = {}
for i in range(self.n):
self.actions[0+(i)*5] = "up"
self.actions[1+(i)*5] = "down"
self.actions[2+(i)*5] = "right"
self.actions[3+(i)*5] = "left"
self.actions[4+(i)*5] = "rotate"
self.actions[len(self.actions)] = "keep"
# 4. Define actions space as Discrete Space
self.action_space = spaces.Discrete(1+5*self.n) #5 actions for each facility: left, up, down, right, rotate + idle action across all
# 5. Set some starting points
self.reward = 0
self.state = None
self.internal_state = None #Placeholder for state variable for internal manipulation in rgb_array mode
if self.w is None or self.l is None:
self.l = np.random.randint(self.min_side_length*self.aspect_ratio, np.min(self.a), size=(self.n, ))
self.w = np.round(self.a/self.l)
# 6. Set upper and lower bound for observation space
# min x position can be point of origin (0,0) [coordinates map to upper left corner]
# min y position can be point of origin (0,0) [coordinates map to upper left corner]
# min width can be smallest area divided by its length
# min lenght can be smallest width (above) multiplied by aspect ratio
# max x pos can be bottom right edge of grid
# max y pos can be bottpm right edge of grid
if self.mode == "rgb_array":
self.observation_space = spaces.Box(low = 0, high = 255, shape= (self.W, self.L,3), dtype = np.uint8) # Image representation
elif self.mode == "human":
#observation_low = np.tile(np.array([0,0,self.min_side_length, self.min_side_length],dtype=float), self.n)
#observation_high = np.tile(np.array([self.L, self.W, max(self.l), max(self.w)], dtype=float), self.n)
observation_low = np.zeros(4* self.n)
observation_high = np.zeros(4* self.n)
observation_low[0::4] = max(self.w)
observation_low[1::4] = max(self.l)
observation_low[2::4] = max(self.w)
observation_low[3::4] = max(self.l)
observation_high[0::4] = self.W - max(self.w)
observation_high[1::4] = self.L - max(self.l)
observation_high[2::4] = self.W - max(self.w)
observation_high[3::4] = self.L - max(self.l)
self.observation_space = spaces.Box(low=observation_low, high=observation_high, dtype = np.uint8) # Vector representation of coordinates
else:
print("Nothing correct selected")
self.MHC = rewards.mhc.MHC()
# Set Boundaries
self.upper_bound = self.L- max(self.l)/2
self.lower_bound = 0 + max(self.l)/2
self.left_bound = 0 + max(self.w)/2
self.right_bound = self.W- max(self.w)/2
def reset(self):
# Start with random x and y positions
if self.mode == 'human':
state_prelim = self.observation_space.sample()
# Override length (l) and width (w) or facilities with data from instances
state_prelim[2::4] = self.w
state_prelim[3::4] = self.l
self.D = getDistances(state_prelim[0::4], state_prelim[1::4])
self.internal_state = np.array(state_prelim)
self.state = np.array(state_prelim)
reward, self.TM = self.MHC.compute(self.D, self.F, np.array(range(1,self.n+1)))
self.counter = 0
self.best_reward = reward
self.reward = 0
elif self.mode == 'rgb_array':
state_prelim = np.zeros((self.W, self.L, 3),dtype=np.uint8)
x = np.random.uniform(0, self.L, size=(self.n,))
y = np.random.uniform(0, self.W, size=(self.n,))
#s = self.constructState(y, x, self.w, self.l, self.n)
s = np.zeros(4*self.n)
s[0::4] = y
s[1::4] = x
s[2::4] = self.w
s[3::4] = self.l
self.internal_state = np.array(s).copy()
#self.state = self.constructState(y, x, self.w, self.l, self.n)
self.D = getDistances(s[0::4], s[1::4])
reward, self.TM = self.MHC.compute(self.D, self.F, np.array(range(1,self.n+1)))
self.state = self.ConvertCoordinatesToState(self.internal_state)
self.counter = 0
self.best_reward = reward
return self.state.copy()
# def offGrid(self, s):
# if np.any(s[0::4]-s[2::4] < 0):
# #print("Bottom bound breached")
# og = True
# elif np.any(s[0::4]+s[2::4] > self.W):
# #print("Top bound breached")
# og = True
# elif np.any(s[1::4]-s[3::4] < 0):
# #print("left bound breached")
# og = True
# elif np.any(s[1::4]+s[3::4] > self.L):
# #print("right bound breached")
# og = True
# else:
# og = False
# return og
# def collision_test(self, y, x, w, l):
# # collision test
# collision = False #initialize collision for each collision test
# for i in range (0, self.n-1):
# for j in range (i+1,self.n):
# if not(x[i]+0.5*l[i] < x[j]-0.5*l[j] or x[i]-0.5*l[i] > x[j]+0.5*l[j] or y[i]-0.5*w[i] > y[j]+0.5*w[j] or y[i]+0.5*w[i] < y[j]-0.5*w[j]):
# collision = True
# break
# return collision
def collision(self,x,y,w,l):
collision = False
for i in range(0,self.n-1):
for j in range(i+1,self.n):
if (abs(int(x[i]) - int(x[j])) < 0.5*self.w[i]+0.5*self.w[j]):
if(abs(int(y[i]) - int(y[j])) < 0.5*self.l[i]+0.5*self.l[j]):
#print(x[i],y[i],x[j],y[j])
collision = True
if (abs(int(y[i]) - int(y[j])) < 0.5*self.l[i]+0.5*self.l[j]):
if(abs(int(x[i]) - int(x[j])) < 0.5*self.w[i]+0.5*self.w[j]):
#print(x[i],y[i],x[j],y[j])
collision = True
return collision
def step(self, action):
self.reward = 0
m = np.int(np.ceil((action+1)/5)) # Facility on which the action is
# Get copy of state to manipulate:
temp_state = self.internal_state[:]
step_size = self.step_size
# Do the action
if self.actions[action] == "up":
if temp_state[4*(m-1)+1] + temp_state[4*(m-1)+3]*0.5 + step_size < self.upper_bound:
temp_state[4*(m-1)+1] += step_size
else:
temp_state[4*(m-1)+1] += 0
#print('Forbidden action: machine', m, 'left grid on upper bound')
elif self.actions[action] == "down":
if temp_state[4*(m-1)+1] - temp_state[4*(m-1)+3]*0.5 + step_size > self.lower_bound:
temp_state[4*(m-1)+1] -= step_size
else:
temp_state[4*(m-1)+1] += 0
#print('Forbidden action: machine', m, 'left grid on lower bound')
elif self.actions[action] == "right":
if temp_state[4*(m-1)]+temp_state[4*(m-1)+2]*0.5 + step_size < self.right_bound:
temp_state[4*(m-1)] += step_size
else:
temp_state[4*(m-1)] += 0
#print('Forbidden action: machine', m, 'left grid on right bound')
elif self.actions[action] == "left":
if temp_state[4*(m-1)]-temp_state[4*(m-1)+2]*0.5 + step_size > self.left_bound:
temp_state[4*(m-1)] -= step_size
else:
temp_state[4*(m-1)] += 0
#print('Forbidden action: machine', m, 'left grid on left bound')
elif self.actions[action] == "keep":
None #Leave everything as is
elif self.actions[action] == "rotate":
temp_state[4*(m-1)+2], temp_state[4*(m-1)+3] = temp_state[4*(m-1)+3], temp_state[4*(m-1)+2]
else:
raise ValueError("Received invalid action={} which is not part of the action space".format(action))
self.fac_x, self.fac_y, self.fac_b, self.fac_h = temp_state[0::4], temp_state[1::4], temp_state[2::4], temp_state[3::4] # ToDo: Read this from self.state
self.D = getDistances(self.fac_x, self.fac_y)
fromState = np.array(range(1,self.n+1)) # Need to create permutation matrix
MHC, self.TM = self.MHC.compute(self.D, self.F, fromState)
self.internal_state = np.array(temp_state) # Keep a copy of the vector representation for future steps
self.state = self.internal_state[:]
# Test if initial state causing a collision. If yes than initialize a new state until there is no collision
collision = self.collision(temp_state[0::4],temp_state[1::4], temp_state[2::4], temp_state[3::4]) # Pass every 4th item starting at 0 (x pos) and 1 (y pos) for checking
if (MHC < self.best_reward) and (collision == False) :
self.best_reward = MHC
self.reward = 50
if collision == True:
self.reward = -2
if self.mode == 'rgb_array':
self.state = self.ConvertCoordinatesToState(self.internal_state) #Retain state for internal use
self.pseudo_stability = self.counter
self.done = True if self.pseudo_stability == 200 else False
self.counter += 1
#print(self.reward)
return self.state,self.reward,self.done,{}
def ConvertCoordinatesToState(self, state_prelim):
data = np.zeros((self.observation_space.shape)) if self.mode == 'rgb_array' else np.zeros((self.W, self.L, 3),dtype=np.uint8)
sources = np.sum(self.TM, axis = 1)
sinks = np.sum(self.TM, axis = 0)
p = np.arange(self.n)
R = np.array((p-np.min(p))/(np.max(p)-np.min(p))*255).astype(int)
R[R<=20] = 255
G = np.array((sources-np.min(sources))/(np.max(sources)-np.min(sources))*255).astype(int)
G[G<=20] = 255
B = np.array((sinks-np.min(sinks))/(np.max(sinks)-np.min(sinks))*255).astype(int)
B[B<=20] = 255
for x, p in enumerate(p):
x_from = state_prelim[4*x+0] -0.5 * state_prelim[4*x+2]
y_from = state_prelim[4*x+1] -0.5 * state_prelim[4*x+3]
x_to = state_prelim[4*x+0] + 0.5 * state_prelim[4*x+2]
y_to = state_prelim[4*x+1] + 0.5 * state_prelim[4*x+3]
data[int(y_from):int(y_to), int(x_from):int(x_to)] = [R[p-1], G[p-1], B[p-1]]
return np.array(data, dtype=np.uint8)
def constructState(self, x, y, b, h, n):
# Construct state
state_prelim = np.zeros((4*n,), dtype=float)
state_prelim[0::4] = x
state_prelim[1::4] = y
state_prelim[2::4] = b
state_prelim[3::4] = h
if self.mode == "human":
self.state = np.array(state_prelim)
elif self.mode == "rgb_array":
self.state = self.ConvertCoordinatesToState(state_prelim)
return self.state[:]
def render(self):
if self.mode == "human":
data = self.ConvertCoordinatesToState(self.state[:])
img = Image.fromarray(data, 'RGB')
if self.mode == "rgb_array":
img = Image.fromarray(self.state, 'RGB')
plt.imshow(img)
plt.axis('off')
plt.show()
return img
def close(self):
pass #Nothing here yet
class stsEnv(gym.Env):
metadata = {'render.modes': ['rgb_array', 'human']}
def __init__(self, mode = None, instance = None):
__location__ = os.path.realpath(os.path.join(os.getcwd(), os.path.dirname(__file__)))
self.problems, self.FlowMatrices, self.sizes, self.LayoutWidths, self.LayoutLengths = pickle.load(open(os.path.join(__location__,'continual', 'cont_instances.pkl'), 'rb'))
self.instance = instance
self.mode = mode
self.MHC = rewards.mhc.MHC()
while not (self.instance in self.FlowMatrices.keys() or self.instance in ['Brewery']):
print('Available Problem Sets:', self.FlowMatrices.keys())
self.instance = input('Pick a problem:').strip()
self.F = self.FlowMatrices[self.instance]
self.n = self.problems[self.instance]
self.AreaData = self.sizes[self.instance]
# Obtain size data: FBS needs a length and area
self.beta, self.l, self.w, self.a, self.min_side_length = getAreaData(self.AreaData) #Investigate available area data and compute missing values if needed
# Check if there are Layout Dimensions available, if not provide enough (sqrt(a)*1.5)
if self.instance in self.LayoutWidths.keys() and self.instance in self.LayoutLengths.keys():
self.L = int(self.LayoutLengths[self.instance]) # We need both values to be integers for converting into image
self.W = int(self.LayoutWidths[self.instance])
else:
self.A = np.sum(self.a)
# Design a squared plant layout
self.L = int(round(math.sqrt(self.A),0)) # We want the plant dimensions to be integers to fit them into an image
self.W = self.L
'''
Nomenclature:
W --> Width of Plant (y coordinate)
L --> Length of Plant (x coordinate)
w --> Width of facility/bay (x coordinate)
l --> Length of facility/bay (y coordinate)
A --> Area of Plant
a --> Area of facility
Point of origin analoguous to numpy indexing (top left corner of plant)
beta --> aspect ratios (as alpha is reserved for learning rate)
'''
# Provide variables for layout encoding (epsilon in doi:10.1016/j.ejor.2018.01.001)
self.permutation = None
self.slicing = None
self.orientation_space = spaces.Box(low=0, high = 1, shape=(self.n-1,), dtype=np.int) # binary vector indicating bay breaks (i = 1 means last facility in bay)
self.state = None
if self.mode == "rgb_array":
self.observation_space = spaces.Box(low = 0, high = 255, shape= (self.W, self.L,3), dtype = np.uint8) # Image representation
elif self.mode == "human":
#observation_low = np.tile(np.array([0,0,self.min_side_length, self.min_side_length],dtype=float), self.n)
#observation_high = np.tile(np.array([self.L, self.W, max(self.l), max(self.w)], dtype=float), self.n)
observation_low = np.zeros(4* self.n)
observation_high = np.zeros(4* self.n)
observation_low[0::4] = 0.0 #Top-left corner y
observation_low[1::4] = 0.0 #Top-left corner x
observation_low[2::4] = 1.0 #Width
observation_low[3::4] = 1.0 #Length
observation_high[0::4] = self.W
observation_high[1::4] = self.L
observation_high[2::4] = self.W
observation_high[3::4] = self.L
self.observation_space = spaces.Box(low=observation_low, high=observation_high, dtype = float) # Vector representation of coordinates
else:
print("Nothing correct selected")
self.action_space = spaces.Discrete(5)
self.actions = {0: 'Permute', 1: 'Slice_Swap', 2: 'Shuffle', 3: 'Bit_Swap', 4: 'Idle'}
def reset(self):
# 1. Get a random permutation, slicing order and orientation
self.permutation, self.slicing, self.orientation = self.sampler()
# 2. Build the tree incl. size information
s = self.TreeBuilder(self.permutation, self.slicing, self.orientation)
centers = np.array([s[0::4] + 0.5*s[2::4], s[1::4] + 0.5* s[3::4]])
self.D = getDistances(centers[0], centers[1])
reward, self.TM = self.MHC.compute(self.D, self.F, np.array(range(1,self.n+1)))
if self.mode == "human":
self.state = np.array(s)
elif self.mode == "rgb_array":
self.state = self.ConvertCoordinatesToState(s)
return self.state
def ConvertCoordinatesToState(self, s):
data = np.zeros((self.observation_space.shape)) if self.mode == 'rgb_array' else np.zeros((self.W, self.L, 3),dtype=np.uint8)
sources = np.sum(self.TM, axis = 1)
sinks = np.sum(self.TM, axis = 0)
p = self.permutation[:]
R = np.array((p-np.min(p))/(np.max(p)-np.min(p))*255).astype(int)
G = np.array((sources-np.min(sources))/(np.max(sources)-np.min(sources))*255).astype(int)
B = np.array((sinks-np.min(sinks))/(np.max(sinks)-np.min(sinks))*255).astype(int)
for x in range(self.n):
y_from = s[4*x+0]
x_from = s[4*x+1]
y_to = y_from + s[4*x+2]
x_to = x_from + s[4*x+3]
data[int(y_from):int(y_to), int(x_from):int(x_to)] = [R[x], G[x], B[x]]
return np.array(data, dtype=np.uint8)
def TreeBuilder(self,p,s,o):
names = {0: 'V', 1: 'H'}
contains = np.array(p)
W = self.W
L = self.L
area = W * L
self.STS = Node(name = None, contains = contains, parent = None, area = area, width = W, length = L, upper_left = np.zeros((2,)), lower_right = np.array([W,L]), dtype = float)
for i,r in enumerate(o):
name = names[r]
cut_after_pos = s[i]
whats_in_pos = p[cut_after_pos-1]
parent = anytree.search.find(self.STS, lambda node: np.any(node.contains==whats_in_pos))
parent.name = name
starting_point = parent.upper_left
cuts = np.split(parent.contains, [np.where(parent.contains == whats_in_pos)[0][0]+1])
for c in cuts:
area = float(np.sum(self.a[c-1]))
length = area/parent.width if name == 'V' else parent.length
width = area/parent.length if name == 'H' else parent.width
starting_point = starting_point
contains = c
new_name = None if not len(c)==1 else c[0]
Node(name = new_name, \
contains = contains, \
parent = parent, \
area = area, \
width = width, \
length = length, \
upper_left = starting_point, \
lower_right = starting_point + np.array([width, length]), \
dtype = float)
starting_point = starting_point + np.array([0, length]) if parent.name == 'V' else starting_point + np.array([width, 0])
parent.contains = None
self.STS.root.area = np.sum([i.area for i in self.STS.root.children])
s = np.zeros((4*self.n,))
for l in self.STS.leaves:
trg = int(l.name)-1
s[4*trg] = l.upper_left[0]
s[4*trg+1] = l.upper_left[1]
s[4*trg+2] = l.width
s[4*trg+3] = l.length
return s
def step(self, a):
action = self.actions[a]
'''
Available actions in STS:
- Random permutation change
- Random slicing order change at two positions
- Shuffle slicing order (new random array)
- Bitswap in Orientation vector
- Do Nothing
'''
if action == 'Permute':
i = np.random.randint(0, len(self.permutation)-1)
j = np.random.randint(0, len(self.permutation)-1)
temp_perm = np.array(self.permutation)
temp_perm[i], temp_perm[j] = temp_perm[j], temp_perm[i]
self.permutation = np.array(temp_perm)
elif action == 'Slice_Swap':
i = np.random.randint(0, len(self.slicing)-1)
j = np.random.randint(0, len(self.slicing)-1)
temp_sli = np.array(self.slicing)
temp_sli[i], temp_sli[j] = temp_sli[j], temp_sli[i]
self.slicing = np.array(temp_sli)
elif action == 'Shuffle':
self.slicing = default_rng().choice(range(1,self.n), size=self.n-1, replace=False)
elif action == 'Bit_Swap':
i = np.random.randint(0, len(self.orientation)-1)
if self.orientation[i] == 1:
self.orientation[i] = 0
elif self.orientation[i] == 0:
self.orientation[i] = 1
elif action == 'Idle':
self.permutation = | np.array(self.permutation) | numpy.array |
# TRANSPORT PROPERTIES OF GASES
# ------------------------------
# import packages/modules
from math import sqrt
import numpy as np
import re
# internals
from PyREMOT.docs.rmtUtility import rmtUtilityClass as rmtUtil
# core
from PyREMOT.core import Tref, R_CONST
from PyREMOT.core import roundNum
from PyREMOT.core import CONST_EQ_GAS_DIFFUSIVITY, CONST_EQ_GAS_VISCOSITY
# data
from PyREMOT.data import viscosityEqList
from PyREMOT.data import viscosityList
from PyREMOT.data.dataGasThermalConductivity import TherConductivityList
from PyREMOT.data.componentData import thermalConductivityEqList
def main():
pass
# NOTE
### diffusivity ###
def calGasDiffusivity(equation, compList, params):
"""
calculate gas diffusivity [m2/s]
args:
params: changes with equation
eq1: Chapman-Enskog
"""
# choose equation
if equation == 1:
return calGaDiEq1(compList, params)
else:
return -1
def calGaDiEq1(compList, params):
"""
calculate based on Chapman-Enskog
args:
params:
compList: component name list
MoFri: mole fraction list
T: temperature [K]
P: pressure [Pa]
MWi: molecular weight list [g/mol]
CrTei: critical temperature [K]
CrPri: critical pressure [bar]
"""
# input
MoFri = params['MoFri']
T = params['T']
P = params['P']
MWi = params['MWi']
CrTei = params['CrTei']
CrPri = params['CrPri']
# component no.
compNo = len(compList)
# e/K
eK_Ratio = np.array([0.75*item for item in CrTei])
# sigma - characteristic length of the intermolecular force law
sigma = np.zeros(compNo)
for i in range(compNo):
_loop = (CrTei[i]/CrPri[i])**(1/3)
sigma[i] = 2.44*_loop
# e[i,j]
eij = | np.zeros((compNo, compNo)) | numpy.zeros |
import copy
import sys
sys.path.append('SetsClustering')
from multiprocessing import Process ,Manager
import numpy as np
import LinearProgrammingInTheDarkClassVersion as LPD
from multiprocessing import Pool
from jgrapht.algorithms.shortestpaths import johnson_allpairs
import jgrapht
from SetsClustering import Utils, PointSet, KMeansAlg
from SetsClustering import KMeansForSetsSensitivityBounder as SensBounder
from SetsClustering import Coreset as CS
from scipy.spatial.distance import cdist
import seaborn as sns
from copy import deepcopy
import itertools
from scipy.ndimage import convolve
from timeit import default_timer as timer
from tqdm import tqdm
import dill
import matplotlib
matplotlib.use('agg')
import matplotlib.pyplot as plt
import matplotlib.pylab as pl
from scipy.linalg import null_space
import scipy.ndimage as ndi
from scipy.spatial import ConvexHull
import argparse, os, pickle
from scipy.io import netcdf
POWER = 4
FORCE_NEIGHBORING = 20
import psutil
CPUS = psutil.cpu_count()
# import multiprocessing
# # from pathos.multiprocessing import ProcessingPool as Pool
# # from sklearn.externals.joblib import Parallel, delayed
# from multiprocessing import Process
parser = argparse.ArgumentParser(description='Initial Location Generator')
parser.add_argument('-d', type=str, default=None, help='Directory containing all maps')
parser.add_argument('-pp', default=False, action='store_true', help='preprocess map')
parser.add_argument('-ft', default='.nc', type=str, help='Type of map file')
parser.add_argument('-nf', default=1, type=int, help='Number of files describing a map of velocities')
parser.add_argument('-eps_g', default=None, type=float, help=r'resolution of the \varepsilon-grid')
parser.add_argument('-eps_b', default=0.08, type=float,
help=r'epsilon approximation for each of the patches of the currents')
parser.add_argument('-k', default=10, type=int, help='Desired number of drifters')
parser.add_argument('-bs', default=2, type=int, help='size of the blob prior to the clustering phase')
parser.add_argument('-coreset_sample_size', default=1000, type=int,
help='The size of the coreset for the clustering phase')
parser.add_argument('-time', default=False, action='store_true', help='Apply our system over time')
parser.add_argument('-tol', default=0.2, type=float, help='Tolerance for minimum volume ellipsoid')
parser.add_argument('-resume', default=False, action='store_true', help='In case of code being killed, you can resume from last map')
parser.add_argument('-show', default=False, action='store_true', help='Show only our segementation and clustering. Must have preporcessed these data before')
class bcolors:
HEADER = '\033[95m'
OKBLUE = '\033[94m'
OKCYAN = '\033[96m'
OKGREEN = '\033[92m'
WARNING = '\033[93m'
FAIL = '\033[91m'
ENDC = '\033[0m'
BOLD = '\033[1m'
UNDERLINE = '\033[4m'
NORMAL = '\033[0m'
plt.rcParams.update({'font.size': 16})
manager = Manager()
def removeInclusionsJob(lst, ids, path_str):
global resdict
for i in range(len(lst)):
resdict[ids[i]] = True
if lst[i] in path_str:
resdict[ids[i]] = False
def removeInclusions(unified_paths, file_path='', file_prefix=''):
global manager
global resdict
global A
unified_paths_strings = [str(x[0]).strip('[]') for x in unified_paths]
unified_paths_strings.sort(key=(lambda x: len(x.split(','))))
lst = [list(grp) for i, grp in itertools.groupby(unified_paths_strings, key=(lambda x: len(x.split(','))))]
sizes = np.cumsum([len(x) for x in lst])
unique_ids = [list(range(sizes[i-1], sizes[i]) if i > 0 else range(sizes[i])) for i in range(len(sizes))]
if len(unified_paths_strings) > 10000:
with Manager() as manager:
proc_list = []
resdict = manager.dict()
for i, item in enumerate(lst):
if i != (len(lst) - 1):
proc_list.append(
Process(target=removeInclusionsJob,
args=(item, unique_ids[i], '\n'.join(unified_paths_strings[sizes[i]:])))
)
proc_list[-1].start()
for proc in proc_list:
proc.join()
mask = [x[1] for x in resdict.items()]
else:
resdict = dict()
for i, item in enumerate(lst):
if i != (len(lst) - 1):
removeInclusionsJob(item, unique_ids[i], '\n'.join(unified_paths_strings[sizes[i]:]))
mask = [x[1] for x in resdict.items()]
mask.extend([True for _ in range(len(lst[-1]))])
np.save('{}mask_unified_paths_{}.npy'.format(file_path, file_prefix), mask)
return [[int(y) for y in x.split(', ')] for x in list(itertools.compress(unified_paths_strings, mask))]
def removeDuplicates(list_1):
list2 = list(set(list_1))
list2.sort(key=list_1.index)
return list2
def makedir(dir_path):
try:
os.mkdir(dir_path)
except OSError as error:
print(error)
def saveVels(data, file_path, smoothed=True):
if smoothed:
file_path += 'Smoothed_Vel/'
else:
file_path += 'Original_Vel/'
makedir(file_path)
temp = np.tile(data[:, :, 0][:, :, np.newaxis], 10)
temp.dump(file_path + 'matrix_vel_x.dat')
temp = np.tile(data[:, :, 1][:, :, np.newaxis], 10)
temp.dump(file_path + 'matrix_vel_y.dat')
def readNetCDFFile(file_path, over_time):
file2read = netcdf.NetCDFFile(file_path, 'r')
U = file2read.variables['u'].data # velocity in x-axis
V = file2read.variables['v'].data # velocity in y-axis
mask = np.logical_and(np.abs(U) <= 1e3, np.abs(V) <= 1e3)
V = np.multiply(V, mask)
U = np.multiply(U, mask)
if not over_time:
U = U[0, :, :, :]
V = V[0, :, :, :]
return U,V
def innerFunction(current_possible_combs, unique_keys):
global resdict
for i, element in enumerate(current_possible_combs):
resdict[unique_keys[i]] = (removeDuplicates(element[0][0] + element[1][0]), element[0][1] + element[1][1])
def getAllPossiblePaths(list1, list2):
global CPUS
global manager
global resdict
if len(list1) * len(list2) > 10000:
manager = Manager()
resdict = manager.dict()
all_possible_combs = np.array_split(list(itertools.product(list1, list2)), CPUS)
unique_ids = np.array_split(np.arange(sum([x.size for x in all_possible_combs])), CPUS)
proc_list = []
for i, item in enumerate(all_possible_combs):
proc_list.append(
Process(target=innerFunction, args=(item, unique_ids[i]))
)
proc_list[-1].start()
for proc in proc_list:
proc.join()
temp = list(resdict.values())
else:
temp = []
for element in itertools.product(list1, list2):
temp.append((removeDuplicates(element[0][0] + element[1][0]), element[0][1] + element[1][1]))
return temp
class CurrentEstimation(object):
def __init__(self, grid, k=10, epsilon_grid=0.06, tolerance=0.001, epsilon_body=2, is_grid=True, is_data_vectorized=True,
blob_size=3, sens_file_name='sens.npz', coreset_sample_size = int(1e3), save_mode=True,
matrix_of_velocities=True, save_path='', file_prefix='', show=False, verbose=False):
self.grid = grid
self.is_grid=is_grid
self.d = (self.grid.ndim - 1) if matrix_of_velocities else self.grid.ndim
self.epsilon_grid = epsilon_grid
self.epsilon_body = epsilon_body
self.tolerance = tolerance
self.g = jgrapht.create_graph(directed=True)
self.cost_func = (lambda x: self.grid[tuple(x.astype("int") if is_grid else x)]) # create a simple membership cost function
self.iocsAlg = None
self.segments = []
self.eps_star = None
self.bodies = []
self.full_bodies = []
self.is_data_vectorized = is_data_vectorized
self.k = k
self.blob_size = blob_size
self.coreset_sample_size = coreset_sample_size
self.save_mode = save_mode
self.binary_grid = None
self.matrix_of_velocities = matrix_of_velocities
self.sens_file_name = sens_file_name
self.ellipsoids = []
self.convex_hulls = []
self.verbose = verbose
self.save_path = save_path
self.file_prefix = file_prefix
self.show = show
def polynomialGridSearchParallelizedVersion(self):
with Pool() as pool:
pass
def checkIfContained(self, point):
for i,body in enumerate((self.full_bodies if self.epsilon_body == 0 else self.bodies)):
if body.ndim > 1:
temp_in_body = np.equal(body, point).all(1).any()
temp_in_CH = False
if self.convex_hulls[i] is not None:
temp_in_CH = np.all(self.convex_hulls[i][:,:-1].dot(point) <= -self.convex_hulls[i][:,-1])
if temp_in_body or temp_in_CH:
return True
else:
if np.linalg.norm(body - point) == 0:
return True
return False
def IOCS(self, p):
cost_func = lambda x: 0.85 <= np.dot(np.nan_to_num(self.grid[tuple(p)]/np.linalg.norm(self.grid[tuple(p)])),
np.nan_to_num(self.grid[tuple(x)]/np.linalg.norm(self.grid[tuple(x)]))) \
<= 1 and 0.5 <= np.linalg.norm(self.grid[tuple(p)])/np.linalg.norm(self.grid[tuple(x)]) <= 2
self.iocsAlg = LPD.LinearProgrammingInTheDark(P=self.grid,cost_func=cost_func, point=p,
d=self.d, epsilon=self.tolerance, hull_hyper=None,
matrix_of_vecs=True)
if self.iocsAlg.lower_d <= 1:
if self.iocsAlg.lower_d == 0:
self.bodies.append(p)
self.full_bodies.append(p)
self.ellipsoids.append(None)
self.convex_hulls.append(None)
else:
idxs = np.where(self.iocsAlg.oracle.flattened_data == 1)[0]
Z = np.empty((idxs.shape[0], p.shape[0]))
Z[:, self.iocsAlg.irrelevant_dims] = p[self.iocsAlg.irrelevant_dims]
Z[:, self.iocsAlg.dims_to_keep[0]] = \
np.arange(*(self.iocsAlg.oracle.bounding_box[self.iocsAlg.dims_to_keep].flatten() +
np.array([0, 1])).tolist())[idxs]
self.bodies.append(Z)
self.full_bodies.append(Z)
self.ellipsoids.append(None)
self.convex_hulls.append(None)
elif self.iocsAlg.get_all_points:
idxs = np.where(self.iocsAlg.oracle.flattened_data == 1)[0]
Z = self.iocsAlg.oracle.coordinates[:-1, idxs].T
self.bodies.append(Z)
self.full_bodies.append(Z)
self.ellipsoids.append(None)
self.convex_hulls.append(None)
else:
self.ellipsoids.append(self.iocsAlg.computeAMVEE() + (p, ))
if self.epsilon_body > 0:
s = timer()
self.approximateBody(self.ellipsoids[-1][0][-1], self.ellipsoids[-1][0][-2],
idx_dims_retrieve=self.ellipsoids[-1][-3], dims_value=self.ellipsoids[-1][-1],
rest_dims=self.ellipsoids[-1][-2])
else:
self.attainWholeBody(self.ellipsoids[-1][0][-1], self.ellipsoids[-1][0][-2],
idx_dims_retrieve=self.ellipsoids[-1][-3], dims_value=self.ellipsoids[-1][-1],
rest_dims=self.ellipsoids[-1][-2])
def polynomialGridSearch(self):
dims = list(self.grid.shape[:-1] if self.matrix_of_velocities else self.grid.shape)
for i in range(len(dims)):
dims[i] = np.arange(0, dims[i], int(np.round(dims[i] * self.epsilon_grid)))
try:
X = np.array(np.meshgrid(*dims)).T.reshape(-1, len(dims))
return X
except MemoryError:
raise MemoryError("Cant handle this much data! Lower your epsilon or simply run the parallelized version")
@staticmethod
def semiBinarizeGrid(grid, kernel_size=None):
# Apply Mean-Filter
kernel = np.ones(tuple([grid.ndim if kernel_size is None else kernel_size for i in range(grid.ndim)]),
np.float32) / (kernel_size ** grid.ndim if kernel_size is not None else grid.ndim ** grid.ndim)
return convolve(grid, kernel, mode='constant', cval=0)
def generateEpsilonStar(self, degree=None):
if degree is None:
degree = self.epsilon_body
Z = np.arange(0, 2*np.pi, degree * np.pi)
V = np.array(np.meshgrid(*[Z for i in range(self.d)])).T.reshape(-1, self.d)
V = np.divide(V, np.linalg.norm(V, axis=1)[:, np.newaxis], out=np.zeros_like(V), where=(V != 0))
V = np.unique(np.around(np.unique(V[1:], axis=0), self.d+1), axis=0)
return V
@staticmethod
def run_dill_encoded(payload):
fun, args = dill.loads(payload)
return fun(*args)
@staticmethod
def apply_async(pool, fun, args):
payload = dill.dumps((fun, args))
return pool.apply_async(CurrentEstimation.run_dill_encoded, (payload,))
def attainWholeBody(self, E, c, idx_dims_retrieve=None, dims_value=None, rest_dims=None):
if self.iocsAlg.oracle.checkIfInsidePixelStyleNumpyVer(np.round(c)) > 1.0:
raise ValueError('Something is wrong with the ellipsoid!')
bounding_box = self.iocsAlg.oracle.bounding_box
indices = np.vstack(map(np.ravel, np.meshgrid(*[np.arange(bounding_box[x, 0], bounding_box[x, 1]+1)
for x in range(bounding_box.shape[0])]))).T
body = []
temp = 0
for idx in indices:
if self.iocsAlg.oracle.checkIfInsidePixelStyleNumpyVer(idx) == 1 and np.linalg.norm(E.dot(idx - c)) <= 1 \
and not self.checkIfContained(idx):
temp += 1
if np.linalg.norm(self.grid[tuple(idx)]) > 1e-10:
body.append(idx)
if len(body) > 0:
self.full_bodies.append(np.vstack(body))
def approximateBody(self, E, c, idx_dims_retrieve=None, dims_value=None, rest_dims=None):
bounding_box = self.iocsAlg.oracle.bounding_box
indices_of_lengths = np.argsort([x[0] - x[1] for x in bounding_box])
coeffs = np.zeros((indices_of_lengths.shape[0],))
for i in range(coeffs.shape[0]):
if i == (coeffs.shape[0] - 1):
coeffs[indices_of_lengths[i]] = 1
else:
coeffs[indices_of_lengths[i]] = max(((bounding_box[indices_of_lengths[i],1] -
bounding_box[indices_of_lengths[i],0]) * self.epsilon_body),1)
V = np.vstack(map(np.ravel, np.meshgrid(*[np.arange(start=x[0], stop=x[1],
step=coeffs[j]) for (j,x) in enumerate(bounding_box)]))).T
V = np.unique(V.astype("int"), axis=0)
body = []
for v in V:
if (self.iocsAlg.oracle.checkIfInsidePixelStyleNumpyVer(v) <= 1.0) and\
(np.linalg.norm(E.dot(v - c)) <= np.sqrt(1 + (1 + self.iocsAlg.eps) * E.shape[0])) and\
(np.linalg.norm(self.grid[tuple(v)]) > 0) and (not self.checkIfContained(v)):
body.append(v)
if len(body) > 0:
self.bodies.append(np.vstack(body))
if len(body) > (self.d + 1):
try:
self.convex_hulls.append(ConvexHull(self.bodies[-1]).equations)
except:
self.convex_hulls.append(None)
else:
self.convex_hulls.append(None)
def createBlobs(self, body):
if body.ndim == 1:
return [PointSet.PointSet(body[np.newaxis,:])]
elif body.shape[0] < self.blob_size:
return [PointSet.PointSet(body)]
else:
blob = []
for x_val in np.unique(body[:,0]):
idxs = np.where(body[:, 0] == x_val)[0]
if body[idxs].shape[0] < self.blob_size:
blob.extend([PointSet.PointSet(body[idxs])])
else:
splitted_array = np.array_split(body[idxs], int(body[idxs].shape[0] / self.blob_size))
blob.extend([PointSet.PointSet(x) for x in splitted_array])
return blob
def clusteringAssignment(self, set_P, Q):
assignments_per_point = []
assignments_per_blob = []
for P in set_P:
dists = cdist(P.P, Q)
cols_idxs = np.argmin(dists, axis=1)
min_idx = np.argmin(np.min(dists, axis=1))
assignments_per_point.extend([cols_idxs[min_idx] for p in P.P])
assignments_per_blob.append(cols_idxs[min_idx])
return assignments_per_point, assignments_per_blob
def clusterWaves(self, continue_from=0,return_full_bodies=True):
P = []
blobs = []
if self.epsilon_body != 0:
for body in self.bodies:
P = []
# need to make a way to make sure that there is a trade-off between the first 3 entries and last two
if body.ndim == 1:
body = body[np.newaxis, :]
for point in body:
a = self.grid[tuple(point.astype("int"))]
b = np.linalg.norm(a)
P.append(
np.hstack((point*FORCE_NEIGHBORING, np.divide(a,b, out=np.zeros_like(a), where=b!=0)
* np.linalg.norm(point))))
blobs.extend(self.createBlobs(np.array(deepcopy(P))))
else:
for body in self.full_bodies:
# need to make a way to make sure that there is a trade-off between the first 3 entries and last two
P = []
if body.ndim == 1:
body = body[np.newaxis, :]
for point in body:
P.append(
np.hstack((point*FORCE_NEIGHBORING, self.grid[tuple(point.astype("int"))] /
np.linalg.norm(self.grid[tuple(point.astype("int"))]) * np.linalg.norm(point))))
blobs.extend(self.createBlobs(np.array(deepcopy(P))))
set_P_indiced = [(P, idx) for (idx, P) in enumerate(blobs)] # taking the full!
if continue_from > 0 or self.show:
sensitivity = np.load(self.save_path + self.file_prefix + self.sens_file_name)['s']
print("Loaded sensitivity for sets clustering!")
else:
k_means_sens_bounder = SensBounder.KMeansForSetsSensitivityBounder(set_P_indiced, self.k, None, None)
sensitivity = k_means_sens_bounder.boundSensitivity()
if self.save_mode:
np.savez(self.save_path + self.file_prefix + self.sens_file_name, s=sensitivity)
print('Sum of sensitivity is {}'.format(np.sum(sensitivity)))
print("Saved sensitivity for sets clustering!")
if continue_from <= 1 and not self.show:
k_means_alg = KMeansAlg.KMeansAlg(blobs[0].d, self.k)
coreset = CS.Coreset()
C = coreset.computeCoreset(set_P_indiced, sensitivity, int(self.coreset_sample_size))
_, Q, _ = k_means_alg.computeKmeans(C[0], False)
np.savez('{}Optimal_clustering_{}.npz'.format(self.save_path, self.file_prefix), Q=Q)
else:
Q = np.load('{}Optimal_clustering_{}.npz'.format(self.save_path,self.file_prefix))['Q']
print("Loaded optimal clustering of coreset")
assignments_per_point, assignments_per_blob = self.clusteringAssignment(blobs, Q)
return np.array(blobs), np.array(assignments_per_blob), assignments_per_point
def addConnections(self, pairs, g_all, i, j, list_of_vertices, shift_idx_root, shift_idx_leaf, is_leaf=None,
enable_weights=False, connections=[]):
dists = np.linalg.norm(self.clustered_bodies[i][pairs[:,0]] - self.clustered_bodies[j][pairs[:,1]], axis=1)
pairs_of_interest = pairs[np.where(dists <= 2)[0]]
if len(pairs_of_interest) != 0:
if enable_weights:
for pair in pairs_of_interest:
root_of_path_of_interest = self.clustered_bodies[i][pair[0]]
leaf_of_path_of_interest = self.clustered_bodies[j][pair[1]]
direction = root_of_path_of_interest - leaf_of_path_of_interest
direction = direction / np.linalg.norm(direction)
target_direction = self.grid[tuple(root_of_path_of_interest.astype("int"))]
alpha = np.dot(direction, target_direction/np.linalg.norm(target_direction))
if alpha > 0.7:
try:
g_all.add_edge(int(pair[0] + shift_idx_root), int(pair[1] + shift_idx_leaf))
list_of_vertices = np.delete(list_of_vertices, np.where(list_of_vertices == (pair[1]+shift_idx_leaf)))
if is_leaf is not None:
is_leaf = np.delete(is_leaf, np.where(is_leaf == (pair[0] + shift_idx_root)))
except:
continue
else:
roots = np.unique(pairs_of_interest[:, 0])
for root in roots:
try:
idxs_of_interest = np.where(pairs_of_interest[:, 0] == root)[0]
pairs_of_interest_per_root = pairs_of_interest[idxs_of_interest, :]
root_of_path_of_interest = self.clustered_bodies[i][root][np.newaxis, :]
leaf_of_path_of_interest = self.clustered_bodies[j][pairs_of_interest_per_root[:, 1]]
directions = leaf_of_path_of_interest - root_of_path_of_interest
directions = np.divide(directions,
np.linalg.norm(directions, axis=1)[:, np.newaxis],
out=np.zeros_like(directions),
where=np.linalg.norm(directions, axis=1)[:, np.newaxis]!=0, casting="unsafe")
target_direction = self.grid[tuple(root_of_path_of_interest.flatten().astype("int"))]
alpha = np.dot(directions, target_direction / np.linalg.norm(target_direction))
l = np.argmax(alpha)
if alpha[l] >= 0.7:
g_all.add_edge(int(root + shift_idx_root),
int(pairs_of_interest[idxs_of_interest[l]][1] + shift_idx_leaf))
list_of_vertices = \
np.delete(list_of_vertices,
np.where(list_of_vertices == (pairs_of_interest[idxs_of_interest[l]][1]
+ shift_idx_leaf)))
if is_leaf is not None:
is_leaf = np.delete(is_leaf, np.where(is_leaf == (root + shift_idx_root)))
connections.append((i, int(root), j, int(pairs_of_interest[idxs_of_interest[l]][1])))
except:
continue
return g_all, list_of_vertices, is_leaf, connections
def containedInMap(self, point):
temp = point + self.grid[tuple(point.astype("int"))]
if np.any(temp < 0) or np.any(temp >= np.array(list(self.grid.shape[:-1]))):
return False
return True
def attainDiameterOfSetOfPoints(self, P):
return np.max(np.linalg.norm(P - P[np.argmax(np.linalg.norm(P - np.mean(P, axis=0)[np.newaxis, :],
axis=1))][np.newaxis, :], axis=1))
def avoidRedundantConnection(self, point, P, orig_idxs):
norms = np.linalg.norm(P - point[np.newaxis, :], axis=1)
idxs = np.argsort(norms)
temp = P - point[np.newaxis, :]
temp = np.around(np.multiply(temp[idxs], (1 / norms[idxs])[:, np.newaxis]), 2)
_, idx2 = np.unique(temp, axis=0, return_index=True)
return orig_idxs[idxs[idx2]]
def generateGraph(self, is_full=True, enable_weights=False, enable_all=False):
leaves = []
roots = []
all_others = []
roots_all = np.array([])
leaves_all = np.array([])
idx_shift = 0
g_all = jgrapht.create_graph(directed=True, weighted=False)
graphs = [jgrapht.create_graph(directed=True, weighted=False) for i in range(self.k)]
counter_bad_vertices = np.zeros((self.k, ))
cnt = 0
for body_idx,body in enumerate(self.clustered_bodies):
idxs_leafs = np.arange(body.shape[0])
idxs_roots = np.arange(body.shape[0])
idxs_all_others = np.arange(body.shape[0])
for i in range(idx_shift, idx_shift + body.shape[0]):
graphs[body_idx].add_vertex(i-idx_shift)
g_all.add_vertex(i)
for i, point in enumerate(body):
temp = body-point[np.newaxis, :]
norms = np.linalg.norm(temp, axis=1)[:, np.newaxis]
if is_full:
norms = norms.flatten()
neighbors = np.where(np.logical_and(norms.flatten() <= np.sqrt(2), norms.flatten() > 0))[0]
norms = norms.flatten()[neighbors][:, np.newaxis]
temp = temp[neighbors,:]
else:
norms = norms.flatten()
min_dist = self.attainDiameterOfSetOfPoints(body) * self.epsilon_body
neighbors = np.where(np.logical_and(norms.flatten() <= min_dist, norms.flatten() > 0))[0]
norms = norms.flatten()[neighbors][:, np.newaxis]
temp = temp[neighbors, :]
dots = np.clip(np.dot(np.multiply(temp, np.divide(1, norms, out=np.zeros_like(norms), where=norms != 0)),
self.grid[tuple(point)] / np.linalg.norm(self.grid[tuple(point)])), -1,1)
vals = np.arccos(dots)
normal = null_space((self.grid[tuple(point)] / np.linalg.norm(self.grid[tuple(point)]))[np.newaxis, :])
vals2 = np.linalg.norm(np.dot(np.multiply(temp, np.divide(1, norms, out=np.zeros_like(norms),
where=norms != 0)), normal), axis=1)
try:
if not self.containedInMap(point):
counter_bad_vertices[body_idx] += 1
idxs_roots = np.delete(idxs_roots, np.where(idxs_roots ==i))
idxs_all_others = np.delete(idxs_all_others, np.where(idxs_all_others == i))
raise ValueError('Will not consider coordinates {} as root.'.format(point))
idxs = np.where(np.logical_and(dots >= 0, np.logical_and(vals <= (15 * np.pi/180), vals2 <= 0.3)))[0]
if idxs.size == 0:
raise ValueError('Continue to next point')
sign_temp = np.sign(temp[idxs])
idxs = idxs[np.where(sign_temp.dot(np.sign(self.grid[tuple(point)])) == point.size)[0]]
idxs = idxs[np.argsort(vals[idxs])[:min(1, idxs.shape[0])]]
if not is_full:
if not enable_all:
l = [np.argmin(vals[idxs.astype("int")])] # take all the points that might be reached from
# current vertex via the dominating direction
# of the body
else:
l = np.arange(idxs.shape[0]).astype("int")
idxs = np.unique(self.avoidRedundantConnection(point, body[neighbors[idxs], :], neighbors[idxs]))
for j in idxs:
edge_endpoint = j
graphs[body_idx].add_edge(int(i), int(edge_endpoint))
idxs_leafs = np.delete(idxs_leafs, np.where(idxs_leafs == i))
idxs_roots = np.delete(idxs_roots, np.where(idxs_roots == edge_endpoint))
g_all.add_edge(int(i+idx_shift), int(edge_endpoint+idx_shift))
cnt+=1
else:
if enable_weights:
for j in idxs: # This requires a graph with weights
edge_endpoint = neighbors[j]
graphs[body_idx].add_edge(int(i), int(edge_endpoint))
idxs_leafs = np.delete(idxs_leafs, np.where(idxs_leafs == (i+idx_shift)))
idxs_roots = np.delete(idxs_roots, np.where(idxs_roots == (edge_endpoint + idx_shift)))
g_all.add_edge(int(i + idx_shift), int(edge_endpoint + idx_shift))
else:
if not enable_all:
l = np.argmin(vals[idxs])
else:
l = np.arange(idxs.shape[0]).astype("int")
for j in l:
edge_endpoint = neighbors[idxs[j]]
graphs[body_idx].add_edge(int(i), int(edge_endpoint))
idxs_leafs = np.delete(idxs_leafs, np.where(idxs_leafs == (i + idx_shift)))
idxs_roots = np.delete(idxs_roots, np.where(idxs_roots == (edge_endpoint + idx_shift)))
g_all.add_edge(int(i + idx_shift), int(edge_endpoint + idx_shift))
except:
continue
idx_shift += body.shape[0]
idxs_leafs = np.array(list(set(idxs_leafs) - set(idxs_roots)))
idxs_all_others = np.array(list(set(idxs_all_others) - (set(idxs_leafs).union(set(idxs_roots)))))
leaves.append(deepcopy(idxs_leafs))
roots.append(deepcopy(idxs_roots))
all_others.append(deepcopy(idxs_all_others))
roots_all = np.hstack((roots_all, idxs_roots+idx_shift))
leaves_all = np.hstack((leaves_all, idxs_leafs+idx_shift))
print(bcolors.BOLD + "Graph {} contains {} vertices and {} edges".format(body_idx, graphs[body_idx].number_of_vertices,
graphs[body_idx].number_of_edges))
print(bcolors.NORMAL)
shifts = np.cumsum([x.shape[0] for x in self.clustered_bodies])
connections = []
for i in range(len(graphs)):
for j in range(len(graphs)):
if i == j:
continue
else:
from_roots = np.array(np.meshgrid(roots[i],
np.unique(np.hstack((roots[j], leaves[j], all_others[j]))))).T.reshape(-1, 2)
from_leaves = np.array(np.meshgrid(leaves[i],
np.unique(np.hstack((roots[j], leaves[j], all_others[j]))))).T.reshape(-1, 2)
from_others = np.array(np.meshgrid(all_others[i],
np.unique(np.hstack((roots[j], leaves[j],all_others[j]))))).T.reshape(-1, 2)
g_all, roots_all, _, connections= \
self.addConnections(from_roots, g_all, i,j,roots_all,
shift_idx_root=(0 if i == 0 else shifts[i-1]),
shift_idx_leaf=(0 if j == 0 else shifts[j-1]),
enable_weights=enable_weights,
connections=connections)
g_all, roots_all, leaves_all, connections = \
self.addConnections(from_leaves, g_all, i,j,roots_all,
shift_idx_root=(0 if i == 0 else shifts[i-1]),
shift_idx_leaf=(0 if j == 0 else shifts[j-1]),
is_leaf=leaves_all,
enable_weights=enable_weights,
connections=connections)
g_all, roots_all, leaves_all, connections = \
self.addConnections(from_others, g_all, i,j, roots_all,
shift_idx_root=(0 if i == 0 else shifts[i-1]),
shift_idx_leaf=(0 if j == 0 else shifts[j-1]),
enable_weights=enable_weights,
connections=connections)
np.savez('{}Graphs_{}.npz'.format(self.save_path, self.file_prefix), g_all=jgrapht.io.exporters.generate_csv(g_all),
graphs=[jgrapht.io.exporters.generate_csv(x) for x in graphs], leaves=leaves, roots=roots,
roots_all=roots_all, leaves_all=leaves_all, connections=connections)
return g_all, graphs, roots, leaves, roots_all, leaves_all, connections
def findTheStartingVertexOfLongestPathInGraph(self, graph=None, return_all=False):
all_paths_alg = johnson_allpairs(self.g if graph is None else graph)
path_lengths = []
all_paths = []
for root in (self.g if graph is None else graph).vertices:
longest_path_len = 0
longest_path = None
for leaf in (self.g if graph is None else graph).vertices:
if root == leaf:
continue
path = all_paths_alg.get_path(root, leaf)
if path is not None:
all_paths.append((path.vertices, len(path.vertices)))
if path is not None and longest_path_len <= len(path.vertices):
longest_path,longest_path_len = path.vertices, len(path.vertices)
if longest_path_len > 0:
path_lengths.append((longest_path, longest_path_len))
if not return_all:
i = np.argmax(np.array([x[1] for x in path_lengths]))
return path_lengths[i][0][0], all_paths
else:
return all_paths,path_lengths
def saveFile(self, file_name, data):
with open(file_name, 'wb') as outfile:
pickle.dump(data, outfile, protocol=pickle.HIGHEST_PROTOCOL)
def loadFile(self, file_name):
with open(file_name, 'rb') as outfile:
return pickle.load(outfile)
def plotResults(self):
x_min, x_max, y_min, y_max = 31.0583, 33.6917, 31.5100, 35.4300
ax = plotMap(self.grid, x_min=x_min, x_max=x_max, y_min=y_min, y_max=y_max)
if self.epsilon_body > 0:
bodies = self.bodies
else:
bodies = self.full_bodies
colors = pl.cm.jet(np.linspace(0, 1, len(bodies)))
for i in range(len(bodies)):
if bodies[i].ndim > 1:
ax.scatter(bodies[i][:, 0] / (self.grid.shape[0] - 1) * (x_max - x_min) + x_min, bodies[i][:, 1]/ (self.grid.shape[1] - 1) * (y_max - y_min) + y_min, color=colors[i])
else:
ax.scatter(bodies[i][0]/ (self.grid.shape[0] - 1) * (x_max - x_min) + x_min, bodies[i][1]/ (self.grid.shape[1] - 1) * (y_max - y_min) + y_min, color=colors[i])
plt.xticks(np.arange(31.5, 34 , 0.5))
plt.yticks(np.arange(32, 35.5 , 0.5))
plt.xlabel('Latitude')
plt.ylabel('Longitude')
plt.gcf().tight_layout()
plt.savefig('{}Segmentation_{}.png'.format(self.save_path,self.file_prefix))
# plot clustering
ax = plotMap(self.grid, x_min=x_min, x_max=x_max, y_min=y_min, y_max=y_max)
colors = pl.cm.jet(np.linspace(0, 1, self.k))
for i in range(self.k):
ax.scatter(self.clustered_bodies[i][:,0]/ (self.grid.shape[0] - 1) * (x_max - x_min) + x_min, self.clustered_bodies[i][:,1]/ (self.grid.shape[1] - 1) * (y_max - y_min) + y_min, color=colors[i])
plt.xticks(np.arange(31.5, 34 , 0.5))
plt.yticks(np.arange(32, 35.5 , 0.5))
plt.xlabel('Latitude')
plt.ylabel('Longitude')
plt.gcf().tight_layout()
plt.savefig('{}Clustering_{}.png'.format(self.save_path,self.file_prefix))
# close all figures
plt.close('all')
def findSubOptimalPlacing(self, continue_from=-1):
if continue_from == -1 and not self.show:
start_ellip = timer()
points = self.polynomialGridSearch()
for point in tqdm(points,ncols=100):
if np.linalg.norm(self.grid[tuple(point)]) > 0 and not self.checkIfContained(point):
self.IOCS(point)
end_ellip = timer()
print(bcolors.BOLD + bcolors.OKGREEN + 'IOCS ended in {} seconds'.format(end_ellip - start_ellip))
print(bcolors.NORMAL)
self.saveFile(file_name=('{}Ellipsoids_{}.dat'.format(self.save_path, self.file_prefix)),
data=dict(zip(['ellipsoids','bodies','full_bodies'],
[self.ellipsoids, self.bodies, self.full_bodies])))
else:
temp = self.loadFile(file_name=('{}Ellipsoids_{}.dat'.format(self.save_path, self.file_prefix)))
self.ellipsoids = temp['ellipsoids']
self.bodies = temp['bodies']
self.full_bodies = temp['full_bodies']
start_clustering = timer()
blobs, assignments_per_blob, assignments_per_point = self.clusterWaves(continue_from)
self.clustered_bodies = []
for idx in range(self.k):
cluster_idx = np.where(assignments_per_blob == idx)[0].astype("int")
self.clustered_bodies.append(np.unique(np.vstack([(x.P[:, [0, 1]] / FORCE_NEIGHBORING).astype("int")
for x in blobs[cluster_idx]]), axis=0))
print(bcolors.BOLD + bcolors.OKGREEN + 'Total time for clustering WC is {} seconds'.format(timer() - start_clustering))
print(bcolors.NORMAL)
self.plotResults()
if self.show:
exit(-9)
start_graph_based = timer()
if continue_from < 3:
g_all, graphs, roots, leaves, roots_all, leaves_all, connections = self.generateGraph(enable_all=True,
is_full=(self.epsilon_body == 0.0))
else:
G = np.load('{}Graphs_{}.npz'.format(self.save_path,self.file_prefix), allow_pickle=True)
g_all = jgrapht.create_graph(directed=True, weighted=False)
graphs_strings = G['graphs']
graphs = [jgrapht.create_graph(directed=True,weighted=False) for i in range(self.k)]
jgrapht.io.importers.parse_csv(g_all, str(G['g_all']))
for i in range(self.k):
jgrapht.io.importers.parse_csv(graphs[i], str(graphs_strings[i]))
roots = G['roots'].tolist()
leaves = G['leaves'].tolist()
roots_all = G['roots_all'].tolist()
leaves_all = G['leaves_all'].tolist()
connections = G['connections'].tolist()
# retrieve only $k$ largest paths where for any two paths, no path is a subpath of the other
positions = np.empty((3,self.k, self.d))
if continue_from < 4:
# Heuristic choice
for i,body in enumerate(self.clustered_bodies):
A = np.vstack([self.grid[tuple(x)] for x in body])
u_vecs, counts = np.unique(np.sign(A), return_counts=True, axis=0)
dominating_vec = u_vecs[np.argmax(counts)] / np.linalg.norm(u_vecs[np.argmax(counts)])
idxs = np.where(np.sign(A).dot(np.sign(dominating_vec)) == dominating_vec.shape[0])[0]
vecs = body[idxs] - np.mean(body[idxs], axis=0)
vals = np.dot(vecs, dominating_vec)
positions[0, i, :] = body[idxs[int(np.argmin(vals))]]
print(bcolors.OKGREEN + 'Finished computing initial positions for drifters via heuristical methods' + bcolors.ENDC)
# Find longest path in each graph seperately
paths_in_graph = [[] for i in range(len(graphs))]
for i,graph in enumerate(graphs):
idx, paths_in_graph[i] = self.findTheStartingVertexOfLongestPathInGraph(graph=graph, return_all=False)
positions[1, i, :] = self.clustered_bodies[i][idx]
print(bcolors.OKGREEN + 'Finished computing initial positions for drifters via graph based methods' + bcolors.ENDC)
np.savez('{}paths_in_graphs_{}.npz'.format(self.save_path, self.file_prefix), positions=positions, paths_in_graph=paths_in_graph)
# Find k longest paths in the combined graph
# old technique
else:
temp = np.load('{}paths_in_graphs_{}.npz'.format(self.save_path, self.file_prefix), allow_pickle=True)
positions = temp['positions']
paths_in_graph = temp['paths_in_graph'].tolist()
print(bcolors.BOLD + 'Starting to compute initial positions for drifters via inter-connected graphs' + bcolors.ENDC)
if continue_from < 5:
parsed_paths = [item for sublist in paths_in_graph for item in sublist]
johnson_graphs = [johnson_allpairs(x) for x in graphs]
shift_idxs = np.hstack((0,np.cumsum([x.number_of_vertices for x in graphs])))
unified_paths = []
for connection in connections:
i, vertex_i, j, vertex_j = connection
temp_paths_from_j = [x for x in paths_in_graph[j] if x[0][0] == vertex_j]
temp_paths_to_i = [x for x in paths_in_graph[i] if x[0][-1] == vertex_i]
unified_temp_paths_to_i = []
# shift indices
for list_i in range(len(temp_paths_to_i)):
if len(temp_paths_to_i) > 0:
temp_paths_to_i[list_i] = ([x + shift_idxs[i] for x in temp_paths_to_i[list_i][0]],
temp_paths_to_i[list_i][1])
for list_j in range(len(temp_paths_from_j)):
if len(temp_paths_from_j) > 0:
temp_paths_from_j[list_j] = ([x + shift_idxs[j] for x in temp_paths_from_j[list_j][0]],
temp_paths_from_j[list_j][1])
# check if there are inter_graph paths including vertex_i
temp_paths_to_i = [x for x in paths_in_graph[i] if x[0][-1] == vertex_i]
if len(unified_paths) > 0:
unified_temp_paths_to_i = [x for x in unified_paths if x[0][-1] == (vertex_i + shift_idxs[i])]
if len(temp_paths_to_i) > 0 and len(temp_paths_from_j) > 0:
temp = getAllPossiblePaths(temp_paths_to_i, temp_paths_from_j)
unified_paths.extend(copy.deepcopy(temp))
if len(unified_temp_paths_to_i) > 0:
temp2 = getAllPossiblePaths(unified_temp_paths_to_i, temp)
print('Length of temp_2 is {}'.format(len(temp2)))
unified_paths.extend(copy.deepcopy(temp2))
unified_paths.sort(key = lambda x: x[1])
i = 0
if False:
while True:
advance_i = True
if i < (len(unified_paths) - 1):
for j in range(i+1, len(unified_paths)):
if set(unified_paths[i][0]).issubset(unified_paths[j][0]):
advance_i = False
del(unified_paths[i])
break
if advance_i:
i += 1
else:
break
else:
print('Removing Inclusions has been initiated')
unified_paths = removeInclusions(unified_paths, self.save_path, self.file_prefix)
print('Number of possibe paths is {}'.format(len(unified_paths)))
np.save('{}unified_paths_{}.npy'.format(self.save_path, self.file_prefix), unified_paths)
print('Saved unified paths')
else:
temp = np.load('{}unified_paths_{}.npy'.format(self.save_path, self.file_prefix), allow_pickle=True)
unified_paths = temp.tolist()
print('length of Connections is {}'.format(len(connections)))
print('length of Unified Paths are {}'.format(len(unified_paths)))
if False:
unified_graph = johnson_allpairs(g_all)
paths = []
for root in roots_all:
for leaf in leaves_all:
try:
path = unified_graph.get_path(int(root), int(leaf))
except:
continue
dont = False
replace_idx = None
if path is not None:
if len(paths) > 0:
if np.any([set(path.vertices).issubset(x[0]) for x in paths]):
dont = True
if np.any([set(x[0]).issubset(path.vertices) for x in paths]):
replace_idx = np.where([set(x[0]).issubset(path.vertices) for x in paths])[0][0]
if not dont:
if replace_idx is None:
paths.append((path.vertices, len(path.vertices)))
else:
paths[replace_idx] = (path.vertices, len(path.vertices))
# make sure that paths chosen that start from different nodes
temp = copy.deepcopy(unified_paths)
while True:
len_paths = np.array([len(x) for x in temp])
sorted_idxs = np.argsort((-1) * len_paths)
idxs = sorted_idxs[:self.k].astype("int")
initials = [temp[x][0] for x in idxs]
to_delete = []
for i in range(self.k):
for j in range(i+1, self.k):
if initials[i] == initials[j]:
to_delete.append(temp[idxs[j]])
if len(to_delete) == 0 or len(len_paths) == self.k:
break
else:
for element in to_delete:
try:
temp.remove(element)
except:
continue
unified_paths = copy.deepcopy(temp)
len_paths = np.array([len(x) for x in unified_paths])
sorted_idxs = np.argsort((-1) * len_paths)
sizes = np.cumsum([x.shape[0] for x in self.clustered_bodies])
idxs = sorted_idxs[:self.k].astype("int")
raw_paths = [unified_paths[x] for x in idxs]
raw_paths_initial_pos = [x[0] for x in raw_paths]
print('raw paths initial are {}'.format(raw_paths_initial_pos))
print('Sizes are {}'.format(sizes))
for i in range(len(raw_paths_initial_pos)):
idx_shift = np.where(raw_paths_initial_pos[i] < sizes)[0][0]
if self.clustered_bodies[idx_shift].shape[0] == (raw_paths_initial_pos[i] -sizes[idx_shift-1]):
idx_shift += 1
positions[2, i, :] = self.clustered_bodies[idx_shift][0]
else:
positions[2, i, :] = self.clustered_bodies[idx_shift][raw_paths_initial_pos[i] -
(0 if idx_shift == 0 else sizes[idx_shift-1])]
print(bcolors.BOLD + 'Finished computing initial positions for drifters via inter-connected graphs' +
bcolors.ENDC)
np.save('{}initial_locations_{}.npy'.format(self.save_path,self.file_prefix), positions)
print(bcolors.BOLD + bcolors.OKGREEN + 'Time for finding suboptimal dropping positions is {} seconds'.format(timer() - start_graph_based))
print(bcolors.NORMAL)
return positions
def plotEllipsoid(self, ellipsoid, center):
"""
This function serves only for plotting a 2D ellipsoid.
:param ellipsoid: An orthogonal matrix representing the ellipsoid's axes lenghts and rotation
:param center: The center of ellipsoid represented by a numpy array.
:return: None.
"""
N = 10000 # numer of points on the boundary of the ellipsoid.
_, D, V = np.linalg.svd(ellipsoid, full_matrices=True) # attain the axes lengthes and rotation of the ellipsoid
a = 1.0 / D[0]
b = 1.0 / D[1]
theta = np.expand_dims(np.arange(start=0, step=1.0 / N, stop=2.0*np.pi + 1.0/N), 1).T
state = np.vstack((a * np.cos(theta), b * np.sin(theta)))
X = np.dot(V, state) + center[:,np.newaxis]
plt.plot(X[0, :], X[1, :], color='blue')
def plotMap(grid, indices=None, x_min=None, x_max=None, y_min=None, y_max=None):
positions = np.indices((grid.shape[0], grid.shape[1])).T.reshape(-1, 2)
fig, ax = plt.subplots()
idxs = [i for i in range(positions.shape[0]) if np.linalg.norm(grid[tuple(positions[i])]) > 0]
if indices is None:
if x_min is None:
q = ax.quiver(positions[idxs,0], positions[idxs,1], grid[positions[idxs,0], positions[idxs,1],0], grid[positions[idxs,0], positions[idxs,1],1], angles='xy')
else:
q = ax.quiver(positions[idxs,0] / (grid.shape[0] - 1) * (x_max - x_min) + x_min, positions[idxs,1] / (grid.shape[1] - 1) * (y_max - y_min) + y_min, grid[positions[idxs,0], positions[idxs,1],0], grid[positions[idxs,0], positions[idxs,1],1], angles='xy')
else:
q = ax.quiver(indices[:, 0], indices[:, 1], grid[indices[:, 0], indices[:, 1],0],
grid[indices[:,0], indices[:, 1], 1], angles='xy')
return ax
def main(data_folder, preprocess=True, file_type='.dat', number_of_files=1, eps_g=None, eps_b=0, k=10,
coreset_sample_size=1000, over_time=False, tol=0.02, resume=False, show=False):
paths = [x for x in os.walk(data_folder)]
done = []
if resume:
with open("resume_from_maps_init.pkl", "rb") as open_file:
paths = pickle.load(open_file)
for i, file_path_tuple in enumerate(paths):
for file_name in file_path_tuple[-1]:
if file_name.endswith(file_type):
if file_type =='.nc':
with open('resume_from_maps_init.pkl', "wb") as open_file:
pickle.dump(paths[i:], open_file)
start_main = timer()
print(bcolors.WARNING + '****************************************************************************')
print(bcolors.BOLD + bcolors.WARNING + "Proccessing File: {}".format(file_name))
print(bcolors.NORMAL)
U, V = readNetCDFFile(file_path_tuple[0]+'/'+file_name, over_time=over_time)
if not over_time:
preprocessed_files = [ndi.correlate(np.mean(x,0), np.full((3, 3), 1 / 9)).T[None] for x in [U,V]]
preprocessed_files_2 = [np.mean(x,0).T[None] for x in [U,V]]
grid = np.append(*preprocessed_files, axis=0).T
grid2 = np.append(*preprocessed_files_2, axis=0).T
saveVels(grid, file_path=file_path_tuple[0]+'/', smoothed=True)
saveVels(grid2, file_path=file_path_tuple[0]+'/', smoothed=False)
if eps_g is None:
eps_g = np.around(10 / grid.shape[0], 2)
drifter_placer = CurrentEstimation(grid, epsilon_grid=eps_g, k=k, epsilon_body=eps_b,
coreset_sample_size=coreset_sample_size, tolerance=tol,
save_path=file_path_tuple[0]+'/', show=show)
drifter_placer.findSubOptimalPlacing(continue_from=-1)
end_main = timer()
print(bcolors.HEADER + bcolors.OKGREEN + 'Whole program took {} seconds'.format(end_main - start_main))
print(bcolors.NORMAL)
| np.save(file_path_tuple[0] + '/' + 'Time.npy', end_main - start_main) | numpy.save |
#
#
# Test of convergence diagnostics
#
#
from __future__ import with_statement
from numpy.testing import assert_equal, assert_array_equal
from numpy.testing import assert_approx_equal, TestCase
import unittest
import nose
import numpy as np
import pymc
import pymc.examples.weibull_fit as model
import os
import warnings
import copy
| np.random.seed(467) | numpy.random.seed |
import os
import sys
import time
import skimage
import numpy as np
import scipy.io as sio
from tqdm import trange
import tensorflow as tf
from sklearn.manifold import TSNE
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt
from sklearn.utils import shuffle
from contextlib import redirect_stdout
from Tools import *
from Networks import *
from flip_gradient import flip_gradient
class Models():
def __init__(self, args, dataset):
self.args = args
# Initializing the placeholders
#Changing the seed at any run
tf.set_random_seed(int(time.time()))
tf.reset_default_graph()
self.learning_rate = tf.placeholder(tf.float32, [], name="learning_rate")
if self.args.compute_ndvi:
self.data = tf.placeholder(tf.float32, [None, self.args.patches_dimension, self.args.patches_dimension, 2 * self.args.image_channels + 2], name = "data")
else:
self.data = tf.placeholder(tf.float32, [None, self.args.patches_dimension, self.args.patches_dimension, 2 * self.args.image_channels], name = "data")
self.label = tf.placeholder(tf.float32, [None, self.args.num_classes], name = "label")
self.label_d = tf.placeholder(tf.float32, [None, 2], name = "label_d")
self.mask_c = tf.placeholder(tf.float32, [None,], name="labeled_samples")
self.L = tf.placeholder(tf.float32, [], name="L" )
# Initializing the network class
self.classifier = EF_CNN(self.args)
# Initializing the models individually
if self.args.FE_Architecture == 'Mabel_Arch':
Encoder_Outputs = self.classifier.build_Mabel_Arch(self.data, reuse = False, name = "FE")
elif self.args.FE_Architecture == 'Ganin_Arch':
Encoder_Outputs = self.classifier.build_Ganin_Arch(self.data, reuse = False, name = "FE")
#Defining the classifier
Classifier_Outputs = self.classifier.build_MLP_1hidden_cl(Encoder_Outputs[-1], reuse = False, name = "MLP_Cl")
self.logits_c = Classifier_Outputs[-2]
self.prediction_c = Classifier_Outputs[-1]
self.features_c = Encoder_Outputs[-1]
if self.args.training_type == 'domain_adaptation':
if 'DR' in self.args.da_type:
flip_feature = flip_gradient(self.features_c, self.L)
self.DR = Domain_Regressors(self.args)
DR_Ouputs = self.DR.build_Domain_Classifier_Arch(flip_feature, name = 'FC_Domain_Classifier')
self.logits_d = DR_Ouputs[-2]
if self.args.phase == 'train':
self.summary(Encoder_Outputs, 'Encoder:')
self.summary(Classifier_Outputs, 'Classifier:')
self.dataset_s = dataset[0]
self.dataset_t = dataset[1]
#Defining losses
temp = tf.nn.softmax_cross_entropy_with_logits(logits = self.logits_c, labels = self.label)
self.classifier_loss = tf.reduce_sum(self.mask_c * temp) / tf.reduce_sum(self.mask_c)
if self.args.training_type == 'classification':
self.total_loss = self.classifier_loss
else:
if 'DR' in self.args.da_type:
self.summary(DR_Ouputs, "Domain_Regressor: ")
self.domainregressor_loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits = self.logits_d, labels = self.label_d))
self.total_loss = self.classifier_loss + self.domainregressor_loss
else:
self.total_loss = self.classifier_loss
#Defining the Optimizers
self.training_optimizer = tf.train.MomentumOptimizer(self.learning_rate, self.args.beta1).minimize(self.total_loss)
self.saver = tf.train.Saver(max_to_keep=5)
self.sess=tf.Session()
self.sess.run(tf.initialize_all_variables())
elif self.args.phase == 'test':
self.dataset = dataset
self.saver = tf.train.Saver(max_to_keep=5)
self.sess=tf.Session()
self.sess.run(tf.initialize_all_variables())
print('[*]Loading the feature extractor and classifier trained models...')
mod = self.load(self.args.trained_model_path)
if mod:
print(" [*] Load with SUCCESS")
else:
print(" [!] Load failed...")
sys.exit()
def Learning_rate_decay(self):
lr = self.args.lr / (1. + 10 * self.p)**0.75
return lr
def summary(self, net, name):
print(net)
f = open(self.args.save_checkpoint_path + "Architecture.txt","a")
f.write(name + "\n")
for i in range(len(net)):
print(net[i].get_shape().as_list())
f.write(str(net[i].get_shape().as_list()) + "\n")
f.close()
def Train(self):
pat = 0
best_val_dr = 0
best_val_fs = 0
if self.args.balanced_tr:
# Shuffling the data and labels
central_pixels_coor_tr = self.dataset_s.central_pixels_coor_tr.copy()
y_train = self.dataset_s.y_train.copy()
central_pixels_coor_tr, y_train = shuffle(central_pixels_coor_tr, y_train, random_state=0)
positive_coordinates = np.transpose(np.array(np.where(y_train == 1)))
negative_coordinates = np.transpose(np.array(np.where(y_train == 0)))
positive_coordinates = positive_coordinates[:,0]
negative_coordinates = negative_coordinates[:,0]
positive_central_pixels_coor_tr = central_pixels_coor_tr[positive_coordinates, :]
if self.args.data_augmentation:
positive_central_pixels_coor_tr, _ = Data_Augmentation_Definition(positive_central_pixels_coor_tr, np.ones((len(positive_coordinates),1)))
#Taking the same amount of negative samples as positive
negative_coordinates = negative_coordinates[:positive_central_pixels_coor_tr.shape[0]]
if self.args.data_augmentation:
negative_central_pixels_coor_tr = np.concatenate((central_pixels_coor_tr[negative_coordinates, :], np.zeros((len(negative_coordinates),1))),axis=1)
else:
negative_central_pixels_coor_tr = central_pixels_coor_tr[negative_coordinates, :]
positive_y_train = np.ones((positive_central_pixels_coor_tr.shape[0],1))
negative_y_train = np.zeros((negative_central_pixels_coor_tr.shape[0],1))
central_pixels_coor_tr = np.concatenate((positive_central_pixels_coor_tr, negative_central_pixels_coor_tr), axis=0)
y_train = np.concatenate((positive_y_train, negative_y_train), axis=0)
# Shuffling again
central_pixels_coor_tr_s, y_train_s = shuffle(central_pixels_coor_tr, y_train,random_state=0)
if self.args.balanced_vl:
central_pixels_coor_vl = self.dataset_s.central_pixels_coor_vl.copy()
y_valid = self.dataset_s.y_valid.copy()
# Shuffling the data and labels
central_pixels_coor_vl, y_valid = shuffle(central_pixels_coor_vl, y_valid,random_state=0)
positive_coordinates = np.transpose(np.array(np.where(y_valid == 1)))
negative_coordinates = np.transpose(np.array(np.where(y_valid == 0)))
positive_coordinates = positive_coordinates[:,0]
negative_coordinates = negative_coordinates[:,0]
positive_central_pixels_coor_vl = central_pixels_coor_vl[positive_coordinates, :]
if self.args.data_augmentation:
positive_central_pixels_coor_vl, _ = Data_Augmentation_Definition(positive_central_pixels_coor_vl, np.ones((len(positive_coordinates),1)))
#Taking the same amount of negative samples as positive
negative_coordinates = negative_coordinates[:positive_central_pixels_coor_vl.shape[0]]
if self.args.data_augmentation:
negative_central_pixels_coor_vl = np.concatenate((central_pixels_coor_vl[negative_coordinates, :] , np.zeros((len(negative_coordinates),1))), axis=1)
else:
negative_central_pixels_coor_vl = central_pixels_coor_vl[negative_coordinates, :]
positive_y_valid = np.ones((positive_central_pixels_coor_vl.shape[0],1))
negative_y_valid = np.zeros((negative_central_pixels_coor_vl.shape[0],1))
central_pixels_coor_vl = np.concatenate((positive_central_pixels_coor_vl, negative_central_pixels_coor_vl), axis=0)
y_valid = np.concatenate((positive_y_valid, negative_y_valid), axis=0)
# Shuffling again
central_pixels_coor_vl_s, y_valid_s = shuffle(central_pixels_coor_vl, y_valid,random_state=0)
print('Source sets dimensions')
print(np.shape(central_pixels_coor_tr_s))
print(np.shape(central_pixels_coor_vl_s))
print( | np.shape(y_train_s) | numpy.shape |
"""
Kravatte Achouffe Cipher Suite: Encryption, Decryption, and Authentication Tools based on the Farfalle modes
Copyright 2018 <NAME>
see LICENSE file
"""
from multiprocessing import Pool
from math import floor, ceil, log2
from typing import Tuple
from os import cpu_count
from ctypes import memset
import numpy as np
KravatteTagOutput = Tuple[bytes, bytes]
KravatteValidatedOutput = Tuple[bytes, bool]
class Kravatte(object):
"""Implementation of the Farfalle Pseudo-Random Function (PRF) construct utilizing the
Keccak-1600 permutation.
"""
KECCAK_BYTES = 200
'''Number of Bytes in Keccak-1600 state'''
KECCAK_LANES = 25
'''Number of 8-Byte lanes in Keccak-1600 state'''
KECCAK_PLANES_SLICES = 5
''' Size of x/y dimensions of Keccak lane array '''
THETA_REORDER = ((4, 0, 1, 2, 3), (1, 2, 3, 4, 0))
IOTA_CONSTANTS = np.array([0x000000000000800A, 0x800000008000000A, 0x8000000080008081,
0x8000000000008080, 0x0000000080000001, 0x8000000080008008],
dtype=np.uint64)
'''Iota Step Round Constants For Keccak-p(1600, 4) and Keccak-p(1600, 6)'''
RHO_SHIFTS = np.array([[0, 36, 3, 41, 18],
[1, 44, 10, 45, 2],
[62, 6, 43, 15, 61],
[28, 55, 25, 21, 56],
[27, 20, 39, 8, 14]], dtype=np.uint64)
'''Lane Shifts for Rho Step'''
CHI_REORDER = ((1, 2, 3, 4, 0), (2, 3, 4, 0, 1))
'''Lane Re-order Mapping for Chi Step'''
PI_ROW_REORDER = np.array([[0, 3, 1, 4, 2],
[1, 4, 2, 0, 3],
[2, 0, 3, 1, 4],
[3, 1, 4, 2, 0],
[4, 2, 0, 3, 1]])
'''Row Re-order Mapping for Pi Step'''
PI_COLUMN_REORDER = np.array([[0, 0, 0, 0, 0],
[1, 1, 1, 1, 1],
[2, 2, 2, 2, 2],
[3, 3, 3, 3, 3],
[4, 4, 4, 4, 4]])
'''Column Re-order Mapping for Pi Step'''
COMPRESS_ROW_REORDER = np.array([[0, 0, 0, 0, 1],
[1, 1, 1, 1, 2],
[2, 2, 2, 2, 3],
[3, 3, 3, 3, 4],
[4, 4, 4, 4, 0]])
'''Row Re-order Mapping for Compress Step'''
COMPRESS_COLUMN_REORDER = np.array([[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4]])
'''Column Re-order Mapping for Compress Step'''
EXPAND_ROW_REORDER = np.array([[0, 0, 0, 1, 1],
[1, 1, 1, 2, 2],
[2, 2, 2, 3, 3],
[3, 3, 3, 4, 4],
[4, 4, 4, 0, 0]])
'''Row Re-order Mapping for Expand Step'''
EXPAND_COLUMN_REORDER = np.array([[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4],
[0, 1, 2, 4, 4]])
'''Column Re-order Mapping for Expand Step'''
def __init__(self, key: bytes=b'', workers: int=None, mp_input: bool=True, mp_output: bool=True):
"""
Initialize Kravatte with user key
Inputs:
key (bytes): encryption/authentication key
workers (int): parallel processes to use in compression/expansion operations
mp_input (bool): Enable multi-processing for calculations on input data
mp_output (bool): Enable multi-processing for calculations on output data
"""
self.update_key(key)
self.reset_state()
# Enable Standard or Optimized Multi-process codepaths
if workers is not None:
self.collect_message = self._collect_message_mp if mp_input else self._collect_message_sp
self.generate_digest = self._generate_digest_mp if mp_output else self._generate_digest_sp
self.workers = cpu_count() if workers == 0 else workers
else:
self.collect_message = self._collect_message_sp
self.generate_digest = self._generate_digest_sp
self.workers = None
def update_key(self, key: bytes) -> None:
"""
Pad and compute new Kravatte base key from bytes source.
Inputs:
key (bytes): user provided bytes to be padded (if necessary) and computed into Kravatte base key
"""
key_pad = self._pad_10_append(key, self.KECCAK_BYTES)
key_array = np.frombuffer(key_pad, dtype=np.uint64, count=self.KECCAK_LANES,
offset=0).reshape([self.KECCAK_PLANES_SLICES,
self.KECCAK_PLANES_SLICES], order='F')
self.kra_key = self._keccak(key_array)
def reset_state(self) -> None:
"""
Clear existing Farfalle/Kravatte state and prepares for new input message collection.
Elements reset include:
- Message block collector
- Rolling key
- Currently stored output digest
- Digest Active and New Collector Flags
Inputs:
None
"""
self.roll_key = np.copy(self.kra_key)
self.collector = np.zeros([5, 5], dtype=np.uint64)
self.digest = bytearray(b'')
self.digest_active = False
self.new_collector = True
def _generate_absorb_queue(self, absorb_steps: int, kra_msg: bytes):
"""
Generator for Keccak-sized blocks of input message for Farfalle compression
Inputs:
absorb_steps (int): Number of blocks to generate for absorption
kra_msg (bytes): padded input message ready for slicing into input blocks
"""
for msg_block in range(absorb_steps):
yield (np.frombuffer(kra_msg, dtype=np.uint64, count=25, offset=msg_block * self.KECCAK_BYTES).reshape([5, 5], order='F') ^ self.roll_key)
self.roll_key = self._kravatte_roll_compress(self.roll_key)
def _collect_message_sp(self, message: bytes, append_bits: int=0, append_bit_count: int=0) -> None:
"""
Pad and Process Blocks of Message into Kravatte collector state
Inputs:
message (bytes): arbitrary number of bytes to be padded into Keccak blocks and absorbed into the collector
append_bits (int): bits to append to the message before padding. Required for more advanced Kravatte modes.
append_bit_count (int): number of bits to append
"""
if self.digest_active:
self.reset_state()
if self.new_collector:
self.new_collector = False
else:
self.roll_key = self._kravatte_roll_compress(self.roll_key)
# Pad Message
msg_len = len(message)
kra_msg = self._pad_10_append(message, msg_len + (self.KECCAK_BYTES - (msg_len % self.KECCAK_BYTES)), append_bits, append_bit_count)
absorb_steps = len(kra_msg) // self.KECCAK_BYTES
# Absorb into Collector
for msg_block in range(absorb_steps):
m = np.frombuffer(kra_msg, dtype=np.uint64, count=25, offset=msg_block * self.KECCAK_BYTES).reshape([5, 5], order='F')
m_k = m ^ self.roll_key
self.roll_key = self._kravatte_roll_compress(self.roll_key)
self.collector = self.collector ^ self._keccak(m_k)
def _collect_message_mp(self, message: bytes, append_bits: int=0, append_bit_count: int=0) -> None:
"""
Pad and Process Blocks of Message into Kravatte collector state - Multi-process Aware Variant
Inputs:
message (bytes): arbitrary number of bytes to be padded into Keccak blocks and absorbed into the collector
append_bits (int): bits to append to the message before padding. Required for more advanced Kravatte modes.
append_bit_count (int): number of bits to append
"""
if self.digest_active:
self.reset_state()
if self.new_collector:
self.new_collector = False
else:
self.roll_key = self._kravatte_roll_compress(self.roll_key)
# Pad Message
msg_len = len(message)
kra_msg = self._pad_10_append(message, msg_len + (self.KECCAK_BYTES - (msg_len % self.KECCAK_BYTES)), append_bits, append_bit_count)
absorb_steps = len(kra_msg) // self.KECCAK_BYTES
workload = 1 if (absorb_steps // self.workers) == 0 else (absorb_steps // self.workers)
with Pool(processes=self.workers) as kravatte_pool:
for output_element in kravatte_pool.imap_unordered(self._keccak, self._generate_absorb_queue(absorb_steps, kra_msg), chunksize=workload):
self.collector ^= output_element
def _generate_digest_sp(self, output_size: int, short_kravatte: bool=False) -> None:
"""
Squeeze an arbitrary number of bytes from collector state
Inputs:
output_size (int): Number of bytes to generate and store in Kravatte digest parameter
short_kravatte (bool): Enable disable short kravatte required for other Kravatte modes
"""
if not self.digest_active:
self.collector = self.collector if short_kravatte else self._keccak(self.collector)
self.roll_key = self._kravatte_roll_compress(self.roll_key)
self.digest_active = True
self.digest = bytearray(b'')
full_output_size = output_size + (200 - (output_size % 200)) if output_size % 200 else output_size
generate_steps = full_output_size // 200
for _ in range(generate_steps):
collector_squeeze = self._keccak(self.collector)
self.collector = self._kravatte_roll_expand(self.collector)
self.digest.extend((collector_squeeze ^ self.roll_key).tobytes('F'))
self.digest = self.digest[:output_size]
def _generate_squeeze_queue(self, generate_steps: int):
"""
Generator for Keccak-sized blocks of expanded collector state for output squeezing
Inputs:
generate_steps (int): Number of blocks to generate and for absorb
"""
for _ in range(generate_steps):
yield self.collector
self.collector = self._kravatte_roll_expand(self.collector)
def _generate_digest_mp(self, output_size: int, short_kravatte: bool=False) -> None:
"""
Squeeze an arbitrary number of bytes from collector state - Multi-process Aware Variant
Inputs:
output_size (int): Number of bytes to generate and store in Kravatte digest parameter
short_kravatte (bool): Enable disable short kravatte required for other Kravatte modes
"""
if not self.digest_active:
self.collector = self.collector if short_kravatte else self._keccak(self.collector)
self.roll_key = self._kravatte_roll_compress(self.roll_key)
self.digest_active = True
self.digest = bytearray(b'')
full_output_size = output_size + (200 - (output_size % 200)) if output_size % 200 else output_size
generate_steps = full_output_size // 200
workload = 1 if (generate_steps // self.workers) == 0 else (generate_steps // self.workers)
with Pool(processes=self.workers) as kravatte_pool:
for digest_block in kravatte_pool.imap(self._keccak_xor_key, self._generate_squeeze_queue(generate_steps), chunksize=workload):
self.digest.extend(digest_block.tobytes('F'))
self.digest = self.digest[:output_size]
def _keccak(self, input_array):
"""
Implementation of Keccak-1600 PRF defined in FIPS 202
Inputs:
input_array (numpy array): Keccak compatible state array: 200-byte as 5x5 64-bit lanes
Return:
numpy array: Keccak compatible state array: 200-byte as 5x5 64-bit lanes
"""
state = np.copy(input_array)
for round_num in range(6):
# theta_step:
# Exclusive-or each slice-lane by state based permutation value
array_shift = state << 1 | state >> 63
state ^= np.bitwise_xor.reduce(state[self.THETA_REORDER[0], ], 1, keepdims=True) ^ np.bitwise_xor.reduce(array_shift[self.THETA_REORDER[1], ], 1, keepdims=True)
# rho_step:
# Left Rotate each lane by pre-calculated value
state = state << self.RHO_SHIFTS | state >> np.uint64(64 - self.RHO_SHIFTS)
# pi_step:
# Shuffle lanes to pre-calculated positions
state = state[self.PI_ROW_REORDER, self.PI_COLUMN_REORDER]
# chi_step:
# Exclusive-or each individual lane based on and/invert permutation
state ^= ~state[self.CHI_REORDER[0], ] & state[self.CHI_REORDER[1], ]
# iota_step:
# Exclusive-or first lane of state with round constant
state[0, 0] ^= self.IOTA_CONSTANTS[round_num]
return state
def _keccak_xor_key(self, input_array):
"""
Implementation of Keccak-1600 PRF defined in FIPS 202 plus an XOR with the current key state
Inputs:
input_array (numpy array): Keccak compatible state array: 200-byte as 5x5 64-bit lanes
Return:
numpy array: Keccak compatible state array: 200-byte as 5x5 64-bit lanes
"""
state = np.copy(input_array)
for round_num in range(6):
# theta_step:
# Exclusive-or each slice-lane by state based permutation value
array_shift = state << 1 | state >> 63
state ^= np.bitwise_xor.reduce(state[self.THETA_REORDER[0], ], 1, keepdims=True) ^ np.bitwise_xor.reduce(array_shift[self.THETA_REORDER[1], ], 1, keepdims=True)
# rho_step:
# Left Rotate each lane by pre-calculated value
state = state << self.RHO_SHIFTS | state >> np.uint64(64 - self.RHO_SHIFTS)
# pi_step:
# Shuffle lanes to pre-calculated positions
state = state[self.PI_ROW_REORDER, self.PI_COLUMN_REORDER]
# chi_step:
# Exclusive-or each individual lane based on and/invert permutation
state ^= ~state[self.CHI_REORDER[0], ] & state[self.CHI_REORDER[1], ]
# iota_step:
# Exclusive-or first lane of state with round constant
state[0, 0] ^= self.IOTA_CONSTANTS[round_num]
return state ^ self.roll_key
def scrub(self):
"""
Explicitly zero out both the key and collector array states. Use prior to reinitialization of
key or when finished with object to help avoid leaving secret/interim data in memory.
WARNING: Does not guarantee other copies of these arrays are not present elsewhere in memory
Not applicable in multi-process mode.
Inputs:
None
Return:
None
"""
# Clear collector array
collector_location = self.collector.ctypes.data
memset(collector_location, 0x00, self.KECCAK_BYTES)
# Clear Kravatte base key array
key_location = self.kra_key.ctypes.data
memset(key_location, 0x00, self.KECCAK_BYTES)
# Clear Kravatte rolling key array
key_location = self.roll_key.ctypes.data
memset(key_location, 0x00, self.KECCAK_BYTES)
def _kravatte_roll_compress(self, input_array):
"""
Kravatte defined roll function for compression side of Farfalle PRF
Inputs:
input_array (numpy array): Keccak compatible state array: 200-byte as 5x5 64-bit lanes
Return:
numpy array: Keccak compatible state array: 200-byte as 5x5 64-bit lanes
"""
state = input_array[self.COMPRESS_ROW_REORDER, self.COMPRESS_COLUMN_REORDER]
state[4, 4] = ((state[4, 4] << np.uint64(7)) | (state[4, 4] >> np.uint64(57))) ^ \
(state[0, 4]) ^ \
(state[0, 4] >> np.uint64(3))
return state
def _kravatte_roll_expand(self, input_array):
"""
Kravatte defined roll function for expansion side of Farfalle PRF
Inputs:
input_array (numpy array): Keccak compatible state array: 200-byte as 5x5 64-bit lanes
Return:
numpy array: Keccak compatible state array: 200-byte as 5x5 64-bit lanes
"""
state = input_array[self.EXPAND_ROW_REORDER, self.EXPAND_COLUMN_REORDER]
state[4, 4] = ((input_array[0, 3] << np.uint64(7)) | (input_array[0, 3] >> np.uint64(57))) ^ \
((input_array[1, 3] << np.uint64(18)) | (input_array[1, 3] >> np.uint64(46))) ^ \
((input_array[1, 3] >> np.uint64(1)) & input_array[2, 3])
return state
@staticmethod
def _pad_10_append(input_bytes: bytes, desired_length: int, append_bits: int=0, append_bit_count: int=0) -> bytes:
"""
Farfalle defined padding function. Limited to byte divisible inputs only
Inputs:
input_bytes (bytes): Collection of bytes
desired_length (int): Number of bytes to pad input len out to
append_bits (int): one or more bits to be inserted before the padding starts. Allows
"appending" bits as required by several Kravatte modes
append_bit_count (int): number of bits to append
Return:
bytes: input bytes with padding applied
"""
start_len = len(input_bytes)
if start_len == desired_length:
return input_bytes
head_pad_byte = bytes([(0b01 << append_bit_count) | (((2**append_bit_count) - 1) & append_bits)])
pad_len = desired_length - (start_len % desired_length)
padded_bytes = input_bytes + head_pad_byte + (b'\x00' * (pad_len - 1))
return padded_bytes
@staticmethod
def compare_bytes(a: bytes, b: bytes) -> bool:
"""
Time Constant Byte Comparison Function
Inputs:
a (bytes): first set of bytes
b (bytes): second set of bytes
Return:
boolean
"""
compare = True
if len(a) != len(b):
return False
for (element_a, element_b) in zip(a, b):
compare = compare and (element_a == element_b)
return compare
def mac(key: bytes, message: bytes, output_size: int, workers: int=None, mp_input: bool=True,
mp_output: bool=True) -> bytearray:
"""
Kravatte Message Authentication Code Generation of given length from a message
based on a user provided key
Args:
key (bytes): User authentication key (0 - 200 bytes)
message (bytes): User message
output_size (int): Size of authenticated digest in bytes
workers (int): parallel processes to use in compression/expansion operations
mp_input (bool): Enable multi-processing for calculations on input data
mp_output (bool): Enable multi-processing for calculations on output data
Returns:
bytes: message authentication bytes of length output_size
"""
kravatte_mac_gen = Kravatte(key, workers=workers, mp_input=mp_input, mp_output=mp_output)
kravatte_mac_gen.collect_message(message)
kravatte_mac_gen.generate_digest(output_size)
kravatte_mac_gen.scrub()
return kravatte_mac_gen.digest
def siv_wrap(key: bytes, message: bytes, metadata: bytes, tag_size: int=32, workers: int=None,
mp_input: bool=True, mp_output: bool=True) -> KravatteTagOutput:
"""
Authenticated Encryption with Associated Data (AEAD) of a provided plaintext using a key and
metadata using the Synthetic Initialization Vector method described in the Farfalle/Kravatte
spec. Generates ciphertext (of equivalent length to the plaintext) and verification tag. Inverse
of siv_unwrap function.
Args:
key (bytes): Encryption key; 0-200 bytes in length
message (bytes): Plaintext message for encryption
metadata (bytes): Nonce/Seed value for authenticated encryption
tag_size (int, optional): The tag size in bytes. Defaults to 32 bytes as defined in the
Kravatte spec
workers (int): parallel processes to use in compression/expansion operations
mp_input (bool): Enable multi-processing for calculations on input data
mp_output (bool): Enable multi-processing for calculations on output data
Returns:
tuple (bytes, bytes): Bytes of ciphertext and tag
"""
# Initialize Kravatte
kravatte_siv_wrap = Kravatte(key, workers=workers, mp_input=mp_input, mp_output=mp_output)
# Generate Tag From Metadata and Plaintext
kravatte_siv_wrap.collect_message(metadata)
kravatte_siv_wrap.collect_message(message)
kravatte_siv_wrap.generate_digest(tag_size)
siv_tag = kravatte_siv_wrap.digest
# Generate Key Stream
kravatte_siv_wrap.collect_message(metadata)
kravatte_siv_wrap.collect_message(siv_tag)
kravatte_siv_wrap.generate_digest(len(message))
ciphertext = bytes([p_text ^ key_stream for p_text, key_stream in zip(message, kravatte_siv_wrap.digest)])
kravatte_siv_wrap.scrub()
return ciphertext, siv_tag
def siv_unwrap(key: bytes, ciphertext: bytes, siv_tag: bytes, metadata: bytes, workers: int=None,
mp_input: bool=True, mp_output: bool=True) -> KravatteValidatedOutput:
"""
Decryption of Synthetic Initialization Vector method described in the Farfalle/Kravatte
spec. Given a key, metadata, and validation tag, generates plaintext (of equivalent length to
the ciphertext) and validates message based on included tag, metadata, and key. Inverse of
siv_wrap function.
Args:
key (bytes): Encryption key; 0-200 bytes in length
ciphertext (bytes): Ciphertext SIV Message
siv_tag (bytes): Authenticating byte string
metadata (bytes): Metadata used to encrypt message and generate tag
workers (int): parallel processes to use in compression/expansion operations
mp_input (bool): Enable multi-processing for calculations on input data
mp_output (bool): Enable multi-processing for calculations on output data
Returns:
tuple (bytes, boolean): Bytes of plaintext and message validation boolean
"""
# Initialize Kravatte
kravatte_siv_unwrap = Kravatte(key, workers=workers, mp_input=mp_input, mp_output=mp_output)
# Re-Generate Key Stream
kravatte_siv_unwrap.collect_message(metadata)
kravatte_siv_unwrap.collect_message(siv_tag)
kravatte_siv_unwrap.generate_digest(len(ciphertext))
siv_plaintext = bytes([p_text ^ key_stream for p_text, key_stream in zip(ciphertext, kravatte_siv_unwrap.digest)])
# Re-Generate Tag From Metadata and Recovered Plaintext
kravatte_siv_unwrap.collect_message(metadata)
kravatte_siv_unwrap.collect_message(siv_plaintext)
kravatte_siv_unwrap.generate_digest(len(siv_tag))
generated_tag = kravatte_siv_unwrap.digest
# Check if tag matches provided tag matches reconstituted tag
valid_tag = kravatte_siv_unwrap.compare_bytes(siv_tag, generated_tag)
kravatte_siv_unwrap.scrub()
return siv_plaintext, valid_tag
class KravatteSAE(Kravatte):
"""
An authenticated encryption mode designed to track a session consisting of a series of messages
and an initialization nonce. ** DEPRECATED in favor of KravatteSANE **
"""
TAG_SIZE = 16
OFFSET = TAG_SIZE
def __init__(self, nonce: bytes, key: bytes=b'', workers: int=None, mp_input: bool=True,
mp_output: bool=True):
"""
Initialize KravatteSAE with user key and nonce
Args:
nonce (bytes) - random unique value to initialize the session with
key (bytes) - secret key for encrypting session messages
workers (int): parallel processes to use in compression/expansion operations
mp_input (bool): Enable multi-processing for calculations on input data
mp_output (bool): Enable multi-processing for calculations on output data
"""
super(KravatteSAE, self).__init__(key, workers, mp_input, mp_output)
self.initialize_history(nonce)
def initialize_history(self, nonce: bytes) -> None:
"""
Initialize session history by storing Keccak collector state and current internal key
Args:
key (bytes): user provided bytes to be padded (if necessary) and computed into Kravatte base key
"""
self.collect_message(nonce)
self.history_collector = np.copy(self.collector)
self.history_key = np.copy(self.roll_key)
self.generate_digest(self.TAG_SIZE)
self.tag = self.digest.copy()
def wrap(self, plaintext: bytes, metadata: bytes) -> KravatteTagOutput:
"""
Encrypt an arbitrary plaintext message using the included metadata as part of an on-going
session. Creates authentication tag for validation during decryption.
Args:
plaintext (bytes): user plaintext of arbitrary length
metadata (bytes): associated data to ensure a unique encryption permutation
Returns:
(bytes, bytes): encrypted cipher text and authentication tag
"""
# Restore Kravatte State to When Latest History was Absorbed
self.collector = np.copy(self.history_collector)
self.roll_key = np.copy(self.history_key)
self.digest = bytearray(b'')
self.digest_active = False
# Generate/Apply Key Stream
self.generate_digest(len(plaintext) + self.OFFSET)
ciphertext = bytes([p_text ^ key_stream for p_text, key_stream in zip(plaintext, self.digest[self.OFFSET:])])
# Update History
if len(metadata) > 0 or len(plaintext) == 0:
self._append_to_history(metadata, 0)
if len(plaintext) > 0:
self._append_to_history(ciphertext, 1)
self.history_collector = np.copy(self.collector)
self.history_key = np.copy(self.roll_key)
# Generate Tag
self.generate_digest(self.TAG_SIZE)
return ciphertext, self.digest
def unwrap(self, ciphertext: bytes, metadata: bytes, validation_tag: bytes) -> KravatteValidatedOutput:
"""
Decrypt an arbitrary ciphertext message using the included metadata as part of an on-going
session. Creates authentication tag for validation during decryption.
Args:
ciphertext (bytes): user ciphertext of arbitrary length
metadata (bytes): associated data from encryption
validation_tag (bytes): collection of bytes that authenticates the decrypted plaintext as
being encrypted with the same secret key
Returns:
(bytes, bool): decrypted plaintext and boolean indicating in decryption was authenticated against secret key
"""
# Restore Kravatte State to When Latest History was Absorbed
self.collector = np.copy(self.history_collector)
self.roll_key = | np.copy(self.history_key) | numpy.copy |
""" test chemkin_io.calculator.mechanism
"""
from __future__ import unicode_literals
from builtins import open
import os
import numpy
import chemkin_io
def _read_file(file_name):
with open(file_name, encoding='utf8', errors='ignore') as file_obj:
file_str = file_obj.read()
return file_str
# Set paths
PATH = os.path.dirname(os.path.realpath(__file__))
DATA_PATH = os.path.join(PATH, 'data')
FAKE1_MECH_NAME = 'fake1_mech.txt'
# Read mechanism files
FAKE1_MECH_STR = _read_file(
os.path.join(DATA_PATH, FAKE1_MECH_NAME))
# Build the reactions blocks and data strings
FAKE1_REACTION_BLOCK = chemkin_io.parser.mechanism.reaction_block(
FAKE1_MECH_STR)
FAKE1_REACTION_STRS = chemkin_io.parser.reaction.data_strings(
FAKE1_REACTION_BLOCK)
FAKE1_REACTION_DCT = chemkin_io.parser.reaction.data_dct(
FAKE1_REACTION_BLOCK)
# Set the reactions to elements of the string, use dct to have DUPs together
GROUPED_REACTION_STRS = list(FAKE1_REACTION_DCT.values())
HIGHP_REACTION = GROUPED_REACTION_STRS[0]
DUP_HIGHP_REACTION = GROUPED_REACTION_STRS[1]
LINDEMANN_REACTION = GROUPED_REACTION_STRS[2]
TROE_REACTION = GROUPED_REACTION_STRS[3]
PLOG_REACTION = GROUPED_REACTION_STRS[5]
DUP_PLOG_REACTION = GROUPED_REACTION_STRS[6]
CHEBYSHEV_REACTION = GROUPED_REACTION_STRS[7]
# Set temperatures and pressures
T_REF = 1.0
UNITS = ('cal/mole', 'moles')
TEMPS = numpy.array([500.0, 1000.0, 1500.0, 2000.0])
PRESSURES = [1.0, 5.0, 10.0]
PRESSURES2 = [0.0100, 0.0700, 0.987]
PRESSURES3 = [0.1, 0.5, 2]
PRESSURES4 = ['high']
def test__high_p_rate_constants():
""" test chemkin_io.calculator.rates.reaction
for a reaction with only high-pressure params
"""
ktp_dct1 = chemkin_io.calculator.rates.reaction(
HIGHP_REACTION, UNITS, T_REF, TEMPS, pressures=PRESSURES4)
ktp_dct2 = chemkin_io.calculator.rates.reaction(
DUP_HIGHP_REACTION, UNITS, T_REF, TEMPS, pressures=PRESSURES4)
assert ktp_dct1.keys() == ktp_dct2.keys() == ['high']
rates1 = ktp_dct1['high']
rates2 = ktp_dct2['high']
ref_rates1 = numpy.array(
[4.43369728e+11, 3.26882402e+12, 6.36209341e+12, 8.87573427e+12])
ref_rates2 = numpy.array(
[1.31390851e+12, 3.43989296e+12, 8.18869558e+12, 1.37943670e+13])
assert | numpy.allclose(rates1, ref_rates1, atol=0.0001) | numpy.allclose |
import logging
import numpy as np
from torch import nn
from core.config import cfg
# import utils.boxes as box_utils
import utils.boxes_3d as box_utils_3d
logger = logging.getLogger(__name__)
class GenerateProposalsOp_3d(nn.Module):
def __init__(self, anchors, spatial_scale):
super().__init__()
self._anchors = anchors
self._num_anchors = self._anchors.shape[0]
self._feat_stride = 1. / spatial_scale
def forward(self, rpn_cls_prob, rpn_bbox_pred, im_info):
"""Op for generating RPN porposals.
blobs_in:
- 'rpn_cls_probs': 5D tensor of shape (N, A, S, H, W), where N is the
number of minibatch images, A is the number of anchors per
locations, and (S, H, W) is the spatial size of the prediction grid.
Each value represents a "probability of object" rating in [0, 1].
- 'rpn_bbox_pred': 5D tensor of shape (N, 4 * A, S, H, W) of predicted
deltas for transformation anchor boxes into RPN proposals.
- 'im_info': 2D tensor of shape (N, 4) where the four columns encode
the input image's [slices, height, width, scale]. Slices, height and
width are for the input to the network, not the original image; scale
is the scale factor used to scale the original image to the network
input size.
blobs_out:
- 'rpn_rois': 2D tensor of shape (R, 7), for R RPN proposals where the
five columns encode [batch ind, x1, y1, z1, x2, y2, z2]. The boxes are
w.r.t. the network input, which is a *scaled* version of the
original image; these proposals must be scaled by 1 / scale (where
scale comes from im_info; see above) to transform it back to the
original input image coordinate system.
- 'rpn_roi_probs': 1D tensor of objectness probability scores
(extracted from rpn_cls_probs; see above).
"""
# 1. for each location i in a (S, H, W) grid:
# generate A anchor boxes centered on cell i
# apply predicted bbox deltas to each of the A anchors at cell i
# 2. clip predicted boxes to image
# 3. remove predicted boxes with either height or width or slices < threshold
# 4. sort all (proposal, score) pairs by score from highest to lowest
# 5. take the top pre_nms_topN proposals before NMS
# 6. apply NMS with a loose threshold (0.7) to the remaining proposals
# 7. take after_nms_topN proposals after NMS
# 8. return the top proposals
"""Type conversion"""
# predicted probability of fg object for each RPN anchor
scores = rpn_cls_prob.data.cpu().numpy()
# predicted achors transformations
bbox_deltas = rpn_bbox_pred.data.cpu().numpy()
# input image (height, width, scale), in which scale is the scale factor
# applied to the original dataset image to get the network input image
im_info = im_info.data.cpu().numpy()
# 1. Generate proposals from bbox deltas and shifted anchors
slices, height, width = scores.shape[-3:]
# Enumerate all shifted positions on the (S, H, W) grid
shift_x = | np.arange(0, width) | numpy.arange |
import time
import tensorflow.compat.v1 as tf
tf.disable_v2_behavior()
import math as m
import numpy as np
import pandas as pd
import tensorflow_probability as tfp
import matplotlib.pyplot as plt
import math
from tensorflow import keras
from tensorflow.keras import layers
from random import shuffle
from keras import backend as K
import numpy as np
import keras.datasets
from keras.layers import Dense, Dropout, Activation, Flatten
from keras.layers import Conv2D, MaxPooling2D
from keras.models import Sequential
from sklearn import model_selection
import scipy
import time
from footprints_and_cutouts import preprocess_scenes
(train_cutouts_blended_allScenes, train_cutouts_unblended_allScenes,
train_blended_mag_filters_allScenes, train_unblended_mag_filters_allScenes) = preprocess_scenes(train=True,use_pipeline_segmap=True)
(test_cutouts_blended_allScenes, test_cutouts_unblended_allScenes,
test_blended_mag_filters_allScenes, test_unblended_mag_filters_allScenes) = preprocess_scenes(train=False,use_pipeline_segmap=True)
train_cutouts_allScenes = []
train_cutouts_labels = []
train_mag_filter = []
count=0
for i in train_cutouts_unblended_allScenes:
train_cutouts_allScenes.append(i)
train_cutouts_labels.append([1,0])
if train_unblended_mag_filters_allScenes[21.5][count]:
train_mag_filter.append(21.5)
elif train_unblended_mag_filters_allScenes[22.5][count]:
train_mag_filter.append(22.5)
elif train_unblended_mag_filters_allScenes[23.5][count]:
train_mag_filter.append(23.5)
elif train_unblended_mag_filters_allScenes[24.5][count]:
train_mag_filter.append(24.5)
elif train_unblended_mag_filters_allScenes[25.5][count]:
train_mag_filter.append(25.5)
elif train_unblended_mag_filters_allScenes[26.5][count]:
train_mag_filter.append(26.5)
else:
train_mag_filter.append(0)
count+=1
count = 0
for i in train_cutouts_blended_allScenes:
train_cutouts_allScenes.append(i)
train_cutouts_labels.append([0,1])
if train_blended_mag_filters_allScenes[21.5][count]:
train_mag_filter.append(21.5)
elif train_blended_mag_filters_allScenes[22.5][count]:
train_mag_filter.append(22.5)
elif train_blended_mag_filters_allScenes[23.5][count]:
train_mag_filter.append(23.5)
elif train_blended_mag_filters_allScenes[24.5][count]:
train_mag_filter.append(24.5)
elif train_blended_mag_filters_allScenes[25.5][count]:
train_mag_filter.append(25.5)
elif train_blended_mag_filters_allScenes[26.5][count]:
train_mag_filter.append(26.5)
else:
train_mag_filter.append(0)
count+=1
test_cutouts_allScenes = []
test_cutouts_labels = []
test_mag_filter = []
count=0
for i in test_cutouts_unblended_allScenes:
test_cutouts_allScenes.append(i)
test_cutouts_labels.append([1,0])
if test_unblended_mag_filters_allScenes[21.5][count]:
test_mag_filter.append(21.5)
elif test_unblended_mag_filters_allScenes[22.5][count]:
test_mag_filter.append(22.5)
elif test_unblended_mag_filters_allScenes[23.5][count]:
test_mag_filter.append(23.5)
elif test_unblended_mag_filters_allScenes[24.5][count]:
test_mag_filter.append(24.5)
elif test_unblended_mag_filters_allScenes[25.5][count]:
test_mag_filter.append(25.5)
elif test_unblended_mag_filters_allScenes[26.5][count]:
test_mag_filter.append(26.5)
else:
test_mag_filter.append(0)
count+=1
count = 0
for i in test_cutouts_blended_allScenes:
test_cutouts_allScenes.append(i)
test_cutouts_labels.append([0,1])
if test_blended_mag_filters_allScenes[21.5][count]:
test_mag_filter.append(21.5)
elif test_blended_mag_filters_allScenes[22.5][count]:
test_mag_filter.append(22.5)
elif test_blended_mag_filters_allScenes[23.5][count]:
test_mag_filter.append(23.5)
elif test_blended_mag_filters_allScenes[24.5][count]:
test_mag_filter.append(24.5)
elif test_blended_mag_filters_allScenes[25.5][count]:
test_mag_filter.append(25.5)
elif test_blended_mag_filters_allScenes[26.5][count]:
test_mag_filter.append(26.5)
else:
test_mag_filter.append(0)
count+=1
for _ in np.arange(23):
trainx,testx,trainy,testy,trainmag,testmag = train_cutouts_allScenes,test_cutouts_allScenes,train_cutouts_labels,test_cutouts_labels,train_mag_filter,test_mag_filter
trainx2 = np.log10(np.array(trainx)+10**-8)
testx2 = np.log10(np.array(testx)+10**-8)
trainxnorm = (trainx2 - np.min(trainx2))/(np.max(trainx2)-np.min(trainx2))
testxnorm = (testx2 - np.min(testx2))/(np.max(testx2)-np.min(testx2))
input_shape = (23, 23, 1)
num_classes=2
model = keras.Sequential()
model.add(Conv2D(128, kernel_size=(3, 3), activation="relu"))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Conv2D(64, kernel_size=(3, 3), activation="relu"))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Flatten())
model.add(Dense(800,activation = 'relu'))
model.add(Dropout(0.2))
model.add(Dense(400,activation = 'relu'))
model.add(Dropout(0.2))
model.add(Dense(200,activation = 'relu'))
model.add(Dense(num_classes, activation="softmax"))
epochs=20
model.compile(loss="binary_crossentropy", optimizer='adam', metrics=["accuracy"])
time_start = time.time()
model.fit(np.reshape(trainxnorm,(len(trainx),23,23,1)), np.array(trainy), epochs=15,verbose=True,batch_size=200,validation_split = .1)
train_time = time.time()-time_start
mean_loss_xxx = model.evaluate(np.array(np.reshape(testxnorm,(len(testx),23,23,1))),np.array(testy))
bce=[]
count = 0
for i in testxnorm:
bce.append(model.evaluate(np.array(np.reshape(i,(1,23,23,1))),np.array([testy[count]]))[0])
count+=1
standard_error_bce = scipy.stats.sem(bce)
classified = []
blended_predict = []
count = []
for i in model.predict(np.reshape(testxnorm,(len(testx),23,23,1))):
if i[0]>i[1]:
classified.append([1,0])
else:
classified.append([0,1])
blended_predict.append(i[1])
blended_predict
arr_21 = []
arr_22 = []
arr_23 = []
arr_24 = []
arr_25 = []
arr_26 = []
count = 0
for i in np.array(testy)==classified:
if testmag[count] == 21.5:
arr_21.append([i[0],testy[count]])
if testmag[count] == 22.5:
arr_22.append([i[0],testy[count]])
if testmag[count] == 23.5:
arr_23.append([i[0],testy[count]])
if testmag[count] == 24.5:
arr_24.append([i[0],testy[count]])
if testmag[count] == 25.5:
arr_25.append([i[0],testy[count]])
if testmag[count] == 26.5:
arr_26.append([i[0],testy[count]])
count+=1
arr_21_unblended = []
arr_21_blended = []
for i in arr_21:
if i[1] == [1,0]:
arr_21_unblended.append(i[0])
else:
arr_21_blended.append(i[0])
arr_22_unblended = []
arr_22_blended = []
for i in arr_22:
if i[1] == [1,0]:
arr_22_unblended.append(i[0])
else:
arr_22_blended.append(i[0])
arr_23_unblended = []
arr_23_blended = []
for i in arr_23:
if i[1] == [1,0]:
arr_23_unblended.append(i[0])
else:
arr_23_blended.append(i[0])
arr_24_unblended = []
arr_24_blended = []
for i in arr_24:
if i[1] == [1,0]:
arr_24_unblended.append(i[0])
else:
arr_24_blended.append(i[0])
arr_25_unblended = []
arr_25_blended = []
for i in arr_25:
if i[1] == [1,0]:
arr_25_unblended.append(i[0])
else:
arr_25_blended.append(i[0])
arr_26_unblended = []
arr_26_blended = []
for i in arr_26:
if i[1] == [1,0]:
arr_26_unblended.append(i[0])
else:
arr_26_blended.append(i[0])
unblended = [['accuracy','# of samples', 'variance of # of accurately classified samples'],[np.count_nonzero(arr_21_unblended)/len(arr_21_unblended),len(arr_21_unblended)],
[np.count_nonzero(arr_22_unblended)/len(arr_22_unblended),len(arr_22_unblended)],
[np.count_nonzero(arr_23_unblended)/len(arr_23_unblended),len(arr_23_unblended)],
[np.count_nonzero(arr_24_unblended)/len(arr_24_unblended),len(arr_24_unblended)],
[np.count_nonzero(arr_25_unblended)/len(arr_25_unblended),len(arr_25_unblended)],
[np.count_nonzero(arr_26_unblended)/len(arr_26_unblended),len(arr_26_unblended)]]
blended = [['accuracy','# of samples', 'variance of # of accurately classified samples'],[np.count_nonzero(arr_21_blended)/len(arr_21_blended),len(arr_21_blended)],
[np.count_nonzero(arr_22_blended)/len(arr_22_blended),len(arr_22_blended)],
[np.count_nonzero(arr_23_blended)/len(arr_23_blended),len(arr_23_blended)],
[np.count_nonzero(arr_24_blended)/len(arr_24_blended),len(arr_24_blended)],
[np.count_nonzero(arr_25_blended)/len(arr_25_blended),len(arr_25_blended)],
[np.count_nonzero(arr_26_blended)/len(arr_26_blended),len(arr_26_blended)]]
for i in unblended[1:]:
i.append(np.sqrt(i[0]*i[1]*(1-i[0])))
for i in blended[1:]:
i.append(np.sqrt(i[0]*i[1]*(1-i[0])))
unblended = np.array(unblended)
blended = np.array(blended)
overall_blended_accuracy = np.sum(i[0].astype(float)*i[1].astype(float) for i in blended[1:].astype(float))/np.sum(i[1].astype(float) for i in blended[1:].astype(float))
overall_unblended_accuracy = np.sum(i[0].astype(float)*i[1].astype(float) for i in unblended[1:].astype(float))/np.sum(i[1].astype(float) for i in unblended[1:].astype(float))
blended_predict_0 = []
blended_predict_1 = []
blended_predict_2 = []
blended_predict_3 = []
blended_predict_4 = []
blended_predict_5 = []
blended_predict_6 = []
blended_predict_7 = []
blended_predict_8 = []
blended_predict_9 = []
count = 0
for i in blended_predict:
if i <.1:
blended_predict_0.append([[0,1]==testy[count],blended_predict[count]])
if i >=.1 and i<.2:
blended_predict_1.append([[0,1]==testy[count],blended_predict[count]])
if i >=.2 and i<.3:
blended_predict_2.append([[0,1]==testy[count],blended_predict[count]])
if i >=.3 and i<.4:
blended_predict_3.append([[0,1]==testy[count],blended_predict[count]])
if i >=.4 and i<.5:
blended_predict_4.append([[0,1]==testy[count],blended_predict[count]])
if i >=.5 and i<.6:
blended_predict_5.append([[0,1]==testy[count],blended_predict[count]])
if i >=.6 and i<.7:
blended_predict_6.append([[0,1]==testy[count],blended_predict[count]])
if i >=.7 and i<.8:
blended_predict_7.append([[0,1]==testy[count],blended_predict[count]])
if i >=.8 and i<.9:
blended_predict_8.append([[0,1]==testy[count],blended_predict[count]])
if i >=.9:
blended_predict_9.append([[0,1]==testy[count],blended_predict[count]])
count+=1
blended_predict_0 = np.array(blended_predict_0)
blended_predict_1 = np.array(blended_predict_1)
blended_predict_2 = np.array(blended_predict_2)
blended_predict_3 = np.array(blended_predict_3)
blended_predict_4 = np.array(blended_predict_4)
blended_predict_5 = np.array(blended_predict_5)
blended_predict_6 = np.array(blended_predict_6)
blended_predict_7 = np.array(blended_predict_7)
blended_predict_8 = np.array(blended_predict_8)
blended_predict_9 = np.array(blended_predict_9)
cal_0 = np.count_nonzero(blended_predict_0[:,0])/len(blended_predict_0)
cal_1 = np.count_nonzero(blended_predict_1[:,0])/len(blended_predict_1)
cal_2 = np.count_nonzero(blended_predict_2[:,0])/len(blended_predict_2)
cal_3 = np.count_nonzero(blended_predict_3[:,0])/len(blended_predict_3)
cal_4 = np.count_nonzero(blended_predict_4[:,0])/len(blended_predict_4)
cal_5 = np.count_nonzero(blended_predict_5[:,0])/len(blended_predict_5)
cal_6 = np.count_nonzero(blended_predict_6[:,0])/len(blended_predict_6)
cal_7 = np.count_nonzero(blended_predict_7[:,0])/len(blended_predict_7)
cal_8 = np.count_nonzero(blended_predict_8[:,0])/len(blended_predict_8)
cal_9 = np.count_nonzero(blended_predict_9[:,0])/len(blended_predict_9)
mean_0 = np.mean(blended_predict_0[:,1])
mean_1 = np.mean(blended_predict_1[:,1])
mean_2 = np.mean(blended_predict_2[:,1])
mean_3 = np.mean(blended_predict_3[:,1])
mean_4 = np.mean(blended_predict_4[:,1])
mean_5 = | np.mean(blended_predict_5[:,1]) | numpy.mean |
import os
from glob import glob
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
plt.rcParams.update({'font.size': 5})
plt.rcParams.update({'lines.linewidth':0.35})
plt.rcParams.update({'axes.linewidth':0.35})
plt.rcParams.update({'lines.markersize':2.5})
plt.rcParams.update({'axes.labelpad':1.5})
fig = plt.figure(figsize=(7.2,6))
grid = plt.GridSpec(18, 10, wspace=4, hspace=15)
ax = fig.add_subplot(grid[:9, :5])
ax.text(0.025, 0.966, 'a', transform=ax.transAxes,
fontsize=8, fontweight='bold', va='top', ha='left')
var_dir = '/home/atom/ongoing/work_worldwide/variance'
region_list = os.listdir(var_dir)
region_nmad = []
region_nsamp = []
for region in region_list:
list_fn_csv = [os.path.join(var_dir,region,f) for f in os.listdir(os.path.join(var_dir,region))]
list_nmad = []
list_nsamp = []
for fn_csv in list_fn_csv:
df = pd.read_csv(fn_csv)
list_nmad.append(df.nmad.values)
list_nsamp.append(df.nsamp.values)
nmad_all = np.stack(list_nmad,axis=1)
nsamp_all = np.stack(list_nsamp,axis=1)
nan_mask = np.all(np.logical_or(np.isnan(nmad_all),nmad_all==0),axis=1)
nmad_final = np.nansum(nmad_all * nsamp_all,axis=1) / np.nansum(nsamp_all,axis=1)
nsamp_final = np.nansum(nsamp_all,axis=1)
nmad_final[nan_mask] = np.nan
nsamp_final[nan_mask] = 0
region_nmad.append(nmad_final)
region_nsamp.append(nsamp_final)
# ax.figure(figsize=(16,9))
slope = df.bin_slope.values
corr = df.bin_corr.values
bin_slope = sorted(list(set(list(slope))))
bin_corr = sorted(list(set(list(corr))))
nb_slope = len(bin_slope)
nb_corr = len(bin_corr)
color_list = ['tab:orange','tab:blue','tab:olive','tab:cyan','tab:red','tab:purple','tab:brown','tab:pink','tab:gray','tab:olive']
ls_list = ['solid','dashed','dotted']
# model_var = np.sqrt(3**2 + (20 * np.tan(np.array(5) * np.pi / 180))**2) + (((100-np.array(bin_corr))/100)*20)**1.25
#
# for i in range(len(region_nmad)):
# i = 0
# for j in range(nb_slope-2):
#
# nmad = region_nmad[i]
#
# ax.plot(corr[1:nb_corr],nmad[j*nb_corr+1:j*nb_corr+nb_corr],label='Slope category: '+str(bin_slope[j]-5)+'-'+str(bin_slope[j]+5)+' degrees',color=color_list[j],linestyle=ls_list[i])
#
#
# # ax.plot(bin_corr,model_var,label='model',linewidth=2)
#
# ax.xlabel('Correlation (percent)')
# ax.ylabel('Stable terrain NMAD (m)')
# ax.ylim([0,50])
# ax.legend()
#
x_slope = np.arange(5,45,0.1)
model_var = np.sqrt(3**2 + (40 * np.tan(np.array(x_slope) * np.pi / 180))**2.5 + (((100-np.array(50))/100)*20)**2)
i=0
# for i in range(len(region_nmad)-1):
u=0
for j in | np.arange(1,nb_corr,2) | numpy.arange |
# Intermediate Python for Data Science on DataCamp
#######################################
# Part 1: matplotlib
#######################################
## Line plot (1)
# Print the last item from year and pop
print(year[-1])
print(pop[-1])
# Import matplotlib.pyplot as plt
import matplotlib.pyplot as plt
# Make a line plot: year on the x-axis, pop on the y-axis
plt.plot(year, pop)
plt.show()
# Print the last item of gdp_cap and life_exp
print(life_exp[-1])
print(gdp_cap[-1])
## Line plot (3)
# Make a line plot, gdp_cap on the x-axis, life_exp on the y-axis
plt.show()
# Display the plot
plt.plot(gdp_cap, life_exp)
## Scatter Plot (1)
# Change the line plot below to a scatter plot
plt.plot(gdp_cap, life_exp)
# Put the x-axis on a logarithmic scale
plt.xscale('log')
plt.scatter(gdp_cap, life_exp)
# Show plot
plt.show()
## Scatter plot (2)
# Import package
import matplotlib.pyplot as plt
# Build Scatter plot
plt.scatter(pop, life_exp)
# Show plot
plt.show()
## Build a histogram (1)
# Create histogram of life_exp data
plt.hist(life_exp)
# Display histogram
plt.show()
## Build a histogram (2): bins
# Build histogram with 5 bins
plt.hist(life_exp, bins = 5)
# Show and clean up plot
plt.show()
plt.clf()
# Build histogram with 20 bins
plt.hist(life_exp, bins = 20)
# Show and clean up again
plt.show()
plt.clf()
## Build a histogram (3): compare
# Histogram of life_exp, 15 bins
plt.hist(life_exp, bins = 15)
# Show and clear plot
plt.show()
plt.clf()
# Histogram of life_exp1950, 15 bins
plt.hist(life_exp1950, bins = 15)
# Show and clear plot again
plt.show()
plt.clf()
## Labels
# Basic scatter plot, log scale
plt.scatter(gdp_cap, life_exp)
plt.xscale('log')
# Strings
xlab = 'GDP per Capita [in USD]'
ylab = 'Life Expectancy [in years]'
title = 'World Development in 2007'
# Add axis labels
plt.xlabel(xlab)
plt.ylabel(ylab)
# Add title
plt.title(title)
# After customizing, display the plot
plt.show()
## Ticks
# Scatter plot
plt.scatter(gdp_cap, life_exp)
# Previous customizations
plt.xscale('log')
plt.xlabel('GDP per Capita [in USD]')
plt.ylabel('Life Expectancy [in years]')
plt.title('World Development in 2007')
# Definition of tick_val and tick_lab
tick_val = [1000,10000,100000]
tick_lab = ['1k','10k','100k']
# Adapt the ticks on the x-axis
plt.xticks(tick_val, tick_lab)
# After customizing, display the plot
plt.show()
## Sizes
# Import numpy as np
import numpy as np
# Store pop as a numpy array: np_pop
np_pop = np.array(pop)
# Double np_pop
np_pop = np_pop * 2
# Update: set s argument to np_pop
plt.scatter(gdp_cap, life_exp, s = np_pop)
# Previous customizations
plt.xscale('log')
plt.xlabel('GDP per Capita [in USD]')
plt.ylabel('Life Expectancy [in years]')
plt.title('World Development in 2007')
plt.xticks([1000, 10000, 100000],['1k', '10k', '100k'])
# Display the plot
plt.show()
## Colors
# Specify c and alpha inside plt.scatter()
plt.scatter(x = gdp_cap, y = life_exp, s = np.array(pop) * 2, c = col, alpha = 0.8)
# Previous customizations
plt.xscale('log')
plt.xlabel('GDP per Capita [in USD]')
plt.ylabel('Life Expectancy [in years]')
plt.title('World Development in 2007')
plt.xticks([1000,10000,100000], ['1k','10k','100k'])
# Show the plot
plt.show()
## Additional Customizations
# Scatter plot
plt.scatter(x = gdp_cap, y = life_exp, s = np.array(pop) * 2, c = col, alpha = 0.8)
# Previous customizations
plt.xscale('log')
plt.xlabel('GDP per Capita [in USD]')
plt.ylabel('Life Expectancy [in years]')
plt.title('World Development in 2007')
plt.xticks([1000,10000,100000], ['1k','10k','100k'])
# Additional customizations
plt.text(1550, 71, 'India')
plt.text(5700, 80, 'China')
# Add grid() call
plt.grid(True)
# Show the plot
plt.show()
#######################################
# Part 2: Dictionaries and Pandas
#######################################
## Motivation for dictionaries
# Definition of countries and capital
countries = ['spain', 'france', 'germany', 'norway']
capitals = ['madrid', 'paris', 'berlin', 'oslo']
# Get index of 'germany': ind_ger
ind_ger = countries.index("germany")
# Use ind_ger to print out capital of Germany
print(capitals[ind_ger])
## Create dictionary
# Definition of countries and capital
countries = ['spain', 'france', 'germany', 'norway']
capitals = ['madrid', 'paris', 'berlin', 'oslo']
# From string in countries and capitals, create dictionary europe
europe = {
"spain": "madrid",
"france": "paris",
"germany": "berlin",
"norway": "oslo"
}
# Print europe
print(europe)
## Access dictionary
# Definition of dictionary
europe = {'spain':'madrid', 'france':'paris', 'germany':'berlin', 'norway':'oslo' }
# Print out the keys in europe
print(europe.keys())
# Print out value that belongs to key 'norway'
print(europe['norway'])
## Dictionary Manipulation (1)
# Definition of dictionary
europe = {'spain':'madrid', 'france':'paris', 'germany':'berlin', 'norway':'oslo' }
# Add italy to europe
europe['italy'] = 'rome'
# Print out italy in europe
print('italy' in europe)
# Add poland to europe
europe['poland'] = 'warsaw'
# Print europe
print(europe)
## Dictionary Manipulation (2)
# Definition of dictionary
europe = {'spain':'madrid', 'france':'paris', 'germany':'bonn',
'norway':'oslo', 'italy':'rome', 'poland':'warsaw',
'australia':'vienna' }
# Update capital of germany
europe['germany'] = 'berlin'
# Remove australia
del(europe['australia'])
# Print europe
print(europe)
## Dictionariception
# Dictionary of dictionaries
europe = { 'spain': { 'capital':'madrid', 'population':46.77 },
'france': { 'capital':'paris', 'population':66.03 },
'germany': { 'capital':'berlin', 'population':80.62 },
'norway': { 'capital':'oslo', 'population':5.084 } }
# Print out the capital of France
print(europe['france']['capital'])
# Create sub-dictionary data
data = {'capital':'rome', 'population':59.83}
# Add data to europe under key 'italy'
europe['italy'] = data
# Print europe
print(europe)
## Dictionary to DataFrame (1)
# Pre-defined lists
names = ['United States', 'Australia', 'Japan', 'India', 'Russia', 'Morocco', 'Egypt']
dr = [True, False, False, False, True, True, True]
cpc = [809, 731, 588, 18, 200, 70, 45]
# Import pandas as pd
import pandas as pd
# Create dictionary my_dict with three key:value pairs: my_dict
my_dict = { 'country': names, 'drives_right': dr, 'cars_per_cap': cpc
}
# Build a DataFrame cars from my_dict: cars
cars = pd.DataFrame(my_dict)
# Print cars
print(cars)
## Dictionary to DataFrame (2)
# Build cars DataFrame
names = ['United States', 'Australia', 'Japan', 'India', 'Russia', 'Morocco', 'Egypt']
dr = [True, False, False, False, True, True, True]
cpc = [809, 731, 588, 18, 200, 70, 45]
dict = { 'country':names, 'drives_right':dr, 'cars_per_cap':cpc }
cars = pd.DataFrame(dict)
print(cars)
# Definition of row_labels
row_labels = ['US', 'AUS', 'JAP', 'IN', 'RU', 'MOR', 'EG']
# Specify row labels of cars
cars.index = row_labels
# Print cars again
print(cars)
## CSV to DataFrame (1)
# Import the cars.csv data: cars
cars = pd.read_csv("cars.csv")
# Print out cars
print(cars)
## CSV to DataFrame (2)
# Fix import by including index_col
cars = pd.read_csv('cars.csv', index_col = 0)
# Print out cars
print(cars)
## Square Brackets (1)
# Import cars data
import pandas as pd
cars = pd.read_csv('cars.csv', index_col = 0)
# Print out country column as Pandas Series
print(cars['country'])
# Print out country column as Pandas DataFrame
print(cars[['country']])
# Print out DataFrame with country and drives_right columns
print(cars[['country', 'drives_right']])
## Square Brackets (2)
# Print out first 3 observations
print(cars[0:3])
# Print out fourth, fifth and sixth observation
print(cars[3:6])
## loc and iloc (1)
# Print out observation for Japan
print(cars.loc['JAP'])
# Print out observations for Australia and Egypt
print(cars.loc[['AUS', 'EG']])
## loc and iloc (2)
# Print out drives_right value of Morocco
print(cars.loc['MOR', 'drives_right'])
# Print sub-DataFrame
print(cars.loc[['RU', 'MOR'], ['country', 'drives_right']])
## loc and iloc (3)
# Import cars data
import pandas as pd
cars = pd.read_csv('cars.csv', index_col = 0)
# Print out drives_right column as Series
print(cars.loc[:, 'drives_right'])
# Print out drives_right column as DataFrame
print(cars.loc[:, ['drives_right']])
# Print out cars_per_cap and drives_right as DataFrame
print(cars.loc[:, ['cars_per_cap', 'drives_right']])
#######################################
# Part 3: Logic, Control Flow and Filters
#######################################
## Equality
# Comparison of booleans
print(True == False)
# Comparison of integers
print(-5 * 15 != 75)
# Comparison of strings
print("pyscript" == "PyScript")
# Compare a boolean with an integer
print(True == 1)
## Greater and less than
# Comparison of integers
x = -3 * 6
print(x >= -10)
# Comparison of strings
y = "test"
print("test" <= y)
# Comparison of booleans
print(True > False)
## Compare arrays
# Create arrays
import numpy as np
my_house = np.array([18.0, 20.0, 10.75, 9.50])
your_house = np.array([14.0, 24.0, 14.25, 9.0])
# my_house greater than or equal to 18
print(my_house >= 18)
# my_house less than your_house
print(my_house < your_house)
## and, or, not (1)
# Define variables
my_kitchen = 18.0
your_kitchen = 14.0
# my_kitchen bigger than 10 and smaller than 18?
print(my_kitchen > 10 and my_kitchen < 18)
# my_kitchen smaller than 14 or bigger than 17?
print(my_kitchen < 14 or my_kitchen > 17)
# Double my_kitchen smaller than triple your_kitchen?
print(my_kitchen*2 < your_kitchen*3)
## Boolean operators with Numpy
# Create arrays
import numpy as np
my_house = np.array([18.0, 20.0, 10.75, 9.50])
your_house = np.array([14.0, 24.0, 14.25, 9.0])
# my_house greater than 18.5 or smaller than 10
print(np.logical_or(my_house > 18.5, my_house < 10))
# Both my_house and your_house smaller than 11
print(np.logical_and(my_house < 11, your_house < 11))
## if
# Define variables
room = "kit"
area = 14.0
# if statement for room
if room == "kit" :
print("looking around in the kitchen.")
# if statement for area
if area > 15:
print("big place!")
## Add else
# if-else construct for room
if room == "kit" :
print("looking around in the kitchen.")
else :
print("looking around elsewhere.")
# if-else construct for area
if area > 15 :
print("big place!")
else:
print("pretty small.")
## Customize further: elif
# Define variables
room = "bed"
area = 14.0
# if-elif-else construct for room
if room == "kit" :
print("looking around in the kitchen.")
elif room == "bed":
print("looking around in the bedroom.")
else :
print("looking around elsewhere.")
# if-elif-else construct for area
if area > 15 :
print("big place!")
elif area > 10:
print("medium size, nice!")
else :
print("pretty small.")
## Driving right (1)
# Import cars data
import pandas as pd
cars = pd.read_csv('cars.csv', index_col = 0)
# Extract drives_right column as Series: dr
dr = cars.loc[:, "drives_right"]
# Use dr to subset cars: sel
sel = cars[dr]
# Print sel
print(sel)
## Driving right (2)
# Import cars data
import pandas as pd
cars = pd.read_csv('cars.csv', index_col = 0)
# Convert code to a one-liner
sel = cars[cars['drives_right']]
# Print sel
print(sel)
## Cars per capita (1)
# Import cars data
import pandas as pd
cars = pd.read_csv('cars.csv', index_col = 0)
# Create car_maniac: observations that have a cars_per_cap over 500
cpc = cars['cars_per_cap']
many_cars = cpc > 500
car_maniac = cars[many_cars]
# Print car_maniac
print(car_maniac)
## Cars per capita (2)
# Import cars data
import pandas as pd
cars = pd.read_csv('cars.csv', index_col = 0)
# Import numpy, you'll need this
import numpy as np
# Create medium: observations with cars_per_cap between 100 and 500
cpc = cars['cars_per_cap']
between = np.logical_and(cpc > 100, cpc < 500)
medium = cars[between]
# Print medium
print(medium)
#######################################
# Part 4: Loops
#######################################
## Basic while loop
# Initialize offset
offset = 8
# Code the while loop
while offset != 0:
print("correcting...")
offset = offset - 1
print(offset)
## Add conditionals
# Initialize offset
offset = -6
# Code the while loop
while offset != 0 :
print("correcting...")
if offset > 0:
offset = offset - 1
else:
offset = offset + 1
print(offset)
## Loop over a list
# areas list
areas = [11.25, 18.0, 20.0, 10.75, 9.50]
# Code the for loop
for i in areas:
print(i)
## Indexes and values (1)
# areas list
areas = [11.25, 18.0, 20.0, 10.75, 9.50]
# Change for loop to use enumerate()
for index, a in enumerate(areas) :
print("room " + str(index) + ": " + str(a))
## Indexes and values (2)
# areas list
areas = [11.25, 18.0, 20.0, 10.75, 9.50]
# Code the for loop
for index, area in enumerate(areas) :
print("room " + str(index + 1) + ": " + str(area))
## Loop over list of lists
# house list of lists
house = [["hallway", 11.25],
["kitchen", 18.0],
["living room", 20.0],
["bedroom", 10.75],
["bathroom", 9.50]]
# Build a for loop from scratch
for area in house :
print("the " + str(area[0]) + " is " + str(area[1]) + " sqm")
## Loop over dictionary
# Definition of dictionary
europe = {'spain':'madrid', 'france':'paris', 'germany':'bonn',
'norway':'oslo', 'italy':'rome', 'poland':'warsaw', 'australia':'vienna' }
# Iterate over europe
for key, value in europe.items() :
print("the capital of " + key + " is " + str(value))
## Loop over Numpy array
# Import numpy as np
import numpy as np
# For loop over np_height
for h in np_height:
print(str(h) + " inches")
# For loop over np_baseball
for x in np.nditer(np_baseball):
print(x)
## Loop over DataFrame (1)
# Import cars data
import pandas as pd
cars = pd.read_csv('cars.csv', index_col = 0)
# Iterate over rows of cars
for lab, row in cars.iterrows() :
print(lab)
print(row)
## Loop over DataFrame (2)
# Import cars data
import pandas as pd
cars = pd.read_csv('cars.csv', index_col = 0)
# Adapt for loop
for lab, row in cars.iterrows() :
print(lab + ": " + str(row['cars_per_cap']))
## Add column (1)
# Import cars data
import pandas as pd
cars = pd.read_csv('cars.csv', index_col = 0)
# Code for loop that adds COUNTRY column
for lab, row in cars.iterrows() :
cars.loc[lab, "COUNTRY"] = row["country"].upper()
# Print cars
print(cars)
## Add column (2)
# Import cars data
import pandas as pd
cars = pd.read_csv('cars.csv', index_col = 0)
# Use .apply(str.upper)
cars["COUNTRY"] = cars["country"].apply(str.upper)
print(cars)
#######################################
# Part 5: Case Study: Hacker Statistics
#######################################
## Random float
# Import numpy as np
import numpy as np
# Set the seed
np.random.seed(123)
# Generate and print random float
print(np.random.rand())
## Roll the dice
# Import numpy and set seed
import numpy as np
np.random.seed(123)
# Use randint() to simulate a dice
print(np.random.randint(1,7))
# Use randint() again
print(np.random.randint(1,7))
## Determine your next move
# Import numpy and set seed
import numpy as np
np.random.seed(123)
# Starting step
step = 50
# Roll the dice
dice = np.random.randint(1,7)
# Finish the control construct
if dice <= 2 :
step = step - 1
elif dice <= 5 :
step = step + 1
else :
step = step + np.random.randint(1,7)
# Print out dice and step
print(dice)
print(step)
## The next step
# Import numpy and set seed
import numpy as np
np.random.seed(123)
# Initialize random_walk
random_walk = [0]
# Complete the ___
for x in range(100) :
# Set step: last element in random_walk
step = random_walk[-1]
# Roll the dice
dice = np.random.randint(1,7)
# Determine next step
if dice <= 2:
step = step - 1
elif dice <= 5:
step = step + 1
else:
step = step + np.random.randint(1,7)
# append next_step to random_walk
random_walk.append(step)
# Print random_walk
print(random_walk)
## How low can you go?
# Import numpy and set seed
import numpy as np
np.random.seed(123)
# Initialize random_walk
random_walk = [0]
for x in range(100) :
step = random_walk[-1]
dice = np.random.randint(1,7)
if dice <= 2:
# Replace below: use max to make sure step can't go below 0
step = max(0, step - 1)
elif dice <= 5:
step = step + 1
else:
step = step + np.random.randint(1,7)
random_walk.append(step)
print(random_walk)
## Visualize the walk
# Initialization
import numpy as np
| np.random.seed(123) | numpy.random.seed |
import os
import scipy
from sklearn import preprocessing
from sklearn.covariance import OAS
os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'
import numpy as np
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
from tensorflow.keras import layers, models
from nas.src import config
from brainflow import BoardShim
from tensorflow.keras.optimizers import Adam
class Classifier:
"""
A class that classifies login EEG data.
:param login_data: Login EEG data. List of login data time windows.
:type login_data: list
:param reg_data: Registration EEG data. List of registration data time windows.
:type reg_data: list
:param reg_data_types: Registration data time windows types.
:type reg_data_types: list
"""
def __init__(self, login_data, reg_data, reg_data_types, login_data_types, user_ids=None):
self.login_data = login_data
self.reg_data = reg_data
self.reg_data_types = reg_data_types
self.login_data_types = login_data_types
self.user_ids = user_ids
# LDA input
self.fit_data = []
self.predict_data = []
self.fit_data_types = []
self.predict_data_types = []
# CNN input
self.training_samples = None
self.predicting_samples = None
self.training_samples_types = []
self.predicting_samples_types = []
# Result
self.result = None
def prepare_cnn_data(self):
"""
Data preparation for CNN.
"""
training_samples = []
predicting_samples = []
predict_data_types = []
training_data_types = []
for i in range(len(self.reg_data)):
epoch = []
norm_data_0 = preprocessing.normalize(np.array([self.reg_data[i][0]]))
norm_data_1 = preprocessing.normalize(np.array([self.reg_data[i][1]]))
norm_data_2 = preprocessing.normalize(np.array([self.reg_data[i][2]]))
norm_data_3 = preprocessing.normalize(np.array([self.reg_data[i][3]]))
epoch = np.array([[norm_data_0[0], norm_data_1[0], norm_data_2[0], norm_data_3[0]]])
training_samples.append(epoch)
training_data_types.append(self.reg_data_types[i])
for i in range(len(self.login_data)):
epoch = []
norm_data_0 = preprocessing.normalize(np.array([self.login_data[i][0]]))
norm_data_1 = preprocessing.normalize(np.array([self.login_data[i][1]]))
norm_data_2 = preprocessing.normalize(np.array([self.login_data[i][2]]))
norm_data_3 = preprocessing.normalize(np.array([self.login_data[i][3]]))
epoch = np.array([[norm_data_0[0], norm_data_1[0], norm_data_2[0], norm_data_3[0]]])
predicting_samples.append(epoch)
predict_data_types.append(self.login_data_types[i])
training_samples = np.array(training_samples)
predicting_samples = np.array(predicting_samples)
training_data_types = np.array(training_data_types)
predict_data_types = np.array(predict_data_types)
num_of_x = round(BoardShim.get_sampling_rate(config.BOARD_TYPE) * 0.8)
training_samples = training_samples.reshape(len(training_samples), 4, num_of_x, 1)
predicting_samples = predicting_samples.reshape(len(predicting_samples), 4, num_of_x, 1)
self.training_samples = training_samples
self.training_samples_types = training_data_types
self.predicting_samples = predicting_samples
self.predicting_samples_types = predict_data_types
def classify(self, classification_method):
"""
Classify login EEG data.
:param classification_method: Method of classification.
:type classification_method: string
:return: Result of classification.
:rtype: list
"""
if classification_method == "LDA" or classification_method == "BOTH":
model = LinearDiscriminantAnalysis(solver='lsqr', shrinkage=0.924)
model.fit(self.fit_data, self.fit_data_types)
self.result = model.predict(self.predict_data)
if classification_method == "CNN" or classification_method == "BOTH":
num_of_x = round(BoardShim.get_sampling_rate(config.BOARD_TYPE) * 0.8)
model = models.Sequential([
layers.Conv2D(filters=32, kernel_size=(3, 3), activation='relu', padding='same',
input_shape=(4, num_of_x, 1), use_bias=True),
layers.MaxPooling2D(pool_size=(1, 4), strides=1),
layers.Conv2D(filters=64, kernel_size=(3, 3), activation='relu', padding='same', use_bias=True),
layers.MaxPooling2D(pool_size=(1, 4), strides=1),
layers.Flatten(),
layers.Dense(units=500, activation='relu'),
layers.BatchNormalization(),
layers.Dropout(0.2),
layers.Dense(units=100, activation='relu'),
layers.Dense(units=2, activation='softmax'),
])
model.compile(optimizer=Adam(learning_rate=0.002), loss='sparse_categorical_crossentropy',
metrics=['accuracy'])
model.fit(x=self.training_samples,
y=self.reg_data_types,
batch_size=10,
epochs=30,
verbose=0,
shuffle=True)
result = model.predict(x=self.predicting_samples, batch_size=1, verbose=0)
result = np.round(result)
result = result[:, 0]
self.result = result
def prepare_lda_data(self):
"""
Data preparation for LDA.
"""
fit_data = []
fit_data_types = []
predict_data = []
predict_data_types = []
for i in range(len(self.reg_data)):
epoch = []
norm_data_0 = preprocessing.normalize(np.array([self.reg_data[i][0]]))
norm_data_1 = preprocessing.normalize(np.array([self.reg_data[i][1]]))
norm_data_2 = preprocessing.normalize(np.array([self.reg_data[i][2]]))
norm_data_3 = preprocessing.normalize(np.array([self.reg_data[i][3]]))
avg = (norm_data_0 + norm_data_1 + norm_data_2 + norm_data_3) / 4
epoch = avg[0]
fit_data.append(epoch)
for i in range(len(self.login_data)):
epoch = []
norm_data_0 = preprocessing.normalize( | np.array([self.login_data[i][0]]) | numpy.array |
# -*- coding: utf-8 -*-
"""Copia di Classification.ipynb
Automatically generated by Colaboratory.
Original file is located at
https://colab.research.google.com/drive/19w462hZ5-StoAmR7fA-GquAcs-hibbSU
"""
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sb
from matplotlib.ticker import AutoMinorLocator
from matplotlib import gridspec
#scaling, normalization
from sklearn.preprocessing import StandardScaler, MinMaxScaler, RobustScaler
from sklearn import metrics
from google.colab import files
#caricamento del dataset
df = pd.read_csv('words_glasgow.csv')
#faccio una copia del dataset in caso di manipolazione dati
dfcopy= df.copy()
df2 = df.copy()
df2["perceivability"] = df2[["imageability", "concreteness"]].mean(axis=1)
df_perc=df2.drop(["concreteness","imageability"], axis=1)
dfprepro= df_perc.copy()
dfprepro=dfprepro.rename(columns={"gender": "masculinity"})
dfprepro.loc[(dfprepro['web_corpus_freq'].isnull() == True), 'web_corpus_freq'] = dfprepro['web_corpus_freq'].mean()
dfprepro["web_corpus_log"] = pd.qcut(dfprepro["web_corpus_freq"], 10) #taglio la variabile web_corpus_freq in 10 gruppi
dataframe = [dfprepro]
for dataset in dataframe:
dataset.loc[(dataset["web_corpus_freq"] > 10000) & (dataset["web_corpus_freq"] <= 100000), "web_corpus_freq"] = 4
dataset.loc[(dataset["web_corpus_freq"] > 100000) & (dataset["web_corpus_freq"] <= 1000000), "web_corpus_freq"] = 5
dataset.loc[(dataset["web_corpus_freq"] > 1000000) & (dataset["web_corpus_freq"] <= 10000000), "web_corpus_freq"] = 6
dataset.loc[(dataset["web_corpus_freq"] > 10000000) & (dataset["web_corpus_freq"] <= 100000000), "web_corpus_freq"] = 7
dataset.loc[(dataset["web_corpus_freq"] > 100000000) & (dataset["web_corpus_freq"] <= 1000000000), "web_corpus_freq"] = 8
dataset.loc[dataset["web_corpus_freq"] > 1000000000, "web_corpus_freq"] = 9
dfprepro = dfprepro.drop(["web_corpus_log","word"], axis=1)
"""# Preprocess for classification"""
# per il decision tree
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import train_test_split
# visualizzarlo
from sklearn import tree
import pydotplus
from IPython.display import Image
# evaluazione
from sklearn.metrics import confusion_matrix
from sklearn.metrics import accuracy_score, f1_score, classification_report
from sklearn.metrics import roc_curve, auc, roc_auc_score
# hyperparameter tuning
from sklearn.model_selection import RandomizedSearchCV, GridSearchCV
# cross-validation
from sklearn.model_selection import cross_val_score
from sklearn.metrics import confusion_matrix
from sklearn.metrics import plot_confusion_matrix
from sklearn.model_selection import cross_val_score
from sklearn.neighbors import KNeighborsClassifier
from sklearn.ensemble import RandomForestClassifier
df_class_ref = dfprepro.copy()
var_to_scale=['aoa',"arousal","valence","dominance","familiarity","semsize","masculinity","perceivability"]
features = df_class_ref[var_to_scale]
scaler = MinMaxScaler().fit(features.values)
features = scaler.transform(features.values)
df_class_ref[var_to_scale] = features
"""#Decision Tree (mostly) and comparison with other methods (binary varaibles only)
### Arousal
"""
refvar="arousal"
taglio=0.55
X=df_class_ref.drop(refvar,axis=1).copy()
y=df_class_ref[refvar].copy()
y_up_index = y >= taglio
y[y_up_index]=1
y_zero_index = y < taglio
y[y_zero_index]=0
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
plt.figure(figsize=(15,7.5))
from sklearn.tree import plot_tree
plot_tree(clf_dt,
filled=True,
rounded=True,
class_names=["not aroused","aroused"],
feature_names=X.columns)
from sklearn.metrics import confusion_matrix
from sklearn.metrics import plot_confusion_matrix
from sklearn.model_selection import cross_val_score
plot_confusion_matrix(clf_dt, X_test, y_test, display_labels=["not aroused","aroused"])
y_pred = clf_dt.predict(X_train)
y_pred = clf_dt.predict(X_test)
print('Accuracy %s' % accuracy_score(y_test, y_pred))
print('F1-score %s' % f1_score(y_test, y_pred, average=None))
print(classification_report(y_test, y_pred))
y_score = clf_dt.predict_proba(X_test)
fpr, tpr, th = roc_curve(y_test, y_score[:,1])
roc_auc = auc(fpr, tpr)
print(roc_auc)
plt.figure(figsize=(8,5))
plt.plot(fpr, tpr, label='$AUC$ = %.3f' % (roc_auc))
plt.legend(loc="lower right", fontsize=14, frameon=False)
plt.plot([0,1], [0,1], 'k--')
plt.xlabel('False Positive Rate', fontsize=20)
plt.ylabel('True Positive Rate', fontsize=20)
plt.tick_params(axis='both', which='major', labelsize=22)
plt.show()
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
fig, ax =plt.subplots()
ax.set_xlabel("alpha")
ax.set_ylabel("accuracy")
ax.set_title("Accuracy vs alpha for training and testing sets")
ax.plot(ccp_alphas,train_scores, marker ='o',label='train',drawstyle='steps-post')
ax.plot(ccp_alphas,test_scores, marker ='o',label='test',drawstyle='steps-post')
ax.legend()
plt.show()
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=0.003)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
df=pd.DataFrame(data={'tree':range(10), 'accuracy':scores})
df.plot(x='tree', y='accuracy',marker='o',linestyle='--')
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(random_state=0, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), np.std(scores)])
alpha_results = pd.DataFrame(alpha_loop_values,
columns=['alpha','mean_accuracy','std'])
alpha_results.plot(x='alpha',
y='mean_accuracy',
marker='o',
linestyle='--')
alpha_results[(alpha_results['alpha']>0.001)
&
(alpha_results['alpha']<0.005)]
indexmax = alpha_results[['mean_accuracy']].idxmax()
maxalpha=alpha_results.loc[indexmax,'alpha']
ideal_ccp_alpha = float(maxalpha)
clf_dt_pruned = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=ideal_ccp_alpha)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
plot_confusion_matrix(clf_dt_pruned,
X_test,
y_test,
display_labels=['not aroused','aroused'])
plt.figure(figsize=(15,7.5))
from sklearn.tree import plot_tree
plot_tree(clf_dt_pruned,
filled=True,
rounded=True,
class_names=["not aroused","aroused"],
feature_names=X.columns)
y_pred = clf_dt_pruned.predict(X_train)
y_pred = clf_dt_pruned.predict(X_test)
print('Accuracy %s' % accuracy_score(y_test, y_pred))
print('F1-score %s' % f1_score(y_test, y_pred,average='weighted'))
print(classification_report(y_test, y_pred))
y_score = clf_dt_pruned.predict_proba(X_test)
fpr_0, tpr_0, th_0 = roc_curve(y_test, y_score[:,1])
roc_auc_0 = auc(fpr_0, tpr_0)
#Entropy
clf_dt = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='entropy',random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=0, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), np.std(scores)])
alpha_results = pd.DataFrame(alpha_loop_values,
columns=['alpha','mean_accuracy','std'])
indexmax = alpha_results[['mean_accuracy']].idxmax()
maxalpha=alpha_results.loc[indexmax,'alpha']
ideal_ccp_alpha = float(maxalpha)
print(ideal_ccp_alpha)
clf_dt_pruned = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=ideal_ccp_alpha)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
y_score = clf_dt_pruned.predict_proba(X_test)
fpr_en, tpr_en, th_en = roc_curve(y_test, y_score[:,1])
roc_auc_en = auc(fpr_en, tpr_en)
y_pred = clf_dt_pruned.predict(X_test)
print('Accuracy %s' % accuracy_score(y_test, y_pred))
print('F1-score %s' % f1_score(y_test, y_pred,average='weighted'))
print(classification_report(y_test, y_pred))
#KNN, find best score
acc = []
# Will take some time
for i in range(1,40):
neigh = KNeighborsClassifier(n_neighbors = i).fit(X_train,y_train)
yhat = neigh.predict(X_test)
acc.append(metrics.accuracy_score(y_test, yhat))
clf_knn = KNeighborsClassifier(n_neighbors=acc.index(max(acc)))
clf_knn.fit(X, y)
y_pred = clf_knn.predict(X_train)
y_score = clf_knn.predict_proba(X_test)
fpr_KNN, tpr_KNN, th_KNN = roc_curve(y_test, y_score[:,1])
roc_auc_KNN = auc(fpr_KNN, tpr_KNN)
y_pred = clf_knn.predict(X_test)
print('Accuracy %s' % accuracy_score(y_test, y_pred))
print('F1-score %s' % f1_score(y_test, y_pred,average='weighted'))
print(classification_report(y_test, y_pred))
# Instantiate model with 380 decision trees
model = RandomForestClassifier(n_estimators = 380, random_state = 42)
# Train the model on training data
ra=model.fit(X_train, y_train)
y_score = model.predict_proba(X_test)
fpr_RF, tpr_RF, th_RF = roc_curve(y_test, y_score[:,1])
roc_auc_RF = auc(fpr_RF, tpr_RF)
y_pred = model.predict(X_test)
print('Accuracy %s' % accuracy_score(y_test, y_pred))
print('F1-score %s' % f1_score(y_test, y_pred,average='weighted'))
print(classification_report(y_test, y_pred))
#Grid Search
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
param_list = {'max_depth': [None] + [2, 3, 4,5,6,7],
'min_samples_split': [2, 5, 10, 15, 20,30,50,60,70,80,90,100],
'min_samples_leaf': [1, 5, 10, 20,25,30,40,50]
}
grid_search = GridSearchCV(clf_dt, param_grid=param_list, scoring='f1')
grid_search.fit(X, y)
res = grid_search.cv_results_
def report(results, n_top=3):
for i in range(1, n_top + 1):
candidates = np.flatnonzero(results['rank_test_score'] == i)
for candidate in candidates:
print("Model with rank: {0}".format(i))
print("Mean validation score: {0:.3f} (std: {1:.3f})".format(
results['mean_test_score'][candidate],
results['std_test_score'][candidate]))
print("Parameters: {0}".format(results['params'][candidate]))
print("")
report(res, n_top=3)
clf_dt_pruned = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=40,random_state=42)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
y_score = clf_dt_pruned.predict_proba(X_test)
fpr_c, tpr_c, th_c = roc_curve(y_test, y_score[:,1])
roc_auc_c = auc(fpr_c, tpr_c)
y_pred = clf_dt_pruned.predict(X_test)
print('Accuracy %s' % accuracy_score(y_test, y_pred))
print('F1-score %s' % f1_score(y_test, y_pred,average='weighted'))
print(classification_report(y_test, y_pred))
plt.figure(figsize=(15,7.5))
from sklearn.tree import plot_tree
plot_tree(clf_dt_pruned,
filled=True,
rounded=True,
class_names=["not aroused","aroused"],
feature_names=X.columns)
plt.figure(figsize=(8,5))
plt.plot(fpr_0, tpr_0,lw=3,label='$GINI_{AUC}$ = %.3f' % (roc_auc_0))
plt.plot(fpr_en, tpr_en,lw=3,label='$ENT_{AUC}$ = %.3f' % (roc_auc_en))
plt.plot(fpr_KNN, tpr_KNN,lw=3,label='$KNN_{AUC}$ = %.3f' % (roc_auc_KNN))
plt.plot(fpr_RF, tpr_RF,lw=3,label='$RAF_{AUC}$ = %.3f' % (roc_auc_RF))
#plt.plot(fpr_c, tpr_c,lw=3,label='$GR_{AUC}$ = %.3f' % (roc_auc_c))
plt.legend(loc="lower right", fontsize=18, frameon=False)
plt.plot([0,1], [0,1], 'k--')
plt.xlabel('False Positive Rate', fontsize=20)
plt.ylabel('True Positive Rate', fontsize=20)
plt.tick_params(axis='both', which='major', labelsize=22)
plt.show()
"""### Valence"""
refvar="valence"
taglio=0.67
X=df_class_ref.drop(refvar,axis=1).copy()
y=df_class_ref[refvar].copy()
y_up_index = y >= taglio
y[y_up_index]=1
y_zero_index = y < taglio
y[y_zero_index]=0
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
fig, ax =plt.subplots()
ax.set_xlabel("alpha")
ax.set_ylabel("accuracy")
ax.set_title("Accuracy vs alpha for training and testing sets")
ax.plot(ccp_alphas,train_scores, marker ='o',label='train',drawstyle='steps-post')
ax.plot(ccp_alphas,test_scores, marker ='o',label='test',drawstyle='steps-post')
ax.legend()
plt.show()
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=0, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), np.std(scores)])
alpha_results = pd.DataFrame(alpha_loop_values,
columns=['alpha','mean_accuracy','std'])
alpha_results.plot(x='alpha',
y='mean_accuracy',
marker='o',
linestyle='--')
indexmax = alpha_results[['mean_accuracy']].idxmax()
maxalpha=alpha_results.loc[indexmax,'alpha']
ideal_ccp_alpha = float(maxalpha)
clf_dt_pruned = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=ideal_ccp_alpha)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
plt.figure(figsize=(15,7.5))
clf_dt_pruned.classes_
from sklearn.tree import plot_tree
plot_tree(clf_dt_pruned,
filled=True,
rounded=True,
class_names=[str(v) for v in clf_dt_pruned.classes_],
feature_names=X.columns)
y_pred = clf_dt_pruned.predict(X_train)
y_pred = clf_dt_pruned.predict(X_test)
print('Accuracy %s' % accuracy_score(y_test, y_pred))
print('F1-score %s' % f1_score(y_test, y_pred,average='weighted'))
print(classification_report(y_test, y_pred))
y_score = clf_dt_pruned.predict_proba(X_test)
plot_confusion_matrix(clf_dt_pruned,
X_test,
y_test,
display_labels=['not val','val'])
fpr, tpr, th = roc_curve(y_test, y_score[:,1])
roc_auc = auc(fpr, tpr)
print(roc_auc)
plt.figure(figsize=(8,5))
plt.plot(fpr, tpr, label='$AUC$ = %.3f' % (roc_auc))
plt.legend(loc="lower right", fontsize=14, frameon=False)
plt.plot([0,1], [0,1], 'k--')
plt.xlabel('False Positive Rate', fontsize=20)
plt.ylabel('True Positive Rate', fontsize=20)
plt.tick_params(axis='both', which='major', labelsize=22)
plt.show()
#ROC for Decision Tree (Gini)
fpr_0, tpr_0, th_0 = roc_curve(y_test, y_score[:,1])
roc_auc_0 = auc(fpr_0, tpr_0)
#Entropy
clf_dt = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='entropy',random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=0, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), np.std(scores)])
alpha_results = pd.DataFrame(alpha_loop_values,
columns=['alpha','mean_accuracy','std'])
indexmax = alpha_results[['mean_accuracy']].idxmax()
maxalpha=alpha_results.loc[indexmax,'alpha']
ideal_ccp_alpha = float(maxalpha)
print(ideal_ccp_alpha)
clf_dt_pruned = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=ideal_ccp_alpha)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
y_score = clf_dt_pruned.predict_proba(X_test)
fpr_en, tpr_en, th_en = roc_curve(y_test, y_score[:,1])
roc_auc_en = auc(fpr_en, tpr_en)
y_pred = clf_dt_pruned.predict(X_test)
print(classification_report(y_test, y_pred))
#KNN, find best score
acc = []
# Will take some time
for i in range(1,40):
neigh = KNeighborsClassifier(n_neighbors = i).fit(X_train,y_train)
yhat = neigh.predict(X_test)
acc.append(metrics.accuracy_score(y_test, yhat))
clf_knn = KNeighborsClassifier(n_neighbors=acc.index(max(acc)))
clf_knn.fit(X, y)
y_pred = clf_knn.predict(X_train)
y_score = clf_knn.predict_proba(X_test)
fpr_KNN, tpr_KNN, th_KNN = roc_curve(y_test, y_score[:,1])
roc_auc_KNN = auc(fpr_KNN, tpr_KNN)
y_pred = clf_knn.predict(X_test)
print(classification_report(y_test, y_pred))
# Instantiate model with 380 decision trees
model = RandomForestClassifier(n_estimators = 380, random_state = 42)
# Train the model on training data
ra=model.fit(X_train, y_train)
y_score = model.predict_proba(X_test)
fpr_RF, tpr_RF, th_RF = roc_curve(y_test, y_score[:,1])
roc_auc_RF = auc(fpr_RF, tpr_RF)
y_pred = model.predict(X_test)
print(classification_report(y_test, y_pred))
plt.figure(figsize=(8,5))
plt.plot(fpr_0, tpr_0,lw=3,label='$GINI_{AUC}$ = %.3f' % (roc_auc_0))
plt.plot(fpr_en, tpr_en,lw=3,label='$ENT_{AUC}$ = %.3f' % (roc_auc_en))
plt.plot(fpr_KNN, tpr_KNN,lw=3,label='$KNN_{AUC}$ = %.3f' % (roc_auc_KNN))
plt.plot(fpr_RF, tpr_RF,lw=3,label='$RAF_{AUC}$ = %.3f' % (roc_auc_RF))
#plt.plot(fpr_c, tpr_c,lw=3,label='$GR_{AUC}$ = %.3f' % (roc_auc_c))
plt.legend(loc="lower right", fontsize=18, frameon=False)
plt.plot([0,1], [0,1], 'k--')
plt.xlabel('False Positive Rate', fontsize=20)
plt.ylabel('True Positive Rate', fontsize=20)
plt.tick_params(axis='both', which='major', labelsize=22)
plt.show()
"""### Dominance
"""
refvar="dominance"
taglio=0.57
X=df_class_ref.drop(refvar,axis=1).copy()
y=df_class_ref[refvar].copy()
y_up_index = y >= taglio
y[y_up_index]=1
y_zero_index = y < taglio
y[y_zero_index]=0
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
fig, ax =plt.subplots()
ax.set_xlabel("alpha")
ax.set_ylabel("accuracy")
ax.set_title("Accuracy vs alpha for training and testing sets")
ax.plot(ccp_alphas,train_scores, marker ='o',label='train',drawstyle='steps-post')
ax.plot(ccp_alphas,test_scores, marker ='o',label='test',drawstyle='steps-post')
ax.legend()
plt.show()
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(random_state=42, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), np.std(scores)])
alpha_results = pd.DataFrame(alpha_loop_values,
columns=['alpha','mean_accuracy','std'])
alpha_results.plot(x='alpha',
y='mean_accuracy',
marker='o',
linestyle='--')
indexmax = alpha_results[['mean_accuracy']].idxmax()
maxalpha=alpha_results.loc[indexmax,'alpha']
ideal_ccp_alpha = float(maxalpha)
clf_dt_pruned = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=ideal_ccp_alpha)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
plot_confusion_matrix(clf_dt_pruned,
X_test,
y_test,
display_labels=['not dominant','dominant'])
plt.figure(figsize=(15,7.5))
from sklearn.tree import plot_tree
plot_tree(clf_dt_pruned,
filled=True,
rounded=True,
class_names=["not dominant","dominant"],
feature_names=X.columns)
y_pred = clf_dt_pruned.predict(X_train)
y_pred = clf_dt_pruned.predict(X_test)
print('Accuracy %s' % accuracy_score(y_test, y_pred))
print('F1-score %s' % f1_score(y_test, y_pred))
print(classification_report(y_test, y_pred))
y_score = clf_dt_pruned.predict_proba(X_test)
fpr, tpr, th = roc_curve(y_test, y_score[:,1])
roc_auc = auc(fpr, tpr)
print(roc_auc)
plt.figure(figsize=(8,5))
plt.plot(fpr, tpr, label='$AUC$ = %.3f' % (roc_auc))
plt.legend(loc="lower right", fontsize=14, frameon=False)
plt.plot([0,1], [0,1], 'k--')
plt.xlabel('False Positive Rate', fontsize=20)
plt.ylabel('True Positive Rate', fontsize=20)
plt.tick_params(axis='both', which='major', labelsize=22)
plt.show()
#ROC for Decision Tree (Gini)
fpr_0, tpr_0, th_0 = roc_curve(y_test, y_score[:,1])
roc_auc_0 = auc(fpr_0, tpr_0)
#Entropy
clf_dt = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='entropy',random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=0, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), np.std(scores)])
alpha_results = pd.DataFrame(alpha_loop_values,
columns=['alpha','mean_accuracy','std'])
indexmax = alpha_results[['mean_accuracy']].idxmax()
maxalpha=alpha_results.loc[indexmax,'alpha']
ideal_ccp_alpha = float(maxalpha)
print(ideal_ccp_alpha)
clf_dt_pruned = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=ideal_ccp_alpha)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
y_score = clf_dt_pruned.predict_proba(X_test)
fpr_en, tpr_en, th_en = roc_curve(y_test, y_score[:,1])
roc_auc_en = auc(fpr_en, tpr_en)
y_pred = clf_dt_pruned.predict(X_test)
print(classification_report(y_test, y_pred))
#KNN, find best score
acc = []
# Will take some time
for i in range(1,40):
neigh = KNeighborsClassifier(n_neighbors = i).fit(X_train,y_train)
yhat = neigh.predict(X_test)
acc.append(metrics.accuracy_score(y_test, yhat))
clf_knn = KNeighborsClassifier(n_neighbors=acc.index(max(acc)))
clf_knn.fit(X, y)
y_pred = clf_knn.predict(X_train)
y_score = clf_knn.predict_proba(X_test)
fpr_KNN, tpr_KNN, th_KNN = roc_curve(y_test, y_score[:,1])
roc_auc_KNN = auc(fpr_KNN, tpr_KNN)
y_pred = clf_knn.predict(X_test)
print(classification_report(y_test, y_pred))
# Instantiate model with 380 decision trees
model = RandomForestClassifier(n_estimators = 380, random_state = 42)
# Train the model on training data
ra=model.fit(X_train, y_train)
y_score = model.predict_proba(X_test)
fpr_RF, tpr_RF, th_RF = roc_curve(y_test, y_score[:,1])
roc_auc_RF = auc(fpr_RF, tpr_RF)
y_pred = model.predict(X_test)
print(classification_report(y_test, y_pred))
plt.figure(figsize=(8,5))
plt.plot(fpr_0, tpr_0,lw=3,label='$GINI_{AUC}$ = %.3f' % (roc_auc_0))
plt.plot(fpr_en, tpr_en,lw=3,label='$ENT_{AUC}$ = %.3f' % (roc_auc_en))
plt.plot(fpr_KNN, tpr_KNN,lw=3,label='$KNN_{AUC}$ = %.3f' % (roc_auc_KNN))
plt.plot(fpr_RF, tpr_RF,lw=3,label='$RAF_{AUC}$ = %.3f' % (roc_auc_RF))
#plt.plot(fpr_c, tpr_c,lw=3,label='$GR_{AUC}$ = %.3f' % (roc_auc_c))
plt.legend(loc="lower right", fontsize=18, frameon=False)
plt.plot([0,1], [0,1], 'k--')
plt.xlabel('False Positive Rate', fontsize=20)
plt.ylabel('True Positive Rate', fontsize=20)
plt.tick_params(axis='both', which='major', labelsize=22)
plt.show()
"""### Familiarity"""
refvar="familiarity"
taglio=0.6
X=df_class_ref.drop(refvar,axis=1).copy()
y=df_class_ref[refvar].copy()
y_up_index = y >= taglio
y[y_up_index]=1
y_zero_index = y < taglio
y[y_zero_index]=0
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
fig, ax =plt.subplots()
ax.set_xlabel("alpha")
ax.set_ylabel("accuracy")
ax.set_title("Accuracy vs alpha for training and testing sets")
ax.plot(ccp_alphas,train_scores, marker ='o',label='train',drawstyle='steps-post')
ax.plot(ccp_alphas,test_scores, marker ='o',label='test',drawstyle='steps-post')
ax.legend()
plt.show()
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=0, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), np.std(scores)])
alpha_results = pd.DataFrame(alpha_loop_values,
columns=['alpha','mean_accuracy','std'])
alpha_results.plot(x='alpha',
y='mean_accuracy',
marker='o',
linestyle='--')
indexmax = alpha_results[['mean_accuracy']].idxmax()
maxalpha=alpha_results.loc[indexmax,'alpha']
ideal_ccp_alpha = float(maxalpha)
clf_dt_pruned = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=ideal_ccp_alpha)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
plot_confusion_matrix(clf_dt_pruned,
X_test,
y_test,
display_labels=['not dominant','dominant'])
plt.figure(figsize=(15,7.5))
from sklearn.tree import plot_tree
plot_tree(clf_dt_pruned,
filled=True,
rounded=True,
class_names=["not familiar","familiar"],
feature_names=X.columns,
max_depth=3,
fontsize=7)
y_pred = clf_dt_pruned.predict(X_train)
y_pred = clf_dt_pruned.predict(X_test)
plt.savefig('plot_of_tree.pdf')
print('Accuracy %s' % accuracy_score(y_test, y_pred))
print('F1-score %s' % f1_score(y_test, y_pred))
print(classification_report(y_test, y_pred))
y_score = clf_dt_pruned.predict_proba(X_test)
fpr, tpr, th = roc_curve(y_test, y_score[:,1])
roc_auc = auc(fpr, tpr)
print(roc_auc)
plt.figure(figsize=(8,5))
plt.plot(fpr, tpr, label='$AUC$ = %.3f' % (roc_auc))
plt.legend(loc="lower right", fontsize=14, frameon=False)
plt.plot([0,1], [0,1], 'k--')
plt.xlabel('False Positive Rate', fontsize=20)
plt.ylabel('True Positive Rate', fontsize=20)
plt.tick_params(axis='both', which='major', labelsize=22)
plt.show()
#ROC for Decision Tree (Gini)
fpr_0, tpr_0, th_0 = roc_curve(y_test, y_score[:,1])
roc_auc_0 = auc(fpr_0, tpr_0)
#Entropy
clf_dt = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='entropy',random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=0, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), np.std(scores)])
alpha_results = pd.DataFrame(alpha_loop_values,
columns=['alpha','mean_accuracy','std'])
indexmax = alpha_results[['mean_accuracy']].idxmax()
maxalpha=alpha_results.loc[indexmax,'alpha']
ideal_ccp_alpha = float(maxalpha)
print(ideal_ccp_alpha)
clf_dt_pruned = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=ideal_ccp_alpha)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
y_score = clf_dt_pruned.predict_proba(X_test)
fpr_en, tpr_en, th_en = roc_curve(y_test, y_score[:,1])
roc_auc_en = auc(fpr_en, tpr_en)
y_pred = clf_dt_pruned.predict(X_test)
print(classification_report(y_test, y_pred))
plt.figure(figsize=(15,7.5))
from sklearn.tree import plot_tree
plot_tree(clf_dt_pruned,
filled=True,
rounded=True,
class_names=["not familiar","familiar"],
feature_names=X.columns,
max_depth=3,
fontsize=7)
#KNN, find best score
acc = []
# Will take some time
for i in range(1,40):
neigh = KNeighborsClassifier(n_neighbors = i).fit(X_train,y_train)
yhat = neigh.predict(X_test)
acc.append(metrics.accuracy_score(y_test, yhat))
clf_knn = KNeighborsClassifier(n_neighbors=acc.index(max(acc)))
clf_knn.fit(X, y)
y_pred = clf_knn.predict(X_train)
y_score = clf_knn.predict_proba(X_test)
fpr_KNN, tpr_KNN, th_KNN = roc_curve(y_test, y_score[:,1])
roc_auc_KNN = auc(fpr_KNN, tpr_KNN)
y_pred = clf_knn.predict(X_test)
print(classification_report(y_test, y_pred))
# Instantiate model with 380 decision trees
model = RandomForestClassifier(n_estimators = 380, random_state = 42)
# Train the model on training data
ra=model.fit(X_train, y_train)
y_score = model.predict_proba(X_test)
fpr_RF, tpr_RF, th_RF = roc_curve(y_test, y_score[:,1])
roc_auc_RF = auc(fpr_RF, tpr_RF)
y_pred = model.predict(X_test)
print(classification_report(y_test, y_pred))
plt.figure(figsize=(8,5))
plt.plot(fpr_0, tpr_0,lw=3,label='$GINI_{AUC}$ = %.3f' % (roc_auc_0))
plt.plot(fpr_en, tpr_en,lw=3,label='$ENT_{AUC}$ = %.3f' % (roc_auc_en))
plt.plot(fpr_KNN, tpr_KNN,lw=3,label='$KNN_{AUC}$ = %.3f' % (roc_auc_KNN))
plt.plot(fpr_RF, tpr_RF,lw=3,label='$RAF_{AUC}$ = %.3f' % (roc_auc_RF))
#plt.plot(fpr_c, tpr_c,lw=3,label='$GR_{AUC}$ = %.3f' % (roc_auc_c))
plt.legend(loc="lower right", fontsize=18, frameon=False)
plt.plot([0,1], [0,1], 'k--')
plt.xlabel('False Positive Rate', fontsize=20)
plt.ylabel('True Positive Rate', fontsize=20)
plt.tick_params(axis='both', which='major', labelsize=22)
plt.show()
"""### Semsize"""
refvar="semsize"
taglio=0.63
X=df_class_ref.drop(refvar,axis=1).copy()
y=df_class_ref[refvar].copy()
y_up_index = y >= taglio
y[y_up_index]=1
y_zero_index = y < taglio
y[y_zero_index]=0
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
fig, ax =plt.subplots()
ax.set_xlabel("alpha")
ax.set_ylabel("accuracy")
ax.set_title("Accuracy vs alpha for training and testing sets")
ax.plot(ccp_alphas,train_scores, marker ='o',label='train',drawstyle='steps-post')
ax.plot(ccp_alphas,test_scores, marker ='o',label='test',drawstyle='steps-post')
ax.legend()
plt.show()
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=0, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), np.std(scores)])
alpha_results = pd.DataFrame(alpha_loop_values,
columns=['alpha','mean_accuracy','std'])
alpha_results.plot(x='alpha',
y='mean_accuracy',
marker='o',
linestyle='--')
indexmax = alpha_results[['mean_accuracy']].idxmax()
maxalpha=alpha_results.loc[indexmax,'alpha']
ideal_ccp_alpha = float(maxalpha)
clf_dt_pruned = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=ideal_ccp_alpha)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
plot_confusion_matrix(clf_dt_pruned,
X_test,
y_test,
display_labels=['small','big'])
plt.figure(figsize=(15,7.5))
from sklearn.tree import plot_tree
plot_tree(clf_dt_pruned,
filled=True,
rounded=True,
class_names=["small","big"],
feature_names=X.columns)
y_pred = clf_dt_pruned.predict(X_train)
y_pred = clf_dt_pruned.predict(X_test)
print('Accuracy %s' % accuracy_score(y_test, y_pred))
print('F1-score %s' % f1_score(y_test, y_pred, average=None))
print(classification_report(y_test, y_pred))
y_score = clf_dt_pruned.predict_proba(X_test)
fpr, tpr, th = roc_curve(y_test, y_score[:,1])
roc_auc = auc(fpr, tpr)
print(roc_auc)
plt.figure(figsize=(8,5))
plt.plot(fpr, tpr, label='$AUC$ = %.3f' % (roc_auc))
plt.legend(loc="lower right", fontsize=14, frameon=False)
plt.plot([0,1], [0,1], 'k--')
plt.xlabel('False Positive Rate', fontsize=20)
plt.ylabel('True Positive Rate', fontsize=20)
plt.tick_params(axis='both', which='major', labelsize=22)
plt.show()
#ROC for Decision Tree (Gini)
fpr_0, tpr_0, th_0 = roc_curve(y_test, y_score[:,1])
roc_auc_0 = auc(fpr_0, tpr_0)
#Entropy
clf_dt = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='entropy',random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=0, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), np.std(scores)])
alpha_results = pd.DataFrame(alpha_loop_values,
columns=['alpha','mean_accuracy','std'])
indexmax = alpha_results[['mean_accuracy']].idxmax()
maxalpha=alpha_results.loc[indexmax,'alpha']
ideal_ccp_alpha = float(maxalpha)
print(ideal_ccp_alpha)
clf_dt_pruned = DecisionTreeClassifier(criterion='entropy', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42, ccp_alpha=ideal_ccp_alpha)
clf_dt_pruned = clf_dt_pruned.fit(X_train, y_train)
y_score = clf_dt_pruned.predict_proba(X_test)
fpr_en, tpr_en, th_en = roc_curve(y_test, y_score[:,1])
roc_auc_en = auc(fpr_en, tpr_en)
y_pred = clf_dt_pruned.predict(X_test)
print(classification_report(y_test, y_pred))
#KNN, find best score
acc = []
# Will take some time
for i in range(1,40):
neigh = KNeighborsClassifier(n_neighbors = i).fit(X_train,y_train)
yhat = neigh.predict(X_test)
acc.append(metrics.accuracy_score(y_test, yhat))
clf_knn = KNeighborsClassifier(n_neighbors=acc.index(max(acc)))
clf_knn.fit(X, y)
y_pred = clf_knn.predict(X_train)
y_score = clf_knn.predict_proba(X_test)
fpr_KNN, tpr_KNN, th_KNN = roc_curve(y_test, y_score[:,1])
roc_auc_KNN = auc(fpr_KNN, tpr_KNN)
y_pred = clf_knn.predict(X_test)
print(classification_report(y_test, y_pred))
# Instantiate model with 380 decision trees
model = RandomForestClassifier(n_estimators = 380, random_state = 42)
# Train the model on training data
ra=model.fit(X_train, y_train)
y_score = model.predict_proba(X_test)
fpr_RF, tpr_RF, th_RF = roc_curve(y_test, y_score[:,1])
roc_auc_RF = auc(fpr_RF, tpr_RF)
y_pred = model.predict(X_test)
print(classification_report(y_test, y_pred))
plt.figure(figsize=(8,5))
plt.plot(fpr_0, tpr_0,lw=3,label='$GINI_{AUC}$ = %.3f' % (roc_auc_0))
plt.plot(fpr_en, tpr_en,lw=3,label='$ENT_{AUC}$ = %.3f' % (roc_auc_en))
plt.plot(fpr_KNN, tpr_KNN,lw=3,label='$KNN_{AUC}$ = %.3f' % (roc_auc_KNN))
plt.plot(fpr_RF, tpr_RF,lw=3,label='$RAF_{AUC}$ = %.3f' % (roc_auc_RF))
#plt.plot(fpr_c, tpr_c,lw=3,label='$GR_{AUC}$ = %.3f' % (roc_auc_c))
plt.legend(loc="lower right", fontsize=18, frameon=False)
plt.plot([0,1], [0,1], 'k--')
plt.xlabel('False Positive Rate', fontsize=20)
plt.ylabel('True Positive Rate', fontsize=20)
plt.tick_params(axis='both', which='major', labelsize=22)
plt.show()
"""### Masculinity"""
refvar="masculinity"
taglio=0.6
X=df_class_ref.drop(refvar,axis=1).copy()
y=df_class_ref[refvar].copy()
y_up_index = y >= taglio
y[y_up_index]=1
y_zero_index = y < taglio
y[y_zero_index]=0
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=42)
clf_dt = clf_dt.fit(X_train, y_train)
path = clf_dt.cost_complexity_pruning_path(X_train, y_train)
ccp_alphas = path.ccp_alphas
ccp_alphas = ccp_alphas[:-1]
clf_dts=[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(random_state=0, ccp_alpha=ccp_alpha)
clf_dt.fit(X_train, y_train)
clf_dts.append(clf_dt)
train_scores = [clf_dt.score(X_train, y_train) for clf_dt in clf_dts]
test_scores = [clf_dt.score(X_test, y_test) for clf_dt in clf_dts]
fig, ax =plt.subplots()
ax.set_xlabel("alpha")
ax.set_ylabel("accuracy")
ax.set_title("Accuracy vs alpha for training and testing sets")
ax.plot(ccp_alphas,train_scores, marker ='o',label='train',drawstyle='steps-post')
ax.plot(ccp_alphas,test_scores, marker ='o',label='test',drawstyle='steps-post')
ax.legend()
plt.show()
alpha_loop_values =[]
for ccp_alpha in ccp_alphas:
clf_dt = DecisionTreeClassifier(criterion='gini', max_depth=None, min_samples_split=2, min_samples_leaf=1,random_state=0, ccp_alpha=ccp_alpha)
scores= cross_val_score(clf_dt,X_train,y_train, cv=10)
alpha_loop_values.append([ccp_alpha,np.mean(scores), | np.std(scores) | numpy.std |
from pandas.io.data import DataReader
from pylab import legend, xlabel, ylabel, sqrt, ylim,\
cov, sqrt, mean, std, plot, show, figure
from numpy import array, zeros, matrix, ones, shape, linspace, hstack
from pandas import Series, DataFrame
from numpy.linalg import inv
# Portfolio class.
class Portfolio:
def __init__(self, symbols, start=None, end=None, bench='^GSPC'):
# Make sure input is a list
if type(symbols) != list:
symbols = [symbols]
# Create distionary to hold assets.
self.asset = {}
# Retrieve assets from data source (IE. Yahoo)
for symbol in symbols:
try:
self.asset[symbol] = DataReader(
symbol, "yahoo", start=start, end=end)
except:
print("Asset " + str(symbol) + " not found!")
# Get Benchmark asset.
self.benchmark = DataReader(bench, "yahoo", start=start, end=end)
self.benchmark['Return'] = self.benchmark['Adj Close'].diff()
# Get returns, beta, alpha, and sharp ratio.
for symbol in symbols:
# Get returns.
self.asset[symbol]['Return'] = \
self.asset[symbol]['Adj Close'].diff()
# Get Beta.
A = self.asset[symbol]['Return'].fillna(0)
B = self.benchmark['Return'].fillna(0)
self.asset[symbol]['Beta'] = cov(A, B)[0, 1] / cov(A, B)[1, 1]
# Get Alpha
self.asset[symbol]['Alpha'] = self.asset[symbol]['Return'] - \
self.asset[symbol]['Beta'] * self.benchmark['Return']
# Get Sharpe Ratio
tmp = self.asset[symbol]['Return']
self.asset[symbol]['Sharpe'] = \
sqrt(len(tmp)) * mean(tmp.fillna(0)) / std(tmp.fillna(0))
def nplot(self, symbol, color='b', nval=0):
tmp = (self.benchmark if symbol == 'bench' else self.asset[symbol]) ['Adj Close']
tmp = tmp / tmp[nval]
tmp.plot(color=color, label=symbol)
legend(loc='best', shadow=True, fancybox=True)
def betas(self):
betas = [v['Beta'][0] for k, v in self.asset.items()]
return Series(betas, index=self.asset.keys())
def returns(self):
returns = [v['Return'].dropna() for k, v in self.asset.items()]
return Series(returns, index=self.asset.keys())
def cov(self):
keys, values = self.returns().keys(), self.returns().values()
return DataFrame(
cov(array(values)), index=keys, columns=keys)
def get_w(self, kind='sharpe'):
V = self.cov()
iV = matrix(inv(V))
if kind == 'characteristic':
e = matrix(ones(len(self.asset.keys()))).T
elif kind == 'sharpe':
suml = [ self.returns()[symbol].sum() for symbol in self.asset.keys()]
e = matrix(suml).T
else:
print('\n *Error: There is no weighting for kind ' + kind)
return
num = iV * e
denom = e.T * iV * e
w = array(num / denom).flatten()
return Series(w, index=self.asset.keys())
def efficient_frontier_w(self, fp):
wc = self.get_w(kind='characteristic')
wq = self.get_w(kind='sharpe')
fc = self.ret_for_w(wc).sum()
fq = self.ret_for_w(wq).sum()
denom = fq - fc
w = (fq - fp) * wc + (fp - fc) * wq
return Series(w / denom, index=self.asset.keys())
def efficient_frontier(self, xi=0.01, xf=4, npts=100, scale=10):
frontier = linspace(xi, xf, npts)
i = 0
rets = zeros(len(frontier))
sharpe = zeros(len(frontier))
for f in frontier:
w = self.efficient_frontier_w(f)
tmp = self.ret_for_w(w)
rets[i] = tmp.sum() * scale
sharpe[i] = mean(tmp) / std(tmp) * sqrt(len(tmp))
i += 1
risk = rets/sharpe
return Series(rets, index=risk), sharpe.max()
def efficient_frontier_plot(self, xi=0.01, xf=4, npts=100, scale=0.1,
col1='b', col2='r', newfig=1, plabel=''):
eff, m = self.efficient_frontier()
if newfig == 1:
figure()
plot(array(eff.index), array(eff), col1, linewidth=2,
label="Efficient Frontier " + plabel)
tmp = zeros(1)
plot(hstack((tmp, array(eff.index))),
hstack((0, m * array(eff.index))),
col2, linewidth=2, label="Max Sharpe Ratio: %6.2g" % m)
legend(loc='best', shadow=True, fancybox=True)
xlabel('Risk %', fontsize=16)
ylabel('Return %', fontsize=16)
show()
def min_var_w_ret(self, ret):
V = self.cov()
suml = [self.returns()[symbol].sum() for symbol in self.asset.keys()]
e = | matrix(suml) | numpy.matrix |
# -*- coding: utf-8 -*-
import numpy as np
from scipy import constants
def B21(A21,nu):
'''Returns the Einstein B21 coefficient for stimulated emission, computed
from the Einstein A21 coefficient and the frequency nu.'''
return constants.c**2/(2*constants.h*nu**3)*A21
def B12(A21,nu,g1,g2):
'''Einstein B12 coefficient for absorption, computed from the Einstein A21
coefficient, the frequency nu, statistical weights g2 and g1 of upper and
lower level respectively.'''
return g2/g1*B21(A21=A21,nu=nu)
def B_nu(nu,T):
"""Planck function
Return the value of the Planck function (black body) in [W/m2/Hz/sr].
Parameters
----------
nu : float or numpy.ndarray
frequency in Hz
T : float or numpy.ndarray
temperature in K
Returns
-------
numpy.ndarray
Value of Planck function in [W/m2/Hz/sr]
"""
T = np.array(T)
return (2*constants.h*nu**3/constants.c**2
*(np.exp(constants.h*nu/(constants.k*T))-1)**-1)
def generate_CMB_background(z=0):
'''generates a function that gives the CMB background at redshift z
Parameters
-----------
z: float
redshift
Returns
--------
function
function giving CMB background in [W/m2/Hz/sr] for an input frequency in [Hz]
'''
T_CMB = 2.73*(1+z)
def CMB_background(nu):
return B_nu(nu=nu,T=T_CMB)
return CMB_background
def zero_background(nu):
'''Zero intensity radiation field
Returns zero intensity for any frequency
Parameters
------------
nu: array_like
frequency in Hz
Returns
---------------
numpy.ndarray
Zero at all requested frequencies'''
return np.zeros_like(nu)
def FWHM2sigma(FWHM):
"""Convert FWHM of a Gaussian to standard deviation.
Parameters
-----------
FWHM: float or numpy.ndarray
FWHM of the Gaussian
Returns
------------
float or numpy.ndarray
the standard deviation of the Gaussian"""
return FWHM/(2*np.sqrt(2*np.log(2)))
def relative_difference(a,b):
"""Computes the elementwise relative difference between a and b.
In general, return |a-b|/a.
Special cases:
a=0 and b=0: return 0
a=0 and b!=0: return 1"""
abs_diff = np.abs(a-b)
with np.errstate(invalid='ignore',divide='ignore'):
rel_diff = np.where((a==0) & (b==0),0,np.where(a==0,1,abs_diff/a))
assert not np.any( | np.isnan(rel_diff) | numpy.isnan |
# standard libraries
import collections
import copy
import functools
import math
import numbers
import operator
import typing
# third party libraries
import numpy
import numpy.fft
import scipy
import scipy.fftpack
import scipy.ndimage
import scipy.ndimage.filters
import scipy.ndimage.fourier
import scipy.signal
# local libraries
from nion.data import Calibration
from nion.data import DataAndMetadata
from nion.data import Image
from nion.data import ImageRegistration
from nion.data import TemplateMatching
from nion.utils import Geometry
DataRangeType = typing.Tuple[float, float]
NormIntervalType = typing.Tuple[float, float]
NormChannelType = float
NormRectangleType = typing.Tuple[typing.Tuple[float, float], typing.Tuple[float, float]]
NormPointType = typing.Tuple[float, float]
NormSizeType = typing.Tuple[float, float]
NormVectorType = typing.Tuple[NormPointType, NormPointType]
def column(data_and_metadata: DataAndMetadata.DataAndMetadata, start: int, stop: int) -> DataAndMetadata.DataAndMetadata:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
def calculate_data():
start_0 = start if start is not None else 0
stop_0 = stop if stop is not None else data_shape(data_and_metadata)[0]
start_1 = start if start is not None else 0
stop_1 = stop if stop is not None else data_shape(data_and_metadata)[1]
return numpy.meshgrid(numpy.linspace(start_1, stop_1, data_shape(data_and_metadata)[1]), numpy.linspace(start_0, stop_0, data_shape(data_and_metadata)[0]), sparse=True)[0]
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=data_and_metadata.dimensional_calibrations)
def row(data_and_metadata: DataAndMetadata.DataAndMetadata, start: int, stop: int) -> DataAndMetadata.DataAndMetadata:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
def calculate_data():
start_0 = start if start is not None else 0
stop_0 = stop if stop is not None else data_shape(data_and_metadata)[0]
start_1 = start if start is not None else 0
stop_1 = stop if stop is not None else data_shape(data_and_metadata)[1]
return numpy.meshgrid(numpy.linspace(start_1, stop_1, data_shape(data_and_metadata)[1]), numpy.linspace(start_0, stop_0, data_shape(data_and_metadata)[0]), sparse=True)[1]
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=data_and_metadata.dimensional_calibrations)
def radius(data_and_metadata: DataAndMetadata.DataAndMetadata, normalize: bool=True) -> DataAndMetadata.DataAndMetadata:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
def calculate_data():
start_0 = -1 if normalize else -data_shape(data_and_metadata)[0] * 0.5
stop_0 = -start_0
start_1 = -1 if normalize else -data_shape(data_and_metadata)[1] * 0.5
stop_1 = -start_1
icol, irow = numpy.meshgrid(numpy.linspace(start_1, stop_1, data_shape(data_and_metadata)[1]), numpy.linspace(start_0, stop_0, data_shape(data_and_metadata)[0]), sparse=True)
return numpy.sqrt(icol * icol + irow * irow)
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=data_and_metadata.dimensional_calibrations)
def full(shape: DataAndMetadata.ShapeType, fill_value, dtype: numpy.dtype = None) -> DataAndMetadata.DataAndMetadata:
"""Generate a constant valued image with the given shape.
full(4, shape(4, 5))
full(0, data_shape(b))
"""
dtype = dtype if dtype else numpy.dtype(numpy.float64)
return DataAndMetadata.new_data_and_metadata(numpy.full(shape, DataAndMetadata.extract_data(fill_value), dtype))
def arange(start: int, stop: int=None, step: int=None) -> DataAndMetadata.DataAndMetadata:
if stop is None:
start = 0
stop = start
if step is None:
step = 1
return DataAndMetadata.new_data_and_metadata(numpy.linspace(int(start), int(stop), int(step)))
def linspace(start: float, stop: float, num: int, endpoint: bool=True) -> DataAndMetadata.DataAndMetadata:
return DataAndMetadata.new_data_and_metadata(numpy.linspace(start, stop, num, endpoint))
def logspace(start: float, stop: float, num: int, endpoint: bool=True, base: float=10.0) -> DataAndMetadata.DataAndMetadata:
return DataAndMetadata.new_data_and_metadata(numpy.logspace(start, stop, num, endpoint, base))
def apply_dist(data_and_metadata: DataAndMetadata.DataAndMetadata, mean: float, stddev: float, dist, fn) -> DataAndMetadata.DataAndMetadata:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
return DataAndMetadata.new_data_and_metadata(getattr(dist(loc=mean, scale=stddev), fn)(data_and_metadata.data))
def take_item(data, key):
return data[key]
def data_shape(data_and_metadata: DataAndMetadata.DataAndMetadata) -> DataAndMetadata.ShapeType:
return data_and_metadata.data_shape
def astype(data: numpy.ndarray, dtype: numpy.dtype) -> numpy.ndarray:
return data.astype(dtype)
dtype_map: typing.Mapping[typing.Any, str] = {int: "int", float: "float", complex: "complex", numpy.int16: "int16",
numpy.int32: "int32", numpy.int64: "int64", numpy.uint8: "uint8",
numpy.uint16: "uint16", numpy.uint32: "uint32", numpy.uint64: "uint64",
numpy.float32: "float32", numpy.float64: "float64",
numpy.complex64: "complex64", numpy.complex128: "complex128"}
dtype_inverse_map = {dtype_map[k]: k for k in dtype_map}
def str_to_dtype(str: str) -> numpy.dtype:
return dtype_inverse_map.get(str, float)
def dtype_to_str(dtype: numpy.dtype) -> str:
return dtype_map.get(dtype, "float")
def function_fft(data_and_metadata: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
data_shape = data_and_metadata.data_shape
data_dtype = data_and_metadata.data_dtype
def calculate_data():
data = data_and_metadata.data
if data is None or not Image.is_data_valid(data):
return None
# scaling: numpy.sqrt(numpy.mean(numpy.absolute(data_copy)**2)) == numpy.sqrt(numpy.mean(numpy.absolute(data_copy_fft)**2))
# see https://gist.github.com/endolith/1257010
if Image.is_data_1d(data):
scaling = 1.0 / numpy.sqrt(data_shape[0])
return scipy.fftpack.fftshift(numpy.multiply(scipy.fftpack.fft(data), scaling))
elif Image.is_data_2d(data):
if Image.is_data_rgb_type(data):
if Image.is_data_rgb(data):
data_copy = numpy.sum(data[..., :] * (0.2126, 0.7152, 0.0722), 2)
else:
data_copy = numpy.sum(data[..., :] * (0.2126, 0.7152, 0.0722, 0.0), 2)
else:
data_copy = data.copy() # let other threads use data while we're processing
scaling = 1.0 / numpy.sqrt(data_shape[1] * data_shape[0])
# note: the numpy.fft.fft2 is faster than scipy.fftpack.fft2, probably either because
# our conda distribution compiles numpy for multiprocessing, the numpy version releases
# the GIL, or both.
return scipy.fftpack.fftshift(numpy.multiply(numpy.fft.fft2(data_copy), scaling))
else:
raise NotImplementedError()
src_dimensional_calibrations = data_and_metadata.dimensional_calibrations
if not Image.is_shape_and_dtype_valid(data_shape, data_dtype) or src_dimensional_calibrations is None:
return None
assert len(src_dimensional_calibrations) == len(
Image.dimensional_shape_from_shape_and_dtype(data_shape, data_dtype))
dimensional_calibrations = [Calibration.Calibration((-0.5 - 0.5 * data_shape_n) / (dimensional_calibration.scale * data_shape_n), 1.0 / (dimensional_calibration.scale * data_shape_n),
"1/" + dimensional_calibration.units) for
dimensional_calibration, data_shape_n in zip(src_dimensional_calibrations, data_shape)]
return DataAndMetadata.new_data_and_metadata(calculate_data(), dimensional_calibrations=dimensional_calibrations)
def function_ifft(data_and_metadata: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
data_shape = data_and_metadata.data_shape
data_dtype = data_and_metadata.data_dtype
def calculate_data():
data = data_and_metadata.data
if data is None or not Image.is_data_valid(data):
return None
# scaling: numpy.sqrt(numpy.mean(numpy.absolute(data_copy)**2)) == numpy.sqrt(numpy.mean(numpy.absolute(data_copy_fft)**2))
# see https://gist.github.com/endolith/1257010
if Image.is_data_1d(data):
scaling = numpy.sqrt(data_shape[0])
return scipy.fftpack.ifft(scipy.fftpack.ifftshift(data) * scaling)
elif Image.is_data_2d(data):
data_copy = data.copy() # let other threads use data while we're processing
scaling = numpy.sqrt(data_shape[1] * data_shape[0])
return scipy.fftpack.ifft2(scipy.fftpack.ifftshift(data_copy) * scaling)
else:
raise NotImplementedError()
src_dimensional_calibrations = data_and_metadata.dimensional_calibrations
if not Image.is_shape_and_dtype_valid(data_shape, data_dtype) or src_dimensional_calibrations is None:
return None
assert len(src_dimensional_calibrations) == len(
Image.dimensional_shape_from_shape_and_dtype(data_shape, data_dtype))
def remove_one_slash(s):
if s.startswith("1/"):
return s[2:]
else:
return "1/" + s
dimensional_calibrations = [Calibration.Calibration(0.0, 1.0 / (dimensional_calibration.scale * data_shape_n),
remove_one_slash(dimensional_calibration.units)) for
dimensional_calibration, data_shape_n in zip(src_dimensional_calibrations, data_shape)]
return DataAndMetadata.new_data_and_metadata(calculate_data(), dimensional_calibrations=dimensional_calibrations)
def function_autocorrelate(data_and_metadata: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
def calculate_data():
data = data_and_metadata.data
if data is None or not Image.is_data_valid(data):
return None
if Image.is_data_2d(data):
data_copy = data.copy() # let other threads use data while we're processing
data_std = data_copy.std(dtype=numpy.float64)
if data_std != 0.0:
data_norm = (data_copy - data_copy.mean(dtype=numpy.float64)) / data_std
else:
data_norm = data_copy
scaling = 1.0 / (data_norm.shape[0] * data_norm.shape[1])
data_norm = numpy.fft.rfft2(data_norm)
return numpy.fft.fftshift(numpy.fft.irfft2(data_norm * numpy.conj(data_norm))) * scaling
# this gives different results. why? because for some reason scipy pads out to 1023 and does calculation.
# see https://github.com/scipy/scipy/blob/master/scipy/signal/signaltools.py
# return scipy.signal.fftconvolve(data_copy, numpy.conj(data_copy), mode='same')
return None
if data_and_metadata is None:
return None
return DataAndMetadata.new_data_and_metadata(calculate_data(), dimensional_calibrations=data_and_metadata.dimensional_calibrations)
def function_crosscorrelate(*args) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
if len(args) != 2:
return None
data_and_metadata1, data_and_metadata2 = args[0], args[1]
data_and_metadata1 = DataAndMetadata.promote_ndarray(data_and_metadata1)
data_and_metadata2 = DataAndMetadata.promote_ndarray(data_and_metadata2)
shape = DataAndMetadata.determine_shape(data_and_metadata1, data_and_metadata2)
data_and_metadata1 = DataAndMetadata.promote_constant(data_and_metadata1, shape)
data_and_metadata2 = DataAndMetadata.promote_constant(data_and_metadata2, shape)
def calculate_data():
data1 = data_and_metadata1.data
data2 = data_and_metadata2.data
if data1 is None or data2 is None:
return None
if Image.is_data_2d(data1) and Image.is_data_2d(data2):
data_std1 = data1.std(dtype=numpy.float64)
if data_std1 != 0.0:
norm1 = (data1 - data1.mean(dtype=numpy.float64)) / data_std1
else:
norm1 = data1
data_std2 = data2.std(dtype=numpy.float64)
if data_std2 != 0.0:
norm2 = (data2 - data2.mean(dtype=numpy.float64)) / data_std2
else:
norm2 = data2
scaling = 1.0 / (norm1.shape[0] * norm1.shape[1])
return numpy.fft.fftshift(numpy.fft.irfft2(numpy.fft.rfft2(norm1) * numpy.conj(numpy.fft.rfft2(norm2)))) * scaling
# this gives different results. why? because for some reason scipy pads out to 1023 and does calculation.
# see https://github.com/scipy/scipy/blob/master/scipy/signal/signaltools.py
# return scipy.signal.fftconvolve(data1.copy(), numpy.conj(data2.copy()), mode='same')
return None
if data_and_metadata1 is None or data_and_metadata2 is None:
return None
return DataAndMetadata.new_data_and_metadata(calculate_data(), dimensional_calibrations=data_and_metadata1.dimensional_calibrations)
def function_register(xdata1: DataAndMetadata.DataAndMetadata, xdata2: DataAndMetadata.DataAndMetadata, upsample_factor: int, subtract_means: bool, bounds: typing.Union[NormRectangleType, NormIntervalType]=None) -> typing.Tuple[float, ...]:
# FUTURE: use scikit.image register_translation
xdata1 = DataAndMetadata.promote_ndarray(xdata1)
xdata2 = DataAndMetadata.promote_ndarray(xdata2)
# data shape and descriptors should match
assert xdata1.data_shape == xdata2.data_shape
assert xdata1.data_descriptor == xdata2.data_descriptor
# get the raw data
data1 = xdata1.data
data2 = xdata2.data
if data1 is None:
return tuple()
if data2 is None:
return tuple()
# take the slice if there is one
if bounds is not None:
d_rank = xdata1.datum_dimension_count
shape = data1.shape
bounds_pixels = numpy.rint(numpy.array(bounds) * numpy.array(shape)).astype(numpy.int_)
bounds_slice: typing.Optional[typing.Union[slice, typing.Tuple[slice, ...]]]
if d_rank == 1:
bounds_slice = slice(max(0, bounds_pixels[0]), min(shape[0], bounds_pixels[1]))
elif d_rank == 2:
bounds_slice = (slice(max(0, bounds_pixels[0][0]), min(shape[0], bounds_pixels[0][0]+bounds_pixels[1][0])),
slice(max(0, bounds_pixels[0][1]), min(shape[1], bounds_pixels[0][1]+bounds_pixels[1][1])))
else:
bounds_slice = None
data1 = data1[bounds_slice]
data2 = data2[bounds_slice]
# subtract the means if desired
if subtract_means:
data1 = data1 - numpy.average(data1)
data2 = data2 - numpy.average(data2)
assert data1 is not None
assert data2 is not None
# adjust the dimensions so 1D data is always nx1
add_before = 0
while len(data1.shape) > 1 and data1.shape[0] == 1:
data1 = numpy.squeeze(data1, axis=0)
data2 = numpy.squeeze(data2, axis=0)
add_before += 1
add_after = 0
while len(data1.shape) > 1 and data1.shape[-1] == 1:
data1 = numpy.squeeze(data1, axis=-1)
data2 = numpy.squeeze(data2, axis=-1)
add_after += 1
do_squeeze = False
if len(data1.shape) == 1:
data1 = data1[..., numpy.newaxis]
data2 = data2[..., numpy.newaxis]
do_squeeze = True
# carry out the registration
result = ImageRegistration.dftregistration(data1, data2, upsample_factor)#[0:d_rank]
# adjust results to match input data
if do_squeeze:
result = result[0:-1]
for _ in range(add_before):
result = (numpy.zeros_like(result[0]), ) + result
for _ in range(add_after):
result = result + (numpy.zeros_like(result[0]), )
return result
def function_match_template(image_xdata: DataAndMetadata.DataAndMetadata, template_xdata: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
"""
Calculates the normalized cross-correlation for a template with an image. The returned xdata will have the same
shape as `image_xdata`.
Inputs can be 1D or 2D and the template must be smaller than or the same size as the image.
"""
image_xdata = DataAndMetadata.promote_ndarray(image_xdata)
template_xdata = DataAndMetadata.promote_ndarray(template_xdata)
assert image_xdata.is_data_2d or image_xdata.is_data_1d
assert template_xdata.is_data_2d or template_xdata.is_data_1d
assert image_xdata.data_descriptor == template_xdata.data_descriptor
# The template needs to be the smaller of the two if they have different shape
assert numpy.less_equal(template_xdata.data_shape, image_xdata.data_shape).all()
image = image_xdata.data
template = template_xdata.data
assert image is not None
assert template is not None
squeeze = False
if image_xdata.is_data_1d:
image = image[..., numpy.newaxis]
template = template[..., numpy.newaxis]
assert image is not None
assert template is not None
squeeze = True
ccorr = TemplateMatching.match_template(image, template)
if squeeze:
ccorr = numpy.squeeze(ccorr)
return DataAndMetadata.new_data_and_metadata(ccorr, dimensional_calibrations=image_xdata.dimensional_calibrations)
def function_register_template(image_xdata: DataAndMetadata.DataAndMetadata, template_xdata: DataAndMetadata.DataAndMetadata) -> typing.Tuple[float, typing.Tuple[float, ...]]:
"""
Calculates and returns the position of a template on an image. The returned values are the intensity if the
normalized cross-correlation peak (between -1 and 1) and the sub-pixel position of the template on the image.
The sub-pixel position is calculated by fitting a parabola to the tip of the cross-correlation peak.
Inputs can be 1D or 2D and the template must be smaller than or the same size as the image.
"""
image_xdata = DataAndMetadata.promote_ndarray(image_xdata)
template_xdata = DataAndMetadata.promote_ndarray(template_xdata)
ccorr_xdata = function_match_template(image_xdata, template_xdata)
if ccorr_xdata:
error, ccoeff, max_pos = TemplateMatching.find_ccorr_max(ccorr_xdata.data)
if not error:
return ccoeff, tuple(max_pos[i] - image_xdata.data_shape[i] * 0.5 for i in range(len(image_xdata.data_shape)))
return 0.0, (0.0, ) * len(image_xdata.data_shape)
def function_shift(src: DataAndMetadata.DataAndMetadata, shift: typing.Tuple[float, ...], *, order: int = 1) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
src = DataAndMetadata.promote_ndarray(src)
if src:
src_data = src._data_ex
shifted = scipy.ndimage.shift(src_data, shift, order=order, cval=numpy.mean(src_data))
return DataAndMetadata.new_data_and_metadata(numpy.squeeze(shifted))
return None
def function_fourier_shift(src: DataAndMetadata.DataAndMetadata, shift: typing.Tuple[float, ...]) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
src = DataAndMetadata.promote_ndarray(src)
src_data = numpy.fft.fftn(src.data)
do_squeeze = False
if len(src_data.shape) == 1:
src_data = src_data[..., numpy.newaxis]
shift = tuple(shift) + (1,)
do_squeeze = True
# NOTE: fourier_shift assumes non-fft-shifted data.
shifted = numpy.fft.ifftn(scipy.ndimage.fourier_shift(src_data, shift)).real
shifted = numpy.squeeze(shifted) if do_squeeze else shifted
return DataAndMetadata.new_data_and_metadata(shifted)
def function_align(src: DataAndMetadata.DataAndMetadata, target: DataAndMetadata.DataAndMetadata, upsample_factor: int, bounds: typing.Union[NormRectangleType, NormIntervalType] = None) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
"""Aligns target to src and returns align target, using Fourier space."""
src = DataAndMetadata.promote_ndarray(src)
target = DataAndMetadata.promote_ndarray(target)
return function_shift(target, function_register(src, target, upsample_factor, True, bounds=bounds))
def function_fourier_align(src: DataAndMetadata.DataAndMetadata, target: DataAndMetadata.DataAndMetadata, upsample_factor: int, bounds: typing.Union[NormRectangleType, NormIntervalType] = None) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
"""Aligns target to src and returns align target, using Fourier space."""
src = DataAndMetadata.promote_ndarray(src)
target = DataAndMetadata.promote_ndarray(target)
return function_fourier_shift(target, function_register(src, target, upsample_factor, True, bounds=bounds))
def function_sequence_register_translation(src: DataAndMetadata.DataAndMetadata, upsample_factor: int, subtract_means: bool, bounds: typing.Union[NormRectangleType, NormIntervalType] = None) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
# measures shift relative to last position in sequence
# only works on sequences
src = DataAndMetadata.promote_ndarray(src)
assert src.is_sequence
d_rank = src.datum_dimension_count
if len(src.data_shape) <= d_rank:
return None
if d_rank < 1 or d_rank > 2:
return None
src_shape = tuple(src.data_shape)
s_shape = src_shape[0:-d_rank]
c = int(numpy.product(s_shape))
result = numpy.empty(s_shape + (d_rank, ))
previous_data = None
src_data = src._data_ex
for i in range(c):
ii = numpy.unravel_index(i, s_shape) + (Ellipsis, )
if previous_data is None:
previous_data = src_data[ii]
result[0, ...] = 0
else:
current_data = src_data[ii]
result[ii] = function_register(previous_data, current_data, upsample_factor, subtract_means, bounds=bounds)
previous_data = current_data
intensity_calibration = src.dimensional_calibrations[1] # not the sequence dimension
return DataAndMetadata.new_data_and_metadata(result, intensity_calibration=intensity_calibration, data_descriptor=DataAndMetadata.DataDescriptor(True, 0, 1))
def function_sequence_measure_relative_translation(src: DataAndMetadata.DataAndMetadata, ref: DataAndMetadata.DataAndMetadata, upsample_factor: int, subtract_means: bool, bounds: typing.Union[NormRectangleType, NormIntervalType] = None) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
# measures shift at each point in sequence/collection relative to reference
src = DataAndMetadata.promote_ndarray(src)
d_rank = src.datum_dimension_count
if len(src.data_shape) <= d_rank:
return None
if d_rank < 1 or d_rank > 2:
return None
src_shape = tuple(src.data_shape)
s_shape = src_shape[0:-d_rank]
c = int(numpy.product(s_shape))
result = numpy.empty(s_shape + (d_rank, ))
src_data = src._data_ex
for i in range(c):
ii = numpy.unravel_index(i, s_shape)
current_data = src_data[ii]
result[ii] = function_register(ref, current_data, upsample_factor, subtract_means, bounds=bounds)
intensity_calibration = src.dimensional_calibrations[1] # not the sequence dimension
return DataAndMetadata.new_data_and_metadata(result, intensity_calibration=intensity_calibration, data_descriptor=DataAndMetadata.DataDescriptor(src.is_sequence, src.collection_dimension_count, 1))
def function_squeeze_measurement(src: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
# squeezes a measurement of a sequence or collection so that it can be sensibly displayed
src = DataAndMetadata.promote_ndarray(src)
data = src._data_ex
descriptor = src.data_descriptor
calibrations = list(src.dimensional_calibrations)
if descriptor.is_sequence and data.shape[0] == 1:
data = numpy.squeeze(data, axis=0)
descriptor = DataAndMetadata.DataDescriptor(False, descriptor.collection_dimension_count, descriptor.datum_dimension_count)
calibrations.pop(0)
for index in reversed(descriptor.collection_dimension_indexes):
if data.shape[index] == 1:
data = numpy.squeeze(data, axis=index)
descriptor = DataAndMetadata.DataDescriptor(descriptor.is_sequence, descriptor.collection_dimension_count - 1, descriptor.datum_dimension_count)
calibrations.pop(index)
for index in reversed(descriptor.datum_dimension_indexes):
if data.shape[index] == 1:
if descriptor.datum_dimension_count > 1:
data = numpy.squeeze(data, axis=index)
descriptor = DataAndMetadata.DataDescriptor(descriptor.is_sequence, descriptor.collection_dimension_count, descriptor.datum_dimension_count - 1)
calibrations.pop(index)
elif descriptor.collection_dimension_count > 0:
data = numpy.squeeze(data, axis=index)
descriptor = DataAndMetadata.DataDescriptor(descriptor.is_sequence, 0, descriptor.collection_dimension_count)
calibrations.pop(index)
elif descriptor.is_sequence:
data = numpy.squeeze(data, axis=index)
descriptor = DataAndMetadata.DataDescriptor(False, 0, 1)
calibrations.pop(index)
intensity_calibration = src.intensity_calibration
intensity_calibration.offset = 0.0
return DataAndMetadata.new_data_and_metadata(data, intensity_calibration=intensity_calibration, dimensional_calibrations=calibrations, data_descriptor=descriptor)
def function_sequence_align(src: DataAndMetadata.DataAndMetadata, upsample_factor: int, bounds: typing.Union[NormRectangleType, NormIntervalType] = None) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
src = DataAndMetadata.promote_ndarray(src)
d_rank = src.datum_dimension_count
if len(src.data_shape) <= d_rank:
return None
if d_rank < 1 or d_rank > 2:
return None
src_shape = list(src.data_shape)
s_shape = src_shape[0:-d_rank]
c = int(numpy.product(s_shape))
ref = src[numpy.unravel_index(0, s_shape) + (Ellipsis, )]
translations = function_sequence_measure_relative_translation(src, ref, upsample_factor, True, bounds=bounds)
if not translations:
return None
result_data = numpy.copy(src.data)
for i in range(1, c):
ii = numpy.unravel_index(i, s_shape) + (Ellipsis, )
current_xdata = DataAndMetadata.new_data_and_metadata(numpy.copy(result_data[ii]))
translation = translations._data_ex[numpy.unravel_index(i, s_shape)]
shift_xdata = function_shift(current_xdata, tuple(translation))
if shift_xdata:
result_data[ii] = shift_xdata.data
return DataAndMetadata.new_data_and_metadata(result_data, intensity_calibration=src.intensity_calibration, dimensional_calibrations=src.dimensional_calibrations, data_descriptor=src.data_descriptor)
def function_sequence_fourier_align(src: DataAndMetadata.DataAndMetadata, upsample_factor: int, bounds: typing.Union[NormRectangleType, NormIntervalType] = None) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
src = DataAndMetadata.promote_ndarray(src)
d_rank = src.datum_dimension_count
if len(src.data_shape) <= d_rank:
return None
if d_rank < 1 or d_rank > 2:
return None
src_shape = list(src.data_shape)
s_shape = src_shape[0:-d_rank]
c = int(numpy.product(s_shape))
ref = src[numpy.unravel_index(0, s_shape) + (Ellipsis, )]
translations = function_sequence_measure_relative_translation(src, ref, upsample_factor, True, bounds=bounds)
if not translations:
return None
result_data = numpy.copy(src.data)
for i in range(1, c):
ii = numpy.unravel_index(i, s_shape) + (Ellipsis, )
current_xdata = DataAndMetadata.new_data_and_metadata(numpy.copy(result_data[ii]))
translation = translations._data_ex[numpy.unravel_index(i, s_shape)]
shift_xdata = function_fourier_shift(current_xdata, tuple(translation))
if shift_xdata:
result_data[ii] = shift_xdata.data
return DataAndMetadata.new_data_and_metadata(result_data, intensity_calibration=src.intensity_calibration, dimensional_calibrations=src.dimensional_calibrations, data_descriptor=src.data_descriptor)
def function_sequence_integrate(src: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
src = DataAndMetadata.promote_ndarray(src)
if not src.is_sequence:
return None
dim = src.data_shape[1:]
if len(dim) < 1:
return None
result = numpy.sum(src._data_ex, axis=0)
intensity_calibration = src.intensity_calibration
dimensional_calibrations = src.dimensional_calibrations[1:]
data_descriptor = DataAndMetadata.DataDescriptor(False, src.data_descriptor.collection_dimension_count, src.data_descriptor.datum_dimension_count)
return DataAndMetadata.new_data_and_metadata(result, intensity_calibration=intensity_calibration, dimensional_calibrations=dimensional_calibrations, data_descriptor=data_descriptor)
def function_sequence_trim(src: DataAndMetadata.DataAndMetadata, trim_start: int, trim_end: int) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
src = DataAndMetadata.promote_ndarray(src)
if not src.is_sequence:
return None
c = src.sequence_dimension_shape[0]
dim = src.data_shape[1:]
if len(dim) < 1:
return None
cs = max(0, int(trim_start))
ce = min(c, max(cs + 1, int(trim_end)))
return src[cs:ce]
def function_sequence_insert(src1: DataAndMetadata.DataAndMetadata, src2: DataAndMetadata.DataAndMetadata, position: int) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
src1 = DataAndMetadata.promote_ndarray(src1)
src2 = DataAndMetadata.promote_ndarray(src2)
if not src1.is_sequence or not src2.is_sequence:
return None
if src1.data_shape[1:] != src2.data_shape[1:]:
return None
c = src1.sequence_dimension_shape[0]
dim = src1.data_shape[1:]
if len(dim) < 1 or len(dim) > 2:
return None
channel = max(0, min(c, int(position)))
result = numpy.vstack([src1._data_ex[:channel], src2._data_ex, src1._data_ex[channel:]])
intensity_calibration = src1.intensity_calibration
dimensional_calibrations = src1.dimensional_calibrations
data_descriptor = src1.data_descriptor
return DataAndMetadata.new_data_and_metadata(result, intensity_calibration=intensity_calibration, dimensional_calibrations=dimensional_calibrations, data_descriptor=data_descriptor)
def function_sequence_concatenate(src1: DataAndMetadata.DataAndMetadata, src2: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
src1 = DataAndMetadata.promote_ndarray(src1)
src2 = DataAndMetadata.promote_ndarray(src2)
return function_sequence_insert(src1, src2, src1.data_shape[0])
def function_sequence_join(data_and_metadata_list: typing.Sequence[DataAndMetadata.DataAndMetadata]) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
if not data_and_metadata_list:
return None
data_and_metadata_list = [DataAndMetadata.promote_ndarray(data_and_metadata) for data_and_metadata in data_and_metadata_list]
def ensure_sequence(xdata):
if xdata.is_sequence:
return xdata
sequence_data = numpy.reshape(xdata.data, (1,) + xdata.data.shape)
dimensional_calibrations = [Calibration.Calibration()] + xdata.dimensional_calibrations
data_descriptor = DataAndMetadata.DataDescriptor(True, xdata.collection_dimension_count, xdata.datum_dimension_count)
return DataAndMetadata.new_data_and_metadata(sequence_data, dimensional_calibrations=dimensional_calibrations, intensity_calibration=xdata.intensity_calibration, data_descriptor=data_descriptor)
sequence_xdata_list = [ensure_sequence(xdata) for xdata in data_and_metadata_list]
xdata_0 = sequence_xdata_list[0]
non_sequence_shape_0 = xdata_0.data_shape[1:]
for xdata in sequence_xdata_list[1:]:
if xdata.data_shape[1:] != non_sequence_shape_0:
return None
return function_concatenate(sequence_xdata_list)
def function_sequence_extract(src: DataAndMetadata.DataAndMetadata, position: int) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
src = DataAndMetadata.promote_ndarray(src)
if not src.is_sequence:
return None
c = src.sequence_dimension_shape[0]
dim = src.data_shape[1:]
if len(dim) < 1:
return None
channel = max(0, min(c, int(position)))
return src[channel]
def function_sequence_split(src: DataAndMetadata.DataAndMetadata) -> typing.Optional[typing.List[DataAndMetadata.DataAndMetadata]]:
src = DataAndMetadata.promote_ndarray(src)
if not src.is_sequence:
return None
dim = src.data_shape[1:]
if len(dim) < 1:
return None
dimensional_calibrations = copy.deepcopy(src.dimensional_calibrations[1:])
data_descriptor = DataAndMetadata.DataDescriptor(False, src.collection_dimension_count, src.datum_dimension_count)
return [
DataAndMetadata.new_data_and_metadata(data, dimensional_calibrations=copy.deepcopy(dimensional_calibrations),
intensity_calibration=copy.deepcopy(src.intensity_calibration),
data_descriptor=copy.copy(data_descriptor)) for data in src._data_ex]
def function_make_elliptical_mask(data_shape: DataAndMetadata.ShapeType, center: NormPointType, size: NormSizeType, rotation: float) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_size = Geometry.IntSize.make(data_shape)
data_rect = Geometry.FloatRect(origin=Geometry.FloatPoint(), size=Geometry.FloatSize.make(data_size))
center_point = Geometry.map_point(Geometry.FloatPoint.make(center), Geometry.FloatRect.unit_rect(), data_rect)
size_size = Geometry.map_size(Geometry.FloatSize.make(size), Geometry.FloatRect.unit_rect(), data_rect)
mask = numpy.zeros((data_size.height, data_size.width))
bounds = Geometry.FloatRect.from_center_and_size(center_point, size_size)
if bounds.height <= 0 or bounds.width <= 0:
return DataAndMetadata.new_data_and_metadata(mask)
a, b = bounds.center.y, bounds.center.x
y, x = numpy.ogrid[-a:data_size.height - a, -b:data_size.width - b]
if rotation:
angle_sin = math.sin(rotation)
angle_cos = math.cos(rotation)
mask_eq = ((x * angle_cos - y * angle_sin) ** 2) / ((bounds.width / 2) * (bounds.width / 2)) + ((y * angle_cos + x * angle_sin) ** 2) / ((bounds.height / 2) * (bounds.height / 2)) <= 1
else:
mask_eq = x * x / ((bounds.width / 2) * (bounds.width / 2)) + y * y / ((bounds.height / 2) * (bounds.height / 2)) <= 1
mask[mask_eq] = 1
return DataAndMetadata.new_data_and_metadata(mask)
def function_fourier_mask(data_and_metadata: DataAndMetadata.DataAndMetadata, mask_data_and_metadata: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
mask_data_and_metadata = DataAndMetadata.promote_ndarray(mask_data_and_metadata)
shape = DataAndMetadata.determine_shape(data_and_metadata, mask_data_and_metadata)
data_and_metadata = DataAndMetadata.promote_constant(data_and_metadata, shape)
mask_data_and_metadata = DataAndMetadata.promote_constant(mask_data_and_metadata, shape)
def calculate_data():
data = data_and_metadata.data
mask_data = mask_data_and_metadata.data
if data is None or mask_data is None:
return None
if Image.is_data_2d(data) and Image.is_data_2d(mask_data):
try:
y_half = data.shape[0] // 2
y_half_p1 = y_half + 1
y_half_m1 = y_half - 1
y_low = 0 if data.shape[0] % 2 == 0 else None
x_half = data.shape[1] // 2
x_half_p1 = x_half + 1
x_half_m1 = x_half - 1
x_low = 0 if data.shape[1] % 2 == 0 else None
fourier_mask_data = numpy.empty_like(mask_data)
fourier_mask_data[y_half_p1:, x_half_p1:] = mask_data[y_half_p1:, x_half_p1:]
fourier_mask_data[y_half_p1:, x_half_m1:x_low:-1] = mask_data[y_half_p1:, x_half_m1:x_low:-1]
fourier_mask_data[y_half_m1:y_low:-1, x_half_m1:x_low:-1] = mask_data[y_half_p1:, x_half_p1:]
fourier_mask_data[y_half_m1:y_low:-1, x_half_p1:] = mask_data[y_half_p1:, x_half_m1:x_low:-1]
fourier_mask_data[0, :] = mask_data[0, :]
fourier_mask_data[:, 0] = mask_data[:, 0]
fourier_mask_data[y_half, :] = mask_data[y_half, :]
fourier_mask_data[:, x_half] = mask_data[:, x_half]
return data * fourier_mask_data
except Exception as e:
print(e)
raise
return None
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=data_and_metadata.dimensional_calibrations)
def function_sobel(data_and_metadata: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
def calculate_data():
data = data_and_metadata.data
if not Image.is_data_valid(data):
return None
if Image.is_shape_and_dtype_rgb(data.shape, data.dtype):
rgb = numpy.empty(data.shape[:-1] + (3,), numpy.uint8)
rgb[..., 0] = scipy.ndimage.sobel(data[..., 0])
rgb[..., 1] = scipy.ndimage.sobel(data[..., 1])
rgb[..., 2] = scipy.ndimage.sobel(data[..., 2])
return rgb
elif Image.is_shape_and_dtype_rgba(data.shape, data.dtype):
rgba = numpy.empty(data.shape[:-1] + (4,), numpy.uint8)
rgba[..., 0] = scipy.ndimage.sobel(data[..., 0])
rgba[..., 1] = scipy.ndimage.sobel(data[..., 1])
rgba[..., 2] = scipy.ndimage.sobel(data[..., 2])
rgba[..., 3] = data[..., 3]
return rgba
else:
return scipy.ndimage.sobel(data)
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=data_and_metadata.dimensional_calibrations)
def function_laplace(data_and_metadata: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
def calculate_data():
data = data_and_metadata.data
if not Image.is_data_valid(data):
return None
if Image.is_shape_and_dtype_rgb(data.shape, data.dtype):
rgb = numpy.empty(data.shape[:-1] + (3,), numpy.uint8)
rgb[..., 0] = scipy.ndimage.laplace(data[..., 0])
rgb[..., 1] = scipy.ndimage.laplace(data[..., 1])
rgb[..., 2] = scipy.ndimage.laplace(data[..., 2])
return rgb
elif Image.is_shape_and_dtype_rgba(data.shape, data.dtype):
rgba = numpy.empty(data.shape[:-1] + (4,), numpy.uint8)
rgba[..., 0] = scipy.ndimage.laplace(data[..., 0])
rgba[..., 1] = scipy.ndimage.laplace(data[..., 1])
rgba[..., 2] = scipy.ndimage.laplace(data[..., 2])
rgba[..., 3] = data[..., 3]
return rgba
else:
return scipy.ndimage.laplace(data)
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=data_and_metadata.dimensional_calibrations)
def function_gaussian_blur(data_and_metadata: DataAndMetadata.DataAndMetadata, sigma: float) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
sigma = float(sigma)
def calculate_data():
data = data_and_metadata.data
if not Image.is_data_valid(data):
return None
return scipy.ndimage.gaussian_filter(data, sigma=sigma)
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=data_and_metadata.dimensional_calibrations)
def function_median_filter(data_and_metadata: DataAndMetadata.DataAndMetadata, size: int) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
size = max(min(int(size), 999), 1)
def calculate_data():
data = data_and_metadata.data
if not Image.is_data_valid(data):
return None
if Image.is_shape_and_dtype_rgb(data.shape, data.dtype):
rgb = numpy.empty(data.shape[:-1] + (3,), numpy.uint8)
rgb[..., 0] = scipy.ndimage.median_filter(data[..., 0], size=size)
rgb[..., 1] = scipy.ndimage.median_filter(data[..., 1], size=size)
rgb[..., 2] = scipy.ndimage.median_filter(data[..., 2], size=size)
return rgb
elif Image.is_shape_and_dtype_rgba(data.shape, data.dtype):
rgba = numpy.empty(data.shape[:-1] + (4,), numpy.uint8)
rgba[..., 0] = scipy.ndimage.median_filter(data[..., 0], size=size)
rgba[..., 1] = scipy.ndimage.median_filter(data[..., 1], size=size)
rgba[..., 2] = scipy.ndimage.median_filter(data[..., 2], size=size)
rgba[..., 3] = data[..., 3]
return rgba
else:
return scipy.ndimage.median_filter(data, size=size)
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=data_and_metadata.dimensional_calibrations)
def function_uniform_filter(data_and_metadata: DataAndMetadata.DataAndMetadata, size: int) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
size = max(min(int(size), 999), 1)
def calculate_data():
data = data_and_metadata.data
if not Image.is_data_valid(data):
return None
if Image.is_shape_and_dtype_rgb(data.shape, data.dtype):
rgb = numpy.empty(data.shape[:-1] + (3,), numpy.uint8)
rgb[..., 0] = scipy.ndimage.uniform_filter(data[..., 0], size=size)
rgb[..., 1] = scipy.ndimage.uniform_filter(data[..., 1], size=size)
rgb[..., 2] = scipy.ndimage.uniform_filter(data[..., 2], size=size)
return rgb
elif Image.is_shape_and_dtype_rgba(data.shape, data.dtype):
rgba = numpy.empty(data.shape[:-1] + (4,), numpy.uint8)
rgba[..., 0] = scipy.ndimage.uniform_filter(data[..., 0], size=size)
rgba[..., 1] = scipy.ndimage.uniform_filter(data[..., 1], size=size)
rgba[..., 2] = scipy.ndimage.uniform_filter(data[..., 2], size=size)
rgba[..., 3] = data[..., 3]
return rgba
else:
return scipy.ndimage.uniform_filter(data, size=size)
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=data_and_metadata.dimensional_calibrations)
def function_transpose_flip(data_and_metadata: DataAndMetadata.DataAndMetadata, transpose: bool=False, flip_v: bool=False, flip_h: bool=False) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
def calculate_data():
data = data_and_metadata.data
data_id = id(data)
if not Image.is_data_valid(data):
return None
if transpose:
if Image.is_shape_and_dtype_rgb_type(data.shape, data.dtype):
data = numpy.transpose(data, [1, 0, 2])
elif len(data_and_metadata.data_shape) == 2:
data = numpy.transpose(data, [1, 0])
if flip_h and len(data_and_metadata.data_shape) == 2:
data = numpy.fliplr(data)
if flip_v and len(data_and_metadata.data_shape) == 2:
data = numpy.flipud(data)
if id(data) == data_id: # ensure real data, not a view
data = data.copy()
return data
data_shape = data_and_metadata.data_shape
data_dtype = data_and_metadata.data_dtype
if not Image.is_shape_and_dtype_valid(data_shape, data_dtype):
return None
if transpose:
dimensional_calibrations = list(reversed(data_and_metadata.dimensional_calibrations))
else:
dimensional_calibrations = list(data_and_metadata.dimensional_calibrations)
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=dimensional_calibrations)
def function_invert(data_and_metadata: DataAndMetadata.DataAndMetadata) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
def calculate_data():
data = data_and_metadata.data
if not Image.is_data_valid(data):
return None
if Image.is_shape_and_dtype_rgb_type(data.shape, data.dtype):
if Image.is_data_rgba(data):
inverted = 255 - data[:]
inverted[...,3] = data[...,3]
return inverted
else:
return 255 - data[:]
else:
return -data[:]
data_shape = data_and_metadata.data_shape
data_dtype = data_and_metadata.data_dtype
if not Image.is_shape_and_dtype_valid(data_shape, data_dtype):
return None
dimensional_calibrations = data_and_metadata.dimensional_calibrations
return DataAndMetadata.new_data_and_metadata(calculate_data(), intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=dimensional_calibrations)
def function_crop(data_and_metadata: DataAndMetadata.DataAndMetadata, bounds: NormRectangleType) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
bounds_rect = Geometry.FloatRect.make(bounds)
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
data_shape = Geometry.IntSize.make(data_and_metadata.data_shape)
data_dtype = data_and_metadata.data_dtype
dimensional_calibrations = data_and_metadata.dimensional_calibrations
data = data_and_metadata._data_ex
if not Image.is_shape_and_dtype_valid(list(data_shape), data_dtype) or dimensional_calibrations is None:
return None
if not Image.is_data_valid(data):
return None
oheight = int(data_shape.height * bounds_rect.height)
owidth = int(data_shape.width * bounds_rect.width)
top = int(data_shape.height * bounds_rect.top)
left = int(data_shape.width * bounds_rect.left)
height = int(data_shape.height * bounds_rect.height)
width = int(data_shape.width * bounds_rect.width)
dtop = 0
dleft = 0
dheight = height
dwidth = width
if top < 0:
dheight += top
dtop -= top
height += top
top = 0
if top + height > data_shape.height:
dheight -= (top + height - data_shape.height)
height = data_shape.height - top
if left < 0:
dwidth += left
dleft -= left
width += left
left = 0
if left + width > data_shape.width:
dwidth -= (left + width- data_shape.width)
width = data_shape.width - left
data_dtype = data.dtype
assert data_dtype is not None
if data_and_metadata.is_data_rgb:
new_data = numpy.zeros((oheight, owidth, 3), dtype=data_dtype)
if height > 0 and width > 0:
new_data[dtop:dtop + dheight, dleft:dleft + dwidth] = data[top:top + height, left:left + width]
elif data_and_metadata.is_data_rgba:
new_data = numpy.zeros((oheight, owidth, 4), dtype=data_dtype)
if height > 0 and width > 0:
new_data[dtop:dtop + dheight, dleft:dleft + dwidth] = data[top:top + height, left:left + width]
else:
new_data = numpy.zeros((oheight, owidth), dtype=data_dtype)
if height > 0 and width > 0:
new_data[dtop:dtop + dheight, dleft:dleft + dwidth] = data[top:top + height, left:left + width]
cropped_dimensional_calibrations = list()
for index, dimensional_calibration in enumerate(dimensional_calibrations):
cropped_calibration = Calibration.Calibration(
dimensional_calibration.offset + data_shape[index] * bounds_rect.origin[index] * dimensional_calibration.scale,
dimensional_calibration.scale, dimensional_calibration.units)
cropped_dimensional_calibrations.append(cropped_calibration)
return DataAndMetadata.new_data_and_metadata(new_data, intensity_calibration=data_and_metadata.intensity_calibration, dimensional_calibrations=cropped_dimensional_calibrations)
def function_crop_rotated(data_and_metadata: DataAndMetadata.DataAndMetadata, bounds: NormRectangleType, angle: float) -> typing.Optional[DataAndMetadata.DataAndMetadata]:
bounds_rect = Geometry.FloatRect.make(bounds)
data_and_metadata = DataAndMetadata.promote_ndarray(data_and_metadata)
data_shape = Geometry.IntSize.make(data_and_metadata.data_shape)
data_dtype = data_and_metadata.data_dtype
dimensional_calibrations = data_and_metadata.dimensional_calibrations
data = data_and_metadata._data_ex
if not Image.is_shape_and_dtype_valid(list(data_shape), data_dtype) or dimensional_calibrations is None:
return None
if not Image.is_data_valid(data):
return None
top = round(data_shape.height * bounds_rect.top)
left = round(data_shape.width * bounds_rect.left)
height = round(data_shape.height * bounds_rect.height)
width = round(data_shape.width * bounds_rect.width)
x, y = numpy.meshgrid(numpy.arange(-(width // 2), width - width // 2), numpy.arange(-(height // 2), height - height // 2))
angle_sin = math.sin(angle)
angle_cos = math.cos(angle)
coords = [top + height // 2 + (y * angle_cos - x * angle_sin), left + width // 2 + (x * angle_cos + y * angle_sin)]
if data_and_metadata.is_data_rgb:
new_data = numpy.zeros(coords[0].shape + (3,), numpy.uint8)
new_data[..., 0] = scipy.ndimage.interpolation.map_coordinates(data[..., 0], coords)
new_data[..., 1] = scipy.ndimage.interpolation.map_coordinates(data[..., 1], coords)
new_data[..., 2] = scipy.ndimage.interpolation.map_coordinates(data[..., 2], coords)
elif data_and_metadata.is_data_rgba:
new_data = | numpy.zeros(coords[0].shape + (4,), numpy.uint8) | numpy.zeros |
import pandas as pd
import numpy as np
import matplotlib
matplotlib.use('agg')
import matplotlib.pyplot as plt
from matplotlib import cm, colors
from astropy.modeling import models, fitting
# Reading in all data files at once
import glob
path_normal ='/projects/p30137/ageller/testing/EBLSST/add_m5/output_files'
allFiles_normal = glob.glob(path_normal + "/*.csv")
path_fast = '/projects/p30137/ageller/testing/EBLSST/add_m5/fast/old/output_files'
allFiles_fast = glob.glob(path_fast + "/*.csv")
path_obsDist = '/projects/p30137/ageller/testing/EBLSST/add_m5/fast/old/obsDist/output_files'
allFiles_obsDist = glob.glob(path_obsDist + "/*.csv")
N_totalnormal_array = []
N_totalobservablenormal_array = []
N_totalrecoverablenormal_array = []
N_totalnormal_array_03 = []
N_totalobservablenormal_array_03 = []
N_totalrecoverablenormal_array_03 = []
N_totalnormal_array_1 = []
N_totalobservablenormal_array_1 = []
N_totalrecoverablenormal_array_1 = []
N_totalnormal_array_10 = []
N_totalobservablenormal_array_10 = []
N_totalrecoverablenormal_array_10 = []
N_totalnormal_array_30 = []
N_totalobservablenormal_array_30 = []
N_totalrecoverablenormal_array_30 = []
N_totalnormal_array_100 = []
N_totalobservablenormal_array_100 = []
N_totalrecoverablenormal_array_100 = []
N_totalnormal_array_1000 = []
N_totalobservablenormal_array_1000 = []
N_totalrecoverablenormal_array_1000 = []
N_totalnormal22_array = []
N_totalobservablenormal22_array = []
N_totalrecoverablenormal22_array = []
N_totalnormal22_array_03 = []
N_totalobservablenormal22_array_03 = []
N_totalrecoverablenormal22_array_03 = []
N_totalnormal22_array_1 = []
N_totalobservablenormal22_array_1 = []
N_totalrecoverablenormal22_array_1 = []
N_totalnormal22_array_10 = []
N_totalobservablenormal22_array_10 = []
N_totalrecoverablenormal22_array_10 = []
N_totalnormal22_array_30 = []
N_totalobservablenormal22_array_30 = []
N_totalrecoverablenormal22_array_30 = []
N_totalnormal22_array_100 = []
N_totalobservablenormal22_array_100 = []
N_totalrecoverablenormal22_array_100 = []
N_totalnormal22_array_1000 = []
N_totalobservablenormal22_array_1000 = []
N_totalrecoverablenormal22_array_1000 = []
N_totalnormal195_array = []
N_totalobservablenormal195_array = []
N_totalrecoverablenormal195_array = []
N_totalnormal195_array_03 = []
N_totalobservablenormal195_array_03 = []
N_totalrecoverablenormal195_array_03 = []
N_totalnormal195_array_1 = []
N_totalobservablenormal195_array_1 = []
N_totalrecoverablenormal195_array_1 = []
N_totalnormal195_array_10 = []
N_totalobservablenormal195_array_10 = []
N_totalrecoverablenormal195_array_10 = []
N_totalnormal195_array_30 = []
N_totalobservablenormal195_array_30 = []
N_totalrecoverablenormal195_array_30 = []
N_totalnormal195_array_100 = []
N_totalobservablenormal195_array_100 = []
N_totalrecoverablenormal195_array_100 = []
N_totalnormal195_array_1000 = []
N_totalobservablenormal195_array_1000 = []
N_totalrecoverablenormal195_array_1000 = []
N_totalfast_array = []
N_totalobservablefast_array = []
N_totalrecoverablefast_array = []
N_totalfast_array_03 = []
N_totalobservablefast_array_03 = []
N_totalrecoverablefast_array_03 = []
N_totalfast_array_1 = []
N_totalobservablefast_array_1 = []
N_totalrecoverablefast_array_1 = []
N_totalfast_array_10 = []
N_totalobservablefast_array_10 = []
N_totalrecoverablefast_array_10 = []
N_totalfast_array_30 = []
N_totalobservablefast_array_30 = []
N_totalrecoverablefast_array_30 = []
N_totalfast_array_100 = []
N_totalobservablefast_array_100 = []
N_totalrecoverablefast_array_100 = []
N_totalfast_array_1000 = []
N_totalobservablefast_array_1000 = []
N_totalrecoverablefast_array_1000 = []
N_totalfast22_array = []
N_totalobservablefast22_array = []
N_totalrecoverablefast22_array = []
N_totalfast22_array_03 = []
N_totalobservablefast22_array_03 = []
N_totalrecoverablefast22_array_03 = []
N_totalfast22_array_1 = []
N_totalobservablefast22_array_1 = []
N_totalrecoverablefast22_array_1 = []
N_totalfast22_array_10 = []
N_totalobservablefast22_array_10 = []
N_totalrecoverablefast22_array_10 = []
N_totalfast22_array_30 = []
N_totalobservablefast22_array_30 = []
N_totalrecoverablefast22_array_30 = []
N_totalfast22_array_100 = []
N_totalobservablefast22_array_100 = []
N_totalrecoverablefast22_array_100 = []
N_totalfast22_array_1000 = []
N_totalobservablefast22_array_1000 = []
N_totalrecoverablefast22_array_1000 = []
N_totalfast195_array = []
N_totalobservablefast195_array = []
N_totalrecoverablefast195_array = []
N_totalfast195_array_03 = []
N_totalobservablefast195_array_03 = []
N_totalrecoverablefast195_array_03 = []
N_totalfast195_array_1 = []
N_totalobservablefast195_array_1 = []
N_totalrecoverablefast195_array_1 = []
N_totalfast195_array_10 = []
N_totalobservablefast195_array_10 = []
N_totalrecoverablefast195_array_10 = []
N_totalfast195_array_30 = []
N_totalobservablefast195_array_30 = []
N_totalrecoverablefast195_array_30 = []
N_totalfast195_array_100 = []
N_totalobservablefast195_array_100 = []
N_totalrecoverablefast195_array_100 = []
N_totalfast195_array_1000 = []
N_totalobservablefast195_array_1000 = []
N_totalrecoverablefast195_array_1000 = []
N_totalobsDist_array = []
N_totalobservableobsDist_array = []
N_totalrecoverableobsDist_array = []
N_totalobsDist_array_03 = []
N_totalobservableobsDist_array_03 = []
N_totalrecoverableobsDist_array_03 = []
N_totalobsDist_array_1 = []
N_totalobservableobsDist_array_1 = []
N_totalrecoverableobsDist_array_1 = []
N_totalobsDist_array_10 = []
N_totalobservableobsDist_array_10 = []
N_totalrecoverableobsDist_array_10 = []
N_totalobsDist_array_30 = []
N_totalobservableobsDist_array_30 = []
N_totalrecoverableobsDist_array_30 = []
N_totalobsDist_array_100 = []
N_totalobservableobsDist_array_100 = []
N_totalrecoverableobsDist_array_100 = []
N_totalobsDist_array_1000 = []
N_totalobservableobsDist_array_1000 = []
N_totalrecoverableobsDist_array_1000 = []
N_totalobsDist22_array = []
N_totalobservableobsDist22_array = []
N_totalrecoverableobsDist22_array = []
N_totalobsDist22_array_03 = []
N_totalobservableobsDist22_array_03 = []
N_totalrecoverableobsDist22_array_03 = []
N_totalobsDist22_array_1 = []
N_totalobservableobsDist22_array_1 = []
N_totalrecoverableobsDist22_array_1 = []
N_totalobsDist22_array_10 = []
N_totalobservableobsDist22_array_10 = []
N_totalrecoverableobsDist22_array_10 = []
N_totalobsDist22_array_30 = []
N_totalobservableobsDist22_array_30 = []
N_totalrecoverableobsDist22_array_30 = []
N_totalobsDist22_array_100 = []
N_totalobservableobsDist22_array_100 = []
N_totalrecoverableobsDist22_array_100 = []
N_totalobsDist22_array_1000 = []
N_totalobservableobsDist22_array_1000 = []
N_totalrecoverableobsDist22_array_1000 = []
N_totalobsDist195_array = []
N_totalobservableobsDist195_array = []
N_totalrecoverableobsDist195_array = []
N_totalobsDist195_array_03 = []
N_totalobservableobsDist195_array_03 = []
N_totalrecoverableobsDist195_array_03 = []
N_totalobsDist195_array_1 = []
N_totalobservableobsDist195_array_1 = []
N_totalrecoverableobsDist195_array_1 = []
N_totalobsDist195_array_10 = []
N_totalobservableobsDist195_array_10 = []
N_totalrecoverableobsDist195_array_10 = []
N_totalobsDist195_array_30 = []
N_totalobservableobsDist195_array_30 = []
N_totalrecoverableobsDist195_array_30 = []
N_totalobsDist195_array_100 = []
N_totalobservableobsDist195_array_100 = []
N_totalrecoverableobsDist195_array_100 = []
N_totalobsDist195_array_1000 = []
N_totalobservableobsDist195_array_1000 = []
N_totalrecoverableobsDist195_array_1000 = []
def fitRagfb():
x = [0.05, 0.1, 1, 8, 15] #estimates of midpoints in bins, and using this: https:/sites.uni.edu/morgans/astro/course/Notes/section2/spectralmasses.html
y = [0.20, 0.35, 0.50, 0.70, 0.75]
init = models.PowerLaw1D(amplitude=0.5, x_0=1, alpha=-1.)
fitter = fitting.LevMarLSQFitter()
fit = fitter(init, x, y)
return fit
fbFit= fitRagfb()
mbins = np.arange(0,10, 0.1, dtype='float')
cutP = 0.10 #condition on recoverability/tolerance
for filenormal_ in sorted(allFiles_normal):
filename = filenormal_[60:]
fileid = filename.strip('output_file.csv')
print ("I'm starting " + fileid)
datnormal = pd.read_csv(filenormal_, sep = ',', header=2)
PeriodIn = datnormal['p'] # input period -- 'p' in data file
##########################################################
datnormal1 = pd.read_csv(filenormal_, sep = ',', header=0, nrows=1)
N_tri = datnormal1["NstarsTRILEGAL"][0]
#print("N_tri = ", N_tri)
Nall = len(PeriodIn)
m1hAll0, m1b = np.histogram(datnormal["m1"], bins=mbins)
dm1 = np.diff(m1b)
m1val = m1b[:-1] + dm1/2.
fb = np.sum(m1hAll0/Nall*fbFit(m1val))
N_mult = N_tri*fb
##########################################################
if len(PeriodIn) == 0.:
continue
if N_tri == 0:
continue
else:
PeriodOut = datnormal['LSM_PERIOD'] #LSM_PERIOD in data file
appMagMean = datnormal['appMagMean'] #apparent magnitude, will use to make cuts for 24 (default), 22, and then Kepler's range (?? -- brighter than LSST can manage-- to 19) OR 19.5 (SNR = 10)
observable = datnormal.loc[PeriodOut != -999].index
observable_03 = datnormal.loc[(PeriodIn <= 0.3) & (PeriodOut != -999)].index
observable_1 = datnormal.loc[(PeriodIn <= 1) & (PeriodOut != -999)].index
observable_10 = datnormal.loc[(PeriodIn <= 10) & (PeriodOut != -999)].index
observable_30 = datnormal.loc[(PeriodIn <= 30) & (PeriodOut != -999)].index
observable_100 = datnormal.loc[(PeriodIn <= 100) & (PeriodOut != -999)].index
observable_1000 = datnormal.loc[(PeriodIn <= 1000) & (PeriodOut != -999)].index
observable_22 = datnormal.loc[(PeriodOut != -999) & (appMagMean <= 22.)].index
observable_03_22 = datnormal.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_1_22 = datnormal.loc[(PeriodIn <= 1) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_10_22 = datnormal.loc[(PeriodIn <= 10) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_30_22 = datnormal.loc[(PeriodIn <= 30) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_100_22 = datnormal.loc[(PeriodIn <= 100) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_1000_22 = datnormal.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_195 = datnormal.loc[(PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_03_195 = datnormal.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_1_195 = datnormal.loc[(PeriodIn <= 1) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_10_195 = datnormal.loc[(PeriodIn <= 10) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_30_195 = datnormal.loc[(PeriodIn <= 30) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_100_195 = datnormal.loc[(PeriodIn <= 100) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_1000_195 = datnormal.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
fullP = abs(PeriodOut - PeriodIn)/PeriodIn
halfP = abs(PeriodOut - 0.5*PeriodIn)/(0.5*PeriodIn)
twiceP = abs(PeriodOut - 2*PeriodIn)/(2*PeriodIn)
recoverable = datnormal.loc[(PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_03 = datnormal.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_1 = datnormal.loc[(PeriodIn <= 1) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_10 = datnormal.loc[(PeriodIn <= 10) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_30 = datnormal.loc[(PeriodIn <= 30) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_100 = datnormal.loc[(PeriodIn <= 100) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_1000 = datnormal.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_22 = datnormal.loc[(PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_03_22 = datnormal.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_1_22 = datnormal.loc[(PeriodIn <= 1) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_10_22 = datnormal.loc[(PeriodIn <= 10) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_30_22 = datnormal.loc[(PeriodIn <= 30) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_100_22 = datnormal.loc[(PeriodIn <= 100) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_1000_22 = datnormal.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_195 = datnormal.loc[(PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_03_195 = datnormal.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_1_195 = datnormal.loc[(PeriodIn <= 1) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_10_195 = datnormal.loc[(PeriodIn <= 10) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_30_195 = datnormal.loc[(PeriodIn <= 30) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_100_195 = datnormal.loc[(PeriodIn <= 100) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_1000_195 = datnormal.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
P03 = datnormal.loc[PeriodIn <= 0.3].index
P1 = datnormal.loc[PeriodIn <= 1].index
P10 = datnormal.loc[PeriodIn <= 10].index
P30 = datnormal.loc[PeriodIn <= 30].index
P100 = datnormal.loc[PeriodIn <= 100].index
P1000 = datnormal.loc[PeriodIn <= 1000].index
P_22 = datnormal.loc[appMagMean <= 22.].index
P03_22 = datnormal.loc[(PeriodIn <= 0.3) & (appMagMean <= 22.)].index
P1_22 = datnormal.loc[(PeriodIn <= 1) & (appMagMean <= 22.)].index
P10_22 = datnormal.loc[(PeriodIn <= 10) & (appMagMean <= 22.)].index
P30_22 = datnormal.loc[(PeriodIn <= 30) & (appMagMean <= 22.)].index
P100_22 = datnormal.loc[(PeriodIn <= 100) & (appMagMean <= 22.)].index
P1000_22 = datnormal.loc[(PeriodIn <= 1000) & (appMagMean <= 22.)].index
P_195 = datnormal.loc[appMagMean <= 19.5].index
P03_195 = datnormal.loc[(PeriodIn <= 0.3) & (appMagMean <= 19.5)].index
P1_195 = datnormal.loc[(PeriodIn <= 1) & (appMagMean <= 19.5)].index
P10_195 = datnormal.loc[(PeriodIn <= 10) & (appMagMean <= 19.5)].index
P30_195 = datnormal.loc[(PeriodIn <= 30) & (appMagMean <= 19.5)].index
P100_195 = datnormal.loc[(PeriodIn <= 100) & (appMagMean <= 19.5)].index
P1000_195 = datnormal.loc[(PeriodIn <= 1000) & (appMagMean <= 19.5)].index
N_all = (len(PeriodIn)/len(PeriodIn))*N_mult
N_all03 = (len(P03)/len(PeriodIn))*N_mult
N_all1 = (len(P1)/len(PeriodIn))*N_mult
N_all10 = (len(P10)/len(PeriodIn))*N_mult
N_all30 = (len(P30)/len(PeriodIn))*N_mult
N_all100 = (len(P100)/len(PeriodIn))*N_mult
N_all1000 = (len(P1000)/len(PeriodIn))*N_mult
N_all_22 = (len(P_22)/len(PeriodIn))*N_mult
N_all03_22 = (len(P03_22)/len(PeriodIn))*N_mult
N_all1_22 = (len(P1_22)/len(PeriodIn))*N_mult
N_all10_22 = (len(P10_22)/len(PeriodIn))*N_mult
N_all30_22 = (len(P30_22)/len(PeriodIn))*N_mult
N_all100_22 = (len(P100_22)/len(PeriodIn))*N_mult
N_all1000_22 = (len(P1000_22)/len(PeriodIn))*N_mult
N_all_195 = (len(P_195)/len(PeriodIn))*N_mult
N_all03_195 = (len(P03_195)/len(PeriodIn))*N_mult
N_all1_195 = (len(P1_195)/len(PeriodIn))*N_mult
N_all10_195 = (len(P10_195)/len(PeriodIn))*N_mult
N_all30_195 = (len(P30_195)/len(PeriodIn))*N_mult
N_all100_195 = (len(P100_195)/len(PeriodIn))*N_mult
N_all1000_195 = (len(P1000_195)/len(PeriodIn))*N_mult
N_obs = (len(observable)/len(PeriodIn))*N_mult
N_obs03 = (len(observable_03)/len(PeriodIn))*N_mult
N_obs1 = (len(observable_1)/len(PeriodIn))*N_mult
N_obs10 = (len(observable_10)/len(PeriodIn))*N_mult
N_obs30 = (len(observable_30)/len(PeriodIn))*N_mult
N_obs100 = (len(observable_100)/len(PeriodIn))*N_mult
N_obs1000 = (len(observable_1000)/len(PeriodIn))*N_mult
N_obs_22 = (len(observable_22)/len(PeriodIn))*N_mult
N_obs03_22 = (len(observable_03_22)/len(PeriodIn))*N_mult
N_obs1_22 = (len(observable_1_22)/len(PeriodIn))*N_mult
N_obs10_22 = (len(observable_10_22)/len(PeriodIn))*N_mult
N_obs30_22 = (len(observable_30_22)/len(PeriodIn))*N_mult
N_obs100_22 = (len(observable_100_22)/len(PeriodIn))*N_mult
N_obs1000_22 = (len(observable_1000_22)/len(PeriodIn))*N_mult
N_obs_195 = (len(observable_195)/len(PeriodIn))*N_mult
N_obs03_195 = (len(observable_03_195)/len(PeriodIn))*N_mult
N_obs1_195 = (len(observable_1_195)/len(PeriodIn))*N_mult
N_obs10_195 = (len(observable_10_195)/len(PeriodIn))*N_mult
N_obs30_195 = (len(observable_30_195)/len(PeriodIn))*N_mult
N_obs100_195 = (len(observable_100_195)/len(PeriodIn))*N_mult
N_obs1000_195 = (len(observable_1000_195)/len(PeriodIn))*N_mult
N_rec = (len(recoverable)/len(PeriodIn))*N_mult
N_rec03 = (len(recoverable_03)/len(PeriodIn))*N_mult
N_rec1 = (len(recoverable_1)/len(PeriodIn))*N_mult
N_rec10 = (len(recoverable_10)/len(PeriodIn))*N_mult
N_rec30 = (len(recoverable_30)/len(PeriodIn))*N_mult
N_rec100 = (len(recoverable_100)/len(PeriodIn))*N_mult
N_rec1000 = (len(recoverable_1000)/len(PeriodIn))*N_mult
N_rec_22 = (len(recoverable_22)/len(PeriodIn))*N_mult
N_rec03_22 = (len(recoverable_03_22)/len(PeriodIn))*N_mult
N_rec1_22 = (len(recoverable_1_22)/len(PeriodIn))*N_mult
N_rec10_22 = (len(recoverable_10_22)/len(PeriodIn))*N_mult
N_rec30_22 = (len(recoverable_30_22)/len(PeriodIn))*N_mult
N_rec100_22 = (len(recoverable_100_22)/len(PeriodIn))*N_mult
N_rec1000_22 = (len(recoverable_1000_22)/len(PeriodIn))*N_mult
N_rec_195 = (len(recoverable_195)/len(PeriodIn))*N_mult
N_rec03_195 = (len(recoverable_03_195)/len(PeriodIn))*N_mult
N_rec1_195 = (len(recoverable_1_195)/len(PeriodIn))*N_mult
N_rec10_195 = (len(recoverable_10_195)/len(PeriodIn))*N_mult
N_rec30_195 = (len(recoverable_30_195)/len(PeriodIn))*N_mult
N_rec100_195 = (len(recoverable_100_195)/len(PeriodIn))*N_mult
N_rec1000_195 = (len(recoverable_1000_195)/len(PeriodIn))*N_mult
N_totalnormal_array.append(float(N_all))
N_totalobservablenormal_array.append(float(N_obs))
N_totalrecoverablenormal_array.append(float(N_rec))
N_totalnormal_array_03.append(float(N_all03))
N_totalobservablenormal_array_03.append(float(N_obs03))
N_totalrecoverablenormal_array_03.append(float(N_rec03))
N_totalnormal_array_1.append(float(N_all1))
N_totalobservablenormal_array_1.append(float(N_obs1))
N_totalrecoverablenormal_array_1.append(float(N_rec1))
N_totalnormal_array_10.append(float(N_all10))
N_totalobservablenormal_array_10.append(float(N_obs10))
N_totalrecoverablenormal_array_10.append(float(N_rec10))
N_totalnormal_array_30.append(float(N_all30))
N_totalobservablenormal_array_30.append(float(N_obs30))
N_totalrecoverablenormal_array_30.append(float(N_rec30))
N_totalnormal_array_100.append(float(N_all100))
N_totalobservablenormal_array_100.append(float(N_obs100))
N_totalrecoverablenormal_array_100.append(float(N_rec100))
N_totalnormal_array_1000.append(float(N_all1000))
N_totalobservablenormal_array_1000.append(float(N_obs1000))
N_totalrecoverablenormal_array_1000.append(float(N_rec1000))
N_totalnormal22_array.append(float(N_all_22))
N_totalobservablenormal22_array.append(float(N_obs_22))
N_totalrecoverablenormal22_array.append(float(N_rec_22))
N_totalnormal22_array_03.append(float(N_all03_22))
N_totalobservablenormal22_array_03.append(float(N_obs03_22))
N_totalrecoverablenormal22_array_03.append(float(N_rec03_22))
N_totalnormal22_array_1.append(float(N_all1_22))
N_totalobservablenormal22_array_1.append(float(N_obs1_22))
N_totalrecoverablenormal22_array_1.append(float(N_rec1_22))
N_totalnormal22_array_10.append(float(N_all10_22))
N_totalobservablenormal22_array_10.append(float(N_obs10_22))
N_totalrecoverablenormal22_array_10.append(float(N_rec10_22))
N_totalnormal22_array_30.append(float(N_all30_22))
N_totalobservablenormal22_array_30.append(float(N_obs30_22))
N_totalrecoverablenormal22_array_30.append(float(N_rec30_22))
N_totalnormal22_array_100.append(float(N_all100_22))
N_totalobservablenormal22_array_100.append(float(N_obs100_22))
N_totalrecoverablenormal22_array_100.append(float(N_rec100_22))
N_totalnormal22_array_1000.append(float(N_all1000_22))
N_totalobservablenormal22_array_1000.append(float(N_obs1000_22))
N_totalrecoverablenormal22_array_1000.append(float(N_rec1000_22))
N_totalnormal195_array.append(float(N_all_195))
N_totalobservablenormal195_array.append(float(N_obs_195))
N_totalrecoverablenormal195_array.append(float(N_rec_195))
N_totalnormal195_array_03.append(float(N_all03_195))
N_totalobservablenormal195_array_03.append(float(N_obs03_195))
N_totalrecoverablenormal195_array_03.append(float(N_rec03_195))
N_totalnormal195_array_1.append(float(N_all1_195))
N_totalobservablenormal195_array_1.append(float(N_obs1_195))
N_totalrecoverablenormal195_array_1.append(float(N_rec1_195))
N_totalnormal195_array_10.append(float(N_all10_195))
N_totalobservablenormal195_array_10.append(float(N_obs10_195))
N_totalrecoverablenormal195_array_10.append(float(N_rec10_195))
N_totalnormal195_array_30.append(float(N_all30_195))
N_totalobservablenormal195_array_30.append(float(N_obs30_195))
N_totalrecoverablenormal195_array_30.append(float(N_rec30_195))
N_totalnormal195_array_100.append(float(N_all100_195))
N_totalobservablenormal195_array_100.append(float(N_obs100_195))
N_totalrecoverablenormal195_array_100.append(float(N_rec100_195))
N_totalnormal195_array_1000.append(float(N_all1000_195))
N_totalobservablenormal195_array_1000.append(float(N_obs1000_195))
N_totalrecoverablenormal195_array_1000.append(float(N_rec1000_195))
N_totalnormal = np.sum(N_totalnormal_array)
N_totalnormal_03 = np.sum(N_totalnormal_array_03)
N_totalnormal_1 = np.sum(N_totalnormal_array_1)
N_totalnormal_10 = np.sum(N_totalnormal_array_10)
N_totalnormal_30 = np.sum(N_totalnormal_array_30)
N_totalnormal_100 = np.sum(N_totalnormal_array_100)
N_totalnormal_1000 = np.sum(N_totalnormal_array_1000)
N_totalobservablenormal = np.sum(N_totalobservablenormal_array)
N_totalobservablenormal_03 = np.sum(N_totalobservablenormal_array_03)
N_totalobservablenormal_1 = np.sum(N_totalobservablenormal_array_1)
N_totalobservablenormal_10 = np.sum(N_totalobservablenormal_array_10)
N_totalobservablenormal_30 = np.sum(N_totalobservablenormal_array_30)
N_totalobservablenormal_100 = np.sum(N_totalobservablenormal_array_100)
N_totalobservablenormal_1000 = np.sum(N_totalobservablenormal_array_1000)
N_totalrecoverablenormal = np.sum(N_totalrecoverablenormal_array)
N_totalrecoverablenormal_03 = np.sum(N_totalrecoverablenormal_array_03)
N_totalrecoverablenormal_1 = np.sum(N_totalrecoverablenormal_array_1)
N_totalrecoverablenormal_10 = np.sum(N_totalrecoverablenormal_array_10)
N_totalrecoverablenormal_30 = np.sum(N_totalrecoverablenormal_array_30)
N_totalrecoverablenormal_100 = np.sum(N_totalrecoverablenormal_array_100)
N_totalrecoverablenormal_1000 = np.sum(N_totalrecoverablenormal_array_1000)
N_totalnormal22 = np.sum(N_totalnormal22_array)
N_totalnormal22_03 = np.sum(N_totalnormal22_array_03)
N_totalnormal22_1 = np.sum(N_totalnormal22_array_1)
N_totalnormal22_10 = np.sum(N_totalnormal22_array_10)
N_totalnormal22_30 = np.sum(N_totalnormal22_array_30)
N_totalnormal22_100 = np.sum(N_totalnormal22_array_100)
N_totalnormal22_1000 = np.sum(N_totalnormal22_array_1000)
N_totalobservablenormal22 = np.sum(N_totalobservablenormal22_array)
N_totalobservablenormal22_03 = np.sum(N_totalobservablenormal22_array_03)
N_totalobservablenormal22_1 = np.sum(N_totalobservablenormal22_array_1)
N_totalobservablenormal22_10 = np.sum(N_totalobservablenormal22_array_10)
N_totalobservablenormal22_30 = np.sum(N_totalobservablenormal22_array_30)
N_totalobservablenormal22_100 = np.sum(N_totalobservablenormal22_array_100)
N_totalobservablenormal22_1000 = np.sum(N_totalobservablenormal22_array_1000)
N_totalrecoverablenormal22 = np.sum(N_totalrecoverablenormal22_array)
N_totalrecoverablenormal22_03 = np.sum(N_totalrecoverablenormal22_array_03)
N_totalrecoverablenormal22_1 = np.sum(N_totalrecoverablenormal22_array_1)
N_totalrecoverablenormal22_10 = np.sum(N_totalrecoverablenormal22_array_10)
N_totalrecoverablenormal22_30 = np.sum(N_totalrecoverablenormal22_array_30)
N_totalrecoverablenormal22_100 = np.sum(N_totalrecoverablenormal22_array_100)
N_totalrecoverablenormal22_1000 = np.sum(N_totalrecoverablenormal22_array_1000)
N_totalnormal195 = np.sum(N_totalnormal195_array)
N_totalnormal195_03 = np.sum(N_totalnormal195_array_03)
N_totalnormal195_1 = np.sum(N_totalnormal195_array_1)
N_totalnormal195_10 = np.sum(N_totalnormal195_array_10)
N_totalnormal195_30 = np.sum(N_totalnormal195_array_30)
N_totalnormal195_100 = np.sum(N_totalnormal195_array_100)
N_totalnormal195_1000 = np.sum(N_totalnormal195_array_1000)
N_totalobservablenormal195 = np.sum(N_totalobservablenormal195_array)
N_totalobservablenormal195_03 = np.sum(N_totalobservablenormal195_array_03)
N_totalobservablenormal195_1 = np.sum(N_totalobservablenormal195_array_1)
N_totalobservablenormal195_10 = np.sum(N_totalobservablenormal195_array_10)
N_totalobservablenormal195_30 = np.sum(N_totalobservablenormal195_array_30)
N_totalobservablenormal195_100 = np.sum(N_totalobservablenormal195_array_100)
N_totalobservablenormal195_1000 = np.sum(N_totalobservablenormal195_array_1000)
N_totalrecoverablenormal195 = np.sum(N_totalrecoverablenormal195_array)
N_totalrecoverablenormal195_03 = np.sum(N_totalrecoverablenormal195_array_03)
N_totalrecoverablenormal195_1 = np.sum(N_totalrecoverablenormal195_array_1)
N_totalrecoverablenormal195_10 = np.sum(N_totalrecoverablenormal195_array_10)
N_totalrecoverablenormal195_30 = np.sum(N_totalrecoverablenormal195_array_30)
N_totalrecoverablenormal195_100 = np.sum(N_totalrecoverablenormal195_array_100)
N_totalrecoverablenormal195_1000 = np.sum(N_totalrecoverablenormal195_array_1000)
wholerecoverypercent_normal = (N_totalrecoverablenormal/N_totalobservablenormal)*100
wholerecoverypercent_normal_03 = (N_totalrecoverablenormal_03/N_totalobservablenormal_03)*100
wholerecoverypercent_normal_1 = (N_totalrecoverablenormal_1/N_totalobservablenormal_1)*100
wholerecoverypercent_normal_10 = (N_totalrecoverablenormal_10/N_totalobservablenormal_10)*100
wholerecoverypercent_normal_30 = (N_totalrecoverablenormal_30/N_totalobservablenormal_30)*100
wholerecoverypercent_normal_100 = (N_totalrecoverablenormal_100/N_totalobservablenormal_100)*100
wholerecoverypercent_normal_1000 = (N_totalrecoverablenormal_1000/N_totalobservablenormal_1000)*100
sigmanormal = ((N_totalrecoverablenormal**(1/2))/N_totalobservablenormal)*100
sigmanormal_03 = ((N_totalrecoverablenormal_03**(1/2))/N_totalobservablenormal_03)*100
sigmanormal_1 = ((N_totalrecoverablenormal_1**(1/2))/N_totalobservablenormal_1)*100
sigmanormal_10 = ((N_totalrecoverablenormal_10**(1/2))/N_totalobservablenormal_10)*100
sigmanormal_30 = ((N_totalrecoverablenormal_30**(1/2))/N_totalobservablenormal_30)*100
sigmanormal_100 = ((N_totalrecoverablenormal_100**(1/2))/N_totalobservablenormal_100)*100
sigmanormal_1000 = ((N_totalrecoverablenormal_1000**(1/2))/N_totalobservablenormal_1000)*100
overallrecoverypercent_normal = (N_totalrecoverablenormal/N_totalnormal)*100
overallrecoverypercent_normal_03 = (N_totalrecoverablenormal_03/N_totalnormal_03)*100
overallrecoverypercent_normal_1 = (N_totalrecoverablenormal_1/N_totalnormal_1)*100
overallrecoverypercent_normal_10 = (N_totalrecoverablenormal_10/N_totalnormal_10)*100
overallrecoverypercent_normal_30 = (N_totalrecoverablenormal_30/N_totalnormal_30)*100
overallrecoverypercent_normal_100 = (N_totalrecoverablenormal_100/N_totalnormal_100)*100
overallrecoverypercent_normal_1000 = (N_totalrecoverablenormal_1000/N_totalnormal_1000)*100
overallsigmanormal = ((N_totalrecoverablenormal**(1/2))/N_totalnormal)*100
overallsigmanormal_03 = ((N_totalrecoverablenormal_03**(1/2))/N_totalnormal_03)*100
overallsigmanormal_1 = ((N_totalrecoverablenormal_1**(1/2))/N_totalnormal_1)*100
overallsigmanormal_10 = ((N_totalrecoverablenormal_10**(1/2))/N_totalnormal_10)*100
overallsigmanormal_30 = ((N_totalrecoverablenormal_30**(1/2))/N_totalnormal_30)*100
overallsigmanormal_100 = ((N_totalrecoverablenormal_100**(1/2))/N_totalnormal_100)*100
overallsigmanormal_1000 = ((N_totalrecoverablenormal_1000**(1/2))/N_totalnormal_1000)*100
wholerecoverypercent_normal22 = (N_totalrecoverablenormal22/N_totalobservablenormal22)*100
wholerecoverypercent_normal22_03 = (N_totalrecoverablenormal22_03/N_totalobservablenormal22_03)*100
wholerecoverypercent_normal22_1 = (N_totalrecoverablenormal22_1/N_totalobservablenormal22_1)*100
wholerecoverypercent_normal22_10 = (N_totalrecoverablenormal22_10/N_totalobservablenormal22_10)*100
wholerecoverypercent_normal22_30 = (N_totalrecoverablenormal22_30/N_totalobservablenormal22_30)*100
wholerecoverypercent_normal22_100 = (N_totalrecoverablenormal22_100/N_totalobservablenormal22_100)*100
wholerecoverypercent_normal22_1000 = (N_totalrecoverablenormal22_1000/N_totalobservablenormal22_1000)*100
sigmanormal22 = ((N_totalrecoverablenormal22**(1/2))/N_totalobservablenormal22)*100
sigmanormal22_03 = ((N_totalrecoverablenormal22_03**(1/2))/N_totalobservablenormal22_03)*100
sigmanormal22_1 = ((N_totalrecoverablenormal22_1**(1/2))/N_totalobservablenormal22_1)*100
sigmanormal22_10 = ((N_totalrecoverablenormal22_10**(1/2))/N_totalobservablenormal22_10)*100
sigmanormal22_30 = ((N_totalrecoverablenormal22_30**(1/2))/N_totalobservablenormal22_30)*100
sigmanormal22_100 = ((N_totalrecoverablenormal22_100**(1/2))/N_totalobservablenormal22_100)*100
sigmanormal22_1000 = ((N_totalrecoverablenormal22_1000**(1/2))/N_totalobservablenormal22_1000)*100
overallrecoverypercent_normal22 = (N_totalrecoverablenormal22/N_totalnormal22)*100
overallrecoverypercent_normal22_03 = (N_totalrecoverablenormal22_03/N_totalnormal22_03)*100
overallrecoverypercent_normal22_1 = (N_totalrecoverablenormal22_1/N_totalnormal22_1)*100
overallrecoverypercent_normal22_10 = (N_totalrecoverablenormal22_10/N_totalnormal22_10)*100
overallrecoverypercent_normal22_30 = (N_totalrecoverablenormal22_30/N_totalnormal22_30)*100
overallrecoverypercent_normal22_100 = (N_totalrecoverablenormal22_100/N_totalnormal22_100)*100
overallrecoverypercent_normal22_1000 = (N_totalrecoverablenormal22_1000/N_totalnormal22_1000)*100
overallsigmanormal22 = ((N_totalrecoverablenormal22**(1/2))/N_totalnormal22)*100
overallsigmanormal22_03 = ((N_totalrecoverablenormal22_03**(1/2))/N_totalnormal22_03)*100
overallsigmanormal22_1 = ((N_totalrecoverablenormal22_1**(1/2))/N_totalnormal22_1)*100
overallsigmanormal22_10 = ((N_totalrecoverablenormal22_10**(1/2))/N_totalnormal22_10)*100
overallsigmanormal22_30 = ((N_totalrecoverablenormal22_30**(1/2))/N_totalnormal22_30)*100
overallsigmanormal22_100 = ((N_totalrecoverablenormal22_100**(1/2))/N_totalnormal22_100)*100
overallsigmanormal22_1000 = ((N_totalrecoverablenormal22_1000**(1/2))/N_totalnormal22_1000)*100
wholerecoverypercent_normal195 = (N_totalrecoverablenormal195/N_totalobservablenormal195)*100
wholerecoverypercent_normal195_03 = (N_totalrecoverablenormal195_03/N_totalobservablenormal195_03)*100
wholerecoverypercent_normal195_1 = (N_totalrecoverablenormal195_1/N_totalobservablenormal195_1)*100
wholerecoverypercent_normal195_10 = (N_totalrecoverablenormal195_10/N_totalobservablenormal195_10)*100
wholerecoverypercent_normal195_30 = (N_totalrecoverablenormal195_30/N_totalobservablenormal195_30)*100
wholerecoverypercent_normal195_100 = (N_totalrecoverablenormal195_100/N_totalobservablenormal195_100)*100
wholerecoverypercent_normal195_1000 = (N_totalrecoverablenormal195_1000/N_totalobservablenormal195_1000)*100
sigmanormal195 = ((N_totalrecoverablenormal195**(1/2))/N_totalobservablenormal195)*100
sigmanormal195_03 = ((N_totalrecoverablenormal195_03**(1/2))/N_totalobservablenormal195_03)*100
sigmanormal195_1 = ((N_totalrecoverablenormal195_1**(1/2))/N_totalobservablenormal195_1)*100
sigmanormal195_10 = ((N_totalrecoverablenormal195_10**(1/2))/N_totalobservablenormal195_10)*100
sigmanormal195_30 = ((N_totalrecoverablenormal195_30**(1/2))/N_totalobservablenormal195_30)*100
sigmanormal195_100 = ((N_totalrecoverablenormal195_100**(1/2))/N_totalobservablenormal195_100)*100
sigmanormal195_1000 = ((N_totalrecoverablenormal195_1000**(1/2))/N_totalobservablenormal195_1000)*100
overallrecoverypercent_normal195 = (N_totalrecoverablenormal195/N_totalnormal195)*100
overallrecoverypercent_normal195_03 = (N_totalrecoverablenormal195_03/N_totalnormal195_03)*100
overallrecoverypercent_normal195_1 = (N_totalrecoverablenormal195_1/N_totalnormal195_1)*100
overallrecoverypercent_normal195_10 = (N_totalrecoverablenormal195_10/N_totalnormal195_10)*100
overallrecoverypercent_normal195_30 = (N_totalrecoverablenormal195_30/N_totalnormal195_30)*100
overallrecoverypercent_normal195_100 = (N_totalrecoverablenormal195_100/N_totalnormal195_100)*100
overallrecoverypercent_normal195_1000 = (N_totalrecoverablenormal195_1000/N_totalnormal195_1000)*100
overallsigmanormal195 = ((N_totalrecoverablenormal195**(1/2))/N_totalnormal195)*100
overallsigmanormal195_03 = ((N_totalrecoverablenormal195_03**(1/2))/N_totalnormal195_03)*100
overallsigmanormal195_1 = ((N_totalrecoverablenormal195_1**(1/2))/N_totalnormal195_1)*100
overallsigmanormal195_10 = ((N_totalrecoverablenormal195_10**(1/2))/N_totalnormal195_10)*100
overallsigmanormal195_30 = ((N_totalrecoverablenormal195_30**(1/2))/N_totalnormal195_30)*100
overallsigmanormal195_100 = ((N_totalrecoverablenormal195_100**(1/2))/N_totalnormal195_100)*100
overallsigmanormal195_1000 = ((N_totalrecoverablenormal195_1000**(1/2))/N_totalnormal195_1000)*100\
print("N_totalnormal = ", N_totalnormal, "and in log = ", np.log10(N_totalnormal), "**** N_totalobservablenormal = ", N_totalobservablenormal, "and in log = ", np.log10(N_totalobservablenormal), "**** N_totalrecoverablenormal = ", N_totalrecoverablenormal, "and in log = ", np.log10(N_totalrecoverablenormal))
print("N_totalnormal_03 = ", N_totalnormal_03, "and in log = ", np.log10(N_totalnormal_03), "**** N_totalobservablenormal_03 = ", N_totalobservablenormal_03, "and in log = ", np.log10(N_totalobservablenormal_03), "**** N_totalrecoverablenormal_03 = ", N_totalrecoverablenormal_03, "and in log = ", np.log10(N_totalrecoverablenormal_03))
print("N_totalnormal_1 = ", N_totalnormal_1, "and in log = ", np.log10(N_totalnormal_1), "**** N_totalobservablenormal_1 = ", N_totalobservablenormal_1, "and in log = ", np.log10(N_totalobservablenormal_1), "**** N_totalrecoverablenormal_1 = ", N_totalrecoverablenormal_1, "and in log = ", np.log10(N_totalrecoverablenormal_1))
print("N_totalnormal_10 = ", N_totalnormal_10, "and in log = ", np.log10(N_totalnormal_10), "**** N_totalobservablenormal_10 = ", N_totalobservablenormal_10, "and in log = ", np.log10(N_totalobservablenormal_10), "**** N_totalrecoverablenormal_10 = ", N_totalrecoverablenormal_10, "and in log = ", np.log10(N_totalrecoverablenormal_10))
print("N_totalnormal_30 = ", N_totalnormal_30, "and in log = ", np.log10(N_totalnormal_30), "**** N_totalobservablenormal_30 = ", N_totalobservablenormal_30, "and in log = ", np.log10(N_totalobservablenormal_30), "**** N_totalrecoverablenormal_30 = ", N_totalrecoverablenormal_30, "and in log = ", np.log10(N_totalrecoverablenormal_30))
print("N_totalnormal_100 = ", N_totalnormal_100, "and in log = ", np.log10(N_totalnormal_100), "**** N_totalobservablenormal_100 = ", N_totalobservablenormal_100, "and in log = ", np.log10(N_totalobservablenormal_100), "**** N_totalrecoverablenormal_100 = ", N_totalrecoverablenormal_100, "and in log = ", np.log10(N_totalrecoverablenormal_100))
print("N_totalnormal_1000 = ", N_totalnormal_1000, "and in log = ", np.log10(N_totalnormal_1000), "**** N_totalobservablenormal_1000 = ", N_totalobservablenormal_1000, "and in log = ", np.log10(N_totalobservablenormal_1000), "**** N_totalrecoverablenormal_1000 = ", N_totalrecoverablenormal_1000, "and in log = ", np.log10(N_totalrecoverablenormal_1000))
print("********************************")
print("wholerecoverypercent_normal = $", wholerecoverypercent_normal, "/pm", sigmanormal, "$")
print("wholerecoverypercent_normal_03 = $", wholerecoverypercent_normal_03, "/pm", sigmanormal_03, "$")
print("wholerecoverypercent_normal_1 = $", wholerecoverypercent_normal_1, "/pm", sigmanormal_1, "$")
print("wholerecoverypercent_normal_10 = $", wholerecoverypercent_normal_10, "/pm", sigmanormal_10, "$")
print("wholerecoverypercent_normal_30 = $", wholerecoverypercent_normal_30, "/pm", sigmanormal_30, "$")
print("wholerecoverypercent_normal_100 = $", wholerecoverypercent_normal_100, "/pm", sigmanormal_100, "$")
print("wholerecoverypercent_normal_1000 = $", wholerecoverypercent_normal_1000, "/pm", sigmanormal_1000, "$")
print("********************************")
print("overallrecoverypercent_normal = $", overallrecoverypercent_normal, "/pm", overallsigmanormal)
print("overallrecoverypercent_normal_03 = $", overallrecoverypercent_normal_03, "/pm", overallsigmanormal_03)
print("overallrecoverypercent_normal_1 = $", overallrecoverypercent_normal_1, "/pm", overallsigmanormal_1)
print("overallrecoverypercent_normal_10 = $", overallrecoverypercent_normal_10, "/pm", overallsigmanormal_10)
print("overallrecoverypercent_normal_30 = $", overallrecoverypercent_normal_30, "/pm", overallsigmanormal_30)
print("overallrecoverypercent_normal_100 = $", overallrecoverypercent_normal_100, "/pm", overallsigmanormal_100)
print("overallrecoverypercent_normal_1000 = $", overallrecoverypercent_normal_1000, "/pm", overallsigmanormal_1000)
print("################################")
print("N_totalnormal22 = ", N_totalnormal22, "and in log = ", np.log10(N_totalnormal22), "**** N_totalobservablenormal22 = ", N_totalobservablenormal22, "and in log = ", np.log10(N_totalobservablenormal22), "**** N_totalrecoverablenormal22 = ", N_totalrecoverablenormal22, "and in log = ", np.log10(N_totalrecoverablenormal22))
print("N_totalnormal22_03 = ", N_totalnormal22_03, "and in log = ", np.log10(N_totalnormal22_03), "**** N_totalobservablenormal22_03 = ", N_totalobservablenormal22_03, "and in log = ", np.log10(N_totalobservablenormal22_03), "**** N_totalrecoverablenormal22_03 = ", N_totalrecoverablenormal22_03, "and in log = ", np.log10(N_totalrecoverablenormal22_03))
print("N_totalnormal22_1 = ", N_totalnormal22_1, "and in log = ", np.log10(N_totalnormal22_1), "**** N_totalobservablenormal22_1 = ", N_totalobservablenormal22_1, "and in log = ", np.log10(N_totalobservablenormal22_1), "**** N_totalrecoverablenormal22_1 = ", N_totalrecoverablenormal22_1, "and in log = ", np.log10(N_totalrecoverablenormal22_1))
print("N_totalnormal22_10 = ", N_totalnormal22_10, "and in log = ", np.log10(N_totalnormal22_10), "**** N_totalobservablenormal22_10 = ", N_totalobservablenormal22_10, "and in log = ", np.log10(N_totalobservablenormal22_10), "**** N_totalrecoverablenormal22_10 = ", N_totalrecoverablenormal22_10, "and in log = ", np.log10(N_totalrecoverablenormal22_10))
print("N_totalnormal22_30 = ", N_totalnormal22_30, "and in log = ", np.log10(N_totalnormal22_30), "**** N_totalobservablenormal22_30 = ", N_totalobservablenormal22_30, "and in log = ", np.log10(N_totalobservablenormal22_30), "**** N_totalrecoverablenormal22_30 = ", N_totalrecoverablenormal22_30, "and in log = ", np.log10(N_totalrecoverablenormal22_30))
print("N_totalnormal22_100 = ", N_totalnormal22_100, "and in log = ", np.log10(N_totalnormal22_100), "**** N_totalobservablenormal22_100 = ", N_totalobservablenormal22_100, "and in log = ", np.log10(N_totalobservablenormal22_100), "**** N_totalrecoverablenormal22_100 = ", N_totalrecoverablenormal22_100, "and in log = ", np.log10(N_totalrecoverablenormal22_100))
print("N_totalnormal22_1000 = ", N_totalnormal22_1000, "and in log = ", np.log10(N_totalnormal22_1000), "**** N_totalobservablenormal22_1000 = ", N_totalobservablenormal22_1000, "and in log = ", np.log10(N_totalobservablenormal22_1000), "**** N_totalrecoverablenormal22_1000 = ", N_totalrecoverablenormal22_1000, "and in log = ", np.log10(N_totalrecoverablenormal22_1000))
print("********************************")
print("wholerecoverypercent_normal22 = $", wholerecoverypercent_normal22, "/pm", sigmanormal22, "$")
print("wholerecoverypercent_normal22_03 = $", wholerecoverypercent_normal22_03, "/pm", sigmanormal22_03, "$")
print("wholerecoverypercent_normal22_1 = $", wholerecoverypercent_normal22_1, "/pm", sigmanormal22_1, "$")
print("wholerecoverypercent_normal22_10 = $", wholerecoverypercent_normal22_10, "/pm", sigmanormal22_10, "$")
print("wholerecoverypercent_normal22_30 = $", wholerecoverypercent_normal22_30, "/pm", sigmanormal22_30, "$")
print("wholerecoverypercent_normal22_100 = $", wholerecoverypercent_normal22_100, "/pm", sigmanormal22_100, "$")
print("wholerecoverypercent_normal22_1000 = $", wholerecoverypercent_normal22_1000, "/pm", sigmanormal22_1000, "$")
print("********************************")
print("overallrecoverypercent_normal22 = $", overallrecoverypercent_normal22, "/pm", overallsigmanormal22, "$")
print("overallrecoverypercent_normal22_03 = $", overallrecoverypercent_normal22_03, "/pm", overallsigmanormal22_03, "$")
print("overallrecoverypercent_normal22_1 = $", overallrecoverypercent_normal22_1, "/pm", overallsigmanormal22_1, "$")
print("overallrecoverypercent_normal22_10 = $", overallrecoverypercent_normal22_10, "/pm", overallsigmanormal22_10, "$")
print("overallrecoverypercent_normal22_30 = $", overallrecoverypercent_normal22_30, "/pm", overallsigmanormal22_30, "$")
print("overallrecoverypercent_normal22_100 = $", overallrecoverypercent_normal22_100, "/pm", overallsigmanormal22_100, "$")
print("overallrecoverypercent_normal22_1000 = $", overallrecoverypercent_normal22_1000, "/pm", overallsigmanormal22_1000, "$")
print("###############################")
print("N_totalnormal195 = ", N_totalnormal195, "and in log = ", np.log10(N_totalnormal195), "**** N_totalobservablenormal195 = ", N_totalobservablenormal195, "and in log = ", np.log10(N_totalobservablenormal195), "**** N_totalrecoverablenormal195 = ", N_totalrecoverablenormal195, "and in log = ", np.log10(N_totalrecoverablenormal195))
print("N_totalnormal195_03 = ", N_totalnormal195_03, "and in log = ", np.log10(N_totalnormal195_03), "**** N_totalobservablenormal195_03 = ", N_totalobservablenormal195_03, "and in log = ", np.log10(N_totalobservablenormal195_03), "**** N_totalrecoverablenormal195_03 = ", N_totalrecoverablenormal195_03, "and in log = ", np.log10(N_totalrecoverablenormal195_03))
print("N_totalnormal195_1 = ", N_totalnormal195_1, "and in log = ", np.log10(N_totalnormal195_1), "**** N_totalobservablenormal195_1 = ", N_totalobservablenormal195_1, "and in log = ", np.log10(N_totalobservablenormal195_1), "**** N_totalrecoverablenormal195_1 = ", N_totalrecoverablenormal195_1, "and in log = ", np.log10(N_totalrecoverablenormal195_1))
print("N_totalnormal195_10 = ", N_totalnormal195_10, "and in log = ", np.log10(N_totalnormal195_10), "**** N_totalobservablenormal195_10 = ", N_totalobservablenormal195_10, "and in log = ", np.log10(N_totalobservablenormal195_10), "**** N_totalrecoverablenormal195_10 = ", N_totalrecoverablenormal195_10, "and in log = ", np.log10(N_totalrecoverablenormal195_10))
print("N_totalnormal195_30 = ", N_totalnormal195_30, "and in log = ", np.log10(N_totalnormal195_30), "**** N_totalobservablenormal195_30 = ", N_totalobservablenormal195_30, "and in log = ", np.log10(N_totalobservablenormal195_30), "**** N_totalrecoverablenormal195_30 = ", N_totalrecoverablenormal195_30, "and in log = ", np.log10(N_totalrecoverablenormal195_30))
print("N_totalnormal195_100 = ", N_totalnormal195_100, "and in log = ", np.log10(N_totalnormal195_100), "**** N_totalobservablenormal195_100 = ", N_totalobservablenormal195_100, "and in log = ", np.log10(N_totalobservablenormal195_100), "**** N_totalrecoverablenormal195_100 = ", N_totalrecoverablenormal195_100, "and in log = ", np.log10(N_totalrecoverablenormal195_100))
print("N_totalnormal195_1000 = ", N_totalnormal195_1000, "and in log = ", np.log10(N_totalnormal195_1000), "**** N_totalobservablenormal195_1000 = ", N_totalobservablenormal195_1000, "and in log = ", np.log10(N_totalobservablenormal195_1000), "**** N_totalrecoverablenormal195_1000 = ", N_totalrecoverablenormal195_1000, "and in log = ", np.log10(N_totalrecoverablenormal195_1000))
print("********************************")
print("wholerecoverypercent_normal195 = $", wholerecoverypercent_normal195, "/pm", sigmanormal195, "$")
print("wholerecoverypercent_normal195_03 = $", wholerecoverypercent_normal195_03, "/pm", sigmanormal195_03, "$")
print("wholerecoverypercent_normal195_1 = $", wholerecoverypercent_normal195_1, "/pm", sigmanormal195_1, "$")
print("wholerecoverypercent_normal195_10 = $", wholerecoverypercent_normal195_10, "/pm", sigmanormal195_10, "$")
print("wholerecoverypercent_normal195_30 = $", wholerecoverypercent_normal195_30, "/pm", sigmanormal195_30, "$")
print("wholerecoverypercent_normal195_100 = $", wholerecoverypercent_normal195_100, "/pm", sigmanormal195_100, "$")
print("wholerecoverypercent_normal195_1000 = $", wholerecoverypercent_normal195_1000, "/pm", sigmanormal195_1000, "$")
print("********************************")
print("overallrecoverypercent_normal195 = $", overallrecoverypercent_normal195, "/pm", overallsigmanormal195, "$")
print("overallrecoverypercent_normal195_03 = $", overallrecoverypercent_normal195_03, "/pm", overallsigmanormal195_03, "$")
print("overallrecoverypercent_normal195_1 = $", overallrecoverypercent_normal195_1, "/pm", overallsigmanormal195_1, "$")
print("overallrecoverypercent_normal195_10 = $", overallrecoverypercent_normal195_10, "/pm", overallsigmanormal195_10, "$")
print("overallrecoverypercent_normal195_30 = $", overallrecoverypercent_normal195_30, "/pm", overallsigmanormal195_30, "$")
print("overallrecoverypercent_normal195_100 = $", overallrecoverypercent_normal195_100, "/pm", overallsigmanormal195_100, "$")
print("overallrecoverypercent_normal195_1000 = $", overallrecoverypercent_normal195_1000, "/pm", overallsigmanormal195_1000, "$")
print("#############################")
print("binarypercent_22 = $", (N_totalnormal22/N_totalnormal)*100, "/pm", ((N_totalnormal22**(1/2))/N_totalnormal)*100, "$")
print("binarypercent_195 = $", (N_totalnormal195/N_totalnormal)*100, "/pm", ((N_totalnormal195**(1/2))/N_totalnormal)*100, "$")
print("binarypercent_03 = $", (N_totalnormal_03/N_totalnormal)*100, "/pm", ((N_totalnormal_03**(1/2))/N_totalnormal)*100, "$")
print("binarypercent_1 = $", (N_totalnormal_1/N_totalnormal)*100, "/pm", ((N_totalnormal_1**(1/2))/N_totalnormal)*100, "$")
print("binarypercent_10 = $", (N_totalnormal_10/N_totalnormal)*100, "/pm", ((N_totalnormal_10**(1/2))/N_totalnormal)*100, "$")
print("binarypercent_30 = $", (N_totalnormal_30/N_totalnormal)*100, "/pm", ((N_totalnormal_30**(1/2))/N_totalnormal)*100, "$")
print("binarypercent_100 = $", (N_totalnormal_100/N_totalnormal)*100, "/pm", ((N_totalnormal_100**(1/2))/N_totalnormal)*100, "$")
print("binarypercent_1000 = $", (N_totalnormal_1000/N_totalnormal)*100, "/pm", ((N_totalnormal_1000**(1/2))/N_totalnormal)*100, "$")
print("observablepercent_03 = $", (N_totalobservablenormal_03/N_totalnormal_03)*100, "/pm", ((N_totalobservablenormal_03**(1/2))/N_totalnormal_03)*100, "$")
print("observablepercent_1 = $", (N_totalobservablenormal_1/N_totalnormal_1)*100, "/pm", ((N_totalobservablenormal_1**(1/2))/N_totalnormal_1)*100, "$")
print("observablepercent_10 = $", (N_totalobservablenormal_10/N_totalnormal_10)*100, "/pm", ((N_totalobservablenormal_10**(1/2))/N_totalnormal_10)*100, "$")
print("observablepercent_30 = $", (N_totalobservablenormal_30/N_totalnormal_30)*100, "/pm", ((N_totalobservablenormal_30**(1/2))/N_totalnormal_30)*100, "$")
print("observablepercent_100 = $", (N_totalobservablenormal_100/N_totalnormal_100)*100, "/pm", ((N_totalobservablenormal_100**(1/2))/N_totalnormal_100)*100, "$")
print("observablepercent_1000 = $", (N_totalobservablenormal_1000/N_totalnormal_1000)*100, "/pm", ((N_totalobservablenormal_1000**(1/2))/N_totalnormal_1000)*100, "$")
print("observablepercent = $", (N_totalobservablenormal/N_totalnormal)*100, "/pm", ((N_totalobservablenormal**(1/2))/N_totalnormal)*100, "$")
print("observablepercent22 = $", (N_totalobservablenormal22/N_totalnormal22)*100, "/pm", ((N_totalobservablenormal22**(1/2))/N_totalnormal22)*100, "$")
print("observablepercent195 = $", (N_totalobservablenormal195/N_totalnormal195)*100, "/pm", ((N_totalobservablenormal195**(1/2))/N_totalnormal195)*100, "$")
for filefast_ in sorted(allFiles_fast):
filename = filefast_[69:] #when file path no longer has /old in it, will be filefast_[65:]
fileid = filename.strip('output_file.csv')
print ("I'm starting " + fileid)
datfast = pd.read_csv(filefast_, sep = ',', header=2)
PeriodIn = datfast['p'] # input period -- 'p' in data file
##########################################################
datfast1 = pd.read_csv(filefast_, sep = ',', header=0, nrows=1)
N_tri = datfast1["NstarsTRILEGAL"][0]
Nall = len(PeriodIn)
m1hAll0, m1b = np.histogram(datfast["m1"], bins=mbins)
dm1 = np.diff(m1b)
m1val = m1b[:-1] + dm1/2.
fb = np.sum(m1hAll0/Nall*fbFit(m1val))
N_mult = N_tri*fb
##########################################################
if len(PeriodIn) == 0.:
continue
if N_tri == 0:
continue
else:
PeriodOut = datfast['LSM_PERIOD'] #LSM_PERIOD in data file
appMagMean = datfast['appMagMean'] #apparent magnitude, will use to make cuts for 24 (default), 22, and then Kepler's range (?? -- brighter than LSST can manage-- to 19) OR 19.5 (SNR = 10)
observable = datfast.loc[PeriodOut != -999].index
observable_03 = datfast.loc[(PeriodIn <= 0.3) & (PeriodOut != -999)].index
observable_1 = datfast.loc[(PeriodIn <= 1) & (PeriodOut != -999)].index
observable_10 = datfast.loc[(PeriodIn <= 10) & (PeriodOut != -999)].index
observable_30 = datfast.loc[(PeriodIn <= 30) & (PeriodOut != -999)].index
observable_100 = datfast.loc[(PeriodIn <= 100) & (PeriodOut != -999)].index
observable_1000 = datfast.loc[(PeriodIn <= 1000) & (PeriodOut != -999)].index
observable_22 = datfast.loc[(PeriodOut != -999) & (appMagMean <= 22.)].index
observable_03_22 = datfast.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_1_22 = datfast.loc[(PeriodIn <= 1) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_10_22 = datfast.loc[(PeriodIn <= 10) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_30_22 = datfast.loc[(PeriodIn <= 30) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_100_22 = datfast.loc[(PeriodIn <= 100) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_1000_22 = datfast.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_195 = datfast.loc[(PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_03_195 = datfast.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_1_195 = datfast.loc[(PeriodIn <= 1) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_10_195 = datfast.loc[(PeriodIn <= 10) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_30_195 = datfast.loc[(PeriodIn <= 30) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_100_195 = datfast.loc[(PeriodIn <= 100) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_1000_195 = datfast.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
fullP = abs(PeriodOut - PeriodIn)/PeriodIn
halfP = abs(PeriodOut - 0.5*PeriodIn)/(0.5*PeriodIn)
twiceP = abs(PeriodOut - 2*PeriodIn)/(2*PeriodIn)
recoverable = datfast.loc[(PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_03 = datfast.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_1 = datfast.loc[(PeriodIn <= 1) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_10 = datfast.loc[(PeriodIn <= 10) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_30 = datfast.loc[(PeriodIn <= 30) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_100 = datfast.loc[(PeriodIn <= 100) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_1000 = datfast.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_22 = datfast.loc[(PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_03_22 = datfast.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_1_22 = datfast.loc[(PeriodIn <= 1) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_10_22 = datfast.loc[(PeriodIn <= 10) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_30_22 = datfast.loc[(PeriodIn <= 30) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_100_22 = datfast.loc[(PeriodIn <= 100) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_1000_22 = datfast.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_195 = datfast.loc[(PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_03_195 = datfast.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_1_195 = datfast.loc[(PeriodIn <= 1) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_10_195 = datfast.loc[(PeriodIn <= 10) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_30_195 = datfast.loc[(PeriodIn <= 30) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_100_195 = datfast.loc[(PeriodIn <= 100) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_1000_195 = datfast.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
P03 = datfast.loc[PeriodIn <= 0.3].index
P1 = datfast.loc[PeriodIn <= 1].index
P10 = datfast.loc[PeriodIn <= 10].index
P30 = datfast.loc[PeriodIn <= 30].index
P100 = datfast.loc[PeriodIn <= 100].index
P1000 = datfast.loc[PeriodIn <= 1000].index
P_22 = datfast.loc[appMagMean <= 22.].index
P03_22 = datfast.loc[(PeriodIn <= 0.3) & (appMagMean <= 22.)].index
P1_22 = datfast.loc[(PeriodIn <= 1) & (appMagMean <= 22.)].index
P10_22 = datfast.loc[(PeriodIn <= 10) & (appMagMean <= 22.)].index
P30_22 = datfast.loc[(PeriodIn <= 30) & (appMagMean <= 22.)].index
P100_22 = datfast.loc[(PeriodIn <= 100) & (appMagMean <= 22.)].index
P1000_22 = datfast.loc[(PeriodIn <= 1000) & (appMagMean <= 22.)].index
P_195 = datfast.loc[appMagMean <= 19.5].index
P03_195 = datfast.loc[(PeriodIn <= 0.3) & (appMagMean <= 19.5)].index
P1_195 = datfast.loc[(PeriodIn <= 1) & (appMagMean <= 19.5)].index
P10_195 = datfast.loc[(PeriodIn <= 10) & (appMagMean <= 19.5)].index
P30_195 = datfast.loc[(PeriodIn <= 30) & (appMagMean <= 19.5)].index
P100_195 = datfast.loc[(PeriodIn <= 100) & (appMagMean <= 19.5)].index
P1000_195 = datfast.loc[(PeriodIn <= 1000) & (appMagMean <= 19.5)].index
N_all = (len(PeriodIn)/len(PeriodIn))*N_mult
N_all03 = (len(P03)/len(PeriodIn))*N_mult
N_all1 = (len(P1)/len(PeriodIn))*N_mult
N_all10 = (len(P10)/len(PeriodIn))*N_mult
N_all30 = (len(P30)/len(PeriodIn))*N_mult
N_all100 = (len(P100)/len(PeriodIn))*N_mult
N_all1000 = (len(P1000)/len(PeriodIn))*N_mult
N_all_22 = (len(P_22)/len(PeriodIn))*N_mult
N_all03_22 = (len(P03_22)/len(PeriodIn))*N_mult
N_all1_22 = (len(P1_22)/len(PeriodIn))*N_mult
N_all10_22 = (len(P10_22)/len(PeriodIn))*N_mult
N_all30_22 = (len(P30_22)/len(PeriodIn))*N_mult
N_all100_22 = (len(P100_22)/len(PeriodIn))*N_mult
N_all1000_22 = (len(P1000_22)/len(PeriodIn))*N_mult
N_all_195 = (len(P_195)/len(PeriodIn))*N_mult
N_all03_195 = (len(P03_195)/len(PeriodIn))*N_mult
N_all1_195 = (len(P1_195)/len(PeriodIn))*N_mult
N_all10_195 = (len(P10_195)/len(PeriodIn))*N_mult
N_all30_195 = (len(P30_195)/len(PeriodIn))*N_mult
N_all100_195 = (len(P100_195)/len(PeriodIn))*N_mult
N_all1000_195 = (len(P1000_195)/len(PeriodIn))*N_mult
N_obs = (len(observable)/len(PeriodIn))*N_mult
N_obs03 = (len(observable_03)/len(PeriodIn))*N_mult
N_obs1 = (len(observable_1)/len(PeriodIn))*N_mult
N_obs10 = (len(observable_10)/len(PeriodIn))*N_mult
N_obs30 = (len(observable_30)/len(PeriodIn))*N_mult
N_obs100 = (len(observable_100)/len(PeriodIn))*N_mult
N_obs1000 = (len(observable_1000)/len(PeriodIn))*N_mult
N_obs_22 = (len(observable_22)/len(PeriodIn))*N_mult
N_obs03_22 = (len(observable_03_22)/len(PeriodIn))*N_mult
N_obs1_22 = (len(observable_1_22)/len(PeriodIn))*N_mult
N_obs10_22 = (len(observable_10_22)/len(PeriodIn))*N_mult
N_obs30_22 = (len(observable_30_22)/len(PeriodIn))*N_mult
N_obs100_22 = (len(observable_100_22)/len(PeriodIn))*N_mult
N_obs1000_22 = (len(observable_1000_22)/len(PeriodIn))*N_mult
N_obs_195 = (len(observable_195)/len(PeriodIn))*N_mult
N_obs03_195 = (len(observable_03_195)/len(PeriodIn))*N_mult
N_obs1_195 = (len(observable_1_195)/len(PeriodIn))*N_mult
N_obs10_195 = (len(observable_10_195)/len(PeriodIn))*N_mult
N_obs30_195 = (len(observable_30_195)/len(PeriodIn))*N_mult
N_obs100_195 = (len(observable_100_195)/len(PeriodIn))*N_mult
N_obs1000_195 = (len(observable_1000_195)/len(PeriodIn))*N_mult
N_rec = (len(recoverable)/len(PeriodIn))*N_mult
N_rec03 = (len(recoverable_03)/len(PeriodIn))*N_mult
N_rec1 = (len(recoverable_1)/len(PeriodIn))*N_mult
N_rec10 = (len(recoverable_10)/len(PeriodIn))*N_mult
N_rec30 = (len(recoverable_30)/len(PeriodIn))*N_mult
N_rec100 = (len(recoverable_100)/len(PeriodIn))*N_mult
N_rec1000 = (len(recoverable_1000)/len(PeriodIn))*N_mult
N_rec_22 = (len(recoverable_22)/len(PeriodIn))*N_mult
N_rec03_22 = (len(recoverable_03_22)/len(PeriodIn))*N_mult
N_rec1_22 = (len(recoverable_1_22)/len(PeriodIn))*N_mult
N_rec10_22 = (len(recoverable_10_22)/len(PeriodIn))*N_mult
N_rec30_22 = (len(recoverable_30_22)/len(PeriodIn))*N_mult
N_rec100_22 = (len(recoverable_100_22)/len(PeriodIn))*N_mult
N_rec1000_22 = (len(recoverable_1000_22)/len(PeriodIn))*N_mult
N_rec_195 = (len(recoverable_195)/len(PeriodIn))*N_mult
N_rec03_195 = (len(recoverable_03_195)/len(PeriodIn))*N_mult
N_rec1_195 = (len(recoverable_1_195)/len(PeriodIn))*N_mult
N_rec10_195 = (len(recoverable_10_195)/len(PeriodIn))*N_mult
N_rec30_195 = (len(recoverable_30_195)/len(PeriodIn))*N_mult
N_rec100_195 = (len(recoverable_100_195)/len(PeriodIn))*N_mult
N_rec1000_195 = (len(recoverable_1000_195)/len(PeriodIn))*N_mult
N_totalfast_array.append(float(N_all))
N_totalobservablefast_array.append(float(N_obs))
N_totalrecoverablefast_array.append(float(N_rec))
N_totalfast_array_03.append(float(N_all03))
N_totalobservablefast_array_03.append(float(N_obs03))
N_totalrecoverablefast_array_03.append(float(N_rec03))
N_totalfast_array_1.append(float(N_all1))
N_totalobservablefast_array_1.append(float(N_obs1))
N_totalrecoverablefast_array_1.append(float(N_rec1))
N_totalfast_array_10.append(float(N_all10))
N_totalobservablefast_array_10.append(float(N_obs10))
N_totalrecoverablefast_array_10.append(float(N_rec10))
N_totalfast_array_30.append(float(N_all30))
N_totalobservablefast_array_30.append(float(N_obs30))
N_totalrecoverablefast_array_30.append(float(N_rec30))
N_totalfast_array_100.append(float(N_all100))
N_totalobservablefast_array_100.append(float(N_obs100))
N_totalrecoverablefast_array_100.append(float(N_rec100))
N_totalfast_array_1000.append(float(N_all1000))
N_totalobservablefast_array_1000.append(float(N_obs1000))
N_totalrecoverablefast_array_1000.append(float(N_rec1000))
N_totalfast22_array.append(float(N_all_22))
N_totalobservablefast22_array.append(float(N_obs_22))
N_totalrecoverablefast22_array.append(float(N_rec_22))
N_totalfast22_array_03.append(float(N_all03_22))
N_totalobservablefast22_array_03.append(float(N_obs03_22))
N_totalrecoverablefast22_array_03.append(float(N_rec03_22))
N_totalfast22_array_1.append(float(N_all1_22))
N_totalobservablefast22_array_1.append(float(N_obs1_22))
N_totalrecoverablefast22_array_1.append(float(N_rec1_22))
N_totalfast22_array_10.append(float(N_all10_22))
N_totalobservablefast22_array_10.append(float(N_obs10_22))
N_totalrecoverablefast22_array_10.append(float(N_rec10_22))
N_totalfast22_array_30.append(float(N_all30_22))
N_totalobservablefast22_array_30.append(float(N_obs30_22))
N_totalrecoverablefast22_array_30.append(float(N_rec30_22))
N_totalfast22_array_100.append(float(N_all100_22))
N_totalobservablefast22_array_100.append(float(N_obs100_22))
N_totalrecoverablefast22_array_100.append(float(N_rec100_22))
N_totalfast22_array_1000.append(float(N_all1000_22))
N_totalobservablefast22_array_1000.append(float(N_obs1000_22))
N_totalrecoverablefast22_array_1000.append(float(N_rec1000_22))
N_totalfast195_array.append(float(N_all_195))
N_totalobservablefast195_array.append(float(N_obs_195))
N_totalrecoverablefast195_array.append(float(N_rec_195))
N_totalfast195_array_03.append(float(N_all03_195))
N_totalobservablefast195_array_03.append(float(N_obs03_195))
N_totalrecoverablefast195_array_03.append(float(N_rec03_195))
N_totalfast195_array_1.append(float(N_all1_195))
N_totalobservablefast195_array_1.append(float(N_obs1_195))
N_totalrecoverablefast195_array_1.append(float(N_rec1_195))
N_totalfast195_array_10.append(float(N_all10_195))
N_totalobservablefast195_array_10.append(float(N_obs10_195))
N_totalrecoverablefast195_array_10.append(float(N_rec10_195))
N_totalfast195_array_30.append(float(N_all30_195))
N_totalobservablefast195_array_30.append(float(N_obs30_195))
N_totalrecoverablefast195_array_30.append(float(N_rec30_195))
N_totalfast195_array_100.append(float(N_all100_195))
N_totalobservablefast195_array_100.append(float(N_obs100_195))
N_totalrecoverablefast195_array_100.append(float(N_rec100_195))
N_totalfast195_array_1000.append(float(N_all1000_195))
N_totalobservablefast195_array_1000.append(float(N_obs1000_195))
N_totalrecoverablefast195_array_1000.append(float(N_rec1000_195))
N_totalfast = np.sum(N_totalfast_array)
N_totalfast_03 = np.sum(N_totalfast_array_03)
N_totalfast_1 = np.sum(N_totalfast_array_1)
N_totalfast_10 = np.sum(N_totalfast_array_10)
N_totalfast_30 = np.sum(N_totalfast_array_30)
N_totalfast_100 = np.sum(N_totalfast_array_100)
N_totalfast_1000 = np.sum(N_totalfast_array_1000)
N_totalobservablefast = np.sum(N_totalobservablefast_array)
N_totalobservablefast_03 = np.sum(N_totalobservablefast_array_03)
N_totalobservablefast_1 = np.sum(N_totalobservablefast_array_1)
N_totalobservablefast_10 = np.sum(N_totalobservablefast_array_10)
N_totalobservablefast_30 = np.sum(N_totalobservablefast_array_30)
N_totalobservablefast_100 = np.sum(N_totalobservablefast_array_100)
N_totalobservablefast_1000 = np.sum(N_totalobservablefast_array_1000)
N_totalrecoverablefast = np.sum(N_totalrecoverablefast_array)
N_totalrecoverablefast_03 = np.sum(N_totalrecoverablefast_array_03)
N_totalrecoverablefast_1 = np.sum(N_totalrecoverablefast_array_1)
N_totalrecoverablefast_10 = np.sum(N_totalrecoverablefast_array_10)
N_totalrecoverablefast_30 = np.sum(N_totalrecoverablefast_array_30)
N_totalrecoverablefast_100 = np.sum(N_totalrecoverablefast_array_100)
N_totalrecoverablefast_1000 = np.sum(N_totalrecoverablefast_array_1000)
N_totalfast22 = np.sum(N_totalfast22_array)
N_totalfast22_03 = np.sum(N_totalfast22_array_03)
N_totalfast22_1 = np.sum(N_totalfast22_array_1)
N_totalfast22_10 = np.sum(N_totalfast22_array_10)
N_totalfast22_30 = np.sum(N_totalfast22_array_30)
N_totalfast22_100 = np.sum(N_totalfast22_array_100)
N_totalfast22_1000 = np.sum(N_totalfast22_array_1000)
N_totalobservablefast22 = np.sum(N_totalobservablefast22_array)
N_totalobservablefast22_03 = np.sum(N_totalobservablefast22_array_03)
N_totalobservablefast22_1 = np.sum(N_totalobservablefast22_array_1)
N_totalobservablefast22_10 = np.sum(N_totalobservablefast22_array_10)
N_totalobservablefast22_30 = np.sum(N_totalobservablefast22_array_30)
N_totalobservablefast22_100 = np.sum(N_totalobservablefast22_array_100)
N_totalobservablefast22_1000 = np.sum(N_totalobservablefast22_array_1000)
N_totalrecoverablefast22 = np.sum(N_totalrecoverablefast22_array)
N_totalrecoverablefast22_03 = np.sum(N_totalrecoverablefast22_array_03)
N_totalrecoverablefast22_1 = np.sum(N_totalrecoverablefast22_array_1)
N_totalrecoverablefast22_10 = np.sum(N_totalrecoverablefast22_array_10)
N_totalrecoverablefast22_30 = np.sum(N_totalrecoverablefast22_array_30)
N_totalrecoverablefast22_100 = np.sum(N_totalrecoverablefast22_array_100)
N_totalrecoverablefast22_1000 = np.sum(N_totalrecoverablefast22_array_1000)
N_totalfast195 = np.sum(N_totalfast195_array)
N_totalfast195_03 = np.sum(N_totalfast195_array_03)
N_totalfast195_1 = np.sum(N_totalfast195_array_1)
N_totalfast195_10 = np.sum(N_totalfast195_array_10)
N_totalfast195_30 = np.sum(N_totalfast195_array_30)
N_totalfast195_100 = np.sum(N_totalfast195_array_100)
N_totalfast195_1000 = np.sum(N_totalfast195_array_1000)
N_totalobservablefast195 = np.sum(N_totalobservablefast195_array)
N_totalobservablefast195_03 = np.sum(N_totalobservablefast195_array_03)
N_totalobservablefast195_1 = np.sum(N_totalobservablefast195_array_1)
N_totalobservablefast195_10 = np.sum(N_totalobservablefast195_array_10)
N_totalobservablefast195_30 = np.sum(N_totalobservablefast195_array_30)
N_totalobservablefast195_100 = np.sum(N_totalobservablefast195_array_100)
N_totalobservablefast195_1000 = np.sum(N_totalobservablefast195_array_1000)
N_totalrecoverablefast195 = np.sum(N_totalrecoverablefast195_array)
N_totalrecoverablefast195_03 = np.sum(N_totalrecoverablefast195_array_03)
N_totalrecoverablefast195_1 = np.sum(N_totalrecoverablefast195_array_1)
N_totalrecoverablefast195_10 = np.sum(N_totalrecoverablefast195_array_10)
N_totalrecoverablefast195_30 = np.sum(N_totalrecoverablefast195_array_30)
N_totalrecoverablefast195_100 = np.sum(N_totalrecoverablefast195_array_100)
N_totalrecoverablefast195_1000 = np.sum(N_totalrecoverablefast195_array_1000)
wholerecoverypercent_fast = (N_totalrecoverablefast/N_totalobservablefast)*100
wholerecoverypercent_fast_03 = (N_totalrecoverablefast_03/N_totalobservablefast_03)*100
wholerecoverypercent_fast_1 = (N_totalrecoverablefast_1/N_totalobservablefast_1)*100
wholerecoverypercent_fast_10 = (N_totalrecoverablefast_10/N_totalobservablefast_10)*100
wholerecoverypercent_fast_30 = (N_totalrecoverablefast_30/N_totalobservablefast_30)*100
wholerecoverypercent_fast_100 = (N_totalrecoverablefast_100/N_totalobservablefast_100)*100
wholerecoverypercent_fast_1000 = (N_totalrecoverablefast_1000/N_totalobservablefast_1000)*100
sigmafast = ((N_totalrecoverablefast**(1/2))/N_totalobservablefast)*100
sigmafast_03 = ((N_totalrecoverablefast_03**(1/2))/N_totalobservablefast_03)*100
sigmafast_1 = ((N_totalrecoverablefast_1**(1/2))/N_totalobservablefast_1)*100
sigmafast_10 = ((N_totalrecoverablefast_10**(1/2))/N_totalobservablefast_10)*100
sigmafast_30 = ((N_totalrecoverablefast_30**(1/2))/N_totalobservablefast_30)*100
sigmafast_100 = ((N_totalrecoverablefast_100**(1/2))/N_totalobservablefast_100)*100
sigmafast_1000 = ((N_totalrecoverablefast_1000**(1/2))/N_totalobservablefast_1000)*100
overallrecoverypercent_fast = (N_totalrecoverablefast/N_totalfast)*100
overallrecoverypercent_fast_03 = (N_totalrecoverablefast_03/N_totalfast_03)*100
overallrecoverypercent_fast_1 = (N_totalrecoverablefast_1/N_totalfast_1)*100
overallrecoverypercent_fast_10 = (N_totalrecoverablefast_10/N_totalfast_10)*100
overallrecoverypercent_fast_30 = (N_totalrecoverablefast_30/N_totalfast_30)*100
overallrecoverypercent_fast_100 = (N_totalrecoverablefast_100/N_totalfast_100)*100
overallrecoverypercent_fast_1000 = (N_totalrecoverablefast_1000/N_totalfast_1000)*100
overallsigmafast = ((N_totalrecoverablefast**(1/2))/N_totalfast)*100
overallsigmafast_03 = ((N_totalrecoverablefast_03**(1/2))/N_totalfast_03)*100
overallsigmafast_1 = ((N_totalrecoverablefast_1**(1/2))/N_totalfast_1)*100
overallsigmafast_10 = ((N_totalrecoverablefast_10**(1/2))/N_totalfast_10)*100
overallsigmafast_30 = ((N_totalrecoverablefast_30**(1/2))/N_totalfast_30)*100
overallsigmafast_100 = ((N_totalrecoverablefast_100**(1/2))/N_totalfast_100)*100
overallsigmafast_1000 = ((N_totalrecoverablefast_1000**(1/2))/N_totalfast_1000)*100
wholerecoverypercent_fast22 = (N_totalrecoverablefast22/N_totalobservablefast22)*100
wholerecoverypercent_fast22_03 = (N_totalrecoverablefast22_03/N_totalobservablefast22_03)*100
wholerecoverypercent_fast22_1 = (N_totalrecoverablefast22_1/N_totalobservablefast22_1)*100
wholerecoverypercent_fast22_10 = (N_totalrecoverablefast22_10/N_totalobservablefast22_10)*100
wholerecoverypercent_fast22_30 = (N_totalrecoverablefast22_30/N_totalobservablefast22_30)*100
wholerecoverypercent_fast22_100 = (N_totalrecoverablefast22_100/N_totalobservablefast22_100)*100
wholerecoverypercent_fast22_1000 = (N_totalrecoverablefast22_1000/N_totalobservablefast22_1000)*100
sigmafast22 = ((N_totalrecoverablefast22**(1/2))/N_totalobservablefast22)*100
sigmafast22_03 = ((N_totalrecoverablefast22_03**(1/2))/N_totalobservablefast22_03)*100
sigmafast22_1 = ((N_totalrecoverablefast22_1**(1/2))/N_totalobservablefast22_1)*100
sigmafast22_10 = ((N_totalrecoverablefast22_10**(1/2))/N_totalobservablefast22_10)*100
sigmafast22_30 = ((N_totalrecoverablefast22_30**(1/2))/N_totalobservablefast22_30)*100
sigmafast22_100 = ((N_totalrecoverablefast22_100**(1/2))/N_totalobservablefast22_100)*100
sigmafast22_1000 = ((N_totalrecoverablefast22_1000**(1/2))/N_totalobservablefast22_1000)*100
overallrecoverypercent_fast22 = (N_totalrecoverablefast22/N_totalfast22)*100
overallrecoverypercent_fast22_03 = (N_totalrecoverablefast22_03/N_totalfast22_03)*100
overallrecoverypercent_fast22_1 = (N_totalrecoverablefast22_1/N_totalfast22_1)*100
overallrecoverypercent_fast22_10 = (N_totalrecoverablefast22_10/N_totalfast22_10)*100
overallrecoverypercent_fast22_30 = (N_totalrecoverablefast22_30/N_totalfast22_30)*100
overallrecoverypercent_fast22_100 = (N_totalrecoverablefast22_100/N_totalfast22_100)*100
overallrecoverypercent_fast22_1000 = (N_totalrecoverablefast22_1000/N_totalfast22_1000)*100
overallsigmafast22 = ((N_totalrecoverablefast22**(1/2))/N_totalfast22)*100
overallsigmafast22_03 = ((N_totalrecoverablefast22_03**(1/2))/N_totalfast22_03)*100
overallsigmafast22_1 = ((N_totalrecoverablefast22_1**(1/2))/N_totalfast22_1)*100
overallsigmafast22_10 = ((N_totalrecoverablefast22_10**(1/2))/N_totalfast22_10)*100
overallsigmafast22_30 = ((N_totalrecoverablefast22_30**(1/2))/N_totalfast22_30)*100
overallsigmafast22_100 = ((N_totalrecoverablefast22_100**(1/2))/N_totalfast22_100)*100
overallsigmafast22_1000 = ((N_totalrecoverablefast22_1000**(1/2))/N_totalfast22_1000)*100
wholerecoverypercent_fast195 = (N_totalrecoverablefast195/N_totalobservablefast195)*100
wholerecoverypercent_fast195_03 = (N_totalrecoverablefast195_03/N_totalobservablefast195_03)*100
wholerecoverypercent_fast195_1 = (N_totalrecoverablefast195_1/N_totalobservablefast195_1)*100
wholerecoverypercent_fast195_10 = (N_totalrecoverablefast195_10/N_totalobservablefast195_10)*100
wholerecoverypercent_fast195_30 = (N_totalrecoverablefast195_30/N_totalobservablefast195_30)*100
wholerecoverypercent_fast195_100 = (N_totalrecoverablefast195_100/N_totalobservablefast195_100)*100
wholerecoverypercent_fast195_1000 = (N_totalrecoverablefast195_1000/N_totalobservablefast195_1000)*100
sigmafast195 = ((N_totalrecoverablefast195**(1/2))/N_totalobservablefast195)*100
sigmafast195_03 = ((N_totalrecoverablefast195_03**(1/2))/N_totalobservablefast195_03)*100
sigmafast195_1 = ((N_totalrecoverablefast195_1**(1/2))/N_totalobservablefast195_1)*100
sigmafast195_10 = ((N_totalrecoverablefast195_10**(1/2))/N_totalobservablefast195_10)*100
sigmafast195_30 = ((N_totalrecoverablefast195_30**(1/2))/N_totalobservablefast195_30)*100
sigmafast195_100 = ((N_totalrecoverablefast195_100**(1/2))/N_totalobservablefast195_100)*100
sigmafast195_1000 = ((N_totalrecoverablefast195_1000**(1/2))/N_totalobservablefast195_1000)*100
overallrecoverypercent_fast195 = (N_totalrecoverablefast195/N_totalfast195)*100
overallrecoverypercent_fast195_03 = (N_totalrecoverablefast195_03/N_totalfast195_03)*100
overallrecoverypercent_fast195_1 = (N_totalrecoverablefast195_1/N_totalfast195_1)*100
overallrecoverypercent_fast195_10 = (N_totalrecoverablefast195_10/N_totalfast195_10)*100
overallrecoverypercent_fast195_30 = (N_totalrecoverablefast195_30/N_totalfast195_30)*100
overallrecoverypercent_fast195_100 = (N_totalrecoverablefast195_100/N_totalfast195_100)*100
overallrecoverypercent_fast195_1000 = (N_totalrecoverablefast195_1000/N_totalfast195_1000)*100
overallsigmafast195 = ((N_totalrecoverablefast195**(1/2))/N_totalfast195)*100
overallsigmafast195_03 = ((N_totalrecoverablefast195_03**(1/2))/N_totalfast195_03)*100
overallsigmafast195_1 = ((N_totalrecoverablefast195_1**(1/2))/N_totalfast195_1)*100
overallsigmafast195_10 = ((N_totalrecoverablefast195_10**(1/2))/N_totalfast195_10)*100
overallsigmafast195_30 = ((N_totalrecoverablefast195_30**(1/2))/N_totalfast195_30)*100
overallsigmafast195_100 = ((N_totalrecoverablefast195_100**(1/2))/N_totalfast195_100)*100
overallsigmafast195_1000 = ((N_totalrecoverablefast195_1000**(1/2))/N_totalfast195_1000)*100\
print("N_totalfast = ", N_totalfast, "and in log = ", np.log10(N_totalfast), "**** N_totalobservablefast = ", N_totalobservablefast, "and in log = ", np.log10(N_totalobservablefast), "**** N_totalrecoverablefast = ", N_totalrecoverablefast, "and in log = ", np.log10(N_totalrecoverablefast))
print("N_totalfast_03 = ", N_totalfast_03, "and in log = ", np.log10(N_totalfast_03), "**** N_totalobservablefast_03 = ", N_totalobservablefast_03, "and in log = ", np.log10(N_totalobservablefast_03), "**** N_totalrecoverablefast_03 = ", N_totalrecoverablefast_03, "and in log = ", np.log10(N_totalrecoverablefast_03))
print("N_totalfast_1 = ", N_totalfast_1, "and in log = ", np.log10(N_totalfast_1), "**** N_totalobservablefast_1 = ", N_totalobservablefast_1, "and in log = ", np.log10(N_totalobservablefast_1), "**** N_totalrecoverablefast_1 = ", N_totalrecoverablefast_1, "and in log = ", np.log10(N_totalrecoverablefast_1))
print("N_totalfast_10 = ", N_totalfast_10, "and in log = ", np.log10(N_totalfast_10), "**** N_totalobservablefast_10 = ", N_totalobservablefast_10, "and in log = ", np.log10(N_totalobservablefast_10), "**** N_totalrecoverablefast_10 = ", N_totalrecoverablefast_10, "and in log = ", np.log10(N_totalrecoverablefast_10))
print("N_totalfast_30 = ", N_totalfast_30, "and in log = ", np.log10(N_totalfast_30), "**** N_totalobservablefast_30 = ", N_totalobservablefast_30, "and in log = ", np.log10(N_totalobservablefast_30), "**** N_totalrecoverablefast_30 = ", N_totalrecoverablefast_30, "and in log = ", np.log10(N_totalrecoverablefast_30))
print("N_totalfast_100 = ", N_totalfast_100, "and in log = ", np.log10(N_totalfast_100), "**** N_totalobservablefast_100 = ", N_totalobservablefast_100, "and in log = ", np.log10(N_totalobservablefast_100), "**** N_totalrecoverablefast_100 = ", N_totalrecoverablefast_100, "and in log = ", np.log10(N_totalrecoverablefast_100))
print("N_totalfast_1000 = ", N_totalfast_1000, "and in log = ", np.log10(N_totalfast_1000), "**** N_totalobservablefast_1000 = ", N_totalobservablefast_1000, "and in log = ", np.log10(N_totalobservablefast_1000), "**** N_totalrecoverablefast_1000 = ", N_totalrecoverablefast_1000, "and in log = ", np.log10(N_totalrecoverablefast_1000))
print("********************************")
print("wholerecoverypercent_fast = $", wholerecoverypercent_fast, "/pm", sigmafast, "$")
print("wholerecoverypercent_fast_03 = $", wholerecoverypercent_fast_03, "/pm", sigmafast_03, "$")
print("wholerecoverypercent_fast_1 = $", wholerecoverypercent_fast_1, "/pm", sigmafast_1, "$")
print("wholerecoverypercent_fast_10 = $", wholerecoverypercent_fast_10, "/pm", sigmafast_10, "$")
print("wholerecoverypercent_fast_30 = $", wholerecoverypercent_fast_30, "/pm", sigmafast_30, "$")
print("wholerecoverypercent_fast_100 = $", wholerecoverypercent_fast_100, "/pm", sigmafast_100, "$")
print("wholerecoverypercent_fast_1000 = $", wholerecoverypercent_fast_1000, "/pm", sigmafast_1000, "$")
print("********************************")
print("overallrecoverypercent_fast = $", overallrecoverypercent_fast, "/pm", overallsigmafast, "$")
print("overallrecoverypercent_fast_03 = $", overallrecoverypercent_fast_03, "/pm", overallsigmafast_03, "$")
print("overallrecoverypercent_fast_1 = $", overallrecoverypercent_fast_1, "/pm", overallsigmafast_1, "$")
print("overallrecoverypercent_fast_10 = $", overallrecoverypercent_fast_10, "/pm", overallsigmafast_10, "$")
print("overallrecoverypercent_fast_30 = $", overallrecoverypercent_fast_30, "/pm", overallsigmafast_30, "$")
print("overallrecoverypercent_fast_100 = $", overallrecoverypercent_fast_100, "/pm", overallsigmafast_100, "$")
print("overallrecoverypercent_fast_1000 = $", overallrecoverypercent_fast_1000, "/pm", overallsigmafast_1000, "$")
print("################################")
print("N_totalfast22 = ", N_totalfast22, "and in log = ", np.log10(N_totalfast22), "**** N_totalobservablefast22 = ", N_totalobservablefast22, "and in log = ", np.log10(N_totalobservablefast22), "**** N_totalrecoverablefast22 = ", N_totalrecoverablefast22, "and in log = ", np.log10(N_totalrecoverablefast22))
print("N_totalfast22_03 = ", N_totalfast22_03, "and in log = ", np.log10(N_totalfast22_03), "**** N_totalobservablefast22_03 = ", N_totalobservablefast22_03, "and in log = ", np.log10(N_totalobservablefast22_03), "**** N_totalrecoverablefast22_03 = ", N_totalrecoverablefast22_03, "and in log = ", np.log10(N_totalrecoverablefast22_03))
print("N_totalfast22_1 = ", N_totalfast22_1, "and in log = ", np.log10(N_totalfast22_1), "**** N_totalobservablefast22_1 = ", N_totalobservablefast22_1, "and in log = ", np.log10(N_totalobservablefast22_1), "**** N_totalrecoverablefast22_1 = ", N_totalrecoverablefast22_1, "and in log = ", np.log10(N_totalrecoverablefast22_1))
print("N_totalfast22_10 = ", N_totalfast22_10, "and in log = ", np.log10(N_totalfast22_10), "**** N_totalobservablefast22_10 = ", N_totalobservablefast22_10, "and in log = ", np.log10(N_totalobservablefast22_10), "**** N_totalrecoverablefast22_10 = ", N_totalrecoverablefast22_10, "and in log = ", np.log10(N_totalrecoverablefast22_10))
print("N_totalfast22_30 = ", N_totalfast22_30, "and in log = ", np.log10(N_totalfast22_30), "**** N_totalobservablefast22_30 = ", N_totalobservablefast22_30, "and in log = ", np.log10(N_totalobservablefast22_30), "**** N_totalrecoverablefast22_30 = ", N_totalrecoverablefast22_30, "and in log = ", np.log10(N_totalrecoverablefast22_30))
print("N_totalfast22_100 = ", N_totalfast22_100, "and in log = ", np.log10(N_totalfast22_100), "**** N_totalobservablefast22_100 = ", N_totalobservablefast22_100, "and in log = ", np.log10(N_totalobservablefast22_100), "**** N_totalrecoverablefast22_100 = ", N_totalrecoverablefast22_100, "and in log = ", np.log10(N_totalrecoverablefast22_100))
print("N_totalfast22_1000 = ", N_totalfast22_1000, "and in log = ", np.log10(N_totalfast22_1000), "**** N_totalobservablefast22_1000 = ", N_totalobservablefast22_1000, "and in log = ", np.log10(N_totalobservablefast22_1000), "**** N_totalrecoverablefast22_1000 = ", N_totalrecoverablefast22_1000, "and in log = ", np.log10(N_totalrecoverablefast22_1000))
print("********************************")
print("wholerecoverypercent_fast22 = $", wholerecoverypercent_fast22, "/pm", sigmafast22, "$")
print("wholerecoverypercent_fast22_03 = $", wholerecoverypercent_fast22_03, "/pm", sigmafast22_03, "$")
print("wholerecoverypercent_fast22_1 = $", wholerecoverypercent_fast22_1, "/pm", sigmafast22_1, "$")
print("wholerecoverypercent_fast22_10 = $", wholerecoverypercent_fast22_10, "/pm", sigmafast22_10, "$")
print("wholerecoverypercent_fast22_30 = $", wholerecoverypercent_fast22_30, "/pm", sigmafast22_30, "$")
print("wholerecoverypercent_fast22_100 = $", wholerecoverypercent_fast22_100, "/pm", sigmafast22_100, "$")
print("wholerecoverypercent_fast22_1000 = $", wholerecoverypercent_fast22_1000, "/pm", sigmafast22_1000, "$")
print("********************************")
print("overallrecoverypercent_fast22 = $", overallrecoverypercent_fast22, "/pm", overallsigmafast22, "$")
print("overallrecoverypercent_fast22_03 = $", overallrecoverypercent_fast22_03, "/pm", overallsigmafast22_03, "$")
print("overallrecoverypercent_fast22_1 = $", overallrecoverypercent_fast22_1, "/pm", overallsigmafast22_1, "$")
print("overallrecoverypercent_fast22_10 = $", overallrecoverypercent_fast22_10, "/pm", overallsigmafast22_10, "$")
print("overallrecoverypercent_fast22_30 = $", overallrecoverypercent_fast22_30, "/pm", overallsigmafast22_30, "$")
print("overallrecoverypercent_fast22_100 = $", overallrecoverypercent_fast22_100, "/pm", overallsigmafast22_100, "$")
print("overallrecoverypercent_fast22_1000 = $", overallrecoverypercent_fast22_1000, "/pm", overallsigmafast22_1000, "$")
print("###############################")
print("N_totalfast195 = ", N_totalfast195, "and in log = ", np.log10(N_totalfast195), "**** N_totalobservablefast195 = ", N_totalobservablefast195, "and in log = ", np.log10(N_totalobservablefast195), "**** N_totalrecoverablefast195 = ", N_totalrecoverablefast195, "and in log = ", np.log10(N_totalrecoverablefast195))
print("N_totalfast195_03 = ", N_totalfast195_03, "and in log = ", np.log10(N_totalfast195_03), "**** N_totalobservablefast195_03 = ", N_totalobservablefast195_03, "and in log = ", np.log10(N_totalobservablefast195_03), "**** N_totalrecoverablefast195_03 = ", N_totalrecoverablefast195_03, "and in log = ", np.log10(N_totalrecoverablefast195_03))
print("N_totalfast195_1 = ", N_totalfast195_1, "and in log = ", np.log10(N_totalfast195_1), "**** N_totalobservablefast195_1 = ", N_totalobservablefast195_1, "and in log = ", np.log10(N_totalobservablefast195_1), "**** N_totalrecoverablefast195_1 = ", N_totalrecoverablefast195_1, "and in log = ", np.log10(N_totalrecoverablefast195_1))
print("N_totalfast195_10 = ", N_totalfast195_10, "and in log = ", np.log10(N_totalfast195_10), "**** N_totalobservablefast195_10 = ", N_totalobservablefast195_10, "and in log = ", np.log10(N_totalobservablefast195_10), "**** N_totalrecoverablefast195_10 = ", N_totalrecoverablefast195_10, "and in log = ", np.log10(N_totalrecoverablefast195_10))
print("N_totalfast195_30 = ", N_totalfast195_30, "and in log = ", np.log10(N_totalfast195_30), "**** N_totalobservablefast195_30 = ", N_totalobservablefast195_30, "and in log = ", np.log10(N_totalobservablefast195_30), "**** N_totalrecoverablefast195_30 = ", N_totalrecoverablefast195_30, "and in log = ", np.log10(N_totalrecoverablefast195_30))
print("N_totalfast195_100 = ", N_totalfast195_100, "and in log = ", np.log10(N_totalfast195_100), "**** N_totalobservablefast195_100 = ", N_totalobservablefast195_100, "and in log = ", np.log10(N_totalobservablefast195_100), "**** N_totalrecoverablefast195_100 = ", N_totalrecoverablefast195_100, "and in log = ", np.log10(N_totalrecoverablefast195_100))
print("N_totalfast195_1000 = ", N_totalfast195_1000, "and in log = ", np.log10(N_totalfast195_1000), "**** N_totalobservablefast195_1000 = ", N_totalobservablefast195_1000, "and in log = ", np.log10(N_totalobservablefast195_1000), "**** N_totalrecoverablefast195_1000 = ", N_totalrecoverablefast195_1000, "and in log = ", np.log10(N_totalrecoverablefast195_1000))
print("********************************")
print("wholerecoverypercent_fast195 = $", wholerecoverypercent_fast195, "/pm", sigmafast195, "$")
print("wholerecoverypercent_fast195_03 = $", wholerecoverypercent_fast195_03, "/pm", sigmafast195_03, "$")
print("wholerecoverypercent_fast195_1 = $", wholerecoverypercent_fast195_1, "/pm", sigmafast195_1, "$")
print("wholerecoverypercent_fast195_10 = $", wholerecoverypercent_fast195_10, "/pm", sigmafast195_10, "$")
print("wholerecoverypercent_fast195_30 = $", wholerecoverypercent_fast195_30, "/pm", sigmafast195_30, "$")
print("wholerecoverypercent_fast195_100 = $", wholerecoverypercent_fast195_100, "/pm", sigmafast195_100, "$")
print("wholerecoverypercent_fast195_1000 = $", wholerecoverypercent_fast195_1000, "/pm", sigmafast195_1000, "$")
print("********************************")
print("overallrecoverypercent_fast195 = $", overallrecoverypercent_fast195, "/pm", overallsigmafast195, "$")
print("overallrecoverypercent_fast195_03 = $", overallrecoverypercent_fast195_03, "/pm", overallsigmafast195_03, "$")
print("overallrecoverypercent_fast195_1 = $", overallrecoverypercent_fast195_1, "/pm", overallsigmafast195_1, "$")
print("overallrecoverypercent_fast195_10 = $", overallrecoverypercent_fast195_10, "/pm", overallsigmafast195_10, "$")
print("overallrecoverypercent_fast195_30 = $", overallrecoverypercent_fast195_30, "/pm", overallsigmafast195_30, "$")
print("overallrecoverypercent_fast195_100 = $", overallrecoverypercent_fast195_100, "/pm", overallsigmafast195_100, "$")
print("overallrecoverypercent_fast195_1000 = $", overallrecoverypercent_fast195_1000, "/pm", overallsigmafast195_1000, "$")
print("#############################")
print("binarypercent_22 = $", (N_totalfast22/N_totalfast)*100, "/pm", ((N_totalfast22**(1/2))/N_totalfast)*100, "$")
print("binarypercent_195 = $", (N_totalfast195/N_totalfast)*100, "/pm", ((N_totalfast195**(1/2))/N_totalfast)*100, "$")
print("binarypercent_03 = $", (N_totalfast_03/N_totalfast)*100, "/pm", ((N_totalfast_03**(1/2))/N_totalfast)*100, "$")
print("binarypercent_1 = $", (N_totalfast_1/N_totalfast)*100, "/pm", ((N_totalfast_1**(1/2))/N_totalfast)*100, "$")
print("binarypercent_10 = $", (N_totalfast_10/N_totalfast)*100, "/pm", ((N_totalfast_10**(1/2))/N_totalfast)*100, "$")
print("binarypercent_30 = $", (N_totalfast_30/N_totalfast)*100, "/pm", ((N_totalfast_30**(1/2))/N_totalfast)*100, "$")
print("binarypercent_100 = $", (N_totalfast_100/N_totalfast)*100, "/pm", ((N_totalfast_100**(1/2))/N_totalfast)*100, "$")
print("binarypercent_1000 = $", (N_totalfast_1000/N_totalfast)*100, "/pm", ((N_totalfast_1000**(1/2))/N_totalfast)*100, "$")
print("observablepercent_03 = $", (N_totalobservablefast_03/N_totalfast_03)*100, "/pm", ((N_totalobservablefast_03**(1/2))/N_totalfast_03)*100, "$")
print("observablepercent_1 = $", (N_totalobservablefast_1/N_totalfast_1)*100, "/pm", ((N_totalobservablefast_1**(1/2))/N_totalfast_1)*100, "$")
print("observablepercent_10 = $", (N_totalobservablefast_10/N_totalfast_10)*100, "/pm", ((N_totalobservablefast_10**(1/2))/N_totalfast_10)*100, "$")
print("observablepercent_30 = $", (N_totalobservablefast_30/N_totalfast_30)*100, "/pm", ((N_totalobservablefast_30**(1/2))/N_totalfast_30)*100, "$")
print("observablepercent_100 = $", (N_totalobservablefast_100/N_totalfast_100)*100, "/pm", ((N_totalobservablefast_100**(1/2))/N_totalfast_100)*100, "$")
print("observablepercent_1000 = $", (N_totalobservablefast_1000/N_totalfast_1000)*100, "/pm", ((N_totalobservablefast_1000**(1/2))/N_totalfast_1000)*100, "$")
print("observablepercent = $", (N_totalobservablefast/N_totalfast)*100, "/pm", ((N_totalobservablefast**(1/2))/N_totalfast)*100, "$")
print("observablepercent22 = $", (N_totalobservablefast22/N_totalfast22)*100, "/pm", ((N_totalobservablefast22**(1/2))/N_totalfast22)*100, "$")
print("observablepercent195 = $", (N_totalobservablefast195/N_totalfast195)*100, "/pm", ((N_totalobservablefast195**(1/2))/N_totalfast195)*100, "$")
for fileobsDist_ in sorted(allFiles_obsDist):
filename = fileobsDist_[77:] #when file path no longer has /old in it, will be fileobsDist_[73:]
fileid = filename.strip('output_file.csv')
print ("I'm starting " + fileid)
datobsDist = pd.read_csv(fileobsDist_, sep = ',', header=2)
PeriodIn = datobsDist['p'] # input period -- 'p' in data file
##########################################################
datobsDist1 = pd.read_csv(fileobsDist_, sep = ',', header=0, nrows=1)
N_tri = datobsDist1["NstarsTRILEGAL"][0]
Nall = len(PeriodIn)
m1hAll0, m1b = np.histogram(datobsDist["m1"], bins=mbins)
dm1 = np.diff(m1b)
m1val = m1b[:-1] + dm1/2.
fb = np.sum(m1hAll0/Nall*fbFit(m1val))
N_mult = N_tri*fb
##########################################################
if len(PeriodIn) == 0.:
continue
if N_tri == 0:
continue
else:
PeriodOut = datobsDist['LSM_PERIOD'] #LSM_PERIOD in data file
appMagMean = datobsDist['appMagMean'] #apparent magnitude, will use to make cuts for 24 (default), 22, and then Kepler's range (?? -- brighter than LSST can manage-- to 19) OR 19.5 (SNR = 10)
observable = datobsDist.loc[PeriodOut != -999].index
observable_03 = datobsDist.loc[(PeriodIn <= 0.3) & (PeriodOut != -999)].index
observable_1 = datobsDist.loc[(PeriodIn <= 1) & (PeriodOut != -999)].index
observable_10 = datobsDist.loc[(PeriodIn <= 10) & (PeriodOut != -999)].index
observable_30 = datobsDist.loc[(PeriodIn <= 30) & (PeriodOut != -999)].index
observable_100 = datobsDist.loc[(PeriodIn <= 100) & (PeriodOut != -999)].index
observable_1000 = datobsDist.loc[(PeriodIn <= 1000) & (PeriodOut != -999)].index
observable_22 = datobsDist.loc[(PeriodOut != -999) & (appMagMean <= 22.)].index
observable_03_22 = datobsDist.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_1_22 = datobsDist.loc[(PeriodIn <= 1) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_10_22 = datobsDist.loc[(PeriodIn <= 10) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_30_22 = datobsDist.loc[(PeriodIn <= 30) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_100_22 = datobsDist.loc[(PeriodIn <= 100) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_1000_22 = datobsDist.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & (appMagMean <= 22.)].index
observable_195 = datobsDist.loc[(PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_03_195 = datobsDist.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_1_195 = datobsDist.loc[(PeriodIn <= 1) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_10_195 = datobsDist.loc[(PeriodIn <= 10) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_30_195 = datobsDist.loc[(PeriodIn <= 30) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_100_195 = datobsDist.loc[(PeriodIn <= 100) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
observable_1000_195 = datobsDist.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & (appMagMean <= 19.5)].index
fullP = abs(PeriodOut - PeriodIn)/PeriodIn
halfP = abs(PeriodOut - 0.5*PeriodIn)/(0.5*PeriodIn)
twiceP = abs(PeriodOut - 2*PeriodIn)/(2*PeriodIn)
recoverable = datobsDist.loc[(PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_03 = datobsDist.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_1 = datobsDist.loc[(PeriodIn <= 1) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_10 = datobsDist.loc[(PeriodIn <= 10) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_30 = datobsDist.loc[(PeriodIn <= 30) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_100 = datobsDist.loc[(PeriodIn <= 100) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_1000 = datobsDist.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP))].index
recoverable_22 = datobsDist.loc[(PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_03_22 = datobsDist.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_1_22 = datobsDist.loc[(PeriodIn <= 1) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_10_22 = datobsDist.loc[(PeriodIn <= 10) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_30_22 = datobsDist.loc[(PeriodIn <= 30) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_100_22 = datobsDist.loc[(PeriodIn <= 100) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_1000_22 = datobsDist.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 22.)].index
recoverable_195 = datobsDist.loc[(PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_03_195 = datobsDist.loc[(PeriodIn <= 0.3) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_1_195 = datobsDist.loc[(PeriodIn <= 1) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_10_195 = datobsDist.loc[(PeriodIn <= 10) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_30_195 = datobsDist.loc[(PeriodIn <= 30) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_100_195 = datobsDist.loc[(PeriodIn <= 100) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
recoverable_1000_195 = datobsDist.loc[(PeriodIn <= 1000) & (PeriodOut != -999) & ((fullP < cutP) | (halfP < cutP) | (twiceP < cutP)) & (appMagMean <= 19.5)].index
P03 = datobsDist.loc[PeriodIn <= 0.3].index
P1 = datobsDist.loc[PeriodIn <= 1].index
P10 = datobsDist.loc[PeriodIn <= 10].index
P30 = datobsDist.loc[PeriodIn <= 30].index
P100 = datobsDist.loc[PeriodIn <= 100].index
P1000 = datobsDist.loc[PeriodIn <= 1000].index
P_22 = datobsDist.loc[appMagMean <= 22.].index
P03_22 = datobsDist.loc[(PeriodIn <= 0.3) & (appMagMean <= 22.)].index
P1_22 = datobsDist.loc[(PeriodIn <= 1) & (appMagMean <= 22.)].index
P10_22 = datobsDist.loc[(PeriodIn <= 10) & (appMagMean <= 22.)].index
P30_22 = datobsDist.loc[(PeriodIn <= 30) & (appMagMean <= 22.)].index
P100_22 = datobsDist.loc[(PeriodIn <= 100) & (appMagMean <= 22.)].index
P1000_22 = datobsDist.loc[(PeriodIn <= 1000) & (appMagMean <= 22.)].index
P_195 = datobsDist.loc[appMagMean <= 19.5].index
P03_195 = datobsDist.loc[(PeriodIn <= 0.3) & (appMagMean <= 19.5)].index
P1_195 = datobsDist.loc[(PeriodIn <= 1) & (appMagMean <= 19.5)].index
P10_195 = datobsDist.loc[(PeriodIn <= 10) & (appMagMean <= 19.5)].index
P30_195 = datobsDist.loc[(PeriodIn <= 30) & (appMagMean <= 19.5)].index
P100_195 = datobsDist.loc[(PeriodIn <= 100) & (appMagMean <= 19.5)].index
P1000_195 = datobsDist.loc[(PeriodIn <= 1000) & (appMagMean <= 19.5)].index
N_all = (len(PeriodIn)/len(PeriodIn))*N_mult
N_all03 = (len(P03)/len(PeriodIn))*N_mult
N_all1 = (len(P1)/len(PeriodIn))*N_mult
N_all10 = (len(P10)/len(PeriodIn))*N_mult
N_all30 = (len(P30)/len(PeriodIn))*N_mult
N_all100 = (len(P100)/len(PeriodIn))*N_mult
N_all1000 = (len(P1000)/len(PeriodIn))*N_mult
N_all_22 = (len(P_22)/len(PeriodIn))*N_mult
N_all03_22 = (len(P03_22)/len(PeriodIn))*N_mult
N_all1_22 = (len(P1_22)/len(PeriodIn))*N_mult
N_all10_22 = (len(P10_22)/len(PeriodIn))*N_mult
N_all30_22 = (len(P30_22)/len(PeriodIn))*N_mult
N_all100_22 = (len(P100_22)/len(PeriodIn))*N_mult
N_all1000_22 = (len(P1000_22)/len(PeriodIn))*N_mult
N_all_195 = (len(P_195)/len(PeriodIn))*N_mult
N_all03_195 = (len(P03_195)/len(PeriodIn))*N_mult
N_all1_195 = (len(P1_195)/len(PeriodIn))*N_mult
N_all10_195 = (len(P10_195)/len(PeriodIn))*N_mult
N_all30_195 = (len(P30_195)/len(PeriodIn))*N_mult
N_all100_195 = (len(P100_195)/len(PeriodIn))*N_mult
N_all1000_195 = (len(P1000_195)/len(PeriodIn))*N_mult
N_obs = (len(observable)/len(PeriodIn))*N_mult
N_obs03 = (len(observable_03)/len(PeriodIn))*N_mult
N_obs1 = (len(observable_1)/len(PeriodIn))*N_mult
N_obs10 = (len(observable_10)/len(PeriodIn))*N_mult
N_obs30 = (len(observable_30)/len(PeriodIn))*N_mult
N_obs100 = (len(observable_100)/len(PeriodIn))*N_mult
N_obs1000 = (len(observable_1000)/len(PeriodIn))*N_mult
N_obs_22 = (len(observable_22)/len(PeriodIn))*N_mult
N_obs03_22 = (len(observable_03_22)/len(PeriodIn))*N_mult
N_obs1_22 = (len(observable_1_22)/len(PeriodIn))*N_mult
N_obs10_22 = (len(observable_10_22)/len(PeriodIn))*N_mult
N_obs30_22 = (len(observable_30_22)/len(PeriodIn))*N_mult
N_obs100_22 = (len(observable_100_22)/len(PeriodIn))*N_mult
N_obs1000_22 = (len(observable_1000_22)/len(PeriodIn))*N_mult
N_obs_195 = (len(observable_195)/len(PeriodIn))*N_mult
N_obs03_195 = (len(observable_03_195)/len(PeriodIn))*N_mult
N_obs1_195 = (len(observable_1_195)/len(PeriodIn))*N_mult
N_obs10_195 = (len(observable_10_195)/len(PeriodIn))*N_mult
N_obs30_195 = (len(observable_30_195)/len(PeriodIn))*N_mult
N_obs100_195 = (len(observable_100_195)/len(PeriodIn))*N_mult
N_obs1000_195 = (len(observable_1000_195)/len(PeriodIn))*N_mult
N_rec = (len(recoverable)/len(PeriodIn))*N_mult
N_rec03 = (len(recoverable_03)/len(PeriodIn))*N_mult
N_rec1 = (len(recoverable_1)/len(PeriodIn))*N_mult
N_rec10 = (len(recoverable_10)/len(PeriodIn))*N_mult
N_rec30 = (len(recoverable_30)/len(PeriodIn))*N_mult
N_rec100 = (len(recoverable_100)/len(PeriodIn))*N_mult
N_rec1000 = (len(recoverable_1000)/len(PeriodIn))*N_mult
N_rec_22 = (len(recoverable_22)/len(PeriodIn))*N_mult
N_rec03_22 = (len(recoverable_03_22)/len(PeriodIn))*N_mult
N_rec1_22 = (len(recoverable_1_22)/len(PeriodIn))*N_mult
N_rec10_22 = (len(recoverable_10_22)/len(PeriodIn))*N_mult
N_rec30_22 = (len(recoverable_30_22)/len(PeriodIn))*N_mult
N_rec100_22 = (len(recoverable_100_22)/len(PeriodIn))*N_mult
N_rec1000_22 = (len(recoverable_1000_22)/len(PeriodIn))*N_mult
N_rec_195 = (len(recoverable_195)/len(PeriodIn))*N_mult
N_rec03_195 = (len(recoverable_03_195)/len(PeriodIn))*N_mult
N_rec1_195 = (len(recoverable_1_195)/len(PeriodIn))*N_mult
N_rec10_195 = (len(recoverable_10_195)/len(PeriodIn))*N_mult
N_rec30_195 = (len(recoverable_30_195)/len(PeriodIn))*N_mult
N_rec100_195 = (len(recoverable_100_195)/len(PeriodIn))*N_mult
N_rec1000_195 = (len(recoverable_1000_195)/len(PeriodIn))*N_mult
N_totalobsDist_array.append(float(N_all))
N_totalobservableobsDist_array.append(float(N_obs))
N_totalrecoverableobsDist_array.append(float(N_rec))
N_totalobsDist_array_03.append(float(N_all03))
N_totalobservableobsDist_array_03.append(float(N_obs03))
N_totalrecoverableobsDist_array_03.append(float(N_rec03))
N_totalobsDist_array_1.append(float(N_all1))
N_totalobservableobsDist_array_1.append(float(N_obs1))
N_totalrecoverableobsDist_array_1.append(float(N_rec1))
N_totalobsDist_array_10.append(float(N_all10))
N_totalobservableobsDist_array_10.append(float(N_obs10))
N_totalrecoverableobsDist_array_10.append(float(N_rec10))
N_totalobsDist_array_30.append(float(N_all30))
N_totalobservableobsDist_array_30.append(float(N_obs30))
N_totalrecoverableobsDist_array_30.append(float(N_rec30))
N_totalobsDist_array_100.append(float(N_all100))
N_totalobservableobsDist_array_100.append(float(N_obs100))
N_totalrecoverableobsDist_array_100.append(float(N_rec100))
N_totalobsDist_array_1000.append(float(N_all1000))
N_totalobservableobsDist_array_1000.append(float(N_obs1000))
N_totalrecoverableobsDist_array_1000.append(float(N_rec1000))
N_totalobsDist22_array.append(float(N_all_22))
N_totalobservableobsDist22_array.append(float(N_obs_22))
N_totalrecoverableobsDist22_array.append(float(N_rec_22))
N_totalobsDist22_array_03.append(float(N_all03_22))
N_totalobservableobsDist22_array_03.append(float(N_obs03_22))
N_totalrecoverableobsDist22_array_03.append(float(N_rec03_22))
N_totalobsDist22_array_1.append(float(N_all1_22))
N_totalobservableobsDist22_array_1.append(float(N_obs1_22))
N_totalrecoverableobsDist22_array_1.append(float(N_rec1_22))
N_totalobsDist22_array_10.append(float(N_all10_22))
N_totalobservableobsDist22_array_10.append(float(N_obs10_22))
N_totalrecoverableobsDist22_array_10.append(float(N_rec10_22))
N_totalobsDist22_array_30.append(float(N_all30_22))
N_totalobservableobsDist22_array_30.append(float(N_obs30_22))
N_totalrecoverableobsDist22_array_30.append(float(N_rec30_22))
N_totalobsDist22_array_100.append(float(N_all100_22))
N_totalobservableobsDist22_array_100.append(float(N_obs100_22))
N_totalrecoverableobsDist22_array_100.append(float(N_rec100_22))
N_totalobsDist22_array_1000.append(float(N_all1000_22))
N_totalobservableobsDist22_array_1000.append(float(N_obs1000_22))
N_totalrecoverableobsDist22_array_1000.append(float(N_rec1000_22))
N_totalobsDist195_array.append(float(N_all_195))
N_totalobservableobsDist195_array.append(float(N_obs_195))
N_totalrecoverableobsDist195_array.append(float(N_rec_195))
N_totalobsDist195_array_03.append(float(N_all03_195))
N_totalobservableobsDist195_array_03.append(float(N_obs03_195))
N_totalrecoverableobsDist195_array_03.append(float(N_rec03_195))
N_totalobsDist195_array_1.append(float(N_all1_195))
N_totalobservableobsDist195_array_1.append(float(N_obs1_195))
N_totalrecoverableobsDist195_array_1.append(float(N_rec1_195))
N_totalobsDist195_array_10.append(float(N_all10_195))
N_totalobservableobsDist195_array_10.append(float(N_obs10_195))
N_totalrecoverableobsDist195_array_10.append(float(N_rec10_195))
N_totalobsDist195_array_30.append(float(N_all30_195))
N_totalobservableobsDist195_array_30.append(float(N_obs30_195))
N_totalrecoverableobsDist195_array_30.append(float(N_rec30_195))
N_totalobsDist195_array_100.append(float(N_all100_195))
N_totalobservableobsDist195_array_100.append(float(N_obs100_195))
N_totalrecoverableobsDist195_array_100.append(float(N_rec100_195))
N_totalobsDist195_array_1000.append(float(N_all1000_195))
N_totalobservableobsDist195_array_1000.append(float(N_obs1000_195))
N_totalrecoverableobsDist195_array_1000.append(float(N_rec1000_195))
N_totalobsDist = np.sum(N_totalobsDist_array)
N_totalobsDist_03 = np.sum(N_totalobsDist_array_03)
N_totalobsDist_1 = np.sum(N_totalobsDist_array_1)
N_totalobsDist_10 = np.sum(N_totalobsDist_array_10)
N_totalobsDist_30 = np.sum(N_totalobsDist_array_30)
N_totalobsDist_100 = np.sum(N_totalobsDist_array_100)
N_totalobsDist_1000 = np.sum(N_totalobsDist_array_1000)
N_totalobservableobsDist = np.sum(N_totalobservableobsDist_array)
N_totalobservableobsDist_03 = np.sum(N_totalobservableobsDist_array_03)
N_totalobservableobsDist_1 = np.sum(N_totalobservableobsDist_array_1)
N_totalobservableobsDist_10 = np.sum(N_totalobservableobsDist_array_10)
N_totalobservableobsDist_30 = np.sum(N_totalobservableobsDist_array_30)
N_totalobservableobsDist_100 = np.sum(N_totalobservableobsDist_array_100)
N_totalobservableobsDist_1000 = np.sum(N_totalobservableobsDist_array_1000)
N_totalrecoverableobsDist = np.sum(N_totalrecoverableobsDist_array)
N_totalrecoverableobsDist_03 = np.sum(N_totalrecoverableobsDist_array_03)
N_totalrecoverableobsDist_1 = np.sum(N_totalrecoverableobsDist_array_1)
N_totalrecoverableobsDist_10 = np.sum(N_totalrecoverableobsDist_array_10)
N_totalrecoverableobsDist_30 = np.sum(N_totalrecoverableobsDist_array_30)
N_totalrecoverableobsDist_100 = np.sum(N_totalrecoverableobsDist_array_100)
N_totalrecoverableobsDist_1000 = np.sum(N_totalrecoverableobsDist_array_1000)
N_totalobsDist22 = np.sum(N_totalobsDist22_array)
N_totalobsDist22_03 = np.sum(N_totalobsDist22_array_03)
N_totalobsDist22_1 = np.sum(N_totalobsDist22_array_1)
N_totalobsDist22_10 = np.sum(N_totalobsDist22_array_10)
N_totalobsDist22_30 = np.sum(N_totalobsDist22_array_30)
N_totalobsDist22_100 = np.sum(N_totalobsDist22_array_100)
N_totalobsDist22_1000 = np.sum(N_totalobsDist22_array_1000)
N_totalobservableobsDist22 = np.sum(N_totalobservableobsDist22_array)
N_totalobservableobsDist22_03 = np.sum(N_totalobservableobsDist22_array_03)
N_totalobservableobsDist22_1 = np.sum(N_totalobservableobsDist22_array_1)
N_totalobservableobsDist22_10 = np.sum(N_totalobservableobsDist22_array_10)
N_totalobservableobsDist22_30 = np.sum(N_totalobservableobsDist22_array_30)
N_totalobservableobsDist22_100 = np.sum(N_totalobservableobsDist22_array_100)
N_totalobservableobsDist22_1000 = np.sum(N_totalobservableobsDist22_array_1000)
N_totalrecoverableobsDist22 = np.sum(N_totalrecoverableobsDist22_array)
N_totalrecoverableobsDist22_03 = np.sum(N_totalrecoverableobsDist22_array_03)
N_totalrecoverableobsDist22_1 = np.sum(N_totalrecoverableobsDist22_array_1)
N_totalrecoverableobsDist22_10 = np.sum(N_totalrecoverableobsDist22_array_10)
N_totalrecoverableobsDist22_30 = np.sum(N_totalrecoverableobsDist22_array_30)
N_totalrecoverableobsDist22_100 = np.sum(N_totalrecoverableobsDist22_array_100)
N_totalrecoverableobsDist22_1000 = np.sum(N_totalrecoverableobsDist22_array_1000)
N_totalobsDist195 = np.sum(N_totalobsDist195_array)
N_totalobsDist195_03 = np.sum(N_totalobsDist195_array_03)
N_totalobsDist195_1 = np.sum(N_totalobsDist195_array_1)
N_totalobsDist195_10 = np.sum(N_totalobsDist195_array_10)
N_totalobsDist195_30 = np.sum(N_totalobsDist195_array_30)
N_totalobsDist195_100 = np.sum(N_totalobsDist195_array_100)
N_totalobsDist195_1000 = np.sum(N_totalobsDist195_array_1000)
N_totalobservableobsDist195 = np.sum(N_totalobservableobsDist195_array)
N_totalobservableobsDist195_03 = np.sum(N_totalobservableobsDist195_array_03)
N_totalobservableobsDist195_1 = np.sum(N_totalobservableobsDist195_array_1)
N_totalobservableobsDist195_10 = np.sum(N_totalobservableobsDist195_array_10)
N_totalobservableobsDist195_30 = np.sum(N_totalobservableobsDist195_array_30)
N_totalobservableobsDist195_100 = np.sum(N_totalobservableobsDist195_array_100)
N_totalobservableobsDist195_1000 = np.sum(N_totalobservableobsDist195_array_1000)
N_totalrecoverableobsDist195 = np.sum(N_totalrecoverableobsDist195_array)
N_totalrecoverableobsDist195_03 = np.sum(N_totalrecoverableobsDist195_array_03)
N_totalrecoverableobsDist195_1 = np.sum(N_totalrecoverableobsDist195_array_1)
N_totalrecoverableobsDist195_10 = np.sum(N_totalrecoverableobsDist195_array_10)
N_totalrecoverableobsDist195_30 = np.sum(N_totalrecoverableobsDist195_array_30)
N_totalrecoverableobsDist195_100 = np.sum(N_totalrecoverableobsDist195_array_100)
N_totalrecoverableobsDist195_1000 = np.sum(N_totalrecoverableobsDist195_array_1000)
wholerecoverypercent_obsDist = (N_totalrecoverableobsDist/N_totalobservableobsDist)*100
wholerecoverypercent_obsDist_03 = (N_totalrecoverableobsDist_03/N_totalobservableobsDist_03)*100
wholerecoverypercent_obsDist_1 = (N_totalrecoverableobsDist_1/N_totalobservableobsDist_1)*100
wholerecoverypercent_obsDist_10 = (N_totalrecoverableobsDist_10/N_totalobservableobsDist_10)*100
wholerecoverypercent_obsDist_30 = (N_totalrecoverableobsDist_30/N_totalobservableobsDist_30)*100
wholerecoverypercent_obsDist_100 = (N_totalrecoverableobsDist_100/N_totalobservableobsDist_100)*100
wholerecoverypercent_obsDist_1000 = (N_totalrecoverableobsDist_1000/N_totalobservableobsDist_1000)*100
sigmaobsDist = ((N_totalrecoverableobsDist**(1/2))/N_totalobservableobsDist)*100
sigmaobsDist_03 = ((N_totalrecoverableobsDist_03**(1/2))/N_totalobservableobsDist_03)*100
sigmaobsDist_1 = ((N_totalrecoverableobsDist_1**(1/2))/N_totalobservableobsDist_1)*100
sigmaobsDist_10 = ((N_totalrecoverableobsDist_10**(1/2))/N_totalobservableobsDist_10)*100
sigmaobsDist_30 = ((N_totalrecoverableobsDist_30**(1/2))/N_totalobservableobsDist_30)*100
sigmaobsDist_100 = ((N_totalrecoverableobsDist_100**(1/2))/N_totalobservableobsDist_100)*100
sigmaobsDist_1000 = ((N_totalrecoverableobsDist_1000**(1/2))/N_totalobservableobsDist_1000)*100
overallrecoverypercent_obsDist = (N_totalrecoverableobsDist/N_totalobsDist)*100
overallrecoverypercent_obsDist_03 = (N_totalrecoverableobsDist_03/N_totalobsDist_03)*100
overallrecoverypercent_obsDist_1 = (N_totalrecoverableobsDist_1/N_totalobsDist_1)*100
overallrecoverypercent_obsDist_10 = (N_totalrecoverableobsDist_10/N_totalobsDist_10)*100
overallrecoverypercent_obsDist_30 = (N_totalrecoverableobsDist_30/N_totalobsDist_30)*100
overallrecoverypercent_obsDist_100 = (N_totalrecoverableobsDist_100/N_totalobsDist_100)*100
overallrecoverypercent_obsDist_1000 = (N_totalrecoverableobsDist_1000/N_totalobsDist_1000)*100
overallsigmaobsDist = ((N_totalrecoverableobsDist**(1/2))/N_totalobsDist)*100
overallsigmaobsDist_03 = ((N_totalrecoverableobsDist_03**(1/2))/N_totalobsDist_03)*100
overallsigmaobsDist_1 = ((N_totalrecoverableobsDist_1**(1/2))/N_totalobsDist_1)*100
overallsigmaobsDist_10 = ((N_totalrecoverableobsDist_10**(1/2))/N_totalobsDist_10)*100
overallsigmaobsDist_30 = ((N_totalrecoverableobsDist_30**(1/2))/N_totalobsDist_30)*100
overallsigmaobsDist_100 = ((N_totalrecoverableobsDist_100**(1/2))/N_totalobsDist_100)*100
overallsigmaobsDist_1000 = ((N_totalrecoverableobsDist_1000**(1/2))/N_totalobsDist_1000)*100
wholerecoverypercent_obsDist22 = (N_totalrecoverableobsDist22/N_totalobservableobsDist22)*100
wholerecoverypercent_obsDist22_03 = (N_totalrecoverableobsDist22_03/N_totalobservableobsDist22_03)*100
wholerecoverypercent_obsDist22_1 = (N_totalrecoverableobsDist22_1/N_totalobservableobsDist22_1)*100
wholerecoverypercent_obsDist22_10 = (N_totalrecoverableobsDist22_10/N_totalobservableobsDist22_10)*100
wholerecoverypercent_obsDist22_30 = (N_totalrecoverableobsDist22_30/N_totalobservableobsDist22_30)*100
wholerecoverypercent_obsDist22_100 = (N_totalrecoverableobsDist22_100/N_totalobservableobsDist22_100)*100
wholerecoverypercent_obsDist22_1000 = (N_totalrecoverableobsDist22_1000/N_totalobservableobsDist22_1000)*100
sigmaobsDist22 = ((N_totalrecoverableobsDist22**(1/2))/N_totalobservableobsDist22)*100
sigmaobsDist22_03 = ((N_totalrecoverableobsDist22_03**(1/2))/N_totalobservableobsDist22_03)*100
sigmaobsDist22_1 = ((N_totalrecoverableobsDist22_1**(1/2))/N_totalobservableobsDist22_1)*100
sigmaobsDist22_10 = ((N_totalrecoverableobsDist22_10**(1/2))/N_totalobservableobsDist22_10)*100
sigmaobsDist22_30 = ((N_totalrecoverableobsDist22_30**(1/2))/N_totalobservableobsDist22_30)*100
sigmaobsDist22_100 = ((N_totalrecoverableobsDist22_100**(1/2))/N_totalobservableobsDist22_100)*100
sigmaobsDist22_1000 = ((N_totalrecoverableobsDist22_1000**(1/2))/N_totalobservableobsDist22_1000)*100
overallrecoverypercent_obsDist22 = (N_totalrecoverableobsDist22/N_totalobsDist22)*100
overallrecoverypercent_obsDist22_03 = (N_totalrecoverableobsDist22_03/N_totalobsDist22_03)*100
overallrecoverypercent_obsDist22_1 = (N_totalrecoverableobsDist22_1/N_totalobsDist22_1)*100
overallrecoverypercent_obsDist22_10 = (N_totalrecoverableobsDist22_10/N_totalobsDist22_10)*100
overallrecoverypercent_obsDist22_30 = (N_totalrecoverableobsDist22_30/N_totalobsDist22_30)*100
overallrecoverypercent_obsDist22_100 = (N_totalrecoverableobsDist22_100/N_totalobsDist22_100)*100
overallrecoverypercent_obsDist22_1000 = (N_totalrecoverableobsDist22_1000/N_totalobsDist22_1000)*100
overallsigmaobsDist22 = ((N_totalrecoverableobsDist22**(1/2))/N_totalobsDist22)*100
overallsigmaobsDist22_03 = ((N_totalrecoverableobsDist22_03**(1/2))/N_totalobsDist22_03)*100
overallsigmaobsDist22_1 = ((N_totalrecoverableobsDist22_1**(1/2))/N_totalobsDist22_1)*100
overallsigmaobsDist22_10 = ((N_totalrecoverableobsDist22_10**(1/2))/N_totalobsDist22_10)*100
overallsigmaobsDist22_30 = ((N_totalrecoverableobsDist22_30**(1/2))/N_totalobsDist22_30)*100
overallsigmaobsDist22_100 = ((N_totalrecoverableobsDist22_100**(1/2))/N_totalobsDist22_100)*100
overallsigmaobsDist22_1000 = ((N_totalrecoverableobsDist22_1000**(1/2))/N_totalobsDist22_1000)*100
wholerecoverypercent_obsDist195 = (N_totalrecoverableobsDist195/N_totalobservableobsDist195)*100
wholerecoverypercent_obsDist195_03 = (N_totalrecoverableobsDist195_03/N_totalobservableobsDist195_03)*100
wholerecoverypercent_obsDist195_1 = (N_totalrecoverableobsDist195_1/N_totalobservableobsDist195_1)*100
wholerecoverypercent_obsDist195_10 = (N_totalrecoverableobsDist195_10/N_totalobservableobsDist195_10)*100
wholerecoverypercent_obsDist195_30 = (N_totalrecoverableobsDist195_30/N_totalobservableobsDist195_30)*100
wholerecoverypercent_obsDist195_100 = (N_totalrecoverableobsDist195_100/N_totalobservableobsDist195_100)*100
wholerecoverypercent_obsDist195_1000 = (N_totalrecoverableobsDist195_1000/N_totalobservableobsDist195_1000)*100
sigmaobsDist195 = ((N_totalrecoverableobsDist195**(1/2))/N_totalobservableobsDist195)*100
sigmaobsDist195_03 = ((N_totalrecoverableobsDist195_03**(1/2))/N_totalobservableobsDist195_03)*100
sigmaobsDist195_1 = ((N_totalrecoverableobsDist195_1**(1/2))/N_totalobservableobsDist195_1)*100
sigmaobsDist195_10 = ((N_totalrecoverableobsDist195_10**(1/2))/N_totalobservableobsDist195_10)*100
sigmaobsDist195_30 = ((N_totalrecoverableobsDist195_30**(1/2))/N_totalobservableobsDist195_30)*100
sigmaobsDist195_100 = ((N_totalrecoverableobsDist195_100**(1/2))/N_totalobservableobsDist195_100)*100
sigmaobsDist195_1000 = ((N_totalrecoverableobsDist195_1000**(1/2))/N_totalobservableobsDist195_1000)*100
overallrecoverypercent_obsDist195 = (N_totalrecoverableobsDist195/N_totalobsDist195)*100
overallrecoverypercent_obsDist195_03 = (N_totalrecoverableobsDist195_03/N_totalobsDist195_03)*100
overallrecoverypercent_obsDist195_1 = (N_totalrecoverableobsDist195_1/N_totalobsDist195_1)*100
overallrecoverypercent_obsDist195_10 = (N_totalrecoverableobsDist195_10/N_totalobsDist195_10)*100
overallrecoverypercent_obsDist195_30 = (N_totalrecoverableobsDist195_30/N_totalobsDist195_30)*100
overallrecoverypercent_obsDist195_100 = (N_totalrecoverableobsDist195_100/N_totalobsDist195_100)*100
overallrecoverypercent_obsDist195_1000 = (N_totalrecoverableobsDist195_1000/N_totalobsDist195_1000)*100
overallsigmaobsDist195 = ((N_totalrecoverableobsDist195**(1/2))/N_totalobsDist195)*100
overallsigmaobsDist195_03 = ((N_totalrecoverableobsDist195_03**(1/2))/N_totalobsDist195_03)*100
overallsigmaobsDist195_1 = ((N_totalrecoverableobsDist195_1**(1/2))/N_totalobsDist195_1)*100
overallsigmaobsDist195_10 = ((N_totalrecoverableobsDist195_10**(1/2))/N_totalobsDist195_10)*100
overallsigmaobsDist195_30 = ((N_totalrecoverableobsDist195_30**(1/2))/N_totalobsDist195_30)*100
overallsigmaobsDist195_100 = ((N_totalrecoverableobsDist195_100**(1/2))/N_totalobsDist195_100)*100
overallsigmaobsDist195_1000 = ((N_totalrecoverableobsDist195_1000**(1/2))/N_totalobsDist195_1000)*100\
print("N_totalobsDist = ", N_totalobsDist, "and in log = ", np.log10(N_totalobsDist), "**** N_totalobservableobsDist = ", N_totalobservableobsDist, "and in log = ", np.log10(N_totalobservableobsDist), "**** N_totalrecoverableobsDist = ", N_totalrecoverableobsDist, "and in log = ", np.log10(N_totalrecoverableobsDist))
print("N_totalobsDist_03 = ", N_totalobsDist_03, "and in log = ", np.log10(N_totalobsDist_03), "**** N_totalobservableobsDist_03 = ", N_totalobservableobsDist_03, "and in log = ", np.log10(N_totalobservableobsDist_03), "**** N_totalrecoverableobsDist_03 = ", N_totalrecoverableobsDist_03, "and in log = ", np.log10(N_totalrecoverableobsDist_03))
print("N_totalobsDist_1 = ", N_totalobsDist_1, "and in log = ", np.log10(N_totalobsDist_1), "**** N_totalobservableobsDist_1 = ", N_totalobservableobsDist_1, "and in log = ", np.log10(N_totalobservableobsDist_1), "**** N_totalrecoverableobsDist_1 = ", N_totalrecoverableobsDist_1, "and in log = ", np.log10(N_totalrecoverableobsDist_1))
print("N_totalobsDist_10 = ", N_totalobsDist_10, "and in log = ", np.log10(N_totalobsDist_10), "**** N_totalobservableobsDist_10 = ", N_totalobservableobsDist_10, "and in log = ", np.log10(N_totalobservableobsDist_10), "**** N_totalrecoverableobsDist_10 = ", N_totalrecoverableobsDist_10, "and in log = ", np.log10(N_totalrecoverableobsDist_10))
print("N_totalobsDist_30 = ", N_totalobsDist_30, "and in log = ", | np.log10(N_totalobsDist_30) | numpy.log10 |
import numpy as np
import matplotlib.pyplot as plt
from scipy import interpolate
from matplotlib.colors import LinearSegmentedColormap
from mpl_toolkits.axes_grid1.inset_locator import (
inset_axes, Bbox, BboxConnector, BboxPatch, TransformedBbox)
import src.visualization.grid_viz as grid_viz
def time_evol_ling(ling_props_dict, x_data, idx_data_to_plot=None,
idx_ling_to_plot=None, figsize=None, bottom_ylim=0, ax=None,
fig_save_path=None, show=True, color_cycle=None, legend=True,
**scatter_kwargs):
'''
Plot the time evolution of the proportions of each ling group whose order
in `ling_props_dict` is contained in `idx_ling_to_plot`. The times are given
by `x_data`, and the indices of the selected data points are in
`idx_ling_to_plot`.
'''
if ax is None:
fig, ax = plt.subplots(1, figsize=figsize)
ling_labels = list(ling_props_dict.keys())
if idx_data_to_plot is None:
idx_data_to_plot = np.arange(0, len(ling_props_dict[ling_labels[0]]))
if idx_ling_to_plot is None:
idx_ling_to_plot = range(len(ling_labels))
if color_cycle is None:
# This selects the default color cycle.
color_cycle = plt.rcParams['axes.prop_cycle'].by_key()['color']
x_plot = x_data[idx_data_to_plot]
for i in idx_ling_to_plot:
ling_label = ling_labels[i]
y_plot = np.array(ling_props_dict[ling_label])[idx_data_to_plot]
# By using the ith element of the color_cycle, we ensure that if we plot
# multiple graphs, a given language will have a consistent colour.
ax.scatter(x_plot, y_plot, label=ling_label, c=(color_cycle[i],),
**scatter_kwargs)
if len(ling_props_dict) > 1:
ax.set_ylim(bottom=bottom_ylim)
if legend:
ax.legend()
ax.set_xlabel('step')
ax.set_ylabel(r'$p_{L}$')
if fig_save_path:
fig.savefig(fig_save_path)
if show:
fig.show()
return ax
def scatter_inset(x_data, ling_props_dict, bbox_to_anchor, inset_interval,
idx_grp_inset, save_path=None, show=True, figsize=None,
ax=None, fig=None, color_cycle=None, top_ylim=None,
inset_left=True):
'''
Makes a scatter plot of the proportions for each group contained in
`ling_props_dict` over the times `x_data`, and adds an inset zooming over
the time interval `inset_interval` of the `idx_grp_inset`-th group. The
inset is placed within `bbox_to_anchor`.
'''
if ax is None:
fig, ax = plt.subplots(1, figsize=figsize)
if color_cycle is None:
color_cycle = plt.rcParams['axes.prop_cycle'].by_key()['color']
ling_labels = list(ling_props_dict.keys())
len_data = len(ling_props_dict[ling_labels[0]])
idx_data_to_plot = | np.arange(0, len_data) | numpy.arange |
from chart import bar, histogram, scatter
from chart.preprocessing import NumberBinarizer
from chart.preprocessing import RangeScaler
# Example 1A
from chart import bar
x = [500, 200, 900, 400]
y = ['marc', 'mummify', 'chart', 'sausagelink']
bar(x, y)
# Example 1B
from chart import bar
import pandas as pd
df = pd.DataFrame({
'artist': ['<NAME>', '<NAME>', 'The Knocks'],
'listens': [8_456_831, 18_185_245, 2_556_448]
})
bar(df.listens, df.artist, width=20, label_width=11, mark='🔊')
# Example 2A
from chart import histogram
x = [1, 2, 4, 3, 3, 1, 7, 9, 9, 1, 3, 2, 1, 2]
histogram(x)
# Example 2B
from chart import histogram
import scipy.stats as stats
import numpy as np
| np.random.seed(14) | numpy.random.seed |
# %%
from functools import partial
import logging
import numpy as np
import torch
import colorsys
from torchvtk.utils import make_5d, tex_from_pts
# Persistent Homology peak extraction
class Peak:
def __init__(self, startidx):
self.born = self.left = self.right = startidx
self.died = None
def get_persistence(self, seq):
return seq[self.born] if self.died is None else seq[self.born] - seq[self.died]
def get_persistent_homology(seq):
peaks = []
# Maps indices to peaks
idxtopeak = [None for s in seq]
# Sequence indices sorted by values
indices = range(len(seq))
indices = sorted(indices, key = lambda i: seq[i], reverse=True)
# Process each sample in descending order
for idx in indices:
lftdone = (idx > 0 and idxtopeak[idx-1] is not None)
rgtdone = (idx < len(seq)-1 and idxtopeak[idx+1] is not None)
il = idxtopeak[idx-1] if lftdone else None
ir = idxtopeak[idx+1] if rgtdone else None
# New peak born
if not lftdone and not rgtdone:
peaks.append(Peak(idx))
idxtopeak[idx] = len(peaks)-1
# Directly merge to next peak left
if lftdone and not rgtdone:
peaks[il].right += 1
idxtopeak[idx] = il
# Directly merge to next peak right
if not lftdone and rgtdone:
peaks[ir].left -= 1
idxtopeak[idx] = ir
# Merge left and right peaks
if lftdone and rgtdone:
# Left was born earlier: merge right to left
if seq[peaks[il].born] > seq[peaks[ir].born]:
peaks[ir].died = idx
peaks[il].right = peaks[ir].right
idxtopeak[peaks[il].right] = idxtopeak[idx] = il
else:
peaks[il].died = idx
peaks[ir].left = peaks[il].left
idxtopeak[peaks[ir].left] = idxtopeak[idx] = ir
# This is optional convenience
return sorted(peaks, key=lambda p: p.get_persistence(seq), reverse=True)
def distinguishable_color_generator():
''' Generates distinguishable colors, compare
http://alumni.media.mit.edu/~wad/color/numbers.html
'''
colors = np.array([
[173, 35, 35],
[42, 75, 215],
[29, 105, 20],
[129, 74, 25],
[129, 38, 192],
[160, 160, 160],
[129, 197, 122],
[157, 175, 255],
[41, 208, 208],
[255, 146, 51],
[255, 238, 51],
[255, 205, 243],
[255, 255, 255]
], dtype=np.float32) / 255.0
np.random.shuffle(colors)
for color in colors:
yield color
def random_color_generator():
''' Generates random colors '''
while True:
h, s, l = np.random.rand(), 0.2 + np.random.rand() * 0.8, 0.35 + np.random.rand() * 0.3
yield np.array([float(255*i) for i in colorsys.hls_to_rgb(h,l,s)], dtype=np.float32) / 255.0
def fixed_color_generator(color=(180, 170, 170.0)):
while True: yield np.array(color).astype(np.float32) / 255.0
def get_histogram_peaks(data, bins=1024, skip_outlier=True):
vals, ranges = np.histogram(data, bins)
peaks = get_persistent_homology(vals)
ret = np.array(list(map(lambda p: (
(ranges[p.born] + ranges[p.born+1])/2.0, # intensity value
p.get_persistence(vals)), peaks # persistence for peak importance
)))
return np.stack([ret[:, 0], ret[:, 1] / peaks[0].get_persistence(vals)], axis=1)
def overlaps_trapeze(trap, ts):
for t in ts:
if trap[0,0] < t[5,0] and trap[5,0] > t[0,0]: return True
return False
def includes_maxvalue(trap, vol=None):
return trap[5, 0] >= (1.0 if vol is None else vol.max())
def includes_minvalue(trap, vol=None, eps=1e-2):
return trap[0, 0] <= (eps if vol is None else vol.min() + eps)
def flatten_clip_sort_peaks(peaks):
if len(peaks) == 0:
peaks = np.zeros((1,5))
arr = np.clip(np.stack(peaks).reshape((-1, 5)), 0, 1)
idx = np.argsort(arr[:, 0])
return arr[idx]
def colorize_trapeze(t, color):
res = np.zeros((t.shape[0], 5))
res[:, 0] = t[:, 0]
res[:, 1:4] = color
res[:, 4] = t[:, 1]
return res
def make_trapezoid(c, top_height, bot_width, fixed_shape=False):
# bot_width = bot_width * c + 1e-2 # allow for wider peaks in higher density
# int_contrib = np.clip(c * (1/0.6), 0, 1) # higher opacity on higher density (usually bones, which are often occluded)
# top_height = (int_contrib + top_height) / 2.0 # allow for mostly low peaks on skin, higher peaks on bones
if fixed_shape:
bot_height = top_height
top_width = bot_width
else:
bot_height = np.random.rand(1).item() * top_height
top_width = np.random.rand(1).item() * bot_width
return np.stack([
np.array([c - bot_width/2 -2e-2, 0]), # left wall ____________ __ top_height
np.array([c - bot_width/2, bot_height]), # bottom left / top_width \
np.array([c - top_width/2, top_height]), # top left /__ bot_width __\__ bot_height
np.array([c + top_width/2, top_height]), # top right | |
np.array([c + bot_width/2, bot_height]), # bottom right | right wall ->|
np.array([c + bot_width/2 +2e-2, 0]) # right wall |<- left wall |
])
def get_tf_pts_from_peaks(peaks, colors='random', height_range=(0.1, 0.9), width_range=(0.02, 0.2), peak_center_noise_std=0.05, max_num_peaks=5, peak_valid_fn=None, fixed_shape=False):
''' Compute transfer function with non-overlapping trapezoids around given peaks
Args:
peaks (np.array of [intensity, persistence]): The histogram peaks
colors (str): Either "distinguishable", "random" or "fixed"
height_range (tuple of floats): Range in which to draw trapezoid height (=opacity). Max range is (0, 1)
width_range (tuple of floats): Range in which to draw trapezoid width around peak. Max range is (0, 1)
peak_center_noise_std (float): Standard deviation of the Gaussian noise applied to peak centers, to shift those randomly.
max_num_peaks (int): Maximum number of peaks in the histogram. The number will be drawn as U(1, max_num_peaks)
peak_valid_fn (func): Function that gets the old TF without a new peak and the TF with the new peak and decides wether to add the peak (return True) or not (return False).
fixed_shape (bool): If True produces a classic ramp peak, if False it has random double ramps
Returns:
[ np.array [x, y] ]: List of TF primitives (List of coordinates [0,1]²) to be lerped
'''
if peak_valid_fn is None: peak_valid_fn = lambda a, b: True
if max_num_peaks is None:
n_peaks = len(peaks)
elif isinstance(max_num_peaks, (tuple, list)) and len(max_num_peaks) == 2:
n_peaks = np.random.randint(max_num_peaks[0], max_num_peaks[1] + 1)
else:
n_peaks = np.random.randint(1, max_num_peaks+1)
height_range_len = height_range[1] - height_range[0]
width_range_len = width_range[1] - width_range[0]
if colors == 'distinguishable': color_gen = distinguishable_color_generator()
elif colors == 'random': color_gen = random_color_generator()
elif colors == 'fixed': color_gen = fixed_color_generator()
else: raise Exception(f'Invalid colors argument ({colors}). Use either "distinguishable" or "random".') # | c |__ 0
if peaks is None:
peaks = np.random.rand(100, 2)
peaks = np.stack([np.linspace(0.05, 0.75, 15)]*2, axis=1)
trapezes = [make_trapezoid(c + np.random.randn() * peak_center_noise_std, # Center of peak
top_height= height_range_len * | np.random.rand(1) | numpy.random.rand |
"""
Test script for PE analysis.
"""
import os
import numpy as np
import pytest
from bilby.core.prior import PriorDict
from cwinpy.data import HeterodynedData
from cwinpy.pe.pe import PERunner, pe
class TestPE(object):
@classmethod
def setup_class(cls):
"""
Create data set files for use.
"""
seed = 88523 # random seed
start = 1000000000 # GPS start
end = 1000086400 # GPS end
step = 60 # time step size
# time stamp array
cls.times = np.arange(start, end, step)
size = len(cls.times)
# create pulsar parameter file
cls.f0 = 100.1 # frequency
parcontent = (
"PSRJ J0341-1253\n"
"F0 {}\n"
"F1 6.5e-12\n"
"RAJ 03:41:00.0\n"
"DECJ -12:53:00.0\n"
"PEPOCH 56789"
)
cls.parfile = "pe_test.par"
with open(cls.parfile, "w") as fp:
fp.write(parcontent.format(cls.f0))
# set random seed
np.random.seed(seed)
# create simulated H1 data (at 1 and 2f)
cls.H1data = []
cls.H1file = []
cls.H1fileh5 = []
H1sigma = 1e-24
for i in [1, 2]:
cls.H1data.append(
np.vstack(
(
cls.times,
H1sigma * np.random.randn(size),
H1sigma * np.random.randn(size),
)
).T
)
cls.H1file.append("H1data{}f.txt".format(i))
np.savetxt(cls.H1file[-1], cls.H1data[-1])
# create HDF5 version of data
cls.H1fileh5.append("H1data{}f.hdf5".format(i))
hd = HeterodynedData(data=cls.H1data[-1], detector="H1", par=cls.parfile)
hd.write(cls.H1fileh5[-1])
# create simulated L1 data
cls.L1data = []
cls.L1file = []
cls.L1fileh5 = []
L1sigma = 0.7e-24
for i in [1, 2]:
cls.L1data.append(
np.vstack(
(
cls.times,
L1sigma * np.random.randn(size),
L1sigma * np.random.randn(size),
)
).T
)
cls.L1file.append("L1data{}f.txt".format(i))
np.savetxt(cls.L1file[-1], cls.L1data[-1])
# create HDF5 version of data
cls.L1fileh5.append("L1data{}f.hdf5".format(i))
hd = HeterodynedData(data=cls.L1data[-1], detector="L1", par=cls.parfile)
hd.write(cls.L1fileh5[-1])
# create a pulsar parameter file containing GW signal parameters
# (for comparison with lalapps_pulsar_parameter_estimation_nested)
parcontent = (
"PSRJ J0341-1253\n"
"F0 {}\n"
"F1 6.5e-12\n"
"RAJ 03:41:00.0\n"
"DECJ -12:53:00.0\n"
"PEPOCH 56789\n"
"C21 6.2e-24\n"
"C22 3.4e-25\n"
"PHI21 0.4\n"
"PHI22 1.3\n"
"PSI 1.1\n"
"IOTA 0.9\n"
"UNITS TCB"
)
cls.parfilesig = "pe_test_sig.par"
with open(cls.parfilesig, "w") as fp:
fp.write(parcontent.format(cls.f0))
# set data pre-produced using lalapps_pulsar_parameter_estimation_nested
# with the same parameter file
cls.sigH11f = np.loadtxt(
os.path.join(
os.path.dirname(os.path.realpath(__file__)),
"data",
"inj_test.txt_H1_1.0_signal_only",
)
)
cls.sigL11f = np.loadtxt(
os.path.join(
os.path.dirname(os.path.realpath(__file__)),
"data",
"inj_test.txt_L1_1.0_signal_only",
)
)
cls.sigH12f = np.loadtxt(
os.path.join(
os.path.dirname(os.path.realpath(__file__)),
"data",
"inj_test.txt_H1_2.0_signal_only",
)
)
cls.sigL12f = np.loadtxt(
os.path.join(
os.path.dirname(os.path.realpath(__file__)),
"data",
"inj_test.txt_L1_2.0_signal_only",
)
)
# create a prior file
cls.priorfile = "pe_test.prior"
cls.priormin = 0.0
cls.priormax = 1e-22
priorcontent = "h0 = Uniform(name='h0', minimum={}, maximum={})"
with open(cls.priorfile, "w") as fp:
fp.write(priorcontent.format(cls.priormin, cls.priormax))
cls.priorbilby = PriorDict(cls.priorfile)
@classmethod
def teardown_class(cls):
"""
Remove data set files.
"""
for dfile in cls.H1file + cls.L1file + cls.H1fileh5 + cls.L1fileh5:
os.remove(dfile)
os.remove(cls.parfile)
os.remove(cls.parfilesig)
os.remove(cls.priorfile)
def test_pe_runner_input(self):
"""
Test the PERunner class fails as expected for wrong input types.
"""
for inputs in [1.0, "hello", 1, True]:
with pytest.raises(TypeError):
PERunner(inputs)
def test_data_input(self):
"""
Test input data
"""
# single detector and single data file
config = "par-file = {}\ndata-file = {}\nprior = {}\ndata-kwargs={}"
configfile = "config_test.ini"
datafile = self.H1file[1]
datakwargs = {"remove_outliers": False}
with open(configfile, "w") as fp:
fp.write(config.format(self.parfile, datafile, self.priorfile, datakwargs))
# no detector specified
with pytest.raises(ValueError):
pe(config=configfile)
with pytest.raises(ValueError):
pe(par_file=self.parfile, data_file=datafile)
# not prior file specified
with pytest.raises(ValueError):
pe(par_file=self.parfile, data_file=datafile, detector="H1")
# comparisons
# pass as keyword arguments (detector as keyword)
t1kw1 = pe(
par_file=self.parfile,
data_file=datafile,
detector="H1",
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file string)
t1kw2 = pe(
par_file=self.parfile,
data_file="{}:{}".format("H1", datafile),
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file dict)
t1kw3 = pe(
par_file=self.parfile,
data_file={"H1": datafile},
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as config file
config = (
"par-file = {}\ndata-file = {}\nprior = {}\ndetector = H1\ndata-kwargs = {}"
)
with open(configfile, "w") as fp:
fp.write(config.format(self.parfile, datafile, self.priorfile, datakwargs))
t1c1 = pe(config=configfile)
# use the data_file_2f option instead
t1kw4 = pe(
par_file=self.parfile,
data_file_2f=datafile,
detector="H1",
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file string)
t1kw5 = pe(
par_file=self.parfile,
data_file_2f="{}:{}".format("H1", datafile),
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file dict)
t1kw6 = pe(
par_file=self.parfile,
data_file_2f={"H1": datafile},
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as config file
config = "par-file = {}\ndata-file-2f = {}\nprior = {}\ndetector = H1\ndata-kwargs = {}"
with open(configfile, "w") as fp:
fp.write(config.format(self.parfile, datafile, self.priorfile, datakwargs))
t1c2 = pe(config=configfile)
# perform consistency checks
for tv in [t1kw1, t1kw2, t1kw3, t1c1, t1kw4, t1kw5, t1kw6, t1c2]:
assert len(tv.hetdata) == 1
assert tv.hetdata["H1"][0].par["F"][0] == self.f0
assert tv.hetdata.detectors[0] == "H1"
assert tv.hetdata.freq_factors[0] == 2
assert np.allclose(tv.hetdata["H1"][0].data.real, self.H1data[1][:, 1])
assert np.allclose(tv.hetdata["H1"][0].data.imag, self.H1data[1][:, 2])
assert np.allclose(tv.hetdata["H1"][0].times.value, self.times)
assert PriorDict(tv.prior) == self.priorbilby
# now pass two detectors
# pass as keyword arguments (detector as keyword)
t2kw1 = pe(
par_file=self.parfile,
data_file=[self.H1file[1], self.L1file[1]],
detector=["H1", "L1"],
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file string)
t2kw2 = pe(
par_file=self.parfile,
data_file=[
"{}:{}".format("H1", self.H1file[1]),
"{}:{}".format("L1", self.L1file[1]),
],
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file dict)
t2kw3 = pe(
par_file=self.parfile,
data_file={"H1": self.H1file[1], "L1": self.L1file[1]},
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as config file
config = (
"par-file = {}\n"
"data-file = [{}, {}]\n"
"prior = {}\n"
"detector = [H1, L1]\n"
"data-kwargs = {}"
)
with open(configfile, "w") as fp:
fp.write(
config.format(
self.parfile,
self.H1file[1],
self.L1file[1],
self.priorfile,
datakwargs,
)
)
t2c1 = pe(config=configfile)
# use the data_file_2f option instead
t2kw4 = pe(
par_file=self.parfile,
data_file_2f=[self.H1file[1], self.L1file[1]],
detector=["H1", "L1"],
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file string)
t2kw5 = pe(
par_file=self.parfile,
data_file_2f=[
"{}:{}".format("H1", self.H1file[1]),
"{}:{}".format("L1", self.L1file[1]),
],
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file dict)
t2kw6 = pe(
par_file=self.parfile,
data_file_2f={"H1": self.H1file[1], "L1": self.L1file[1]},
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as config file
config = (
"par-file = {}\n"
"data-file-2f = [{}, {}]\n"
"prior = {}\n"
"detector = [H1, L1]\n"
"data-kwargs = {}"
)
with open(configfile, "w") as fp:
fp.write(
config.format(
self.parfile,
self.H1file[1],
self.L1file[1],
self.priorfile,
datakwargs,
)
)
t2c2 = pe(config=configfile)
# perform consistency checks
for tv in [t2kw1, t2kw2, t2kw3, t2c1, t2kw4, t2kw5, t2kw6, t2c2]:
assert len(tv.hetdata) == 2
for i, det, data in zip(
range(2), ["H1", "L1"], [self.H1data[1], self.L1data[1]]
):
assert tv.hetdata.detectors[i] == det
assert tv.hetdata.freq_factors[0] == 2
assert tv.hetdata[det][0].par["F"][0] == self.f0
assert np.allclose(tv.hetdata[det][0].data.real, data[:, 1])
assert np.allclose(tv.hetdata[det][0].data.imag, data[:, 2])
assert np.allclose(tv.hetdata[det][0].times.value, self.times)
assert PriorDict(tv.prior) == self.priorbilby
# pass data at 1f
datafile = self.H1file[0]
t3kw1 = pe(
par_file=self.parfile,
data_file_1f=datafile,
detector="H1",
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file string)
t3kw2 = pe(
par_file=self.parfile,
data_file_1f="{}:{}".format("H1", datafile),
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file dict)
t3kw3 = pe(
par_file=self.parfile,
data_file_1f={"H1": datafile},
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as config file
config = "par-file = {}\ndata-file-1f = {}\nprior = {}\ndetector = H1\ndata-kwargs = {}"
with open(configfile, "w") as fp:
fp.write(config.format(self.parfile, datafile, self.priorfile, datakwargs))
t3c1 = pe(config=configfile)
# perform consistency checks
for tv in [t3kw1, t3kw2, t3kw3, t3c1]:
assert len(tv.hetdata) == 1
assert tv.hetdata.detectors[0] == "H1"
assert tv.hetdata.freq_factors[0] == 1
assert tv.hetdata["H1"][0].par["F"][0] == self.f0
assert np.allclose(tv.hetdata["H1"][0].data.real, self.H1data[0][:, 1])
assert np.allclose(tv.hetdata["H1"][0].data.imag, self.H1data[0][:, 2])
assert np.allclose(tv.hetdata["H1"][0].times.value, self.times)
assert PriorDict(tv.prior) == self.priorbilby
# test with two detectors and two frequencies
# pass as keyword arguments (detector as keyword)
t4kw1 = pe(
par_file=self.parfile,
data_file_1f=[self.H1file[0], self.L1file[0]],
data_file_2f=[self.H1file[1], self.L1file[1]],
detector=["H1", "L1"],
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file string)
t4kw2 = pe(
par_file=self.parfile,
data_file_1f=[
"{}:{}".format("H1", self.H1file[0]),
"{}:{}".format("L1", self.L1file[0]),
],
data_file_2f=[
"{}:{}".format("H1", self.H1file[1]),
"{}:{}".format("L1", self.L1file[1]),
],
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as keyword arguments (detector in data file dict)
t4kw3 = pe(
par_file=self.parfile,
data_file_1f={"H1": self.H1file[0], "L1": self.L1file[0]},
data_file_2f={"H1": self.H1file[1], "L1": self.L1file[1]},
prior=self.priorbilby,
data_kwargs=datakwargs,
)
# pass as config file
config = (
"par-file = {}\n"
"data-file-1f = [{}, {}]\n"
"data-file-2f = [{}, {}]\n"
"prior = {}\n"
"detector = [H1, L1]\n"
"data-kwargs = {}"
)
with open(configfile, "w") as fp:
fp.write(
config.format(
self.parfile,
self.H1file[0],
self.L1file[0],
self.H1file[1],
self.L1file[1],
self.priorfile,
datakwargs,
)
)
t4c1 = pe(config=configfile)
# perform consistency checks
for tv in [t4kw1, t4kw2, t4kw3, t4c1]:
assert len(tv.hetdata) == 4
for i, det, data1f, data2f in zip(
range(2),
["H1", "L1"],
[self.H1data[0], self.L1data[0]],
[self.H1data[1], self.L1data[1]],
):
assert tv.hetdata.detectors[i] == det
assert tv.hetdata[det][0].freq_factor == 1.0
assert tv.hetdata[det][1].freq_factor == 2.0
assert tv.hetdata[det][0].par["F"][0] == self.f0
assert np.allclose(tv.hetdata[det][0].data.real, data1f[:, 1])
assert | np.allclose(tv.hetdata[det][0].data.imag, data1f[:, 2]) | numpy.allclose |
from des_model import DES_model
from des_simulator import DES_simulator
import numpy as np
import matplotlib.pyplot as plt
# build model
d = np.array([[320.0e3]]) # port-terminal distance (m)
tu = np.array([[4 * 3600.0]]) # unloading time (s)
tl = np.array([[8 * 3600.0]]) # loading time (s)
v = np.array([40 / 3.6]) # train speed (m/s)
L = np.array([5.0e6]) # train load (kg)
ntmax = 8 # maximum number of trains
tc = tu[0][0] + tl[0][0] + 2 * d[0][0] / v[0]
ntm = tc / tl[0][0]
# simulate model
T = 50 * 24 * 3600 # time horizon (s)
Pn = [0] # numerical productivity (kg/s)
Pa = [0] # analytical productivity (kg/s)
tq = [0] # queue time (s)
n = [0] # number of trains
for i in range(1, ntmax):
# model
nt = np.array([i], dtype=int) # train count of each model
model = DES_model(d, tu, tl, nt, v, L)
# simulation
simulator = DES_simulator()
simulator.simulate(model, T)
Pt, P, t = model.productivity() # [kg/s], [kg], [s]
tq.append(model.queue_time())
# log
n.append(i)
Pn.append(Pt[-1])
Pa.append(min(nt[0], ntm) * L[0] / tc)
# line command output
print('\n Numerical productivity {:.0f}'.format(Pt[-1] * 3.6))
print('Analytical productivity {:.0f}'.format(Pa[-1] * 3.6))
# graphical output
if False:
hf, ha = plt.subplots()
plt.plot(t / 3600, Pt * 3.6)
plt.xlabel('time (hours)')
plt.ylabel('productivity (ton/hour)')
plt.title('{} trains'.format(i))
# graphical ouptut
hf, ha = plt.subplots()
plt.plot(np.array(n), | np.array(Pn) | numpy.array |
#!/usr/bin/env python
# -*- coding: utf-8 -*-
""" Plot ranks of top 100 users in the cyberbullying dataset
Usage: python plot_fig4_top_entities.py
Input data files: ../data/[app_name]_out/complete_user_[app_name].txt, ../data/[app_name]_out/user_[app_name]_all.txt
Time: ~8M
"""
import sys, os, platform
from collections import defaultdict
from datetime import datetime
import numpy as np
from scipy.stats import entropy, kendalltau
import matplotlib as mpl
if platform.system() == 'Linux':
mpl.use('Agg') # no UI backend
import matplotlib.pyplot as plt
sys.path.append(os.path.join(os.path.dirname(__file__), '../'))
from utils.helper import Timer, melt_snowflake
from utils.metrics import mean_absolute_percentage_error as mape
cm = plt.cm.get_cmap('RdBu')
def write_to_file(filepath, header, datalist):
with open(filepath, 'w') as fout:
for user_idx, user_id in enumerate(header):
fout.write('{0}\t{1}\t{2}\n'.format(user_id, sum(datalist[user_idx]), ','.join(map(str, datalist[user_idx]))))
def read_from_file(filepath, dtype=0):
datalist = []
with open(filepath, 'r') as fin:
for line in fin:
user_id, total, records = line.rstrip().split('\t')
if dtype == 0:
records = list(map(int, records.split(',')))
else:
records = list(map(float, records.split(',')))
datalist.append(records)
return datalist
def main():
timer = Timer()
timer.start()
app_name = 'cyberbullying'
hours_in_day = 24
minutes_in_hour = 60
seconds_in_minute = 60
ms_in_second = 1000
num_bins = 100
width = ms_in_second // num_bins
num_top = 500
fig, axes = plt.subplots(1, 2, figsize=(7.2, 4.8), gridspec_kw={'width_ratios': [2.75, 3]})
axes = axes.ravel()
confusion_sampling_rate = np.load('../data/{0}_out/{0}_confusion_sampling_rate.npy'.format(app_name))
confusion_sampling_rate = np.nan_to_num(confusion_sampling_rate)
load_external_data = True
if not load_external_data:
sample_entity_stats = defaultdict(int)
with open('../data/{0}_out/user_{0}_all.txt'.format(app_name), 'r') as fin:
for line in fin:
split_line = line.rstrip().split(',')
sample_entity_stats[split_line[1]] += 1
# == == == == == == Part 2: Plot entity rank == == == == == == #
print('>>> found top {0} users in sample set...'.format(num_top))
sample_top = [kv[0] for kv in sorted(sample_entity_stats.items(), key=lambda x: x[1], reverse=True)[:num_top]]
# == == == == == == Part 1: Find tweets appearing in complete set == == == == == == #
complete_post_lists_hour = [[0] * hours_in_day for _ in range(num_top)]
complete_post_lists_min = [[0] * minutes_in_hour for _ in range(num_top)]
complete_post_lists_sec = [[0] * seconds_in_minute for _ in range(num_top)]
complete_post_lists_10ms = [[0] * num_bins for _ in range(num_top)]
complete_entity_stats = defaultdict(int)
with open('../data/{0}_out/complete_user_{0}.txt'.format(app_name), 'r') as fin:
for line in fin:
split_line = line.rstrip().split(',')
user_id = split_line[1]
if user_id in sample_top:
complete_entity_stats[user_id] += 1
user_idx = sample_top.index(user_id)
tweet_id = split_line[0]
timestamp_ms = melt_snowflake(tweet_id)[0]
dt_obj = datetime.utcfromtimestamp(timestamp_ms // 1000)
hour = dt_obj.hour
minute = dt_obj.minute
second = dt_obj.second
millisec = timestamp_ms % 1000
ms_idx = (millisec-7) // width if millisec >= 7 else (1000 + millisec-7) // width
complete_post_lists_hour[user_idx][hour] += 1
complete_post_lists_min[user_idx][minute] += 1
complete_post_lists_sec[user_idx][second] += 1
complete_post_lists_10ms[user_idx][ms_idx] += 1
write_to_file('./complete_post_lists_hour.txt', sample_top, complete_post_lists_hour)
write_to_file('./complete_post_lists_min.txt', sample_top, complete_post_lists_min)
write_to_file('./complete_post_lists_sec.txt', sample_top, complete_post_lists_sec)
write_to_file('./complete_post_lists_10ms.txt', sample_top, complete_post_lists_10ms)
print('>>> finish dumping complete lists...')
timer.stop()
# == == == == == == Part 2: Find appearing tweets in sample set == == == == == == #
sample_post_lists_hour = [[0] * hours_in_day for _ in range(num_top)]
sample_post_lists_min = [[0] * minutes_in_hour for _ in range(num_top)]
sample_post_lists_sec = [[0] * seconds_in_minute for _ in range(num_top)]
sample_post_lists_10ms = [[0] * num_bins for _ in range(num_top)]
estimated_post_lists_hour = [[0] * hours_in_day for _ in range(num_top)]
estimated_post_lists_min = [[0] * minutes_in_hour for _ in range(num_top)]
estimated_post_lists_sec = [[0] * seconds_in_minute for _ in range(num_top)]
estimated_post_lists_10ms = [[0] * num_bins for _ in range(num_top)]
hourly_conversion = np.mean(confusion_sampling_rate, axis=(1, 2, 3))
minutey_conversion = np.mean(confusion_sampling_rate, axis=(2, 3))
secondly_conversion = np.mean(confusion_sampling_rate, axis=(3))
with open('../data/{0}_out/user_{0}_all.txt'.format(app_name), 'r') as fin:
for line in fin:
split_line = line.rstrip().split(',')
user_id = split_line[1]
if user_id in sample_top:
user_idx = sample_top.index(user_id)
tweet_id = split_line[0]
timestamp_ms = melt_snowflake(tweet_id)[0]
dt_obj = datetime.utcfromtimestamp(timestamp_ms // 1000)
hour = dt_obj.hour
minute = dt_obj.minute
second = dt_obj.second
millisec = timestamp_ms % 1000
ms_idx = (millisec-7) // width if millisec >= 7 else (1000 + millisec-7) // width
sample_post_lists_hour[user_idx][hour] += 1
sample_post_lists_min[user_idx][minute] += 1
sample_post_lists_sec[user_idx][second] += 1
sample_post_lists_10ms[user_idx][ms_idx] += 1
estimated_post_lists_hour[user_idx][hour] += 1 / hourly_conversion[hour]
estimated_post_lists_min[user_idx][minute] += 1 / minutey_conversion[hour, minute]
estimated_post_lists_sec[user_idx][second] += 1 / secondly_conversion[hour, minute, second]
estimated_post_lists_10ms[user_idx][ms_idx] += 1 / confusion_sampling_rate[hour, minute, second, ms_idx]
write_to_file('./sample_post_lists_hour.txt', sample_top, sample_post_lists_hour)
write_to_file('./sample_post_lists_min.txt', sample_top, sample_post_lists_min)
write_to_file('./sample_post_lists_sec.txt', sample_top, sample_post_lists_sec)
write_to_file('./sample_post_lists_10ms.txt', sample_top, sample_post_lists_10ms)
write_to_file('./estimated_post_lists_hour.txt', sample_top, estimated_post_lists_hour)
write_to_file('./estimated_post_lists_min.txt', sample_top, estimated_post_lists_min)
write_to_file('./estimated_post_lists_sec.txt', sample_top, estimated_post_lists_sec)
write_to_file('./estimated_post_lists_10ms.txt', sample_top, estimated_post_lists_10ms)
print('>>> finish dumping sample and estimated lists...')
timer.stop()
else:
sample_top = []
complete_post_lists_hour = []
with open('./complete_post_lists_hour.txt', 'r') as fin:
for line in fin:
user_id, total, records = line.rstrip().split('\t')
sample_top.append(user_id)
records = list(map(int, records.split(',')))
complete_post_lists_hour.append(records)
sample_post_lists_hour = read_from_file('./sample_post_lists_hour.txt', dtype=0)
sample_post_lists_min = read_from_file('./sample_post_lists_min.txt', dtype=0)
sample_post_lists_sec = read_from_file('./sample_post_lists_sec.txt', dtype=0)
sample_post_lists_10ms = read_from_file('./sample_post_lists_10ms.txt', dtype=0)
estimated_post_lists_hour = read_from_file('./estimated_post_lists_hour.txt', dtype=1)
estimated_post_lists_min = read_from_file('./estimated_post_lists_min.txt', dtype=1)
estimated_post_lists_sec = read_from_file('./estimated_post_lists_sec.txt', dtype=1)
estimated_post_lists_10ms = read_from_file('./estimated_post_lists_10ms.txt', dtype=1)
# == == == == == == Part 3: Find the best estimation by comparing JS distance == == == == == == #
ret = {}
num_estimate_list = []
num_sample_list = []
num_complete_list = []
sample_entity_stats = {user_id: sum(sample_post_lists_hour[user_idx]) for user_idx, user_id in enumerate(sample_top)}
complete_entity_stats = {user_id: sum(complete_post_lists_hour[user_idx]) for user_idx, user_id in enumerate(sample_top)}
min_mat = np.array([], dtype=np.int64).reshape(0, 60)
sec_mat = np.array([], dtype=np.int64).reshape(0, 60)
for user_idx, user_id in enumerate(sample_top):
num_sample = sample_entity_stats[user_id]
num_complete = complete_entity_stats[user_id]
hour_entropy = entropy(sample_post_lists_hour[user_idx], base=hours_in_day)
min_entropy = entropy(sample_post_lists_min[user_idx], base=minutes_in_hour)
sec_entropy = entropy(sample_post_lists_sec[user_idx], base=seconds_in_minute)
ms10_entropy = entropy(sample_post_lists_10ms[user_idx], base=num_bins)
min_mat = np.vstack((min_mat, np.array(sample_post_lists_min[user_idx]).reshape(1, -1)))
sec_mat = np.vstack((sec_mat, np.array(sample_post_lists_sec[user_idx]).reshape(1, -1)))
min_entropy, min_entropy_idx = min((min_entropy, min_entropy_idx) for (min_entropy_idx, min_entropy) in enumerate([hour_entropy, min_entropy, sec_entropy]))
if ms10_entropy < 0.87:
min_entropy_idx = 3
else:
min_entropy_idx = 2
# # if they are all very large
# if min_entropy >= msly_entropy_benchmark:
# min_entropy_idx = 2
num_estimate = sum([estimated_post_lists_hour[user_idx], estimated_post_lists_min[user_idx],
estimated_post_lists_sec[user_idx], estimated_post_lists_10ms[user_idx]][min_entropy_idx])
num_estimate_list.append(num_estimate)
num_sample_list.append(num_sample)
num_complete_list.append(num_complete)
ret[user_id] = (num_sample, num_complete, num_estimate, min_entropy_idx)
np.savetxt('min_sample.npy', min_mat, delimiter=',')
np.savetxt('sec_sample.npy', sec_mat, delimiter=',')
rank_by_sample = [k for k, v in sorted(ret.items(), key=lambda item: item[1][0], reverse=True)]
rank_by_complete = [k for k, v in sorted(ret.items(), key=lambda item: item[1][1], reverse=True)]
rank_by_estimated = [k for k, v in sorted(ret.items(), key=lambda item: item[1][2], reverse=True)]
for user_idx, user_id in enumerate(sample_top):
print(user_id, ret[user_id][:-1], (rank_by_sample.index(user_id)+1, rank_by_complete.index(user_id)+1, rank_by_estimated.index(user_id)+1))
print(ret[user_id][0]/ret[user_id][1], mape(ret[user_id][1], ret[user_id][2])[0], rank_by_sample.index(user_id)-rank_by_complete.index(user_id), rank_by_estimated.index(user_id)-rank_by_complete.index(user_id))
print(np.sum(np.array(sample_post_lists_min[user_idx]) > 0), np.sum(np.array(sample_post_lists_sec[user_idx]) > 0), np.sum( | np.array(sample_post_lists_10ms[user_idx]) | numpy.array |
'''
Created by SJWANG 07/21/2018
For refuge image segmentation
'''
# from __future__ import print_function
from keras.preprocessing.image import ImageDataGenerator
import numpy as np
import os
import glob
import skimage.io as io
import skimage.transform as trans
import cv2
from skimage.transform import rotate
from keras.preprocessing import image
import scipy
from PIL import Image
from skimage.measure import label, regionprops
from keras.applications import imagenet_utils
from matplotlib.pyplot import imshow, imsave
import math
from Utils.random_eraser import get_random_eraser
import random
from keras.preprocessing import image
from skimage.transform import rotate, resize
from skimage.measure import label, regionprops
from skimage.exposure import adjust_log, equalize_adapthist
from skimage.filters.rank import median
from skimage.morphology import disk
from scipy.ndimage.interpolation import map_coordinates
from scipy.ndimage.filters import gaussian_filter
eraser = get_random_eraser()
def pro_process(temp_img, input_size):
img = np.asarray(temp_img).astype('float32')
img = scipy.misc.imresize(img, (input_size, input_size, 3))
return img
def elastic_transform(image, label, alpha, sigma, random_state=None):
"""Elastic deformation of images as described in [Simard2003]_.
.. [Simard2003] <NAME> Platt, "Best Practices for
Convolutional Neural Networks applied to Visual Document Analysis", in
Proc. of the International Conference on Document Analysis and
Recognition, 2003.
"""
seed = random.random()
if seed > 0.5:
assert len(image.shape) == 3
if random_state is None:
random_state = np.random.RandomState(None)
shape = image.shape[0:2]
dx = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma, mode="constant", cval=0) * alpha
dy = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma, mode="constant", cval=0) * alpha
x, y = np.meshgrid(np.arange(shape[0]), np.arange(shape[1]), indexing='ij')
indices = np.reshape(x + dx, (-1, 1)), np.reshape(y + dy, (-1, 1))
transformed_image = np.zeros(image.shape)
transformed_label = np.zeros(image.shape)
for i in range(image.shape[-1]):
transformed_image[:, :, i] = map_coordinates(image[:, :, i], indices, order=1).reshape(shape)
if label is not None:
transformed_label[:, :, i] = map_coordinates(label[:, :, i], indices, order=1).reshape(shape)
else:
transformed_label = None
transformed_image = transformed_image.astype(np.uint8)
if label is not None:
transformed_label = transformed_label.astype(np.uint8)
return transformed_image, transformed_label
else:
return image, label
def add_salt_pepper_noise(image):
# Need to produce a copy as to not modify the original image
X_imgs_copy = image.copy()
row, col, _ = image.shape
salt_vs_pepper = 0.2
amount = 0.004
num_salt = np.ceil(amount * X_imgs_copy.size * salt_vs_pepper)
num_pepper = np.ceil(amount * X_imgs_copy.size * (1.0 - salt_vs_pepper))
seed = random.random()
if seed > 0.75:
# Add Salt noise
coords = [np.random.randint(0, i - 1, int(num_salt)) for i in X_imgs_copy.shape]
X_imgs_copy[coords[0], coords[1], :] = 1
elif seed > 0.5:
# Add Pepper noise
coords = [np.random.randint(0, i - 1, int(num_pepper)) for i in X_imgs_copy.shape]
X_imgs_copy[coords[0], coords[1], :] = 0
else:
return image
return X_imgs_copy
def adjust_light(image):
seed = random.random()
if seed > 0.5:
gamma = random.random() * 3 + 0.5
invGamma = 1.0 / gamma
table = np.array([((i / 255.0) ** invGamma) * 255 for i in np.arange(0, 256)]).astype(np.uint8)
image = cv2.LUT(image.astype(np.uint8), table).astype(np.uint8)
return image
def adjust_contrast(image):
seed = random.random()
if seed > 0.5:
image = adjust_log(image, 1)
return image
def ad_blur(image):
seed = random.random()
if seed > 0.5:
image = image / 127.5 - 1
image[:,:,0] = median(image[:,:,0], disk(3))
image[:,:,1] = median(image[:,:,1], disk(3))
image[:,:,2] = median(image[:,:,2], disk(3))
image = (image + 1) * 127.5
image = image.astype(np.uint8)
return image
def data_augmentation(img, mask=None, flip=True, ifrotate=True, ifelastic=True, scale=True, noise=True, light=True, erasing=True, ad_contrast=False, clahe=False, blur=False):
if mask is not None:
if scale:
seed = random.random()
if seed > 0.5:
img_ = np.zeros([img.shape[0], img.shape[1], img.shape[2]])
mask_ = | np.zeros([mask.shape[0], mask.shape[1], mask.shape[2]]) | numpy.zeros |
#!/usr/bin/env python
'''
Diffraction functions require for fitting and analyzing data.
mkak 2017.02.06 (originally written spring 2016)
'''
##########################################################################
# IMPORT PYTHON PACKAGES
import math
import numpy as np
from numpy import cos, sin, arcsin, degrees
from ..utils.physical_constants import PLANCK_HC, TAU, DEG2RAD, RAD2DEG
import re
import os
import cmath
##########################################################################
# FUNCTIONS
def d_from_q(q):
'''
Converts q axis into d (returned units inverse of provided units)
d = 2*PI/q
'''
return TAU/q
def d_from_twth(twth,wavelength,ang_units='degrees'):
'''
Converts 2th axis into d (returned units same as wavelength units)
d = lambda/[2*sin(2th/2)]
ang_unit : default in degrees; will convert from 'rad' if given
'''
if not ang_units.startswith('rad'):
twth = DEG2RAD*twth
return wavelength/(2*sin(twth/2.))
def twth_from_d(d,wavelength,ang_units='degrees'):
'''
Converts d axis into 2th (d and wavelength must be in same units)
2th = 2*sin^-1(lambda/[2*d])
ang_unit : default in degrees; will convert to 'rad' if given
'''
twth = 2*arcsin(wavelength/(2.*d))
if ang_units.startswith('rad'):
return twth
else:
return RAD2DEG*twth
def twth_from_q(q,wavelength,ang_units='degrees'):
'''
Converts q axis into 2th (q and wavelength will have inverse units)
2th = 2*sin^-1(lambda/[2*d])
ang_unit : default in degrees; will convert to 'rad' if given
'''
twth = 2*arcsin((q*wavelength)/(2*TAU))
if ang_units.startswith('rad'):
return twth
else:
return RAD2DEG*twth
def q_from_d(d):
'''
Converts d axis into q (returned units inverse of provided units)
q = 2*PI/d
'''
return TAU/d
def q_from_twth(twth, wavelength, ang_units='degrees'):
'''
Converts 2th axis into q (q returned in inverse units of wavelength)
q = [(4*PI)/lamda]*sin(2th/2)
ang_unit : default in degrees; will convert from 'rad' if given
'''
if not ang_units.startswith('rad'):
twth = DEG2RAD*twth
return ((2*TAU)/wavelength)*sin(twth/2.)
def qv_from_hkl(hklall, a, b, c, alpha, beta, gamma):
qv = np.zeros(np.shape(hklall))
uvol = unit_cell_volume(a,b,c,alpha,beta,gamma)
alpha, beta, gamma = DEG2RAD*alpha, DEG2RAD*beta, DEG2RAD*gamma
q0 = [(b*c*sin(alpha))/uvol,(c*a*sin(beta))/uvol,(a*b*sin(gamma))/uvol]
for i, hkl in enumerate(hklall):
qv[i] = [TAU*hkl[0]*q0[0], TAU*hkl[1]*q0[1], TAU*hkl[2]*q0[2]]
return qv
def d_from_hkl(hkl, a, b, c, alpha, beta, gamma):
h, k, l = hkl[:, 0], hkl[:, 1], hkl[:, 2]
alpha, beta, gamma = DEG2RAD*alpha, DEG2RAD*beta, DEG2RAD*gamma
x = 1-cos(alpha)**2 - cos(beta)**2 - cos(gamma)**2 \
+ 2*cos(alpha)*cos(beta)*cos(gamma)
y = (h*sin(alpha)/a)**2 + 2*k*l*(cos(beta)*cos(gamma)-cos(alpha))/(b*c) + \
(k*sin(beta)/b)**2 + 2*l*h*(cos(gamma)*cos(alpha)-cos(beta))/(c*a) + \
(l*sin(gamma)/c)**2 + 2*h*k*(cos(alpha)*cos(beta)-cos(gamma))/(a*b)
d = np.sqrt(x/y)
return d
def d_from_hkl_orig(hklall, a, b, c, alpha, beta, gamma):
d = np.zeros(len(hklall))
alpha, beta, gamma = DEG2RAD*alpha, DEG2RAD*beta, DEG2RAD*gamma
for i,hkl in enumerate(hklall):
h,k,l = hkl
x = 1-cos(alpha)**2 - cos(beta)**2 - cos(gamma)**2 \
+ 2*cos(alpha)* | cos(beta) | numpy.cos |
# Author : <NAME> <EMAIL> (2012)
# License : BSD 3-clause
# Parts of this code were copied from NiTime http://nipy.sourceforge.net/nitime
import operator
import numpy as np
from scipy import linalg
from ..parallel import parallel_func
from ..utils import sum_squared, warn, verbose, logger
def tridisolve(d, e, b, overwrite_b=True):
"""Symmetric tridiagonal system solver, from Golub and Van Loan p157.
.. note:: Copied from NiTime.
Parameters
----------
d : ndarray
main diagonal stored in d[:]
e : ndarray
superdiagonal stored in e[:-1]
b : ndarray
RHS vector
Returns
-------
x : ndarray
Solution to Ax = b (if overwrite_b is False). Otherwise solution is
stored in previous RHS vector b
"""
N = len(b)
# work vectors
dw = d.copy()
ew = e.copy()
if overwrite_b:
x = b
else:
x = b.copy()
for k in range(1, N):
# e^(k-1) = e(k-1) / d(k-1)
# d(k) = d(k) - e^(k-1)e(k-1) / d(k-1)
t = ew[k - 1]
ew[k - 1] = t / dw[k - 1]
dw[k] = dw[k] - t * ew[k - 1]
for k in range(1, N):
x[k] = x[k] - ew[k - 1] * x[k - 1]
x[N - 1] = x[N - 1] / dw[N - 1]
for k in range(N - 2, -1, -1):
x[k] = x[k] / dw[k] - ew[k] * x[k + 1]
if not overwrite_b:
return x
def tridi_inverse_iteration(d, e, w, x0=None, rtol=1e-8):
"""Perform an inverse iteration.
This will find the eigenvector corresponding to the given eigenvalue
in a symmetric tridiagonal system.
..note:: Copied from NiTime.
Parameters
----------
d : ndarray
main diagonal of the tridiagonal system
e : ndarray
offdiagonal stored in e[:-1]
w : float
eigenvalue of the eigenvector
x0 : ndarray
initial point to start the iteration
rtol : float
tolerance for the norm of the difference of iterates
Returns
-------
e: ndarray
The converged eigenvector
"""
eig_diag = d - w
if x0 is None:
x0 = np.random.randn(len(d))
x_prev = np.zeros_like(x0)
norm_x = np.linalg.norm(x0)
# the eigenvector is unique up to sign change, so iterate
# until || |x^(n)| - |x^(n-1)| ||^2 < rtol
x0 /= norm_x
while np.linalg.norm(np.abs(x0) - np.abs(x_prev)) > rtol:
x_prev = x0.copy()
tridisolve(eig_diag, e, x0)
norm_x = np.linalg.norm(x0)
x0 /= norm_x
return x0
def dpss_windows(N, half_nbw, Kmax, low_bias=True, interp_from=None,
interp_kind='linear'):
"""Compute Discrete Prolate Spheroidal Sequences.
Will give of orders [0,Kmax-1] for a given frequency-spacing multiple
NW and sequence length N.
.. note:: Copied from NiTime.
Parameters
----------
N : int
Sequence length
half_nbw : float, unitless
Standardized half bandwidth corresponding to 2 * half_bw = BW*f0
= BW*N/dt but with dt taken as 1
Kmax : int
Number of DPSS windows to return is Kmax (orders 0 through Kmax-1)
low_bias : Bool
Keep only tapers with eigenvalues > 0.9
interp_from : int (optional)
The dpss can be calculated using interpolation from a set of dpss
with the same NW and Kmax, but shorter N. This is the length of this
shorter set of dpss windows.
interp_kind : str (optional)
This input variable is passed to scipy.interpolate.interp1d and
specifies the kind of interpolation as a string ('linear', 'nearest',
'zero', 'slinear', 'quadratic, 'cubic') or as an integer specifying the
order of the spline interpolator to use.
Returns
-------
v, e : tuple,
v is an array of DPSS windows shaped (Kmax, N)
e are the eigenvalues
Notes
-----
Tridiagonal form of DPSS calculation from:
<NAME>. Prolate spheroidal wave functions, Fourier analysis, and
uncertainty V: The discrete case. Bell System Technical Journal,
Volume 57 (1978), 1371430
"""
from scipy import interpolate
from ..filter import next_fast_len
# This np.int32 business works around a weird Windows bug, see
# gh-5039 and https://github.com/scipy/scipy/pull/8608
Kmax = np.int32(operator.index(Kmax))
N = np.int32(operator.index(N))
W = float(half_nbw) / N
nidx = np.arange(N, dtype='d')
# In this case, we create the dpss windows of the smaller size
# (interp_from) and then interpolate to the larger size (N)
if interp_from is not None:
if interp_from > N:
e_s = 'In dpss_windows, interp_from is: %s ' % interp_from
e_s += 'and N is: %s. ' % N
e_s += 'Please enter interp_from smaller than N.'
raise ValueError(e_s)
dpss = []
d, e = dpss_windows(interp_from, half_nbw, Kmax, low_bias=False)
for this_d in d:
x = np.arange(this_d.shape[-1])
tmp = interpolate.interp1d(x, this_d, kind=interp_kind)
d_temp = tmp(np.linspace(0, this_d.shape[-1] - 1, N,
endpoint=False))
# Rescale:
d_temp = d_temp / np.sqrt(sum_squared(d_temp))
dpss.append(d_temp)
dpss = np.array(dpss)
else:
# here we want to set up an optimization problem to find a sequence
# whose energy is maximally concentrated within band [-W,W].
# Thus, the measure lambda(T,W) is the ratio between the energy within
# that band, and the total energy. This leads to the eigen-system
# (A - (l1)I)v = 0, where the eigenvector corresponding to the largest
# eigenvalue is the sequence with maximally concentrated energy. The
# collection of eigenvectors of this system are called Slepian
# sequences, or discrete prolate spheroidal sequences (DPSS). Only the
# first K, K = 2NW/dt orders of DPSS will exhibit good spectral
# concentration
# [see http://en.wikipedia.org/wiki/Spectral_concentration_problem]
# Here I set up an alternative symmetric tri-diagonal eigenvalue
# problem such that
# (B - (l2)I)v = 0, and v are our DPSS (but eigenvalues l2 != l1)
# the main diagonal = ([N-1-2*t]/2)**2 cos(2PIW), t=[0,1,2,...,N-1]
# and the first off-diagonal = t(N-t)/2, t=[1,2,...,N-1]
# [see Percival and Walden, 1993]
diagonal = ((N - 1 - 2 * nidx) / 2.) ** 2 * np.cos(2 * np.pi * W)
off_diag = np.zeros_like(nidx)
off_diag[:-1] = nidx[1:] * (N - nidx[1:]) / 2.
# put the diagonals in LAPACK "packed" storage
ab = np.zeros((2, N), 'd')
ab[1] = diagonal
ab[0, 1:] = off_diag[:-1]
# only calculate the highest Kmax eigenvalues
w = linalg.eigvals_banded(ab, select='i',
select_range=(N - Kmax, N - 1))
w = w[::-1]
# find the corresponding eigenvectors via inverse iteration
t = np.linspace(0, np.pi, N)
dpss = np.zeros((Kmax, N), 'd')
for k in range(Kmax):
dpss[k] = tridi_inverse_iteration(diagonal, off_diag, w[k],
x0=np.sin((k + 1) * t))
# By convention (Percival and Walden, 1993 pg 379)
# * symmetric tapers (k=0,2,4,...) should have a positive average.
# * antisymmetric tapers should begin with a positive lobe
fix_symmetric = (dpss[0::2].sum(axis=1) < 0)
for i, f in enumerate(fix_symmetric):
if f:
dpss[2 * i] *= -1
# rather than test the sign of one point, test the sign of the
# linear slope up to the first (largest) peak
pk = np.argmax(np.abs(dpss[1::2, :N // 2]), axis=1)
for i, p in enumerate(pk):
if np.sum(dpss[2 * i + 1, :p]) < 0:
dpss[2 * i + 1] *= -1
# Now find the eigenvalues of the original spectral concentration problem
# Use the autocorr sequence technique from Percival and Walden, 1993 pg 390
# compute autocorr using FFT (same as nitime.utils.autocorr(dpss) * N)
rxx_size = 2 * N - 1
n_fft = next_fast_len(rxx_size)
dpss_fft = np.fft.rfft(dpss, n_fft)
dpss_rxx = np.fft.irfft(dpss_fft * dpss_fft.conj(), n_fft)
dpss_rxx = dpss_rxx[:, :N]
r = 4 * W * np.sinc(2 * W * nidx)
r[0] = 2 * W
eigvals = np.dot(dpss_rxx, r)
if low_bias:
idx = (eigvals > 0.9)
if not idx.any():
warn('Could not properly use low_bias, keeping lowest-bias taper')
idx = [np.argmax(eigvals)]
dpss, eigvals = dpss[idx], eigvals[idx]
assert len(dpss) > 0 # should never happen
assert dpss.shape[1] == N # old nitime bug
return dpss, eigvals
def _psd_from_mt_adaptive(x_mt, eigvals, freq_mask, max_iter=150,
return_weights=False):
r"""Use iterative procedure to compute the PSD from tapered spectra.
.. note:: Modified from NiTime.
Parameters
----------
x_mt : array, shape=(n_signals, n_tapers, n_freqs)
The DFTs of the tapered sequences (only positive frequencies)
eigvals : array, length n_tapers
The eigenvalues of the DPSS tapers
freq_mask : array
Frequency indices to keep
max_iter : int
Maximum number of iterations for weight computation
return_weights : bool
Also return the weights
Returns
-------
psd : array, shape=(n_signals, np.sum(freq_mask))
The computed PSDs
weights : array shape=(n_signals, n_tapers, np.sum(freq_mask))
The weights used to combine the tapered spectra
Notes
-----
The weights to use for making the multitaper estimate, such that
:math:`S_{mt} = \sum_{k} |w_k|^2S_k^{mt} / \sum_{k} |w_k|^2`
"""
n_signals, n_tapers, n_freqs = x_mt.shape
if len(eigvals) != n_tapers:
raise ValueError('Need one eigenvalue for each taper')
if n_tapers < 3:
raise ValueError('Not enough tapers to compute adaptive weights.')
rt_eig = np.sqrt(eigvals)
# estimate the variance from an estimate with fixed weights
psd_est = _psd_from_mt(x_mt, rt_eig[np.newaxis, :, np.newaxis])
x_var = np.trapz(psd_est, dx=np.pi / n_freqs) / (2 * np.pi)
del psd_est
# allocate space for output
psd = np.empty((n_signals, np.sum(freq_mask)))
# only keep the frequencies of interest
x_mt = x_mt[:, :, freq_mask]
if return_weights:
weights = | np.empty((n_signals, n_tapers, psd.shape[1])) | numpy.empty |
"""
This file contains all helper utility functions.
"""
import os
import sys
import math
import importlib
from scipy.optimize import linear_sum_assignment
import torch
import numpy as np
import trimesh, configparser
from pyquaternion import Quaternion
import h5py
def worker_init_fn(worker_id):
""" The function is designed for pytorch multi-process dataloader.
Note that we use the pytorch random generator to generate a base_seed.
Please try to be consistent.
References:
https://pytorch.org/docs/stable/notes/faq.html#dataloader-workers-random-seed
"""
base_seed = torch.IntTensor(1).random_().item()
#print(worker_id, base_seed)
np.random.seed(base_seed + worker_id)
def save_checkpoint(models, model_names, dirname, epoch=None, prepend_epoch=False, optimizers=None, optimizer_names=None):
if len(models) != len(model_names) or (optimizers is not None and len(optimizers) != len(optimizer_names)):
raise ValueError('Number of models, model names, or optimizers does not match.')
for model, model_name in zip(models, model_names):
filename = f'net_{model_name}.pth'
if prepend_epoch:
filename = f'{epoch}_' + filename
torch.save(model.state_dict(), os.path.join(dirname, filename))
if optimizers is not None:
filename = 'checkpt.pth'
if prepend_epoch:
filename = f'{epoch}_' + filename
checkpt = {'epoch': epoch}
for opt, optimizer_name in zip(optimizers, optimizer_names):
checkpt[f'opt_{optimizer_name}'] = opt.state_dict()
torch.save(checkpt, os.path.join(dirname, filename))
def load_checkpoint(models, model_names, dirname, epoch=None, device="cuda:0", optimizers=None, optimizer_names=None, strict=True):
if len(models) != len(model_names) or (optimizers is not None and len(optimizers) != len(optimizer_names)):
raise ValueError('Number of models, model names, or optimizers does not match.')
for model, model_name in zip(models, model_names):
filename = f'net_{model_name}.pth'
if epoch is not None:
filename = f'{epoch}_' + filename
state_dict = torch.load(os.path.join(dirname, filename), map_location=torch.device(device))
current_state_dict = model.state_dict()
firstkey = [k for k in current_state_dict.keys()]
if firstkey[0].find('module.')>=0:
from collections import OrderedDict
new_state_dict = OrderedDict()
# state_dict = torch.load(os.path.join(dirname, filename))
for k, v in state_dict.items():
name = 'module.' + k # remove `module.`
new_state_dict[name] = v
model.load_state_dict(new_state_dict, strict=strict)
else:
model.load_state_dict(state_dict, strict=strict)
start_epoch = 0
if optimizers is not None:
filename = 'checkpt.pth'
if epoch is not None:
filename = f'{epoch}_' + filename
filename = os.path.join(dirname, filename)
if os.path.exists(filename):
checkpt = torch.load(filename)
start_epoch = checkpt['epoch']
for opt, optimizer_name in zip(optimizers, optimizer_names):
opt.load_state_dict(checkpt[f'opt_{optimizer_name}'])
print(f'resuming from checkpoint {filename}')
else:
response = input(f'Checkpoint {filename} not found for resuming, refine saved models instead? (y/n) ')
if response != 'y':
sys.exit()
return start_epoch
def optimizer_to_device(optimizer, device):
for state in optimizer.state.values():
for k, v in state.items():
if torch.is_tensor(v):
state[k] = v.to(device)
def optimizer_to_device1(optimizer, device):
for state in optimizer.state.values():
for k, v in state.items():
if torch.is_tensor(v):
state[k] = v.cuda(device)
def vrrotvec2mat(rotvector):
s = math.sin(rotvector[3])
c = math.cos(rotvector[3])
t = 1 - c
x = rotvector[0]
y = rotvector[1]
z = rotvector[2]
m = rotvector.new_tensor([[t*x*x+c, t*x*y-s*z, t*x*z+s*y], [t*x*y+s*z, t*y*y+c, t*y*z-s*x], [t*x*z-s*y, t*y*z+s*x, t*z*z+c]])
return m
def get_model_module(model_version):
importlib.invalidate_caches()
return importlib.import_module(model_version)
# row_counts, col_counts: row and column counts of each distance matrix (assumed to be full if given)
def linear_assignment(distance_mat, row_counts=None, col_counts=None):
batch_ind = []
row_ind = []
col_ind = []
for i in range(distance_mat.shape[0]):
# print(f'{i} / {distance_mat.shape[0]}')
dmat = distance_mat[i, :, :]
if row_counts is not None:
dmat = dmat[:row_counts[i], :]
if col_counts is not None:
dmat = dmat[:, :col_counts[i]]
rind, cind = linear_sum_assignment(dmat.to('cpu').detach().numpy())
rind = list(rind)
cind = list(cind)
# print(dmat)
# print(rind)
# print(cind)
if len(rind) > 0:
rind, cind = zip(*sorted(zip(rind, cind)))
rind = list(rind)
cind = list(cind)
# complete the assignemnt for any remaining non-active elements (in case row_count or col_count was given),
# by assigning them randomly
#if len(rind) < distance_mat.shape[1]:
# rind.extend(set(range(distance_mat.shape[1])).difference(rind))
# cind.extend(set(range(distance_mat.shape[1])).difference(cind))
batch_ind += [i]*len(rind)
row_ind += rind
col_ind += cind
return batch_ind, row_ind, col_ind
def object_batch_boxes(objects, max_box_num):
box_num = []
boxes = torch.zeros(len(objects), 12, max_box_num)
for oi, obj in enumerate(objects):
obj_boxes = obj.boxes()
box_num.append(len(obj_boxes))
if box_num[-1] > max_box_num:
print(f'WARNING: too many boxes in object, please use a dataset that does not have objects with too many boxes, clipping the object for now.')
box_num[-1] = max_box_num
obj_boxes = obj_boxes[:box_num[-1]]
obj_boxes = [o.view(-1, 1) for o in obj_boxes]
boxes[oi, :, :box_num[-1]] = torch.cat(obj_boxes, dim=1)
return boxes, box_num
# out shape: (label_count, in shape)
def one_hot(inp, label_count):
out = torch.zeros(label_count, inp.numel(), dtype=torch.uint8, device=inp.device)
out[inp.view(-1), torch.arange(out.shape[1])] = 1
out = out.view((label_count,) + inp.shape)
return out
def collate_feats(b):
return list(zip(*b))
def export_ply_with_label(out, v, l):
num_colors = len(colors)
with open(out, 'w') as fout:
fout.write('ply\n')
fout.write('format ascii 1.0\n')
fout.write('element vertex '+str(v.shape[0])+'\n')
fout.write('property float x\n')
fout.write('property float y\n')
fout.write('property float z\n')
fout.write('property uchar red\n')
fout.write('property uchar green\n')
fout.write('property uchar blue\n')
fout.write('end_header\n')
for i in range(v.shape[0]):
cur_color = colors[l[i]%num_colors]
fout.write('%f %f %f %d %d %d\n' % (v[i, 0], v[i, 1], v[i, 2], \
int(cur_color[0]*255), int(cur_color[1]*255), int(cur_color[2]*255)))
def load_pts(fn):
with open(fn, 'r') as fin:
lines = [item.rstrip() for item in fin]
pts = np.array([[float(line.split()[0]), float(line.split()[1]), float(line.split()[2])] for line in lines], dtype=np.float32)
return pts
def export_pts(out, v):
with open(out, 'w') as fout:
for i in range(v.shape[0]):
fout.write('%f %f %f\n' % (v[i, 0], v[i, 1], v[i, 2]))
def load_obj(fn):
fin = open(fn, 'r')
lines = [line.rstrip() for line in fin]
fin.close()
vertices = []; faces = [];
for line in lines:
if line.startswith('v '):
vertices.append(np.float32(line.split()[1:4]))
elif line.startswith('f '):
faces.append(np.int32([item.split('/')[0] for item in line.split()[1:4]]))
f = np.vstack(faces)
v = np.vstack(vertices)
return v, f
def export_obj(out, v, f):
with open(out, 'w') as fout:
for i in range(v.shape[0]):
fout.write('v %f %f %f\n' % (v[i, 0], v[i, 1], v[i, 2]))
for i in range(f.shape[0]):
fout.write('f %d %d %d\n' % (f[i, 0], f[i, 1], f[i, 2]))
def color2mtl(colorfile):
from vis_utils import load_semantic_colors
from datav1 import Tree
filepath, fullflname = os.path.split(colorfile)
fname, ext = os.path.splitext(fullflname)
Tree.load_category_info(fname)
sem_colors = load_semantic_colors(filename=colorfile)
for sem in sem_colors:
sem_colors[sem] = (float(sem_colors[sem][0]) / 255.0, float(sem_colors[sem][1]) / 255.0, float(sem_colors[sem][2]) / 255.0)
mtl_fid = open(os.path.join(filepath, fname + '.mtl'), 'w')
for i in range(len(Tree.part_id2name)):
partname = Tree.part_id2name[i + 1]
color = sem_colors[partname]
mtl_fid.write('newmtl m_%s\nKd %f %f %f\nKa 0 0 0\n' % (partname.replace('/', '-'), color[0], color[1], color[2]))
mtl_fid.close()
def qrot(q, v):
"""
Rotate vector(s) v about the rotation described by quaternion(s) q.
Expects a tensor of shape (*, 4) for q and a tensor of shape (*, 3) for v,
where * denotes any number of dimensions.
Returns a tensor of shape (*, 3).
"""
assert q.shape[-1] == 4
assert v.shape[-1] == 3
assert q.shape[:-1] == v.shape[:-1]
original_shape = list(v.shape)
q = q.view(-1, 4)
v = v.view(-1, 3)
qvec = q[:, 1:]
uv = torch.cross(qvec, v, dim=1)
uuv = torch.cross(qvec, uv, dim=1)
return (v + 2 * (q[:, :1] * uv + uuv)).view(original_shape)
# pc is N x 3, feat is 10-dim
def transform_pc(pc, feat):
num_point = pc.size(0)
center = feat[:3]
shape = feat[3:6]
quat = feat[6:]
pc = pc * shape.repeat(num_point, 1)
pc = qrot(quat.repeat(num_point, 1), pc)
pc = pc + center.repeat(num_point, 1)
return pc
# pc is N x 3, feat is B x 10-dim
def transform_pc_batch(pc, feat, anchor=False):
batch_size = feat.size(0)
num_point = pc.size(0)
pc = pc.repeat(batch_size, 1, 1)
center = feat[:, :3].unsqueeze(dim=1).repeat(1, num_point, 1)
shape = feat[:, 3:6].unsqueeze(dim=1).repeat(1, num_point, 1)
quat = feat[:, 6:].unsqueeze(dim=1).repeat(1, num_point, 1)
if not anchor:
pc = pc * shape
pc = qrot(quat.view(-1, 4), pc.view(-1, 3)).view(batch_size, num_point, 3)
if not anchor:
pc = pc + center
return pc
def get_surface_reweighting(xyz, cube_num_point):
x = xyz[0]
y = xyz[1]
z = xyz[2]
assert cube_num_point % 6 == 0, 'ERROR: cube_num_point %d must be dividable by 6!' % cube_num_point
np = cube_num_point // 6
out = torch.cat([(x*y).repeat(np*2), (y*z).repeat(np*2), (x*z).repeat(np*2)])
out = out / (out.sum() + 1e-12)
return out
def get_surface_reweighting_batch(xyz, cube_num_point):
x = xyz[:, 0]
y = xyz[:, 1]
z = xyz[:, 2]
assert cube_num_point % 6 == 0, 'ERROR: cube_num_point %d must be dividable by 6!' % cube_num_point
np = cube_num_point // 6
out = torch.cat([(x*y).unsqueeze(dim=1).repeat(1, np*2), \
(y*z).unsqueeze(dim=1).repeat(1, np*2), \
(x*z).unsqueeze(dim=1).repeat(1, np*2)], dim=1)
out = out / (out.sum(dim=1).unsqueeze(dim=1) + 1e-12)
return out
def gen_obb_mesh(obbs):
# load cube
cube_v, cube_f = load_obj('cube.obj')
all_v = []; all_f = []; vid = 0;
for pid in range(obbs.shape[0]):
p = obbs[pid, :]
center = p[0: 3]
lengths = p[3: 6]
dir_1 = p[6: 9]
dir_2 = p[9: ]
dir_1 = dir_1/np.linalg.norm(dir_1)
dir_2 = dir_2/np.linalg.norm(dir_2)
dir_3 = np.cross(dir_1, dir_2)
dir_3 = dir_3/np.linalg.norm(dir_3)
v = np.array(cube_v, dtype=np.float32)
f = np.array(cube_f, dtype=np.int32)
rot = np.vstack([dir_1, dir_2, dir_3])
v *= lengths
v = np.matmul(v, rot)
v += center
all_v.append(v)
all_f.append(f+vid)
vid += v.shape[0]
all_v = np.vstack(all_v)
all_f = np.vstack(all_f)
return all_v, all_f
def sample_pc(v, f, n_points=2048):
mesh = trimesh.Trimesh(vertices=v, faces=f-1)
points, __ = trimesh.sample.sample_surface(mesh=mesh, count=n_points)
return points
def set_requires_grad(nets, requires_grad=False):
"""Set requies_grad=Fasle for all the networks to avoid unnecessary computations
Parameters:
nets (network list) -- a list of networks
requires_grad (bool) -- whether the networks require gradients or not
"""
if not isinstance(nets, list):
nets = [nets]
for net in nets:
if net is not None:
for param in net.parameters():
param.requires_grad = requires_grad
def argpaser2file(args, name='example.ini'):
d = args.__dict__
cfpar = configparser.ConfigParser()
cfpar['default'] = {}
for key in sorted(d.keys()):
cfpar['default'][str(key)]=str(d[key])
print('%s = %s'%(key,d[key]))
with open(name, 'w') as configfile:
cfpar.write(configfile)
def inifile2args(args, ininame='example.ini'):
config = configparser.ConfigParser()
config.read(ininame)
defaults = config['default']
result = dict(defaults)
# print(result)
# print('\n')
# print(args)
args1 = vars(args)
# print(args1)
args1.update({k: v for k, v in result.items() if v is not None}) # Update if v is not None
# print(args1)
args.__dict__.update(args1)
# print(args)
return args
def neighbour2vdiff(neighbour, ref_V):
neighbour = neighbour - 1
pointnum = neighbour.shape[0]
maxdim = neighbour.shape[1]
vdiff = np.zeros((pointnum, maxdim, 3), dtype=np.float32)
for point_i in range(pointnum):
for j in range(maxdim):
curneighbour = neighbour[point_i][j]
if curneighbour == -1:
break
vdiff[point_i][j] = ref_V[point_i] - ref_V[curneighbour]
return vdiff
# ----------------------------------------------------------- ICP -------------------------------------------------------------
def best_fit_transform(A, B):
'''
Calculates the least-squares best-fit transform that maps corresponding points A to B in m spatial dimensions
Input:
A: Nxm numpy array of corresponding points
B: Nxm numpy array of corresponding points
Returns:
T: (m+1)x(m+1) homogeneous transformation matrix that maps A on to B
R: mxm rotation matrix
t: mx1 translation vector
'''
#print(A.shape, B.shape)
assert A.shape == B.shape
# get number of dimensions
m = A.shape[1]
# translate points to their centroids
centroid_A = np.mean(A, axis=0)
centroid_B = np.mean(B, axis=0)
AA = A - centroid_A
BB = B - centroid_B
# rotation matrix
H = np.dot(AA.T, BB)
U, S, Vt = np.linalg.svd(H)
R = np.dot(Vt.T, U.T)
# special reflection case
if np.linalg.det(R) < 0:
Vt[m-1,:] *= -1
R = np.dot(Vt.T, U.T)
# translation
t = centroid_B.T - np.dot(R,centroid_A.T)
# homogeneous transformation
T = np.identity(m+1)
T[:m, :m] = R
T[:m, m] = t
return T, R, t
def nearest_neighbor(src, dst):
'''
Find the nearest (Euclidean) neighbor in dst for each point in src
Input:
src: Nxm array of points
dst: Nxm array of points
Output:
distances: Euclidean distances of the nearest neighbor
indices: dst indices of the nearest neighbor
'''
assert src.shape == dst.shape
neigh = NearestNeighbors(n_neighbors=1)
neigh.fit(dst)
distances, indices = neigh.kneighbors(src, return_distance=True)
return distances.ravel(), indices.ravel()
def icp(A, B, init_pose=None, max_iterations=20, tolerance=0.001):
'''
The Iterative Closest Point method: finds best-fit transform that maps points A on to points B
Input:
A: Nxm numpy array of source mD points
B: Nxm numpy array of destination mD point
init_pose: (m+1)x(m+1) homogeneous transformation
max_iterations: exit algorithm after max_iterations
tolerance: convergence criteria
Output:
T: final homogeneous transformation that maps A on to B
distances: Euclidean distances (errors) of the nearest neighbor
i: number of iterations to converge
'''
assert A.shape == B.shape
# get number of dimensions
m = A.shape[1]
# make points homogeneous, copy them to maintain the originals
src = np.ones((m+1,A.shape[0]))
dst = np.ones((m+1,B.shape[0]))
src[:m,:] = np.copy(A.T)
dst[:m,:] = np.copy(B.T)
# apply the initial pose estimation
if init_pose is not None:
src = np.dot(init_pose, src)
prev_error = 0
for i in range(max_iterations):
# find the nearest neighbors between the current source and destination points
distances, indices = nearest_neighbor(src[:m,:].T, dst[:m,:].T)
# compute the transformation between the current source and nearest destination points
T,_,_ = best_fit_transform(src[:m,:].T, dst[:m,indices].T)
# update the current source
src = np.dot(T, src)
# check error
mean_error = np.mean(distances)
if np.abs(prev_error - mean_error) < tolerance:
break
prev_error = mean_error
# calculate final transformation
T,_,_ = best_fit_transform(A, src[:m,:].T)
return T, distances, i
class ConcatDataset(torch.utils.data.Dataset):
def __init__(self, *datasets):
self.datasets = datasets
def __getitem__(self, i):
return tuple(d[i] for d in self.datasets)
def __len__(self):
return min(len(d) for d in self.datasets)
class MeshDataLoader():
def __init__(self, data_path):
meshfile = os.path.join(data_path, '..', 'cube_meshinfo.mat')
if os.path.exists(meshfile):
print(meshfile)
meshdata = h5py.File(meshfile, mode = 'r')
self.num_point = meshdata['neighbour'].shape[0]
self.edge_index = np.array(meshdata['edge_index']).astype('int64')
self.reconmatrix = np.array(meshdata['recon']).astype('float32')
self.ref_V = np.array(meshdata['ref_V']).astype('float32')
self.ref_F = np.array(meshdata['ref_F']).astype('int64')
self.vdiff = np.array(meshdata['vdiff']).astype('float32')
self.nb = | np.array(meshdata['neighbour']) | numpy.array |
'''
'''
import os
import sys
import numpy as np
import matplotlib.pyplot as plt
import astropy.coordinates as coordinates
import astropy.units as units
if sys.version_info.major == 2:
fmap = map
elif sys.version_info.major == 3:
fmap = lambda x, *args: list(map(x, *args))
xrange = range
ON = "ON"
OFF = "OFF"
class Calibrator(object):
def __init__(self, freqs, S, Serr=None, pol_type='Coherence', fd_poln='LIN', verbose=True):
self.pol_type = pol_type
self.freqs = np.array(freqs)
self.S = np.array(S)
if Serr is None:
Serr = np.zeros(4, dtype=np.float32)
self.Serr = np.array(Serr)
self.verbose = verbose
if self.pol_type == 'Coherence' or self.pol_type == 'AABBCRCI':
A, B, C, D = S
Aerr, Berr, Cerr, Derr = Serr
if fd_poln == 'LIN':
S0 = A+B #I
S1 = A-B #Q
S2 = 2*C #U
S3 = 2*D #V
S0err = np.sqrt(Aerr**2 + Berr**2)
S1err = S0err
S2err = 2*Cerr
S3err = 2*Derr
elif self.pol_type == 'Stokes' or self.pol_type == 'IQUV':
S0, S1, S2, S3 = S
S0err, S1err, S2err, S3err = Serr
else:
raise SystemExit
self.I = S0
self.Q = S1
self.U = S2
self.V = S3
self.Ierr = S0err
self.Qerr = S1err
self.Uerr = S2err
self.Verr = S3err
def pacv(self):
'''
Emulates pacv <archive>
See More/Polarimetry/SingleAxisSolver.C
'''
dG = 2*self.Q/self.I
dpsi = np.arctan2(self.V, self.U)
plt.subplot(311)
plt.plot(dpsi, 'k.')
plt.subplot(312)
plt.plot(100*dG, 'k.')
plt.subplot(313)
U_0 = self.U/np.cos(dpsi)
#plot(self.I)
#plot(np.sqrt(self.U**2+self.V**2)/U_0, 'k.')
plt.show()
def pacv_csu(self):
'''
Emulates pacv -n csu <archive>
'''
plt.errorbar(self.freqs, self.I, yerr=self.Ierr, fmt='k.')
plt.errorbar(self.freqs, self.Q, yerr=self.Qerr, fmt='r.')
plt.errorbar(self.freqs, self.U, yerr=self.Uerr, fmt='g.')
plt.errorbar(self.freqs, self.V, yerr=self.Verr, fmt='b.')
plt.xlabel('Frequency')
plt.ylabel('Calibrator Stokes')
plt.show()
def applyFluxcal(self, fluxcalonar, fluxcaloffar=None):
if fluxcaloffar is None: #The fluxcalon file contains both ON and OFF observations
pass
else:
fluxcalonfreqs, fluxcalondatalow, fluxcalondatahigh, fluxcalonerrslow, fluxcalonerrshigh = fluxcalonar.getLevels()
fluxcalofffreqs, fluxcaloffdatalow, fluxcaloffdatahigh, fluxcalofferrslow, fluxcalofferrshigh = fluxcaloffar.getLevels()
source = fluxcalonar.getName()
if source != fluxcaloffar.getName():
raise ValueError("Mismatch in fluxcal names")
config = CalibratorConfig()
calflux = config.calculateCalibratorFlux(source, self.freqs)
# Flux calibrator amplitudes, the difference between on and off source without the noise diode operational.
S_cal = fluxcalondatalow - fluxcaloffdatalow
#print np.shape(calflux), np.shape(S_cal)
#self.I = self.I
def applyCalibration(self, ar):
M_PAs = []
PAR_ANG = ar.getSubintinfo('PAR_ANG')
if PAR_ANG is None:
POS_ANG = ar.getSubintinfo('POS_ANG')
if POS_ANG is None:
print("No parallactic/position angle information")
elif self.verbose:
print("Calibrating using position angles")
PAR_ANG = POS_ANG
elif self.verbose:
print("Calibrating using parallactic angles")
if PAR_ANG is not None:
PAR_ANG *= np.pi/180 #check if degrees!
dG = 2*self.Q/self.I
dpsi = np.arctan2(self.V, self.U)
data = ar.getData(squeeze=False) #perform checks here
# Remove baselines?
POL_TYPE = ar.subintheader['POL_TYPE']
I = xrange(ar.getNsubint())
J = xrange(ar.getNchan())
K = xrange(ar.getNbin())
calibrated_data = np.zeros_like(data)
for i in I:
print(i)
if PAR_ANG is not None:
M_PA = self.buildMuellerMatrixPA(PAR_ANG[i])
for j in J:
M_differential = self.buildMuellerMatrixDifferential((dG[j], dpsi[j])) # must match exactly
if PAR_ANG is not None:
M = np.dot(M_differential, M_PA)
else:
M = M_differential
Minv = np.linalg.inv(M)
for k in K:
S = self.convertPolarization(data[i, :, j, k], POL_TYPE, "IQUV")
#print np.shape(Minv), np.shape(S), np.shape(calibrated_data[i, :, j, k])
calibrated_data[i, :, j, k] = self.convertPolarization(np.dot(Minv, S), "IQUV", POL_TYPE)
# reset baseline
#if i == 5 and j == 50:
# plot(calibrated_data[i, 0, j, :])
# show()
#imshow(calibrated_data[i, 1, :, :])
#show()
#imshow(calibrated_data[i, 2, :, :])
#show()
#imshow(calibrated_data[i, 3, :, :])
#show()
# raise SystemExit
#calibrated_data[i, :, j, :] -= np.mean(calibrated_data[i, :, j, ar.opw])
#if i == 10:
# imshow(calibrated_data[i, 0, :, :])
# show()
# raise SystemExit
#print np.mean(calibrated_data[5, :, 25, :])
ar.setData(calibrated_data)
def buildMuellerMatrixPA(self, PA):
if PA is None:
M_PA = np.identity(4)
else:
cos = np.cos(2*PA)
sin = np.sin(2*PA)
M_PA = [[1, 0, 0, 0],
[0, cos, sin, 0],
[0, -sin, cos, 0],
[0, 0, 0, 1]]
return M_PA
def buildMuellerMatrixDifferential(self, differential):
if differential is None:
M_differential = np.identity(4)
else:
dG, dpsi = differential
cos = np.cos(dpsi)
sin = np.sin(dpsi)
M_differential = [[1, dG/2.0, 0, 0],
[dG/2.0, 1, 0, 0],
[0, 0, cos, -sin],
[0, 0, sin, cos]]
return M_differential
def convertPolarization(self, S, intype, outtype, linear=True):
if intype == outtype:
return S
elif intype == "AABBCRCI" and outtype == "IQUV": # Coherence -> Stokes
A, B, C, D = S
if linear:
I = A+B
Q = A-B
U = 2*C
V = 2*D
else:
I = A+B
Q = 2*C
U = 2*D
V = A-B
outS = [I, Q, U, V]
elif intype == "IQUV" and outtype == "AABBCRCI": # Stokes -> Coherence
I, Q, U, V = S
if linear:
pass
A = (I+Q)/2.0
B = (I-Q)/2.0
C = U/2.0
D = V/2.0
else:
A = (I+V)/2.0
B = (I-V)/2.0
C = Q/2.0
D = U/2.0
outS = [A, B, C, D]
if isinstance(S, np.ndarray):
return np.array(outS)
elif isinstance(S, list):
return outS
def buildMuellerMatrix(self, PA=None, feed=None, CC=None, differential=None):
"""
Following Lorimer & Kramer methodology
PA = parallactic angle (scalar)
feed =
CC = cross coupling (4-vector of )
differential = differential gain and phase (2-vector)
"""
if PA is None:
M_PA = np.identity(4)
else:
cos = np.cos(2*PA)
sin = np.sin(2*PA)
M_PA = [[1, 0, 0, 0],
[0, cos, sin, 0],
[0, -sin, cos, 0],
[0, 0, 0, 1]]
if feed is None:
M_feed = np.identity(4)
else:
cos = np.cos(2*feed)
sin = np.sin(2*feed)
M_feed = [[1, 0, 0, 0],
[0, cos, 0, sin],
[0, 0, 1, 0],
[0, -sin, 0, cos]]
if CC is None:
M_CC = np.identity(4)
else:
M_CC = np.identity(4) #NOT YET IMPLEMENTED
if differential is None:
M_differential = np.identity(4)
else:
dG, dpsi = differential
cos = np.cos(dpsi)
sin = | np.sin(dpsi) | numpy.sin |
#!/usr/bin/env python
# Test QP solver against Maros Mezaros Benchmark suite
from __future__ import print_function
import sys
import scipy.io as spio
import scipy.sparse as spspa
import scipy as sp
import numpy as np
import ipdb
import mathprogbasepy as mpbpy
import mathprogbasepy.quadprog.problem as mpbpy_prob
def load_maros_meszaros_problem(f):
# Load file
m = spio.loadmat(f)
# Convert matrices
P = m['Q'].astype(float)
n = P.shape[0]
q = m['c'].T.flatten().astype(float)
A = m['A'].astype(float)
A = spspa.vstack([A, spspa.eye(n)])
u = np.append(m['ru'].T.flatten().astype(float),
m['ub'].T.flatten().astype(float))
l = np.append(m['rl'].T.flatten().astype(float),
m['lb'].T.flatten().astype(float))
# Define problem
p = mpbpy.QuadprogProblem(P, q, A, l, u)
return p
def main():
sp.random.seed(1)
# Possible ops: {'small1', 'small2', 'random',
# 'primal_infeasible', 'random_primal_infeasible',
# 'maros_meszaros', 'lp', 'dual_infeasible_lp',
# 'dual_infeasible_qp'}
example = 'random_primal_infeasible'
if example == 'maros_meszaros':
# Maros Meszaros Examples
# f = 'tests/maros_meszaros/CVXQP2_S.mat'
# f = 'tests/maros_meszaros/CVXQP1_S.mat'
# f = 'tests/maros_meszaros/AUG2D.mat'
f = 'maros_meszaros/CONT-200.mat'
# f = 'tests/maros_meszaros/PRIMAL3.mat'
# f = 'tests/maros_meszaros/QBANDM.mat'
p = load_maros_meszaros_problem(f)
elif example == 'small1':
# Our Examples
# Small Example 1
P = spspa.csc_matrix(np.array([[4., 1.], [1., 2.]]))
q = np.ones(2)
A = spspa.vstack([spspa.csc_matrix(np.ones((1, 2))),
spspa.eye(P.shape[0])]).tocsc()
l = np.array([1.0, 0.0, 0.0])
u = np.array([1.0, 0.7, 0.7])
p = mpbpy.QuadprogProblem(P, q, A, l, u)
elif example == 'small2':
# Small Example 2
P = spspa.csc_matrix(np.array([[11., 0.], [0., 0.]]))
q = np.array([3, 4])
A = spspa.csc_matrix(np.array([[-1, 0], [0, -1], [-1, -3],
[2, 5], [3, 4]]))
u = np.array([0., 0., -15, 100, 80])
l = -np.inf * np.ones(len(u))
p = mpbpy.QuadprogProblem(P, q, A, l, u)
elif example == 'primal_infeasible':
# primal_infeasible example
# P = spspa.eye(2)
P = spspa.csc_matrix((2, 2))
q = np.ones(2)
A = spspa.csc_matrix(np.array([[1, 0], [0, 1], [1, 1]]))
l = np.array([0., 0., -1.])
u = np.array([np.inf, np.inf, -1.])
p = mpbpy.QuadprogProblem(P, q, A, l, u)
elif example == 'random_primal_infeasible':
# Random Example
n = 50
m = 500
# Generate random Matrices
Pt = sp.randn(n, n)
P = spspa.csc_matrix(np.dot(Pt.T, Pt))
q = sp.randn(n)
A = spspa.csc_matrix(sp.randn(m, n))
u = 3 + sp.randn(m)
# l = u
l = -3 + sp.randn(m)
# Make random problem primal_infeasible
A[int(n/2), :] = A[int(n/2)+1, :]
l[int(n/2)] = u[int(n/2)+1] + 100 * sp.rand()
u[int(n/2)] = l[int(n/2)] + 0.5
# l[int(n/3)] = u[int(n/3)] + 100 * sp.rand()
# l[int(n/4)] = u[int(n/4)] + 50. * sp.rand()
p = mpbpy.QuadprogProblem(P, q, A, l, u)
elif example == 'dual_infeasible_lp':
# Dual infeasible example
P = spspa.csc_matrix((2, 2))
q = np.array([2, -1])
A = spspa.eye(2)
l = np.array([0., 0.])
u = np.array([np.inf, np.inf])
p = mpbpy.QuadprogProblem(P, q, A, l, u)
elif example == 'dual_infeasible_qp':
# Dual infeasible example
P = spspa.csc_matrix(np.diag(np.array([4., 0.])))
q = np.array([0, 2])
A = spspa.csc_matrix([[1., 1.], [-1., 1.]])
l = | np.array([-np.inf, -np.inf]) | numpy.array |
from __future__ import print_function
from __future__ import division
from tensorflow.python.util import compat
import numpy as np
import tensorflow as tf
from ._layers_common import add_const, identity, make_tensor, skip, _get_const_tensor_value
from . import _shape_sensitive_layers as ss_layers
_SKIP_OP_TYPES = ['NoOp', 'ExpandDims', 'Cast', 'Squeeze']
def _compare(a, b, encoding="utf8"): #type: (Text, Text, Text) -> bool
if isinstance(a, bytes):
a = a.decode(encoding)
if isinstance(b, bytes):
b = b.decode(encoding)
return a == b
def _is_skip_type(op):
return op.type in _SKIP_OP_TYPES
def _backtrace_skip_ops(start_op):
# if start_op is skippable, trace down its path to an unskippable op.
op = start_op
if not _is_skip_type(op):
return op
pred = None if len(op.inputs) == 0 else op.inputs[0].op
while pred is not None and (_is_skip_type(pred)):
op = pred
pred = None if len(op.inputs) == 0 else op.inputs[0].op
return pred
def add_tensor_sub(builder, name, x_name, y_name, output_name):
y_out_name = 'negated_' + y_name + '_' + output_name
builder.add_activation(y_out_name, 'LINEAR', y_name, y_out_name, [-1.0, 0])
builder.add_elementwise(name, [x_name, y_out_name], output_name, 'ADD')
def add_tensor_div(builder, name, x_name, y_name, output_name):
y_out_name = 'inversed_' + y_name + '_' + output_name
builder.add_unary(y_out_name, y_name, y_out_name, 'inverse')
builder.add_elementwise(name, [x_name, y_out_name], output_name, 'MULTIPLY')
def _update_padding_and_crop_values_2D(pad_values, crop_values, params):
def _new_pad_crop_1D(p1,p2,c1,c2,k,s,n1):
n2 = np.floor((n1+p1+p2-k)/s) + 1
if 1+c1*s <= p1:
p1 -= c1*s
c1 = 0
if k+(n2-c2-1)*s > p1+n1:
p2 = k + (n2-c2-1) - (p1+n1)
c2 = 0
return p1,p2,c1,c2
p1,p2,c1,c2 = _new_pad_crop_1D(pad_values[2],pad_values[3],
crop_values[2],crop_values[3],
params['kh'],params['sh'],params['Hin'])
pad_values[2:] = | np.array([p1,p2],dtype=np.int) | numpy.array |
import h5py
import numpy
import scipy.stats
from sklearn.metrics import confusion_matrix
from crowdastro.experiment.results import Results
from crowdastro.crowd.raykar import RaykarClassifier
def raykar_params(crowdastro_path, results_path, method, n_annotators=50):
results = Results.from_path(results_path)
n_splits = results.n_splits
assert method in results.methods
alphas = []
betas = []
for split_id in range(n_splits):
model = results.get_model(method, split_id)
rc = RaykarClassifier.unserialise(model)
alphas.append(rc.a_)
betas.append(rc.b_)
alphas = numpy.array(alphas)
betas = numpy.array(betas)
print('estimated alphas:', alphas.mean(axis=0))
print('stdevs:', alphas.std(axis=0))
print('estimated betas:', betas.mean(axis=0))
print('stdevs:', betas.std(axis=0))
# Get the "true" alpha/beta.
with h5py.File(crowdastro_path, 'r') as f:
norris = f['/wise/cdfs/norris_labels'].value
labels = numpy.ma.MaskedArray(
f['/wise/cdfs/rgz_raw_labels'],
mask=f['/wise/cdfs/rgz_raw_labels_mask'])
annotator_accuracies = []
true_alphas = []
true_betas = []
for t in range(labels.shape[0]):
cm = confusion_matrix(norris[~labels[t].mask],
labels[t][~labels[t].mask])
if cm.shape[0] == 1:
continue
tp = cm[1, 1]
n, p = cm.sum(axis=1)
tn = cm[0, 0]
if not n or not p or p + n < 700:
annotator_accuracies.append(0)
true_alphas.append(tp / p)
true_betas.append(tn / n)
continue
ba = (tp / p + tn / n) / 2
annotator_accuracies.append(ba)
true_alphas.append(tp / p)
true_betas.append(tn / n)
assert len(annotator_accuracies) == len(true_alphas)
ranked_annotators = numpy.argsort(annotator_accuracies)
top_n_annotators = ranked_annotators[-n_annotators:]
true_alphas = numpy.array(true_alphas)[top_n_annotators]
true_betas = | numpy.array(true_betas) | numpy.array |
import matplotlib.pyplot as plt
import matplotlib.dates as mpldates
from datetime import datetime
from floodsystem.analysis import polyfit
from .flood import flood_risk, increase_rate
import numpy as np
import matplotlib.patches as mpatches
def plot_water_levels(station_levels_list):
'''plots water level data and typical low and high for up to 6 different stations.
must be fed a list of (station,dates,levels) tuples'''
locations = [321,322,323,324,325,326]
for entry in station_levels_list:
station = entry[0]
dates = entry[1]
levels = entry[2]
plt.subplot(locations[station_levels_list.index(entry)])
typical_low = [station.typical_range[0]]*len(dates)
typical_high = [station.typical_range[1]]*len(dates)
dates = | np.array(dates) | numpy.array |
'''
Created on Sep 24, 2013
@author: fan
'''
"""
ax1 = plt.subplot2grid((3,3), (0,0), colspan=3)
ax2 = plt.subplot2grid((3,3), (1,0), colspan=2)
ax3 = plt.subplot2grid((3,3), (1, 2), rowspan=2)
ax4 = plt.subplot2grid((3,3), (2, 0))
ax5 = plt.subplot2grid((3,3), (2, 1))
"""
import logging
logger = logging.getLogger(__name__)
import matplotlib
# matplotlib.use('Agg')
# matplotlib.use('qt5agg')
# import matplotlib.pyplot as pylab
import pylab as pylab
# import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import gaussian_kde
# from matplotlib.mlab import griddata
import mpl_toolkits.mplot3d.axes3d as p3
import itertools
from matplotlib.patches import Polygon
from matplotlib import cm
import seaborn as sns
# ===============================================================================
# pylab.tight_layout(pad=0.4, w_pad=0.5, h_pad=1.0)
# pylab.subplots_adjust(left=None, bottom=None, right=None, top=None, wspace=None, hspace=None)
# ===============================================================================
def contourAnd3D(xData, yData, zData,
xLabStr, yLabStr, zLabStr,
graphTitleDisp, graphTitleSave,
savedpi=125, angleType=[1, [1, 2, 3]],
drawContour=False, draw3D=True,
draw3DSurf=False,
contourXres=100, contourYres=100,
s=20, alpha=0.6,
subplot=None, fig=None):
if (fig == None):
fig = pylab.figure()
'''
Contour
'''
if (drawContour == True):
try:
pylab.clf()
if (subplot is not None):
pylab.subplot(subplot['rows'], subplot['cols'], subplot['cur'])
xN, yN, zN = grid(xData, yData, zData, resX=contourXres, resY=contourYres)
pylab.contour(xN, yN, zN)
pylab.xlabel(xLabStr)
pylab.ylabel(yLabStr)
pylab.title(graphTitleDisp)
pylab.grid()
# pylab.show()
pylab.savefig(graphTitleSave + '_contour', dpi=savedpi, papertype='a1')
except:
pass
'''
3D
'''
if (draw3D == True):
try:
pylab.clf()
if (subplot is not None):
pylab.subplot(subplot['rows'], subplot['cols'], subplot['cur'])
ax = p3.Axes3D(fig)
ax.scatter3D(xData, yData, zData, marker='o', s=s, c=np.ravel(zData), alpha=alpha)
tripleAngle3dSave(ax, graphTitleDisp, xLabStr, yLabStr, zLabStr, graphTitleSave + '_3D', savedpi=savedpi,
angleType=angleType)
except:
pass
if (draw3DSurf == True):
try:
# pylab.clf()
if (subplot is not None):
ax = fig.add_subplot(subplot['rows'], subplot['cols'], subplot['cur'], projection='3d')
else:
ax = p3.Axes3D(fig)
ax.plot_surface(xData, yData, zData, cmap=cm.coolwarm, linewidth=0, antialiased=False)
tripleAngle3dSave(ax, graphTitleDisp, xLabStr, yLabStr, zLabStr, graphTitleSave + '_3DS', savedpi=savedpi,
angleType=angleType)
except:
pass
return fig
# pylab.close(fig)
"""
angleType: [1, [1, 2, 3]]
this menas
"""
def tripleAngle3dSave(ax, graphTitleDisp, xLabStr, yLabStr, zLabStr, graphTitleSave, savedpi=125,
angleType=[1, [1, 2, 3]]):
ax.set_title(graphTitleDisp)
# pylab.show()
# for graphICur in [1, 2, 3]:
for graphICur in angleType[1]:
ax.set_xlabel(xLabStr)
ax.set_ylabel(yLabStr)
ax.set_zlabel(zLabStr)
if (angleType[0] == 1):
if (graphICur == 1):
ax.view_init(elev=0, azim=-180)
ax.set_xlabel('')
if (graphICur == 2):
ax.view_init(elev=0, azim=-90)
ax.set_ylabel('')
if (graphICur == 3):
ax.view_init(elev=90, azim=-90)
ax.set_zlabel('')
if (graphICur == 4):
ax.view_init(elev=-90, azim=0)
ax.set_ylabel('')
if (graphICur == 5):
ax.view_init(elev=0, azim=-145)
ax.set_ylabel('')
if (graphICur == 6):
ax.view_init(elev=22., azim=-115)
ax.set_ylabel('')
if (angleType[0] == 2):
if (graphICur == 1):
ax.view_init(elev=-90, azim=0)
if (graphICur == 2):
ax.view_init(elev=0, azim=-145)
if (angleType[0] == 3):
if (graphICur == 1):
ax.view_init(elev=22., azim=-115)
pylab.savefig(graphTitleSave + str(graphICur), dpi=savedpi, papertype='a1')
# ===========================================================================
#
# angleColl_elevAndAzim_set1 = [[90,-90],[0,-180],[0,-90]]
# angleColl_elevAndAzim_set2 = [[-90,0],[0,-145]]
# angleColl_elevAndAzim = [angleColl_elevAndAzim_set1,angleColl_elevAndAzim_set2]
#
# if (angleColl_elevAndAzim[0] == 1):
# ax.set_title(graphTitleDisp)
# # pylab.show()
# #for graphICur in [1, 2, 3]:
# for graphICur in angleType[1]:
# ax.set_xlabel(xLabStr)
# ax.set_ylabel(yLabStr)
# ax.set_zlabel(zLabStr)
# (curElev,curAxzim) = angleColl_elevAndAzim[angleType[0]][graphICur]
# ax.view_init(elev=curElev, azim=curAxzim)
# if (graphICur == 1):
# ax.set_zlabel('')
# if (graphICur == 2):
# ax.set_xlabel('')
# if (graphICur == 3):
# ax.set_ylabel('')
#
# pylab.savefig(graphTitleSave+str(graphICur), dpi=savedpi, papertype='a1')
#
# if (angleType[0] == 2):
# ax.view_init(elev=-90, azim=0)
# ===========================================================================
'''
Essential function for turning scatter 3d plot into contour 3d plot
'''
def grid(x, y, z, resX=100, resY=100):
"Convert 3 column data to matplotlib grid"
xi = np.linspace(min(x), max(x), resX)
yi = np.linspace(min(y), max(y), resY)
Z = griddata(x, y, z, xi, yi)
X, Y = np.meshgrid(xi, yi)
return X, Y, Z
toGraphHere = False
def graph_emaxKCash_Value(soluSupObj, resources, k_vec, emaxValsCur, emaxChoicesCur, emaxChoiceOfMaxCollCur,
predictUtil):
grapher = graphFunc()
pylab.clf()
toGraphHere = False
if (toGraphHere == True):
# fig=pylab.figure()
xLabStr = 'Cash on Hand'
yLabStr = 'Physical Capital'
xData = resources
yData = k_vec
'''
Resource and K State Space Ranges
'''
# ===================================================================
# grapher = grpSup.graphFunc()
# pylab.clf()
# grapher.xyPlotMultiYOneX(yDataMat=resources, saveOrNot=True, showOrNot=False, graphType='hist',
# saveDirectory=fobj.support_args['IO'],
# saveFileName='ResStateHist'+str(fobj.support_args['cur_round']),
# basicTitle='Resource Histogram', basicXLabel='Resource State Points', basicYLabel='Density')
#
# pylab.clf()
# grapher.xyPlotMultiYOneX(yDataMat=k_vec, saveOrNot=True, showOrNot=False, graphType='hist',
# saveDirectory=fobj.support_args['IO'],
# saveFileName='KStateHist'+str(fobj.support_args['cur_round']),
# basicTitle='K Histogram', basicXLabel='K State Points', basicYLabel='Density')
# ===================================================================
titleStrList = ['Utility', 'Consumption Choice', 'Kapital Choice', 'B Formal Choice', 'B Informal Choice']
titleStringList = ['Informal Borrow', 'Informal Save/Lend', 'Formal Borrow', 'Formal Save',
'Formal and Informal Borrow', 'Formal Borrow and Informal Save/Lend', 'None']
titleStringList = ['Inf Borr', 'Inf Save', 'For Borr', 'Form Save',
'FB+IB', 'FB+IS', 'None']
drawHere2DGraph = True
drawHere3DGraph = False
"""
3D and Contour
"""
curRound = str(soluSupObj.sa['cur_round'])
if (int(curRound) % 1 == 0):
"""
Look over Value and Choices
"""
# for curCol in range(0,0):
if (drawHere2DGraph == True):
pylab.clf()
fig, ((ax1, ax2, ax3), (ax4, ax5, ax6)) = pylab.subplots(2, 3)
axisList = [ax1, ax2, ax3, ax4, ax5, ax6]
for curCol in range(0, 5):
pylab.sca(axisList[curCol])
titlStr = titleStrList[curCol]
labelArray_coll = [titlStr]
noLabel = True
if (titlStr == 'Utility'):
zData = emaxValsCur[:, 0]
angleType = [1, [1, 2, 3]]
else:
zData = emaxChoicesCur[:, curCol - 1]
angleType = [3, [1]]
if (drawHere2DGraph == True):
"""
Draw Prediction Line
"""
if (curCol == 0):
xDataSortedIdx = np.argsort(xData)
xDataSorted = xData[xDataSortedIdx]
predictUtilSorted = predictUtil[xDataSortedIdx]
grapher.xyPlotMultiYOneX(yDataMat=predictUtilSorted, xData=xDataSorted,
labelArray=labelArray_coll, noLabel=noLabel,
saveOrNot=False, graphType='plot')
"""
Draw Choices and Value along resources, scatter, color showing K value
"""
line45Deg = False
if (curCol == 1):
line45Deg = True
grapher.xyPlotMultiYOneX(yDataMat=zData, xData=xData, colorVar=yData,
labelArray=labelArray_coll, noLabel=noLabel,
saveOrNot=False, graphType='scatter', scattersize=1,
labelLoc1t0=4, basicTitle=titlStr,
basicXLabel='Cash on Hand', basicYLabel='Consumption Unit',
line45Deg=line45Deg)
if (drawHere3DGraph == True and curCol <= 4):
graphTitleDisp = titlStr
saveTitleFull = soluSupObj.sa['IO'] + 'EmaxApprox_VCKnBn_t' + str(curCol) + 'iter' + curRound
graphTitleSave = saveTitleFull
zLabStr = 'Choices'
contourAnd3D(xData, yData, zData, xLabStr, yLabStr, zLabStr,
graphTitleDisp, graphTitleSave, angleType=angleType, drawContour=True, draw3D=True)
if (drawHere2DGraph == True):
grapher.savingFig(saveDirectory=soluSupObj.sa['IO'],
saveFileName='EmaxApprox_VCKnBn_iter' + str(curRound),
saveDPI=200, pylabUse=fig)
"""
Probability of Choices Graphs along 3D
"""
# for curCol in range(4,4,1):
if (drawHere2DGraph == True):
pylab.clf()
fig, ((ax1, ax2, ax3, ax4), (ax5, ax6, ax7, ax8)) = pylab.subplots(2, 4)
axisList = [ax1, ax2, ax3, ax4, ax5, ax6, ax7]
maxProb = np.max(emaxChoiceOfMaxCollCur[:, 4:11])
for curCol in range(4, 11, 1):
pylab.sca(axisList[curCol - 4])
xLabStr = 'Cash on Hand'
yLabStr = 'Physical Capital'
titlStr = 'Probability of ' + titleStringList[curCol - 4]
zData = emaxChoiceOfMaxCollCur[:, curCol]
if (drawHere3DGraph == True):
graphTitleDisp = titlStr
saveTitleFull = soluSupObj.sa['IO'] + 'EmaxApprox_Prob_t' + str(curCol) + 'iter' + curRound
graphTitleSave = saveTitleFull
zLabStr = 'Probability of Choice'
contourAnd3D(xData, yData, zData, xLabStr, yLabStr, zLabStr,
graphTitleDisp, graphTitleSave, angleType=[3, [1]], drawContour=True, draw3D=True)
if (drawHere2DGraph == True):
grapher.xyPlotMultiYOneX(yDataMat=zData, xData=xData, colorVar=yData,
saveOrNot=False, graphType='scatter', scattersize=1,
basicTitle=titleStringList[curCol - 4],
basicXLabel='Cash on Hand', basicYLabel='Probability',
ylim=[-0.05, maxProb], xlim=[0 - 5000, np.max(xData) + 5000])
"""
sumProb Should be 1, but maybe not due to code issues, need to check here
"""
pylab.sca(ax8)
sumProb = np.sum((emaxChoiceOfMaxCollCur[:, 4:11]), axis=1)
grapher.xyPlotMultiYOneX(yDataMat=sumProb, xData=xData,
saveOrNot=False, graphType='scatter', scattersize=1, basicTitle='Sum Prob',
basicXLabel='Cash on Hand', basicYLabel='Probability', ylim=[-0.05, 1.05],
xlim=[0 - 5000, np.max(xData) + 5000])
if (drawHere2DGraph == True):
grapher.savingFig(saveDirectory=soluSupObj.sa['IO'],
saveFileName='EmaxApprox_Prob_iter' + str(curRound),
saveDPI=200, pylabUse=fig)
def OLSEmaxValAndChoicesGraphs(allDataY, allDataX,
saveFileSuffix='', yLabelNames=['Emax', 'Choice'],
xLabelNames=['Height', 'Weight', 'Income'],
saveDirectory='default', saveFileName='default'):
# toGraphHere = False
if (toGraphHere == True):
loopCountY = len(yLabelNames)
for graphI in range(0, loopCountY, 1):
yData = allDataY[graphI]
OLSEmaxGraphs(saveFileSuffix, yVal=yData, allDataX=allDataX,
yLabelName=yLabelNames[graphI], xLabelNames=xLabelNames,
saveDirectory=saveDirectory, saveFileName=saveFileName)
def OLSEmaxGraphs(saveFileSuffix,
yVal, allDataX,
saveDirectory='default', saveFileName='default', yLabelName='yLabelName',
xLabelNames=['Height', 'Weight', 'Income']):
if (saveDirectory == 'default'):
saveDirectory = 'C:\\Users\\fan\\Documents\\Dropbox\\Height_Production_Function\\Results--HD on HL WL--Linear--Protein and Calorie With Price Instruments\\ProduWithPref\\'
saveFileName = saveFileName + '_' + str(yLabelName) + str(saveFileSuffix)
if (saveFileName == 'default'):
saveFileName = 'EmaxApprox'
grapher = graphFunc()
pylab.clf()
loopCount = len(xLabelNames)
for graphI in range(0, loopCount, 1):
xData = allDataX[graphI]
yDataMat = yVal
pylab.subplot(2, loopCount, graphI + 1)
basicTitle = xLabelNames[graphI] + ' and ' + yLabelName
basicXLabel = xLabelNames[graphI]
basicYLabel = yLabelName
grapher.xyPlotMultiYOneX(yDataMat=yDataMat, xData=xData, saveOrNot=False, graphType='scatterregline',
basicTitle=basicTitle, basicXLabel=basicXLabel, basicYLabel=basicYLabel, noLabel=True,
scattersize=0.1)
xData = allDataX[graphI]
pylab.subplot(2, loopCount, graphI + 1 + loopCount)
basicTitle = xLabelNames[graphI] + ' Histogram'
basicXLabel = xLabelNames[graphI]
basicYLabel = 'Frequency'
grapher.xyPlotMultiYOneX(yDataMat=xData, saveOrNot=False, graphType='hist',
basicTitle=basicTitle, basicXLabel=basicXLabel, basicYLabel=basicYLabel, noLabel=True,
bins=30)
pylab.tight_layout(pad=0.4, w_pad=0.5, h_pad=1.0)
pylab.subplots_adjust(left=None, bottom=None, right=None, top=None, wspace=None, hspace=None)
grapher.savingFig(saveDirectory=saveDirectory, saveFileName=saveFileName)
class graphFunc:
points = 200
xData = np.linspace(-1, 1, points)
xData = | np.random.normal(10, 2, points) | numpy.random.normal |
# Copyright 2020 The Cirq Developers
#
# 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
#
# https://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 dataclasses
import datetime
import time
import numpy as np
import pytest
import cirq
import cirq.work as cw
from cirq.work.observable_measurement_data import (
_check_and_get_real_coef,
_obs_vals_from_measurements,
_stats_from_measurements,
)
from cirq.work.observable_settings import _MeasurementSpec
def test_get_real_coef():
q0 = cirq.LineQubit(0)
assert _check_and_get_real_coef(cirq.Z(q0) * 2, atol=1e-8) == 2
assert _check_and_get_real_coef(cirq.Z(q0) * complex(2.0), atol=1e-8) == 2
with pytest.raises(ValueError):
_check_and_get_real_coef(cirq.Z(q0) * 2.0j, atol=1e-8)
def test_obs_vals_from_measurements():
bitstrings = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
a = cirq.NamedQubit('a')
b = cirq.NamedQubit('b')
qubit_to_index = {a: 0, b: 1}
obs = cirq.Z(a) * cirq.Z(b) * 10
vals = _obs_vals_from_measurements(bitstrings, qubit_to_index, obs, atol=1e-8)
should_be = [10, -10, -10, 10]
np.testing.assert_equal(vals, should_be)
def test_stats_from_measurements():
bitstrings = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
a = cirq.NamedQubit('a')
b = cirq.NamedQubit('b')
qubit_to_index = {a: 0, b: 1}
obs = cirq.Z(a) * cirq.Z(b) * 10
mean, err = _stats_from_measurements(bitstrings, qubit_to_index, obs, atol=1e-8)
# The mean is zero since our bitstrings have balanced even- and odd-
# parity cases.
assert mean == 0
# Since we multiplied our observable by 10, the standard deviation is
# 10 [each obs val deviates by 10]. The variance is 10**2 and the
# squared-standard-error-of-the-mean can be found by dividing by the
# number of samples minus 1.
assert err == 10**2 / (4 - 1)
def test_observable_measured_result():
a = cirq.NamedQubit('a')
b = cirq.NamedQubit('b')
omr = cw.ObservableMeasuredResult(
setting=cw.InitObsSetting(
init_state=cirq.Z(a) * cirq.Z(b), observable=cirq.Y(a) * cirq.Y(b)
),
mean=0,
variance=5**2,
repetitions=4,
circuit_params={'phi': 52},
)
assert omr.stddev == 5
assert omr.observable == cirq.Y(a) * cirq.Y(b)
assert omr.init_state == cirq.Z(a) * cirq.Z(b)
cirq.testing.assert_equivalent_repr(omr)
assert omr.as_dict() == {
'init_state': cirq.Z(a) * cirq.Z(b),
'observable': cirq.Y(a) * cirq.Y(b),
'mean': 0,
'variance': 25,
'repetitions': 4,
'param.phi': 52,
}
omr2 = dataclasses.replace(
omr,
circuit_params={
'phi': 52,
'observable': 3.14, # this would be a bad but legal parameter name
'param.phi': -1,
},
)
assert omr2.as_dict() == {
'init_state': cirq.Z(a) * cirq.Z(b),
'observable': cirq.Y(a) * cirq.Y(b),
'mean': 0,
'variance': 25,
'repetitions': 4,
'param.phi': 52,
'param.observable': 3.14,
'param.param.phi': -1,
}
@pytest.fixture()
def example_bsa() -> 'cw.BitstringAccumulator':
"""Test fixture to create an (empty) example BitstringAccumulator"""
q0, q1 = cirq.LineQubit.range(2)
setting = cw.InitObsSetting(
init_state=cirq.KET_ZERO(q0) * cirq.KET_ZERO(q1), observable=cirq.X(q0) * cirq.Y(q1)
)
meas_spec = _MeasurementSpec(
max_setting=setting, circuit_params={'beta': 0.123, 'gamma': 0.456}
)
bsa = cw.BitstringAccumulator(
meas_spec=meas_spec,
simul_settings=[
setting,
cw.InitObsSetting(init_state=setting.init_state, observable=cirq.X(q0)),
cw.InitObsSetting(init_state=setting.init_state, observable=cirq.Y(q1)),
],
qubit_to_index={q0: 0, q1: 1},
)
return bsa
def test_bitstring_accumulator(example_bsa):
# test initialization
assert example_bsa.bitstrings.shape == (0, 2)
assert example_bsa.chunksizes.shape == (0,)
assert example_bsa.timestamps.shape == (0,)
# test consume_results
bitstrings = np.array([[0, 0], [0, 1], [1, 0], [1, 1]], dtype=np.uint8)
example_bsa.consume_results(bitstrings)
assert example_bsa.bitstrings.shape == (4, 2)
assert example_bsa.chunksizes.shape == (1,)
assert example_bsa.timestamps.shape == (1,)
assert example_bsa.n_repetitions == 4
with pytest.raises(ValueError):
example_bsa.consume_results(bitstrings.astype(int))
# test results
results = list(example_bsa.results)
assert len(results) == 3
for r in results:
assert r.repetitions == 4
# test records
for r in example_bsa.records:
assert isinstance(r, dict)
assert 'repetitions' in r
assert r['repetitions'] == 4
def test_bitstring_accumulator_strings(example_bsa):
bitstrings = np.array([[0, 0], [0, 1], [1, 0], [1, 1]], dtype=np.uint8)
example_bsa.consume_results(bitstrings)
q0, q1 = cirq.LineQubit.range(2)
settings = cw.observables_to_settings(
[cirq.X(q0), cirq.Y(q1), cirq.X(q0) * cirq.Y(q1)], qubits=[q0, q1]
)
strings_should_be = [
'+Z(q(0)) * +Z(q(1)) → X(q(0)): 0.000 +- 0.577',
'+Z(q(0)) * +Z(q(1)) → Y(q(1)): 0.000 +- 0.577',
'+Z(q(0)) * +Z(q(1)) → X(q(0))*Y(q(1)): 0.000 +- 0.577',
]
for setting, ssb in zip(settings, strings_should_be):
assert example_bsa.summary_string(setting) == ssb, ssb
assert (
str(example_bsa)
== """Accumulator +Z(q(0)) * +Z(q(1)) → X(q(0))*Y(q(1)); 4 repetitions
+Z(q(0)) * +Z(q(1)) → X(q(0))*Y(q(1)): 0.000 +- 0.577
+Z(q(0)) * +Z(q(1)) → X(q(0)): 0.000 +- 0.577
+Z(q(0)) * +Z(q(1)) → Y(q(1)): 0.000 +- 0.577"""
)
def test_bitstring_accumulator_equality():
et = cirq.testing.EqualsTester()
bitstrings = np.array([[0, 0], [0, 1], [1, 0], [1, 1]], dtype=np.uint8)
chunksizes = np.asarray([4])
timestamps = np.asarray([datetime.datetime.now()])
a = cirq.NamedQubit('a')
b = cirq.NamedQubit('b')
qubit_to_index = {a: 0, b: 1}
obs = cirq.Z(a) * cirq.Z(b) * 10
setting = cw.InitObsSetting(init_state=cirq.Z(a) * cirq.Z(b), observable=obs)
meas_spec = _MeasurementSpec(setting, {})
cirq.testing.assert_equivalent_repr(
cw.BitstringAccumulator(
meas_spec=meas_spec,
simul_settings=[setting],
qubit_to_index=qubit_to_index,
bitstrings=bitstrings.copy(),
chunksizes=chunksizes.copy(),
timestamps=timestamps.copy(),
)
)
et.add_equality_group(
cw.BitstringAccumulator(
meas_spec=meas_spec,
simul_settings=[setting],
qubit_to_index=qubit_to_index,
bitstrings=bitstrings.copy(),
chunksizes=chunksizes.copy(),
timestamps=timestamps.copy(),
),
cw.BitstringAccumulator(
meas_spec=meas_spec,
simul_settings=[setting],
qubit_to_index=qubit_to_index,
bitstrings=bitstrings.copy(),
chunksizes=chunksizes.copy(),
timestamps=timestamps.copy(),
),
)
time.sleep(1)
timestamps = np.asarray([datetime.datetime.now()])
et.add_equality_group(
cw.BitstringAccumulator(
meas_spec=meas_spec,
simul_settings=[setting],
qubit_to_index=qubit_to_index,
bitstrings=bitstrings,
chunksizes=chunksizes,
timestamps=timestamps,
)
)
et.add_equality_group(
cw.BitstringAccumulator(
meas_spec=_MeasurementSpec(setting, {'a': 2}),
simul_settings=[setting],
qubit_to_index=qubit_to_index,
bitstrings=bitstrings,
chunksizes=chunksizes,
timestamps=timestamps,
)
)
bitstrings = bitstrings.copy()
bitstrings[0] = [1, 1]
et.add_equality_group(
cw.BitstringAccumulator(
meas_spec=meas_spec,
simul_settings=[setting],
qubit_to_index=qubit_to_index,
bitstrings=bitstrings,
chunksizes=chunksizes,
timestamps=timestamps,
)
)
chunksizes = np.asarray([2, 2])
timestamps = np.asarray(list(timestamps) * 2)
et.add_equality_group(
cw.BitstringAccumulator(
meas_spec=meas_spec,
simul_settings=[setting],
qubit_to_index=qubit_to_index,
bitstrings=bitstrings,
chunksizes=chunksizes,
timestamps=timestamps,
)
)
def _get_ZZ_Z_Z_bsa_constructor_args():
bitstrings = np.array([[0, 0], [0, 1], [1, 0], [1, 1]], dtype=np.uint8)
chunksizes = np.asarray([4])
timestamps = np.asarray([datetime.datetime.now()])
a = cirq.NamedQubit('a')
b = cirq.NamedQubit('b')
qubit_to_index = {a: 0, b: 1}
settings = list(
cw.observables_to_settings(
[cirq.Z(a) * cirq.Z(b) * 7, cirq.Z(a) * 5, cirq.Z(b) * 3], qubits=[a, b]
)
)
meas_spec = _MeasurementSpec(settings[0], {})
return {
'meas_spec': meas_spec,
'simul_settings': settings,
'qubit_to_index': qubit_to_index,
'bitstrings': bitstrings,
'chunksizes': chunksizes,
'timestamps': timestamps,
}
def test_bitstring_accumulator_stats():
kwargs = _get_ZZ_Z_Z_bsa_constructor_args()
settings = kwargs['simul_settings']
a, b = kwargs['qubit_to_index']
bsa = cw.BitstringAccumulator(**kwargs)
# There are three observables, each with mean 0 because
# the four 2-bit strings have even numbers of a) ones in the
# first position b) ones in the second position c) even parity
# pairs.
np.testing.assert_allclose([0, 0, 0], bsa.means())
# Covariance: Sum[(x - xbar)(y - ybar)] / (N-1)
# where xbar and ybar are 0, per above. Each individual observed
# value is +-1, so (x-xbar)(y-bar) is +-1 (neglecting observable coefficients)
# For off-diagonal elements, there are two +1 and two -1 terms for each entry
# so the total contribution is zero, and the matrix is diagonal
should_be = np.array([[4 * 7**2, 0, 0], [0, 4 * 5**2, 0], [0, 0, 4 * 3**2]])
should_be = should_be / (4 - 1) # covariance formula
should_be = should_be / 4 # cov of the distribution of sample mean
np.testing.assert_allclose(should_be, bsa.covariance())
for setting, var in zip(settings, [4 * 7**2, 4 * 5**2, 4 * 3**2]):
np.testing.assert_allclose(0, bsa.mean(setting))
np.testing.assert_allclose(var / 4 / (4 - 1), bsa.variance(setting))
np.testing.assert_allclose( | np.sqrt(var / 4 / (4 - 1)) | numpy.sqrt |
# 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]) | numpy.array |
# Copyright (c) 2020 @ FBK - Fondazione B<NAME>
# Author: <NAME>
# Project: LUCID: A Practical, Lightweight Deep Learning Solution for DDoS Attack Detection
#
# 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 copy
import os
import sys
import csv
import glob
import h5py
import time
import pyshark
import socket
import pickle
import random
import hashlib
import argparse
import ipaddress
import numpy as np
from lxml import etree
from collections import OrderedDict
from sklearn.feature_extraction.text import CountVectorizer
from sklearn.utils import shuffle as sklearn_shuffle
from multiprocessing import Process, Manager, Value, Queue
from util_functions import *
# Sample commands
# split a pcap file into smaller chunks to leverage multi-core CPUs: tcpdump -r dataset.pcap -w dataset-chunk -C 1000
# dataset parsing (first step): python3 lucid_dataset_parser.py --dataset_type SYN2020 --dataset_folder ./sample-dataset/ --packets_per_flow 10 --dataset_id SYN2020 --traffic_type all --time_window 10
# dataset parsing (second step): python3 lucid_dataset_parser.py --preprocess_folder ./sample-dataset/
IDS2018_DDOS_FLOWS = {'attackers': ['192.168.127.12', '192.168.3.11','192.168.127.12','192.168.127.12','192.168.3.11','172.16.17.32','192.168.127.12','172.16.17.32','192.168.3.11','192.168.127.12'],
'victims': ['172.16.17.32','172.31.69.28']}
IDS2017_DDOS_FLOWS = {'attackers': ['172.16.0.1'],
'victims': ['192.168.10.50']}
CUSTOM_DDOS_SYN = {'attackers': ['11.0.0.' + str(x) for x in range(1,255)],
'victims': ['10.42.0.2']}
DDOS_ATTACK_SPECS = {
'IDS2017' : IDS2017_DDOS_FLOWS,
'IDS2018' : IDS2018_DDOS_FLOWS,
'SYN2020' : CUSTOM_DDOS_SYN
}
vector_proto = CountVectorizer()
vector_proto.fit_transform(protocols).todense()
random.seed(SEED)
np.random.seed(SEED)
def get_pkt_direction(srcIP,dstIP):
internalIP = "192.168"
if internalIP in srcIP and internalIP in dstIP:
return 0
elif internalIP in srcIP:
return 1
elif internalIP in dstIP:
return 2
else:
print ("No private address in this flow!!!!")
return 3
class packet_features:
def __init__(self):
self.id_fwd = (0,0,0,0,0) # 5-tuple src_ip_addr, src_port,,dst_ip_addr,dst_port,protocol
self.id_bwd = (0,0,0,0,0) # 5-tuple src_ip_addr, src_port,,dst_ip_addr,dst_port,protocol
self.features_list = []
def __str__(self):
return "{} -> {}".format(self.id_fwd, self.features_list)
def get_ddos_flows(attackers,victims):
DDOS_FLOWS = {}
if '/' in attackers: # subnet
DDOS_FLOWS['attackers'] = [str(ip) for ip in list(ipaddress.IPv4Network(attackers).hosts())]
else: # single address
DDOS_FLOWS['attackers'] = [str(ipaddress.IPv4Address(attackers))]
if '/' in victims: # subnet
DDOS_FLOWS['victims'] = [str(ip) for ip in list(ipaddress.IPv4Network(victims).hosts())]
else: # single address
DDOS_FLOWS['victims'] = [str(ipaddress.IPv4Address(victims))]
return DDOS_FLOWS
# function that build the labels based on the dataset type
def parse_labels(dataset_type=None, attackers=None,victims=None):
output_dict = {}
if attackers is not None and victims is not None:
DDOS_FLOWS = get_ddos_flows(attackers, victims)
elif dataset_type is not None and dataset_type in DDOS_ATTACK_SPECS:
DDOS_FLOWS = DDOS_ATTACK_SPECS[dataset_type]
else:
return None
for attacker in DDOS_FLOWS['attackers']:
for victim in DDOS_FLOWS['victims']:
ip_src = str(attacker)
ip_dst = str(victim)
key_fwd = (ip_src, ip_dst)
key_bwd = (ip_dst, ip_src)
if key_fwd not in output_dict:
output_dict[key_fwd] = 1
if key_bwd not in output_dict:
output_dict[key_bwd] = 1
return output_dict
def parse_packet(pkt):
pf = packet_features()
tmp_id = [0,0,0,0,0]
try:
pf.features_list.append(float(pkt.sniff_timestamp)) # timestampchild.find('Tag').text
pf.features_list.append(int(pkt.ip.len)) # packet length
pf.features_list.append(int(hashlib.sha256(str(pkt.highest_layer).encode('utf-8')).hexdigest(),
16) % 10 ** 8) # highest layer in the packet
pf.features_list.append(int(int(pkt.ip.flags, 16))) # IP flags
tmp_id[0] = str(pkt.ip.src) # int(ipaddress.IPv4Address(pkt.ip.src))
tmp_id[2] = str(pkt.ip.dst) # int(ipaddress.IPv4Address(pkt.ip.dst))
protocols = vector_proto.transform([pkt.frame_info.protocols]).toarray().tolist()[0]
protocols = [1 if i >= 1 else 0 for i in
protocols] # we do not want the protocols counted more than once (sometimes they are listed twice in pkt.frame_info.protocols)
protocols_value = int(np.dot(np.array(protocols), powers_of_two))
pf.features_list.append(protocols_value)
protocol = int(pkt.ip.proto)
tmp_id[4] = protocol
if pkt.transport_layer != None:
if protocol == socket.IPPROTO_TCP:
tmp_id[1] = int(pkt.tcp.srcport)
tmp_id[3] = int(pkt.tcp.dstport)
pf.features_list.append(int(pkt.tcp.len)) # TCP length
pf.features_list.append(int(pkt.tcp.ack)) # TCP ack
pf.features_list.append(int(pkt.tcp.flags, 16)) # TCP flags
pf.features_list.append(int(pkt.tcp.window_size_value)) # TCP window size
pf.features_list = pf.features_list + [0, 0] # UDP + ICMP positions
elif protocol == socket.IPPROTO_UDP:
pf.features_list = pf.features_list + [0, 0, 0, 0] # TCP positions
tmp_id[1] = int(pkt.udp.srcport)
pf.features_list.append(int(pkt.udp.length)) # UDP length
tmp_id[3] = int(pkt.udp.dstport)
pf.features_list = pf.features_list + [0] # ICMP position
elif protocol == socket.IPPROTO_ICMP:
pf.features_list = pf.features_list + [0, 0, 0, 0, 0] # TCP and UDP positions
pf.features_list.append(int(pkt.icmp.type)) # ICMP type
else:
pf.features_list = pf.features_list + [0, 0, 0, 0, 0, 0] # padding for layer3-only packets
tmp_id[4] = 0
pf.id_fwd = (tmp_id[0], tmp_id[1], tmp_id[2], tmp_id[3], tmp_id[4])
pf.id_bwd = (tmp_id[2], tmp_id[3], tmp_id[0], tmp_id[1], tmp_id[4])
return pf
except AttributeError as e:
# ignore packets that aren't TCP/UDP or IPv4
return None
# Offline preprocessing of pcap files for model training, validation and testing
def process_pcap(pcap_file,dataset_type,in_labels,max_flow_len,labelled_flows,traffic_type='all',time_window=TIME_WINDOW):
start_time = time.time()
temp_dict = OrderedDict()
start_time_window = -1
pcap_name = pcap_file.split("/")[-1]
print("Processing file: ", pcap_name)
cap = pyshark.FileCapture(pcap_file)
for i, pkt in enumerate(cap):
if i % 1000 == 0:
print(pcap_name + " packet #", i)
# start_time_window is used to group packets/flows captured in a time-window
if start_time_window == -1 or float(pkt.sniff_timestamp) > start_time_window + time_window:
start_time_window = float(pkt.sniff_timestamp)
pf = parse_packet(pkt)
temp_dict = store_packet(pf, temp_dict, start_time_window, max_flow_len)
apply_labels(temp_dict, labelled_flows, in_labels, traffic_type)
print('Completed file {} in {} seconds.'.format(pcap_name, time.time() - start_time))
# Transforms live traffic into input samples for inference
def process_live_traffic(cap, dataset_type, in_labels, max_flow_len, traffic_type='all',time_window=TIME_WINDOW):
start_time = time.time()
temp_dict = OrderedDict()
labelled_flows = []
start_time_window = start_time
time_window = start_time_window + time_window
if isinstance(cap, pyshark.LiveCapture) == True:
for pkt in cap.sniff_continuously():
if time.time() >= time_window:
break
pf = parse_packet(pkt)
temp_dict = store_packet(pf, temp_dict, start_time_window, max_flow_len)
elif isinstance(cap, pyshark.FileCapture) == True:
while time.time() < time_window:
pkt = cap.next()
pf = parse_packet(pkt)
temp_dict = store_packet(pf,temp_dict,start_time_window,max_flow_len)
apply_labels(temp_dict,labelled_flows, in_labels,traffic_type)
return labelled_flows
def store_packet(pf,temp_dict,start_time_window, max_flow_len):
if pf is not None:
if pf.id_fwd in temp_dict and start_time_window in temp_dict[pf.id_fwd] and \
temp_dict[pf.id_fwd][start_time_window].shape[0] < max_flow_len:
temp_dict[pf.id_fwd][start_time_window] = np.vstack(
[temp_dict[pf.id_fwd][start_time_window], pf.features_list])
elif pf.id_bwd in temp_dict and start_time_window in temp_dict[pf.id_bwd] and \
temp_dict[pf.id_bwd][start_time_window].shape[0] < max_flow_len:
temp_dict[pf.id_bwd][start_time_window] = np.vstack(
[temp_dict[pf.id_bwd][start_time_window], pf.features_list])
else:
if pf.id_fwd not in temp_dict and pf.id_bwd not in temp_dict:
temp_dict[pf.id_fwd] = {start_time_window: np.array([pf.features_list]), 'label': 0}
elif pf.id_fwd in temp_dict and start_time_window not in temp_dict[pf.id_fwd]:
temp_dict[pf.id_fwd][start_time_window] = np.array([pf.features_list])
elif pf.id_bwd in temp_dict and start_time_window not in temp_dict[pf.id_bwd]:
temp_dict[pf.id_bwd][start_time_window] = np.array([pf.features_list])
return temp_dict
def apply_labels(flows, labelled_flows, labels, traffic_type):
for five_tuple, flow in flows.items():
if labels is not None:
short_key = (five_tuple[0], five_tuple[2]) # for IDS2017/IDS2018 dataset the labels have shorter keys
flow['label'] = labels.get(short_key, 0)
for flow_key, packet_list in flow.items():
# relative time wrt the time of the first packet in the flow
if flow_key != 'label':
amin = np.amin(packet_list,axis=0)[0]
packet_list[:, 0] = packet_list[:, 0] - amin
if traffic_type == 'ddos' and flow['label'] == 0: # we only want malicious flows from this dataset
continue
elif traffic_type == 'benign' and flow['label'] > 0: # we only want benign flows from this dataset
continue
else:
labelled_flows.append((five_tuple,flow))
# returns the total number of flows
def count_flows(preprocessed_flows):
ddos_flows = 0
total_flows = len(preprocessed_flows)
ddos_fragments = 0
total_fragments = 0
for flow in preprocessed_flows:
flow_fragments = len(flow[1]) - 1
total_fragments += flow_fragments
if flow[1]['label'] > 0:
ddos_flows += 1
ddos_fragments += flow_fragments # the label does not count
return (total_flows, ddos_flows, total_flows - ddos_flows), (total_fragments, ddos_fragments, total_fragments-ddos_fragments)
# balance the dataset based on the number of benign and malicious fragments of flows
def balance_dataset(flows,total_fragments=float('inf')):
new_flow_list = []
_,(_, ddos_fragments, benign_fragments) = count_flows(flows)
if ddos_fragments == 0 or benign_fragments == 0:
min_fragments = total_fragments
else:
min_fragments = min(total_fragments/2,ddos_fragments,benign_fragments)
random.shuffle(flows)
new_benign_fragments = 0
new_ddos_fragments = 0
for flow in flows:
if flow[1]['label'] == 0 and (new_benign_fragments < min_fragments ):
new_benign_fragments += len(flow[1]) - 1
new_flow_list.append(flow)
elif flow[1]['label'] == 1 and (new_ddos_fragments < min_fragments):
new_ddos_fragments += len(flow[1]) - 1
new_flow_list.append(flow)
return new_flow_list, new_benign_fragments, new_ddos_fragments
# convert the dataset from dictionaries with 5-tuples keys into a list of flow fragments and another list of labels
def dataset_to_list_of_fragments(dataset):
keys = []
X = []
y = []
for flow in dataset:
tuple = flow[0]
flow_data = flow[1]
label = flow_data['label']
for key, fragment in flow_data.items():
if key != 'label':
X.append(fragment)
y.append(label)
keys.append(tuple)
return X,y,keys
def train_test_split(flow_list,train_size=TRAIN_SIZE, shuffle=True):
test_list = []
_,(total_examples,_,_) = count_flows(flow_list)
test_examples = total_examples - total_examples*train_size
if shuffle == True:
random.shuffle(flow_list)
current_test_examples = 0
while current_test_examples < test_examples:
flow = flow_list.pop(0)
test_list.append(flow)
current_test_examples += len(flow[1])-1
return flow_list,test_list
def main(argv):
command_options = " ".join(str(x) for x in argv[1:])
help_string = 'Usage[0]: python3 lucid_dataset_parser.py --dataset_type <dataset_name> --dataset_folder <folder path> --dataset_id <dataset identifier> --packets_per_flow <n> --time_window <t>\n' \
'Usage[1]: python3 lucid_dataset_parser.py --preprocess_folder <folder path>'
manager = Manager()
parser = argparse.ArgumentParser(
description='Dataset parser',
formatter_class=argparse.ArgumentDefaultsHelpFormatter)
parser.add_argument('-d', '--dataset_folder', nargs='+', type=str,
help='Folder with the dataset')
parser.add_argument('-o', '--output_folder', nargs='+', type=str,
help='Output folder')
parser.add_argument('-f', '--traffic_type', default='all', nargs='+', type=str,
help='Type of flow to process (all, benign, ddos)')
parser.add_argument('-p', '--preprocess_folder', nargs='+', type=str,
help='Folder with preprocessed data')
parser.add_argument('--preprocess_file', nargs='+', type=str,
help='File with preprocessed data')
parser.add_argument('-b', '--balance_folder', nargs='+', type=str,
help='Folder where balancing datasets')
parser.add_argument('-n', '--packets_per_flow', nargs='+', type=str,
help='Packet per flow sample')
parser.add_argument('-s', '--samples', default=float('inf'), type=int,
help='Number of training samples in the reduced output')
parser.add_argument('-i', '--dataset_id', nargs='+', type=str,
help='String to append to the names of output files')
parser.add_argument('-t', '--dataset_type', nargs='+', type=str,
help='Type of the dataset. Available options are: IDS2017, IDS2018, SYN2020')
parser.add_argument('-w', '--time_window', nargs='+', type=str,
help='Length of the time window')
parser.add_argument('--no_split', help='Do not split the dataset', action='store_true')
args = parser.parse_args()
if args.packets_per_flow is not None:
max_flow_len = int(args.packets_per_flow[0])
else:
max_flow_len = MAX_FLOW_LEN
if args.time_window is not None:
time_window = float(args.time_window[0])
else:
time_window = TIME_WINDOW
if args.dataset_id is not None:
dataset_id = str(args.dataset_id[0])
else:
dataset_id = ''
if args.traffic_type is not None:
traffic_type = str(args.traffic_type[0])
else:
traffic_type = 'all'
if args.dataset_folder is not None and args.dataset_type is not None:
process_list = []
flows_list = []
if args.output_folder is not None and os.path.isdir(args.output_folder[0]) is True:
output_folder = args.output_folder[0]
else:
output_folder = args.dataset_folder[0]
filelist = glob.glob(args.dataset_folder[0]+ '/*.pcap')
in_labels = parse_labels(args.dataset_type[0],args.dataset_folder[0])
start_time = time.time()
for file in filelist:
try:
flows = manager.list()
p = Process(target=process_pcap,args=(file,args.dataset_type[0],in_labels,max_flow_len,flows,traffic_type,time_window))
process_list.append(p)
flows_list.append(flows)
except FileNotFoundError as e:
continue
for p in process_list:
p.start()
for p in process_list:
p.join()
np.seterr(divide='ignore', invalid='ignore')
preprocessed_flows = list(flows_list[0])
#concatenation of the features
for results in flows_list[1:]:
preprocessed_flows = preprocessed_flows + list(results)
process_time = time.time()-start_time
if dataset_id == '':
dataset_id = str(args.dataset_type[0])
filename = str(int(time_window)) + 't-' + str(max_flow_len) + 'n-' + dataset_id + '-preprocess'
output_file = output_folder + '/' + filename
output_file = output_file.replace("//", "/") # remove double slashes when needed
with open(output_file + '.data', 'wb') as filehandle:
# store the data as binary data stream
pickle.dump(preprocessed_flows, filehandle)
(total_flows, ddos_flows, benign_flows), (total_fragments, ddos_fragments, benign_fragments) = count_flows(preprocessed_flows)
log_string = time.strftime("%Y-%m-%d %H:%M:%S") + " | dataset_type:" + args.dataset_type[0] + \
" | flows (tot,ben,ddos):(" + str(total_flows) + "," + str(benign_flows) + "," + str(ddos_flows) + \
") | fragments (tot,ben,ddos):(" + str(total_fragments) + "," + str(benign_fragments) + "," + str(ddos_fragments) + \
") | options:" + command_options + " | process_time:" + str(process_time) + " |\n"
print (log_string)
# saving log file
with open(output_folder + '/history.log', "a") as myfile:
myfile.write(log_string)
if args.preprocess_folder is not None or args.preprocess_file is not None:
if args.preprocess_folder is not None:
output_folder = args.output_folder[0] if args.output_folder is not None else args.preprocess_folder[0]
filelist = glob.glob(args.preprocess_folder[0] + '/*.data')
else:
output_folder = args.output_folder[0] if args.output_folder is not None else os.path.dirname(os.path.realpath(args.preprocess_file[0]))
filelist = args.preprocess_file
# obtain time_window and flow_len from filename and ensure that all files have the same values
time_window = None
max_flow_len = None
dataset_id = None
for file in filelist:
filename = file.split('/')[-1].strip()
current_time_window = int(filename.split('-')[0].strip().replace('t',''))
current_max_flow_len = int(filename.split('-')[1].strip().replace('n',''))
current_dataset_id = str(filename.split('-')[2].strip())
if time_window != None and current_time_window != time_window:
print ("Incosistent time windows!!")
exit()
else:
time_window = current_time_window
if max_flow_len != None and current_max_flow_len != max_flow_len:
print ("Incosistent flow lengths!!")
exit()
else:
max_flow_len = current_max_flow_len
if dataset_id != None and current_dataset_id != dataset_id:
dataset_id = "IDS201X"
else:
dataset_id = current_dataset_id
preprocessed_flows = []
for file in filelist:
with open(file, 'rb') as filehandle:
# read the data as binary data stream
preprocessed_flows = preprocessed_flows + pickle.load(filehandle)
# balance samples and redux the number of samples when requested
preprocessed_flows, benign_fragments, ddos_fragments = balance_dataset(preprocessed_flows,args.samples)
if len(preprocessed_flows) == 0:
print("Empty dataset!")
exit()
preprocessed_train, preprocessed_test = train_test_split(preprocessed_flows,train_size=TRAIN_SIZE, shuffle=True)
preprocessed_train, preprocessed_val = train_test_split(preprocessed_train, train_size=TRAIN_SIZE, shuffle=True)
X_train, y_train, _ = dataset_to_list_of_fragments(preprocessed_train)
X_val, y_val, _ = dataset_to_list_of_fragments(preprocessed_val)
X_test, y_test, _ = dataset_to_list_of_fragments(preprocessed_test)
# normalization and padding
X_full = X_train + X_val + X_test
y_full = y_train + y_val + y_test
mins,maxs = static_min_max(time_window=time_window)
total_examples = len(y_full)
total_ddos_examples = sum(y_full)
total_benign_examples = len(y_full) - sum(y_full)
output_file = output_folder + '/' + str(time_window) + 't-' + str(max_flow_len) + 'n-' + dataset_id + '-dataset'
if args.no_split == True: # don't split the dataset
norm_X_full = normalize_and_padding(X_full, mins, maxs, max_flow_len)
#norm_X_full = padding(X_full,max_flow_len) # only padding
norm_X_full_np = np.array(norm_X_full)
y_full_np = np.array(y_full)
hf = h5py.File(output_file + '-full.hdf5', 'w')
hf.create_dataset('set_x', data=norm_X_full_np)
hf.create_dataset('set_y', data=y_full_np)
hf.close()
[full_packets] = count_packets_in_dataset([norm_X_full_np])
log_string = time.strftime("%Y-%m-%d %H:%M:%S") + " | Total examples (tot,ben,ddos):(" + str(total_examples) + "," + str(total_benign_examples) + "," + str(total_ddos_examples) + \
") | Total packets:(" + str(full_packets) + \
") | options:" + command_options + " |\n"
else:
norm_X_train = normalize_and_padding(X_train,mins,maxs,max_flow_len)
norm_X_val = normalize_and_padding(X_val, mins, maxs, max_flow_len)
norm_X_test = normalize_and_padding(X_test, mins, maxs, max_flow_len)
norm_X_train_np = np.array(norm_X_train)
y_train_np = np.array(y_train)
norm_X_val_np = np.array(norm_X_val)
y_val_np = np.array(y_val)
norm_X_test_np = np.array(norm_X_test)
y_test_np = np.array(y_test)
hf = h5py.File(output_file + '-train.hdf5', 'w')
hf.create_dataset('set_x', data=norm_X_train_np)
hf.create_dataset('set_y', data=y_train_np)
hf.close()
hf = h5py.File(output_file + '-val.hdf5', 'w')
hf.create_dataset('set_x', data=norm_X_val_np)
hf.create_dataset('set_y', data=y_val_np)
hf.close()
hf = h5py.File(output_file + '-test.hdf5', 'w')
hf.create_dataset('set_x', data=norm_X_test_np)
hf.create_dataset('set_y', data=y_test_np)
hf.close()
[train_packets, val_packets, test_packets] = count_packets_in_dataset([norm_X_train_np, norm_X_val_np, norm_X_test_np])
log_string = time.strftime("%Y-%m-%d %H:%M:%S") + " | examples (tot,ben,ddos):(" + str(total_examples) + "," + str(total_benign_examples) + "," + str(total_ddos_examples) + \
") | Train/Val/Test sizes: (" + str(norm_X_train_np.shape[0]) + "," + str(norm_X_val_np.shape[0]) + "," + str(norm_X_test_np.shape[0]) + \
") | Packets (train,val,test):(" + str(train_packets) + "," + str(val_packets) + "," + str(test_packets) + \
") | options:" + command_options + " |\n"
print(log_string)
# saving log file
with open(output_folder + '/history.log', "a") as myfile:
myfile.write(log_string)
if args.balance_folder is not None and args.output_folder is not None:
output_folder = args.output_folder[0] if args.output_folder is not None else args.balance_folder[0]
datasets = []
for folder in args.balance_folder:
datasets += glob.glob(folder + '/*.hdf5')
train_filelist = {}
val_filelist = {}
test_filelist = {}
min_samples_train = float('inf')
min_samples_val = float('inf')
min_samples_test = float('inf')
output_filename_prefix = None
for file in datasets:
filename = file.split('/')[-1].strip()
dataset = h5py.File(file, "r")
X = np.array(dataset["set_x"][:]) # features
Y = np.array(dataset["set_y"][:]) # labels
if 'train' in filename:
key = filename.split('dataset')[0].strip() + 'dataset-balanced-train.hdf5'
if output_filename_prefix ==None:
output_filename_prefix = filename.split('IDS')[0].strip()
else:
if filename.split('IDS')[0].strip() != output_filename_prefix:
print ("Inconsistent datasets!")
exit()
train_filelist[key] = (X,Y)
if X.shape[0] < min_samples_train:
min_samples_train = X.shape[0]
elif 'val' in filename:
key = filename.split('dataset')[0].strip() + 'dataset-balanced-val.hdf5'
if output_filename_prefix ==None:
output_filename_prefix = filename.split('IDS')[0].strip()
else:
if filename.split('IDS')[0].strip() != output_filename_prefix:
print ("Inconsistent datasets!")
exit()
val_filelist[key] = (X,Y)
if X.shape[0] < min_samples_val:
min_samples_val = X.shape[0]
elif 'test' in filename:
key = filename.split('dataset')[0].strip() + 'dataset-balanced-test.hdf5'
if output_filename_prefix ==None:
output_filename_prefix = filename.split('IDS')[0].strip()
else:
if filename.split('IDS')[0].strip() != output_filename_prefix:
print ("Inconsistent datasets!")
exit()
test_filelist[key] = (X, Y)
if X.shape[0] < min_samples_test:
min_samples_test = X.shape[0]
final_X = {'train':None,'val':None,'test':None}
final_y = {'train':None,'val':None,'test':None}
for key,value in train_filelist.items():
X_short = value[0][:min_samples_train,...]
y_short = value[1][:min_samples_train,...]
if final_X['train'] is None:
final_X['train'] = X_short
final_y['train'] = y_short
else:
final_X['train'] = np.vstack((final_X['train'],X_short))
final_y['train'] = np.hstack((final_y['train'],y_short))
for key,value in val_filelist.items():
X_short = value[0][:min_samples_val,...]
y_short = value[1][:min_samples_val,...]
if final_X['val'] is None:
final_X['val'] = X_short
final_y['val'] = y_short
else:
final_X['val'] = np.vstack((final_X['val'],X_short))
final_y['val'] = np.hstack((final_y['val'],y_short))
for key,value in test_filelist.items():
X_short = value[0][:min_samples_test,...]
y_short = value[1][:min_samples_test,...]
if final_X['test'] is None:
final_X['test'] = X_short
final_y['test'] = y_short
else:
final_X['test'] = | np.vstack((final_X['test'],X_short)) | numpy.vstack |
from __future__ import print_function, division
import os, sys, warnings, platform
from time import time
import numpy as np
#if "PyPy" not in platform.python_implementation():
# from scipy.io import loadmat, savemat
from Kuru.Tensor import unique2d, itemfreq, in2d, makezero
#from Florence.Utils import insensitive
#from .vtk_writer import write_vtu
#try:
# import meshpy.triangle as triangle
# has_meshpy = True
#except ImportError:
# has_meshpy = False
from .HigherOrderMeshing import *
from .NodeArrangement import *
#from .GeometricPath import *
from warnings import warn
from copy import deepcopy
"""
Mesh class providing most of the pre-processing functionalities of the Core module
<NAME> - 13/06/2015
"""
class Mesh(object):
"""Mesh class provides the following functionalities:
1. Generating higher order meshes based on a linear mesh, for tris, tets, quads and hexes
2. Generating linear tri and tet meshes based on meshpy back-end
3. Generating linear tri meshes based on distmesh back-end
4. Finding bounary edges and faces for tris and tets, in case they are not provided by the mesh generator
5. Reading Salome meshes in binary (.dat/.txt/etc) format
6. Reading gmsh files .msh
7. Checking for node numbering order of elements and fixing it if desired
8. Writing meshes to unstructured vtk file format (.vtu) in xml and binary formats,
including high order elements
"""
def __init__(self, element_type=None):
super(Mesh, self).__init__()
# self.faces and self.edges ARE BOUNDARY FACES
# AND BOUNDARY EDGES, RESPECTIVELY
self.degree = None
self.ndim = None
self.edim = None
self.nelem = None
self.nnode = None
self.elements = None
self.points = None
self.corners = None
self.edges = None
self.faces = None
self.element_type = element_type
self.face_to_element = None
self.edge_to_element = None
self.boundary_edge_to_element = None
self.boundary_face_to_element = None
self.all_faces = None
self.all_edges = None
self.interior_faces = None
self.interior_edges = None
# TYPE OF BOUNDARY FACES/EDGES
self.boundary_element_type = None
# FOR GEOMETRICAL CURVES/SURFACES
self.edge_to_curve = None
self.face_to_surface = None
self.spatial_dimension = None
self.reader_type = None
self.reader_type_format = None
self.reader_type_version = None
self.writer_type = None
self.filename = None
self.element_to_set = None
def GetEdges(self):
assert self.element_type is not None
if self.element_type == "tri":
self.GetEdgesTri()
elif self.element_type == "quad":
self.GetEdgesQuad()
elif self.element_type == "pent":
self.GetEdgesPent()
elif self.element_type == "tet":
self.GetEdgesTet()
elif self.element_type == "hex":
self.GetEdgesHex()
else:
raise ValueError('Type of element not understood')
return self.all_edges
def GetBoundaryEdges(self):
assert self.element_type is not None
if self.element_type == "tri":
self.GetBoundaryEdgesTri()
elif self.element_type == "quad":
self.GetBoundaryEdgesQuad()
elif self.element_type == "pent":
self.GetBoundaryEdgesPent()
elif self.element_type == "tet":
self.GetBoundaryEdgesTet()
elif self.element_type == "hex":
self.GetBoundaryEdgesHex()
else:
raise ValueError('Type of element not understood')
return self.edges
def GetEdgesQuad(self):
"""Find the all edges of a quadrilateral mesh.
Sets all_edges property and returns it
returns:
arr: numpy ndarray of all edges"""
p = self.InferPolynomialDegree()
# DO NOT COMPUTE IF ALREADY COMPUTED
if isinstance(self.all_edges,np.ndarray):
if self.all_edges.shape[0] > 1:
# IF LINEAR VERSION IS COMPUTED, DO COMPUTE HIGHER VERSION
if self.all_edges.shape[1]==2 and p > 1:
pass
else:
return self.all_edges
node_arranger = NodeArrangementQuad(p-1)[0]
# GET ALL EDGES FROM THE ELEMENT CONNECTIVITY
edges = np.concatenate((self.elements[:,node_arranger[0,:]],self.elements[:,node_arranger[1,:]],
self.elements[:,node_arranger[2,:]],self.elements[:,node_arranger[3,:]]),axis=0).astype(np.uint64)
# REMOVE DUPLICATES
edges, idx = unique2d(edges,consider_sort=True,order=False,return_index=True)
edge_to_element = np.zeros((edges.shape[0],2),np.int64)
edge_to_element[:,0] = idx % self.elements.shape[0]
edge_to_element[:,1] = idx // self.elements.shape[0]
self.edge_to_element = edge_to_element
# DO NOT SET all_edges IF THE CALLER FUNCTION IS GetBoundaryEdgesHex
import inspect
curframe = inspect.currentframe()
calframe = inspect.getouterframes(curframe, 2)[1][3]
if calframe != "GetBoundaryEdgesHex":
self.all_edges = edges
return edges
def GetBoundaryEdgesQuad(self):
"""Find boundary edges (lines) of a quadrilateral mesh"""
p = self.InferPolynomialDegree()
# DO NOT COMPUTE IF ALREADY COMPUTED
if isinstance(self.edges,np.ndarray):
if self.edges.shape[0] > 1:
# IF LINEAR VERSION IS COMPUTED, DO COMPUTE HIGHER VERSION
if self.edges.shape[1] == 2 and p > 1:
pass
else:
return
node_arranger = NodeArrangementQuad(p-1)[0]
# GET ALL EDGES FROM THE ELEMENT CONNECTIVITY
all_edges = np.concatenate((self.elements[:,node_arranger[0,:]],self.elements[:,node_arranger[1,:]],
self.elements[:,node_arranger[2,:]],self.elements[:,node_arranger[3,:]]),axis=0).astype(np.uint64)
# GET UNIQUE ROWS
uniques, idx, inv = unique2d(all_edges,consider_sort=True,order=False,return_index=True,return_inverse=True)
# ROWS THAT APPEAR ONLY ONCE CORRESPOND TO BOUNDARY EDGES
freqs_inv = itemfreq(inv)
edges_ext_flags = freqs_inv[freqs_inv[:,1]==1,0]
# NOT ARRANGED
self.edges = uniques[edges_ext_flags,:]
# DETERMINE WHICH FACE OF THE ELEMENT THEY ARE
boundary_edge_to_element = np.zeros((edges_ext_flags.shape[0],2),dtype=np.int64)
# FURTHER RE-ARRANGEMENT / ARANGE THE NODES BASED ON THE ORDER THEY APPEAR
# IN ELEMENT CONNECTIVITY
# THIS STEP IS NOT NECESSARY INDEED - ITS JUST FOR RE-ARANGMENT OF EDGES
all_edges_in_edges = in2d(all_edges,self.edges,consider_sort=True)
all_edges_in_edges = np.where(all_edges_in_edges==True)[0]
boundary_edge_to_element[:,0] = all_edges_in_edges % self.elements.shape[0]
boundary_edge_to_element[:,1] = all_edges_in_edges // self.elements.shape[0]
# ARRANGE FOR ANY ORDER OF BASES/ELEMENTS AND ASSIGN DATA MEMBERS
self.edges = self.elements[boundary_edge_to_element[:,0][:,None],node_arranger[boundary_edge_to_element[:,1],:]]
self.edges = self.edges.astype(np.uint64)
self.boundary_edge_to_element = boundary_edge_to_element
return self.edges
def GetBoundaryEdgesHex(self):
"""Find boundary edges (lines) of hexahedral mesh.
"""
p = self.InferPolynomialDegree()
# DO NOT COMPUTE IF ALREADY COMPUTED
if isinstance(self.edges,np.ndarray):
if self.edges.shape[0] > 1:
# IF LINEAR VERSION IS COMPUTED, DO COMPUTE HIGHER VERSION
if self.edges.shape[1] == 2 and p > 1:
pass
else:
return
# FIRST GET BOUNDARY FACES
if not isinstance(self.faces,np.ndarray):
self.GetBoundaryFacesHex()
# BUILD A 2D MESH
tmesh = Mesh()
tmesh.element_type = "quad"
tmesh.elements = self.faces
tmesh.nelem = tmesh.elements.shape[0]
del tmesh.faces
del tmesh.points
# ALL THE EDGES CORRESPONDING TO THESE BOUNDARY FACES ARE BOUNDARY EDGES
self.edges = tmesh.GetEdgesQuad()
@property
def Bounds(self):
"""Returns bounds of a mesh i.e. the minimum and maximum coordinate values
in every direction
"""
assert self.points is not None
if self.points.shape[1] == 3:
bounds = np.array([[np.min(self.points[:,0]),
np.min(self.points[:,1]),
np.min(self.points[:,2])],
[np.max(self.points[:,0]),
np.max(self.points[:,1]),
np.max(self.points[:,2])]])
makezero(bounds)
return bounds
elif self.points.shape[1] == 2:
bounds = np.array([[np.min(self.points[:,0]),
np.min(self.points[:,1])],
[np.max(self.points[:,0]),
np.max(self.points[:,1])]])
makezero(bounds)
return bounds
elif self.points.shape[1] == 1:
bounds = np.array([[np.min(self.points[:,0])],
[np.max(self.points[:,0])]])
makezero(bounds)
return bounds
else:
raise ValueError("Invalid dimension for mesh coordinates")
def GetElementsEdgeNumberingQuad(self):
"""Finds edges of elements and their flags saying which edge they are [0,1,2,3].
At most a quad can have all its four edges on the boundary.
output:
edge_elements: [1D array] array containing elements which have edges
on the boundary
Note that this method sets the self.edge_to_element to edge_elements,
so the return value is not strictly necessary
"""
if isinstance(self.edge_to_element,np.ndarray):
if self.edge_to_element.shape[0] > 1:
return self.edge_to_element
# GET ALL EDGES FROM THE ELEMENT CONNECTIVITY
if self.all_edges is None:
self.GetEdgesQuad()
p = self.InferPolynomialDegree()
# FIND WHICH FACE NODES ARE IN WHICH ELEMENT
node_arranger = NodeArrangementQuad(p-1)[0]
# GET ALL EDGES FROM THE ELEMENT CONNECTIVITY
all_edges = np.concatenate((self.elements[:,node_arranger[0,:]],self.elements[:,node_arranger[1,:]],
self.elements[:,node_arranger[2,:]],self.elements[:,node_arranger[3,:]]),axis=0).astype(np.int64)
all_edges, idx = unique2d(all_edges,consider_sort=True,order=False, return_index=True)
edge_elements = np.zeros((all_edges.shape[0],2),dtype=np.int64)
# edge_elements = np.zeros((self.edges.shape[0],2),dtype=np.int64)
edge_elements[:,0] = idx % self.elements.shape[0]
edge_elements[:,1] = idx // self.elements.shape[0]
self.edge_to_element = edge_elements
return self.edge_to_element
def GetFaces(self):
assert self.element_type is not None
if self.element_type == "tet":
self.GetFacesTet()
elif self.element_type == "hex":
self.GetFacesHex()
elif self.element_type=="tri" or self.element_type=="quad":
raise ValueError("2D mesh does not have faces")
else:
raise ValueError('Type of element not understood')
return self.all_faces
def GetBoundaryFaces(self):
assert self.element_type is not None
if self.element_type == "tet":
self.GetBoundaryFacesTet()
elif self.element_type == "hex":
self.GetBoundaryFacesHex()
elif self.element_type=="tri" or self.element_type=="quad":
raise ValueError("2D mesh does not have faces")
else:
raise ValueError('Type of element not understood')
return self.faces
def GetBoundaryFacesHex(self):
"""Find boundary faces (surfaces) of a hexahedral mesh"""
p = self.InferPolynomialDegree()
# DO NOT COMPUTE IF ALREADY COMPUTED
if isinstance(self.faces,np.ndarray):
if self.faces.shape[0] > 1:
# IF LINEAR VERSION IS COMPUTED, DO COMPUTE HIGHER VERSION
if self.faces.shape[1] == 4 and p > 1:
pass
else:
return
node_arranger = NodeArrangementHex(p-1)[0]
# CONCATENATE ALL THE FACES MADE FROM ELEMENTS
all_faces = np.concatenate((np.concatenate((
np.concatenate((np.concatenate((np.concatenate((self.elements[:,node_arranger[0,:]],
self.elements[:,node_arranger[1,:]]),axis=0),self.elements[:,node_arranger[2,:]]),axis=0),
self.elements[:,node_arranger[3,:]]),axis=0),self.elements[:,node_arranger[4,:]]),axis=0),
self.elements[:,node_arranger[5,:]]),axis=0).astype(np.int64)
# GET UNIQUE ROWS
uniques, idx, inv = unique2d(all_faces,consider_sort=True,order=False,return_index=True,return_inverse=True)
# ROWS THAT APPEAR ONLY ONCE CORRESPOND TO BOUNDARY FACES
freqs_inv = itemfreq(inv)
faces_ext_flags = freqs_inv[freqs_inv[:,1]==1,0]
# NOT ARRANGED
self.faces = uniques[faces_ext_flags,:]
# DETERMINE WHICH FACE OF THE ELEMENT THEY ARE
boundary_face_to_element = np.zeros((faces_ext_flags.shape[0],2),dtype=np.int64)
# FURTHER RE-ARRANGEMENT / ARANGE THE NODES BASED ON THE ORDER THEY APPEAR
# IN ELEMENT CONNECTIVITY
# THIS STEP IS NOT NECESSARY INDEED - ITS JUST FOR RE-ARANGMENT OF FACES
all_faces_in_faces = in2d(all_faces,self.faces,consider_sort=True)
all_faces_in_faces = np.where(all_faces_in_faces==True)[0]
# boundary_face_to_element = np.zeros((all_faces_in_faces.shape[0],2),dtype=np.int64)
boundary_face_to_element[:,0] = all_faces_in_faces % self.elements.shape[0]
boundary_face_to_element[:,1] = all_faces_in_faces // self.elements.shape[0]
# ARRANGE FOR ANY ORDER OF BASES/ELEMENTS AND ASSIGN DATA MEMBERS
self.faces = self.elements[boundary_face_to_element[:,0][:,None],node_arranger[boundary_face_to_element[:,1],:]]
self.faces = self.faces.astype(np.uint64)
self.boundary_face_to_element = boundary_face_to_element
def GetElementsWithBoundaryEdgesQuad(self):
"""Finds elements which have edges on the boundary.
At most a quad can have all its four edges on the boundary.
output:
boundary_edge_to_element: [2D array] array containing elements which have face
on the boundary [cloumn 0] and a flag stating which edges they are [column 1]
"""
if isinstance(self.boundary_edge_to_element,np.ndarray):
if self.boundary_edge_to_element.shape[1] > 1 and self.boundary_edge_to_element.shape[0] > 1:
return self.boundary_edge_to_element
# DO NOT COMPUTE EDGES AND RAISE BECAUSE OF CYCLIC DEPENDENCIES
assert self.elements is not None
assert self.edges is not None
p = self.InferPolynomialDegree()
# FIND WHICH FACE NODES ARE IN WHICH ELEMENT
node_arranger = NodeArrangementQuad(p-1)[0]
# GET ALL EDGES FROM THE ELEMENT CONNECTIVITY
all_edges = np.concatenate((self.elements[:,node_arranger[0,:]],self.elements[:,node_arranger[1,:]],
self.elements[:,node_arranger[2,:]],self.elements[:,node_arranger[3,:]]),axis=0).astype(self.edges.dtype)
# GET UNIQUE ROWS
uniques, idx, inv = unique2d(all_edges,consider_sort=True,order=False,return_index=True,return_inverse=True)
# ROWS THAT APPEAR ONLY ONCE CORRESPOND TO BOUNDARY EDGES
freqs_inv = itemfreq(inv)
edges_ext_flags = freqs_inv[freqs_inv[:,1]==1,0]
# NOT ARRANGED
edges = uniques[edges_ext_flags,:]
# DETERMINE WHICH FACE OF THE ELEMENT THEY ARE
boundary_edge_to_element = np.zeros((edges_ext_flags.shape[0],2),dtype=np.int64)
# FURTHER RE-ARRANGEMENT / ARANGE THE NODES BASED ON THE ORDER THEY APPEAR
# IN ELEMENT CONNECTIVITY
# THIS STEP IS NOT NECESSARY INDEED - ITS JUST FOR RE-ARANGMENT OF EDGES
all_edges_in_edges = in2d(all_edges,self.edges,consider_sort=True)
all_edges_in_edges = np.where(all_edges_in_edges==True)[0]
boundary_edge_to_element[:,0] = all_edges_in_edges % self.elements.shape[0]
boundary_edge_to_element[:,1] = all_edges_in_edges // self.elements.shape[0]
# ARRANGE FOR ANY ORDER OF BASES/ELEMENTS AND ASSIGN DATA MEMBERS
self.boundary_edge_to_element = boundary_edge_to_element
return self.boundary_edge_to_element
def GetElementsWithBoundaryFacesHex(self):
"""Finds elements which have faces on the boundary.
At most a hexahedral can have all its 8 faces on the boundary.
output:
boundary_face_to_element: [2D array] array containing elements which have face
on the boundary [column 0] and a flag stating which faces they are [column 1]
"""
# DO NOT COMPUTE FACES AND RAISE BECAUSE OF CYCLIC DEPENDENCIES
assert self.elements is not None
assert self.faces is not None
if self.boundary_face_to_element is not None:
return self.boundary_face_to_element
# THIS METHOD ALWAYS RETURNS THE FACE TO ELEMENT ARRAY, AND DOES NOT CHECK
# IF THIS HAS BEEN COMPUTED BEFORE, THE REASON BEING THAT THE FACES CAN COME
# EXTERNALLY WHOSE ARRANGEMENT WOULD NOT CORRESPOND TO THE ONE USED INTERNALLY
# HENCE THIS MAPPING BECOMES NECESSARY
C = self.InferPolynomialDegree() - 1
node_arranger = NodeArrangementHex(C)[0]
all_faces = np.concatenate((np.concatenate((
np.concatenate((np.concatenate((np.concatenate((self.elements[:,node_arranger[0,:]],
self.elements[:,node_arranger[1,:]]),axis=0),self.elements[:,node_arranger[2,:]]),axis=0),
self.elements[:,node_arranger[3,:]]),axis=0),self.elements[:,node_arranger[4,:]]),axis=0),
self.elements[:,node_arranger[5,:]]),axis=0).astype(self.faces.dtype)
all_faces_in_faces = in2d(all_faces,self.faces[:,:4],consider_sort=True)
all_faces_in_faces = np.where(all_faces_in_faces==True)[0]
boundary_face_to_element = np.zeros((all_faces_in_faces.shape[0],2),dtype=np.int64)
boundary_face_to_element[:,0] = all_faces_in_faces % self.elements.shape[0]
boundary_face_to_element[:,1] = all_faces_in_faces // self.elements.shape[0]
# SO FAR WE HAVE COMPUTED THE ELEMENTS THAT CONTAIN FACES, HOWEVER
# NOTE THAT WE STILL HAVE NOT COMPUTED A MAPPING BETWEEN ELEMENTS AND
# FACES. WE ONLY KNOW WHICH ELEMENTS CONTAIN FACES FROM in2d.
# WE NEED TO FIND THIS MAPPING NOW
# WE NEED TO DO THIS DUMMY RECONSTRUCTION OF FACES BASED ON ELEMENTS
faces = self.elements[boundary_face_to_element[:,0][:,None],
node_arranger[boundary_face_to_element[:,1],:]].astype(self.faces.dtype)
# CHECK FOR THIS CONDITION AS ARRANGEMENT IS NO LONGER MAINTAINED
assert np.sum(faces[:,:4].astype(np.int64) - self.faces[:,:4].astype(np.int64)) == 0
# NOW GET THE ROW MAPPING BETWEEN OLD FACES AND NEW FACES
from Kuru.Tensor import shuffle_along_axis
row_mapper = shuffle_along_axis(faces[:,:4],self.faces[:,:4],consider_sort=True)
# UPDATE THE MAP
boundary_face_to_element[:,:] = boundary_face_to_element[row_mapper,:]
self.boundary_face_to_element = boundary_face_to_element
return self.boundary_face_to_element
def GetFacesHex(self):
"""Find all faces (surfaces) in the hexahedral mesh (boundary & interior).
Sets all_faces property and returns it
returns:
arr: numpy ndarray of all faces
"""
# DETERMINE DEGREE
p = self.InferPolynomialDegree()
# DO NOT COMPUTE IF ALREADY COMPUTED
if isinstance(self.all_faces,np.ndarray):
if self.all_faces.shape[0] > 1:
# IF LINEAR VERSION IS COMPUTED, DO COMPUTE HIGHER VERSION
if self.all_faces.shape[1] == 4 and p > 1:
pass
else:
return self.all_faces
node_arranger = NodeArrangementHex(p-1)[0]
fsize = int((p+1)**3)
# GET ALL FACES FROM THE ELEMENT CONNECTIVITY
faces = np.concatenate((np.concatenate((
np.concatenate((np.concatenate((np.concatenate((self.elements[:,node_arranger[0,:]],
self.elements[:,node_arranger[1,:]]),axis=0),self.elements[:,node_arranger[2,:]]),axis=0),
self.elements[:,node_arranger[3,:]]),axis=0),self.elements[:,node_arranger[4,:]]),axis=0),
self.elements[:,node_arranger[5,:]]),axis=0).astype(np.int64)
# REMOVE DUPLICATES
self.all_faces, idx = unique2d(faces,consider_sort=True,order=False,return_index=True)
face_to_element = np.zeros((self.all_faces.shape[0],2),np.int64)
face_to_element[:,0] = idx % self.elements.shape[0]
face_to_element[:,1] = idx // self.elements.shape[0]
self.face_to_element = face_to_element
return self.all_faces
def GetHighOrderMesh(self,p=1, silent=True, **kwargs):
"""Given a linear tri, tet, quad or hex mesh compute high order mesh based on it.
This is a static method linked to the HigherOrderMeshing module"""
if not isinstance(p,int):
raise ValueError("p must be an integer")
else:
if p < 1:
raise ValueError("Value of p={} is not acceptable. Provide p>=1.".format(p))
if self.degree is None:
self.InferPolynomialDegree()
C = p-1
if 'C' in kwargs.keys():
if kwargs['C'] != p - 1:
raise ValueError("Did not understand the specified interpolation degree of the mesh")
del kwargs['C']
# DO NOT COMPUTE IF ALREADY COMPUTED FOR THE SAME ORDER
if self.degree == None:
self.degree = self.InferPolynomialDegree()
if self.degree == p:
return
# SITUATIONS WHEN ANOTHER HIGH ORDER MESH IS REQUIRED, WITH ONE HIGH
# ORDER MESH ALREADY AVAILABLE
if self.degree != 1 and self.degree - 1 != C:
dum = self.GetLinearMesh(remap=True)
self.__dict__.update(dum.__dict__)
if not silent:
print('Generating p = '+str(C+1)+' mesh based on the linear mesh...')
t_mesh = time()
# BUILD A NEW MESH BASED ON THE LINEAR MESH
if self.element_type == 'line':
nmesh = HighOrderMeshLine(C,self,**kwargs)
if self.element_type == 'tri':
if self.edges is None:
self.GetBoundaryEdgesTri()
# nmesh = HighOrderMeshTri(C,self,**kwargs)
nmesh = HighOrderMeshTri_SEMISTABLE(C,self,**kwargs)
elif self.element_type == 'tet':
# nmesh = HighOrderMeshTet(C,self,**kwargs)
nmesh = HighOrderMeshTet_SEMISTABLE(C,self,**kwargs)
elif self.element_type == 'quad':
if self.edges is None:
self.GetBoundaryEdgesTri()
nmesh = HighOrderMeshQuad(C,self,**kwargs)
elif self.element_type == 'hex':
nmesh = HighOrderMeshHex(C,self,**kwargs)
self.points = nmesh.points
self.elements = nmesh.elements.astype(np.uint64)
if isinstance(self.corners,np.ndarray):
# NOT NECESSARY BUT GENERIC
self.corners = nmesh.corners.astype(np.uint64)
if isinstance(self.edges,np.ndarray):
self.edges = nmesh.edges.astype(np.uint64)
if isinstance(self.faces,np.ndarray):
if isinstance(nmesh.faces,np.ndarray):
self.faces = nmesh.faces.astype(np.uint64)
self.nelem = nmesh.nelem
self.nnode = self.points.shape[0]
self.element_type = nmesh.info
self.degree = C+1
self.ChangeType()
if not silent:
print('Finished generating the high order mesh. Time taken', time()-t_mesh,'sec')
def Line(self, left_point=0., right_point=1., n=10, p=1):
"""Creates a mesh of on a line for 1D rods/beams"""
self.__reset__()
assert p > 0
if not isinstance(left_point,float):
if not isinstance(left_point,int):
raise ValueError("left_point must be a number")
if not isinstance(right_point,float):
if not isinstance(right_point,int):
raise ValueError("right_point must be a number")
left_point = float(left_point)
right_point = float(right_point)
n = int(n)
if n <= 0:
raise ValueError("Number of discretisation cannot be zero or negative: n={}".format(n))
self.element_type = "line"
self.points = np.linspace(left_point,right_point,p*n+1)[:,None]
self.elements = np.zeros((n,p+1),dtype=np.int64)
for i in range(p+1):
self.elements[:,i] = p*np.arange(0,n)+i
self.nelem = self.elements.shape[0]
self.nnode = self.points.shape[0]
def Rectangle(self,lower_left_point=(0,0), upper_right_point=(2,1),
nx=5, ny=5, element_type="tri"):
"""Creates a quad/tri mesh of a rectangle"""
if element_type != "tri" and element_type != "quad":
raise ValueError("Element type should either be tri or quad")
if self.elements is not None and self.points is not None:
self.__reset__()
if (lower_left_point[0] > upper_right_point[0]) or \
(lower_left_point[1] > upper_right_point[1]):
raise ValueError("Incorrect coordinate for lower left and upper right vertices")
nx, ny = int(nx), int(ny)
if nx <= 0 or ny <= 0:
raise ValueError("Number of discretisation cannot be zero or negative: nx={} ny={}".format(nx,ny))
from scipy.spatial import Delaunay
x=np.linspace(lower_left_point[0],upper_right_point[0],nx+1)
y=np.linspace(lower_left_point[1],upper_right_point[1],ny+1)
X,Y = np.meshgrid(x,y)
coordinates = np.dstack((X.ravel(),Y.ravel()))[0,:,:]
if element_type == "tri":
tri_func = Delaunay(coordinates)
self.element_type = "tri"
self.elements = tri_func.simplices
self.nelem = self.elements.shape[0]
self.points = tri_func.points
self.nnode = self.points.shape[0]
self.GetBoundaryEdgesTri()
elif element_type == "quad":
self.nelem = int(nx*ny)
elements = np.zeros((self.nelem,4),dtype=np.int64)
dum_0 = np.arange((nx+1)*ny)
dum_1 = np.array([(nx+1)*i+nx for i in range(ny)])
col0 = np.delete(dum_0,dum_1)
elements[:,0] = col0
elements[:,1] = col0 + 1
elements[:,2] = col0 + nx + 2
elements[:,3] = col0 + nx + 1
self.nnode = int((nx+1)*(ny+1))
self.element_type = "quad"
self.elements = elements
self.points = coordinates
self.nnode = self.points.shape[0]
self.GetBoundaryEdgesQuad()
self.GetEdgesQuad()
def GetNodeCommonality(self):
"""Finds the elements sharing a node.
The return values are linked lists [list of numpy of arrays].
Each numpy array within the list gives the elements that contain a given node.
As a result the size of the linked list is nnode
outputs:
els: [list of numpy arrays] element numbers containing nodes
pos: [list of numpy arrays] elemental positions of the nodes
res_flat: [list of numpy arrays] position of nodes in the
flattened element connectivity.
"""
self.__do_essential_memebers_exist__()
elements = self.elements.ravel()
idx_sort = np.argsort(elements)
sorted_elements = elements[idx_sort]
vals, idx_start = np.unique(sorted_elements, return_index=True)
# Sets of indices
flat_pos = np.split(idx_sort, idx_start[1:])
els = np.split(idx_sort // int(self.elements.shape[1]), idx_start[1:])
pos = np.split(idx_sort % int(self.elements.shape[1]), idx_start[1:])
# In case one wants to return only the duplicates i.e. filter keeping only items occurring more than once
# vals, idx_start, count = np.unique(sorted_elements, return_counts=True, return_index=True)
# vals = vals[count > 1]
# res = filter(lambda x: x.size > 1, res)
return els, pos, flat_pos
def Read(self, filename=None, element_type="tri", reader_type=None, reader_type_format=None,
reader_type_version=None, order=0, read_surface_info=False, read_curve_info=False, **kwargs):
"""Convenience mesh reader method to dispatch call to subsequent apporpriate methods"""
if not isinstance(filename,str):
raise ValueError("filename must be a string")
return
if reader_type is not None:
if not isinstance(filename,str):
raise ValueError("filename must be a string")
return
if reader_type is None:
if filename.split('.')[-1] == "msh":
reader_type = "gmsh"
elif filename.split('.')[-1] == "obj":
reader_type = "obj"
elif filename.split('.')[-1] == "unv":
reader_type = "unv"
elif filename.split('.')[-1] == "fro":
reader_type = "fro"
elif filename.split('.')[-1] == "dat":
for key in kwargs.keys():
inkey = insensitive(key)
if "connectivity" in inkey and "delimiter" not in inkey:
reader_type = "read_separate"
break
if reader_type is None:
raise ValueError("Mesh file format was not undertood. Please specify it using reader_type keyword")
self.filename = filename
self.reader_type = reader_type
self.reader_type_format = reader_type_format
self.reader_type_version = reader_type_version
if self.reader_type is 'salome':
#self.ReadSalome(filename, element_type=element_type, read_surface_info=read_surface_info)
raise ValueError("Reader not implemented yet")
elif reader_type is 'GID':
#self.ReadGIDMesh(filename, element_type, order)
raise ValueError("Reader not implemented yet")
elif self.reader_type is 'gmsh':
self.ReadGmsh(filename, element_type=element_type, read_surface_info=read_surface_info, read_curve_info=read_curve_info)
elif self.reader_type is 'obj':
self.ReadOBJ(filename, element_type=element_type, read_surface_info=read_surface_info)
elif self.reader_type is 'fenics':
#self.ReadFenics(filename, element_type)
raise ValueError("Reader not implemented yet")
elif self.reader_type is 'vtu':
self.ReadVTK(filename)
elif self.reader_type is 'abaqus':
self.ReadAbaqus(filename)
elif self.reader_type is 'unv':
#self.ReadUNV(filename, element_type)
raise ValueError("Reader not implemented yet")
elif self.reader_type is 'fro':
#self.ReadFRO(filename, element_type)
raise ValueError("Reader not implemented yet")
elif self.reader_type is 'read_separate':
# READ MESH FROM SEPARATE FILES FOR CONNECTIVITY AND COORDINATES
raise ValueError("Reader not implemented yet")
from Kuru.Utils import insensitive
# return insensitive(kwargs.keys())
#for key in kwargs.keys():
# inkey = insensitive(key)
# if "connectivity" in inkey and "delimiter" not in inkey:
# connectivity_file = kwargs.get(key)
# if "coordinate" in insensitive(key) and "delimiter" not in inkey:
# coordinates_file = kwargs.get(key)
#self.ReadSeparate(connectivity_file,coordinates_file,element_type,
# delimiter_connectivity=',',delimiter_coordinates=',')
elif self.reader_type is 'ReadHDF5':
#self.ReadHDF5(filename)
raise ValueError("Reader not implemented yet")
self.nnode = self.points.shape[0]
# MAKE SURE MESH DATA IS CONTIGUOUS
self.points = np.ascontiguousarray(self.points)
self.elements = np.ascontiguousarray(self.elements)
return
def ReadVTK(self, filename, element_type=None):
"""Read mesh from a vtu file"""
try:
import vtk
except IOError:
raise IOError("vtk is not installed. Please install it first using 'pip install vtk'")
self.__reset__()
reader = vtk.vtkXMLUnstructuredGridReader()
reader.SetFileName(filename)
reader.Update()
vmesh = reader.GetOutput()
npieces = vmesh.GetNumberOfPieces()
if npieces > 1:
raise IOError("VTK reader is not prepare to read more than one piece.")
piece = vmesh.GetPiece()
flat_elements, celltypes, element_to_set = [], [], []
for cellid in range(vmesh.GetNumberOfCells()):
cell = vmesh.GetCell(cellid)
celltypes.append(vmesh.GetCellType(cellid))
element_to_set.append(piece)
for ptid in range(cell.GetNumberOfPoints()):
flat_elements.append(cell.GetPointId(ptid))
celltypes = np.array(celltypes, copy=True)
flat_elements = np.array(flat_elements, copy=True)
if not np.all(celltypes == celltypes[0]):
raise IOError("Cannot read VTK files with hybrid elements")
cellflag = celltypes[0]
if cellflag == 5:
self.element_type = "tri"
divider = 3
elif cellflag == 9:
self.element_type = "quad"
divider = 4
elif cellflag == 10:
self.element_type = "tet"
divider = 4
elif cellflag == 12:
self.element_type = "hex"
divider = 8
elif cellflag == 3:
self.element_type = "line"
divider = 2
else:
raise IOError("VTK element type not understood")
if element_type is not None:
if self.element_type != element_type:
raise ValueError("VTK file does not contain {} elements".format(element_type))
points = np.array([vmesh.GetPoint(ptid) for ptid in range(vmesh.GetNumberOfPoints())])
self.elements = np.ascontiguousarray(flat_elements.reshape(int(flat_elements.shape[0]/divider),divider), dtype=np.uint64)
self.points = np.ascontiguousarray(points, dtype=np.float64)
self.nelem = self.elements.shape[0]
self.nnode = self.points.shape[0]
if self.points.shape[1] == 3:
if np.allclose(self.points[:,2],0.):
self.points = np.ascontiguousarray(self.points[:,:2])
if self.element_type == "tri" or self.element_type == "quad":
self.GetEdges()
self.GetBoundaryEdges()
elif self.element_type == "tet" or self.element_type == "hex":
self.GetFaces()
self.GetBoundaryFaces()
self.GetBoundaryEdges()
# SET OF SETS TO EACH ELEMENTS
element_to_set = np.array(element_to_set, dtype=np.int64, copy=True).flatten()
self.element_to_set = element_to_set
return
def ReadAbaqus(self, filename, element_type=None):
"""Read INP file meshes from Abaqus"""
try:
fid = open(filename, "r")
except IOError:
print("File '%s' not found." % (filename))
sys.exit()
fid.close()
#FAST READER
head_node, head_elem = int(1e09), int(1e09)
tail_node, tail_elem = int(1e09), int(1e09)
head_elset, tail_elset = [], []
open_set = False
for line_counter, line in enumerate(open(filename)):
item = line.rstrip()
plist = item.split(",")
if plist[0] == "*End Part":
break
if plist[0] == "*Node":
head_node = line_counter
continue
elif plist[0] == "*Element":
tail_node = line_counter
head_elem = line_counter
elem_flag = plist[1][-4:]
continue
elif head_elem != int(1e09) and tail_elem == int(1e09) and plist[0][0] == "*":
tail_elem = line_counter
continue
elif plist[0] == "*Elset":
open_set = True
head_elset.append(line_counter)
continue
elif plist[0][0] == "*" and open_set:
open_set = False
tail_elset.append(line_counter)
continue
if elem_flag == "C3D8":
self.element_type = "hex"
else:
raise IOError("Abaqus element type not understood")
points, elements = [], []
element_set_list = [[] for j in range(len(head_elset))]
# RE-READ
for line_counter, line in enumerate(open(filename)):
item = line.rstrip()
plist = item.split(",")
if line_counter > head_node and line_counter < tail_node:
points.append([float(i) for i in plist[1:]])
if line_counter > head_elem and line_counter < tail_elem:
elements.append([int(i) for i in plist[-8:]])
for j in range(len(head_elset)):
if line_counter > head_elset[j] and line_counter < tail_elset[j]:
element_set_list[j].extend([int(i) for i in plist])
self.points = np.array(points,copy=True)
self.elements = np.array(elements,copy=True) - 1
# CORRECT
self.nelem = self.elements.shape[0]
self.nnode = self.points.shape[0]
if self.nelem == 0:
raise ValueError("mesh file does not contain {} elements".format(element_type))
if self.points.shape[1] == 3:
if np.allclose(self.points[:,2],0.):
self.points = np.ascontiguousarray(self.points[:,:2])
if self.element_type == "tri" or self.element_type == "quad":
self.GetEdges()
self.GetBoundaryEdges()
elif self.element_type == "tet" or self.element_type == "hex":
self.GetFaces()
self.GetBoundaryFaces()
self.GetBoundaryEdges()
## SET OF SETS TO EACH ELEMENTS
element_to_set = np.zeros(self.elements.shape[0], dtype=np.int64)
element_set = [[] for j in range(len(head_elset))]
for j in range(len(head_elset)):
element_set[j] = np.array(element_set_list[j],dtype=np.int64,copy=True).flatten() - 1
element_to_set[element_set[j]] = j
self.element_to_set = element_to_set
return
def ReadGmsh(self, filename, element_type, read_surface_info=False,read_curve_info=False):
"""Read gmsh (.msh) file"""
try:
fid = open(filename, "r")
except IOError:
print("File '%s' not found." % (filename))
sys.exit()
msh_version = None
# CHECK MSH FILE VERSION
if "MeshFormat" in fid.readline():
msh_version = int(np.floor(float(fid.readline().split(" ")[0])))
if 4 != msh_version and 2 != msh_version:
raise IOError("Only ASCII version 2 and 4 (>=4.1) .msh file formats are supported")
if 4 != msh_version and 2 != msh_version:
raise IOError("Only ASCII version 2 and 4 (>=4.1) .msh file formats are supported")
fid.close()
if self.elements is not None and self.points is not None:
self.__reset__()
self.filename = filename
bel = -1
if element_type == "line":
el = 1
elif element_type == "tri":
el = 2
bel = 2
cel = 1
elif element_type == "quad":
el = 3
bel = 3
cel = 1
elif element_type == "tet":
el = 4
bel = 2
elif element_type == "hex":
el = 5
bel = 3
else:
raise ValueError("Element type not understood")
# NEW FAST READER
var = 0 # for old gmsh versions - needs checks
node_blocks, elem_blocks, face_blocks = None, None, None
rem_nnode, rem_nelem, rem_faces = int(1e09), int(1e09), int(1e09)
face_counter = 0
for line_counter, line in enumerate(open(filename)):
item = line.rstrip()
plist = item.split()
if plist[0] == "Dimension":
self.ndim = plist[1]
elif plist[0] == "Vertices":
rem_nnode = line_counter+1
continue
elif plist[0] == "$Nodes":
rem_nnode = line_counter+1
continue
elif plist[0] == "Triangles":
rem_faces = line_counter+1
continue
elif plist[0] == "Tetrahedra":
rem_nelem = line_counter+1
continue
elif plist[0] == "$Elements":
rem_nelem = line_counter+1
var = 1
continue
if msh_version == 2:
if rem_nnode == line_counter:
self.nnode = int(plist[0])
if rem_faces == line_counter:
face_counter = int(plist[0])
if rem_nelem == line_counter:
self.nelem = int(plist[0])
break
else:
if rem_nnode == line_counter:
node_blocks, self.nnode = int(plist[0]), int(plist[1])
if rem_faces == line_counter:
face_blocks, face_counter = int(plist[0]), int(plist[1])
if rem_nelem == line_counter:
elem_blocks, self.nelem = int(plist[0]), int(plist[1])
break
points, elements, element_to_set, faces, face_to_surface, edges, curve = [], [], [], [], [], [], []
if msh_version == 2:
# RE-READ
ns = self.InferNumberOfNodesPerElement(p=1,element_type=element_type)
for line_counter, line in enumerate(open(filename)):
item = line.rstrip()
plist = item.split()
if var == 0:
if line_counter > rem_nnode and line_counter < self.nnode+rem_nnode+1:
points.append([float(i) for i in plist[:3]])
if line_counter > rem_nelem and line_counter < self.nelem+rem_nelem+1:
elements.append([int(i) for i in plist[:4]])
elif var == 1:
if line_counter > rem_nnode and line_counter < self.nnode+rem_nnode+1:
points.append([float(i) for i in plist[1:]])
if line_counter > rem_nelem and line_counter < self.nelem+rem_nelem+1:
if int(plist[1]) == el:
elements.append([int(i) for i in plist[-ns:]])
element_to_set.append(int(plist[4]))
# READ SURFACE INFO - CERTAINLY ONLY IF SURFACE ELEMENT TYPE IS QUADS/TRIS
if read_surface_info:
if int(plist[1]) == bel:
faces.append([int(i) for i in plist[5:]])
face_to_surface.append(int(plist[4]))
elif msh_version == 4:
# RE-READ
fid = open(filename)
content = fid.readlines()
# READ NODES
nodes_content = content[rem_nnode+1:2*self.nnode+node_blocks+rem_nnode+1]
incrementer, line_number = 0, 0
# LOOP OVER BLOCKS
for i in range(node_blocks):
incrementer = int(nodes_content[line_number].rstrip().split()[3])
# LOOP OVER NODES OF EACH BLOCK
for j in range(line_number+1, line_number+2*incrementer+1):
plist = nodes_content[j].rstrip().split()
if len(plist) == 1:
continue
points.append([float(plist[k]) for k in range(0,len(plist))])
line_number += 2*incrementer + 1
# READ ELEMENTS
elems_content = content[rem_nelem+1:self.nelem+elem_blocks+rem_nelem+1]
incrementer, line_number = 0, 0
# LOOP OVER BLOCKS
for i in range(elem_blocks):
incrementer = int(elems_content[line_number].rstrip().split()[3])
volume_tag = int(elems_content[line_number].rstrip().split()[1])
if el == int(elems_content[line_number].rstrip().split()[2]):
# LOOP OVER ELEMENTS OF EACH BLOCK
for j in range(line_number+1, line_number+incrementer+1):
plist = elems_content[j].rstrip().split()
elements.append([int(plist[k]) for k in range(1,len(plist))])
element_to_set.append(volume_tag)
line_number += incrementer + 1
if read_surface_info:
# READ FACES
incrementer, line_number = 0, 0
# LOOP OVER BLOCKS
for i in range(elem_blocks):
incrementer = int(elems_content[line_number].rstrip().split()[3])
surface_tag = int(elems_content[line_number].rstrip().split()[1])
if bel == int(elems_content[line_number].rstrip().split()[2]):
# LOOP OVER FACES OF EACH BLOCK
for j in range(line_number+1, line_number+incrementer+1):
plist = elems_content[j].rstrip().split()
faces.append([int(plist[k]) for k in range(1,len(plist))])
face_to_surface.append(surface_tag)
line_number += incrementer + 1
self.points = np.array(points,copy=True)
self.elements = np.array(elements,copy=True) - 1
# CORRECT
self.nelem = self.elements.shape[0]
self.nnode = self.points.shape[0]
if self.nelem == 0:
raise ValueError("msh file does not contain {} elements".format(element_type))
if read_surface_info:
self.faces = np.array(faces,copy=True) - 1
self.face_to_surface = np.array(face_to_surface, dtype=np.int64, copy=True).flatten()
self.face_to_surface -= 1
# CHECK IF FILLED
if isinstance(self.face_to_surface,list):
if not self.face_to_surface:
self.face_to_surface = None
elif isinstance(self.face_to_surface,np.ndarray):
if self.face_to_surface.shape[0]==0:
self.face_to_surface = None
if self.points.shape[1] == 3:
if np.allclose(self.points[:,2],0.):
self.points = np.ascontiguousarray(self.points[:,:2])
self.element_type = element_type
if self.element_type == "tri" or self.element_type == "quad":
self.GetEdges()
self.GetBoundaryEdges()
elif self.element_type == "tet" or self.element_type == "hex":
self.GetFaces()
self.GetBoundaryFaces()
self.GetBoundaryEdges()
# SET OF SETS TO EACH ELEMENTS
element_to_set = np.array(element_to_set, dtype=np.int64, copy=True).flatten()
element_to_set -= 1
self.element_to_set = element_to_set
return
def ReadOBJ(self, filename, element_type="tri"):
try:
fid = open(filename, "r")
except IOError:
print("File '%s' not found." % (filename))
sys.exit()
if self.elements is not None and self.points is not None:
self.__reset__()
self.filename = filename
bel = -1
if element_type == "line":
el = 2
elif element_type == "tri":
el = 3
bel = 2
elif element_type == "quad":
el = 4
bel = 2
elif element_type == "tet":
el = 4
bel = 3
elif element_type == "hex":
el = 8
bel = 4
else:
raise ValueError("Element type not understood")
# Read
points, elements, faces = [],[], []
vertex_normal, vertex_texture = [], []
for line_counter, line in enumerate(open(filename)):
item = line.rstrip()
plist = item.split()
if not plist:
continue
if plist[0] == 'v':
points.append([float(i) for i in plist[1:4]])
if plist[0] == 'f' and len(plist) > el:
for i in range(1,el+1):
if "/" in plist[i]:
plist[i] = plist[i].split("//")[0]
elements.append([int(i) for i in plist[1:el+1]])
if plist[0] == 'vn':
vertex_normal.append([float(i) for i in plist[1:4]])
self.points = np.array(points,copy=True)
self.elements = np.array(elements,copy=True) - 1
if not vertex_normal:
self.vertex_normal = np.array(vertex_normal,copy=True)
# CORRECT
self.nelem = self.elements.shape[0]
self.nnode = self.points.shape[0]
if self.nelem == 0:
raise ValueError("obj file does not contain {} elements".format(element_type))
if self.points.shape[1] == 3:
if np.allclose(self.points[:,2],0.):
self.points = np.ascontiguousarray(self.points[:,:2])
self.element_type = element_type
ndim = self.InferSpatialDimension()
if self.element_type == "tri" or self.element_type == "quad":
self.GetEdges()
self.GetBoundaryEdges()
elif self.element_type == "tet" or self.element_type == "hex":
self.GetFaces()
self.GetBoundaryFaces()
self.GetBoundaryEdges()
def WriteGmsh(self, filename, write_surface_info=False):
"""Write mesh to a .msh (gmsh format) file"""
self.__do_essential_memebers_exist__()
mesh = deepcopy(self)
p = self.InferPolynomialDegree()
if p > 1:
mesh = self.GetLinearMesh(remap=True)
element_type = mesh.element_type
edim = mesh.InferElementalDimension()
# THESE TAGS ARE DIFFERENT FROM THE GMSH READER TAGS
bel = -1
if element_type == "line":
el = 1
elif element_type == "tri":
el = 2
bel = 1
elif element_type == "quad":
el = 3
bel = 1
elif element_type == "tet":
el = 4
bel = 2
elif element_type == "hex":
el = 5
bel = 3
else:
raise ValueError("Element type not understood")
elements = np.copy(mesh.elements).astype(np.int64)
points = mesh.points[np.unique(elements),:]
# Take care of a corner case where nnode != points.shape[0]
if mesh.nnode != points.shape[0]:
mesh.nnode = points.shape[0]
if points.shape[1] == 2:
points = np.hstack((points,np.zeros((points.shape[0],1))))
points_repr = np.zeros((points.shape[0],points.shape[1]+1), dtype=object)
points_repr[:,0] = np.arange(mesh.nnode) + 1
points_repr[:,1:] = points
if self.element_to_set is None:
element_to_set = 0
else:
element_to_set = self.element_to_set
elements_repr = np.zeros((elements.shape[0],elements.shape[1]+5), dtype=object)
elements_repr[:,0] = np.arange(mesh.nelem) + 1
elements_repr[:,1] = el
elements_repr[:,2] = 2
elements_repr[:,3] = 0
elements_repr[:,4] = element_to_set + 1
elements_repr[:,5:] = elements + 1
if write_surface_info:
if edim == 3:
boundary = np.copy(mesh.faces).astype(np.int64)
elif edim == 2:
boundary = np.copy(mesh.edges).astype(np.int64)
if self.face_to_surface is None:
face_to_surface = 0
else:
face_to_surface = self.face_to_surface
boundary_repr = np.zeros((boundary.shape[0],boundary.shape[1]+5), dtype=object)
boundary_repr[:,0] = np.arange(boundary.shape[0]) + 1
boundary_repr[:,1] = bel
boundary_repr[:,2] = 2
boundary_repr[:,3] = 0
boundary_repr[:,4] = face_to_surface + 1
boundary_repr[:,5:] = boundary + 1
elements_repr[:,0] += boundary.shape[0]
gmsh_nelem = mesh.nelem + boundary.shape[0]
else:
gmsh_nelem = mesh.nelem
with open(filename, 'w') as f:
f.write("$MeshFormat\n")
f.write("2.2 0 8\n")
f.write("$EndMeshFormat\n")
f.write("$Nodes\n")
f.write(str(mesh.nnode) + "\n")
np.savetxt(f, points_repr, fmt="%s")
f.write("$EndNodes\n")
f.write("$Elements\n")
f.write(str(gmsh_nelem) + "\n")
if write_surface_info:
np.savetxt(f, boundary_repr, fmt="%s")
np.savetxt(f, elements_repr, fmt="%s")
f.write("$EndElements\n")
def WriteOBJ(self, filename):
"""Write mesh to an obj file. For 3D elements writes the faces only
"""
self.__do_essential_memebers_exist__()
mesh = deepcopy(self)
p = self.InferPolynomialDegree()
if p > 1:
mesh = self.GetLinearMesh(remap=True)
edim = mesh.InferElementalDimension()
if edim == 2:
elements = np.copy(mesh.elements).astype(np.int64)
elif edim == 3:
elements = np.copy(mesh.faces).astype(np.int64)
else:
raise RuntimeError("Writing obj file for {} elements not supported".format(mesh.element_type))
points = mesh.points[np.unique(elements),:]
if points.shape[1] == 2:
points = np.hstack((points,np.zeros((points.shape[0],1))))
points_repr = np.zeros((points.shape[0],points.shape[1]+1), dtype=object)
points_repr[:,0] = "v "
points_repr[:,1:] = points
elements_repr = np.zeros((elements.shape[0],elements.shape[1]+1), dtype=object)
elements_repr[:,0] = "f "
elements_repr[:,1:] = elements + 1
with open(filename, "w") as f:
f.write("# "+ str(mesh.nnode))
f.write('\n')
f.write("# "+ str(mesh.nelem))
f.write('\n')
np.savetxt(f, points_repr, fmt="%s")
f.write('\n')
np.savetxt(f, elements_repr, fmt="%s")
f.write('\n')
def ChangeType(self):
"""Change mesh data type from signed to unsigned"""
self.__do_essential_memebers_exist__()
self.points = np.ascontiguousarray(self.points.astype(np.float64))
if isinstance(self.elements,np.ndarray):
self.elements = np.ascontiguousarray(self.elements.astype(np.uint64))
if hasattr(self, 'edges'):
if isinstance(self.edges,np.ndarray):
self.edges = np.ascontiguousarray(self.edges.astype(np.uint64))
if hasattr(self, 'faces'):
if isinstance(self.faces,np.ndarray):
self.faces = np.ascontiguousarray(self.faces.astype(np.uint64))
@property
def IsHighOrder(self):
is_high_order = False
if self.InferPolynomialDegree() > 1:
is_high_order = True
return is_high_order
def InferPolynomialDegree(self):
"""Infer the degree of interpolation (p) based on the shape of
self.elements
returns: [int] polynomial degree
"""
assert self.element_type is not None
assert self.elements is not None
if self.degree is not None:
if isinstance(self.degree,np.ndarray):
self.degree = np.asscalar(self.degree)
i = self.degree
if self.element_type == "tet" and (i+1)*(i+2)*(i+3)/6==self.elements.shape[1]:
return self.degree
if self.element_type == "tri" and (i+1)*(i+2)/2==self.elements.shape[1]:
return self.degree
p = 0
if self.element_type == "tet":
for i in range(100):
if (i+1)*(i+2)*(i+3)/6==self.elements.shape[1]:
p = i
break
elif self.element_type == "tri":
for i in range(100):
if (i+1)*(i+2)/2==self.elements.shape[1]:
p = i
break
elif self.element_type == "hex":
for i in range(100):
if int((i+1)**3)==self.elements.shape[1]:
p = i
break
elif self.element_type == "quad":
for i in range(100):
if int((i+1)**2)==self.elements.shape[1]:
p = i
break
elif self.element_type == "line":
for i in range(100):
if int(i+1)==self.elements.shape[1]:
p = i
break
elif self.element_type == "pent":
if 5==self.elements.shape[1]:
p = 1
else:
raise NotImplementedError("High order pentagonal elements are not supported yet")
self.degree = p
return p
def InferNumberOfNodesPerElement(self, p=None, element_type=None):
"""Infers number of nodes per element. If p and element_type are
not None then returns the number of nodes required for the given
element type with the given polynomial degree"""
if p is not None and element_type is not None:
if element_type=="line":
return int(p+1)
elif element_type=="tri":
return int((p+1)*(p+2)/2)
elif element_type=="quad":
return int((p+1)**2)
elif element_type=="tet":
return int((p+1)*(p+2)*(p+3)/6)
elif element_type=="hex":
return int((p+1)**3)
else:
raise ValueError("Did not understand element type")
assert self.elements.shape[0] is not None
return self.elements.shape[1]
def InferElementalDimension(self):
"""Infer the actual dimension of the element. This is 3 for tet and hex,
2 for tri and quad, 1 for line etc
"""
assert self.element_type is not None
if self.element_type == "tet" or self.element_type == "hex":
self.edim = 3
elif self.element_type == "tri" or self.element_type == "quad" or self.element_type == "pent":
self.edim = 2
elif self.element_type == "line":
self.edim = 1
else:
raise RuntimeError("Could not infer element type")
return self.edim
def InferNumberOfNodesPerLinearElement(self, element_type=None):
"""Infers number of nodes per element. If element_type are
not None then returns the number of nodes required for the given
element type"""
if element_type is None and self.element_type is None:
raise ValueError("Did not understand element type")
if element_type is None:
element_type = self.element_type
tmp = self.element_type
if element_type != self.element_type:
self.element_type = element_type
nodeperelem = None
if element_type=="line":
nodeperelem = 2
elif element_type=="tri":
nodeperelem = 3
elif element_type=="quad":
nodeperelem = 4
elif element_type=="tet":
nodeperelem = 4
elif element_type=="hex":
nodeperelem = 8
else:
raise ValueError("Did not understand element type")
self.element_type = tmp
return nodeperelem
def InferSpatialDimension(self):
"""Infer the spatial dimension of the mesh"""
assert self.points is not None
# if self.points.shape[1] == 3:
# if self.element_type == "tri" or self.element_type == "quad":
# print("3D surface mesh of ", self.element_type)
return self.points.shape[1]
def InferElementType(self):
if self.element_type is not None:
return self.element_type
assert self.elements is not None
assert self.points is not None
ndim = self.InferSpatialDimension()
nodeperelem = self.InferNumberOfNodesPerElement()
nn = 20
if ndim==3:
if nodeperelem in [int((i+1)*(i+2)*(i+3)/6) for i in range(1,nn)]:
self.element_type = "tet"
elif nodeperelem in [int((i+1)**3) for i in range(1,nn)]:
self.element_type = "hex"
else:
if nodeperelem in [int((i+1)*(i+2)/2) for i in range(1,nn)]:
self.element_type = "tri"
elif nodeperelem in [int((i+1)**2) for i in range(1,nn)]:
self.element_type = "quad"
else:
raise ValueError("Element type not understood")
elif ndim==2:
if nodeperelem in [int((i+1)*(i+2)/2) for i in range(1,nn)]:
self.element_type = "tri"
elif nodeperelem in [int((i+1)**2) for i in range(1,nn)]:
self.element_type = "quad"
else:
raise ValueError("Element type not understood")
elif ndim==1:
self.element_type = "line"
else:
raise ValueError("Element type not understood")
# IF POINTS ARE CO-PLANAR THEN IT IS NOT TET BUT QUAD
if ndim == 3 and self.element_type == "tet":
a = self.points[self.elements[:,0],:]
b = self.points[self.elements[:,1],:]
c = self.points[self.elements[:,2],:]
d = self.points[self.elements[:,3],:]
det_array = np.dstack((a-d,b-d,c-d))
# FIND VOLUME OF ALL THE ELEMENTS
volume = 1./6.*np.linalg.det(det_array)
if np.allclose(volume,0.0):
self.element_type = "quad"
return self.element_type
def InferBoundaryElementType(self):
self.InferElementType()
if self.element_type == "hex":
self.boundary_element_type = "quad"
elif self.element_type == "tet":
self.boundary_element_type = "tri"
elif self.element_type == "quad" or self.element_type == "tri":
self.boundary_element_type = "line"
elif self.element_type == "line":
self.boundary_element_type = "point"
else:
raise ValueError("Could not understand element type")
return self.boundary_element_type
def CreateDummyLowerDimensionalMesh(self):
"""Create a dummy lower dimensional mesh that would have some specific mesh attributes at least.
The objective is that the lower dimensional mesh should have the same element type as the
boundary faces/edges of the actual mesh and be the same order"""
sys.stdout = open(os.devnull, "w")
p = self.InferPolynomialDegree()
mesh = Mesh()
if self.element_type == "tet":
mesh.Rectangle(nx=1,ny=1, element_type="tri")
mesh.GetHighOrderMesh(p=p)
elif self.element_type == "hex":
mesh.Rectangle(nx=1,ny=1, element_type="quad")
mesh.GetHighOrderMesh(p=p)
elif self.element_type == "tri" or self.element_type == "quad":
mesh.Line(n=1, p=p)
sys.stdout = sys.__stdout__
return mesh
def GetLinearMesh(self, solution=None, remap=False):
"""Returns the linear mesh from a high order mesh. If mesh is already linear returns the same mesh.
Also maps any solution vector/tensor of high order mesh to the linear mesh, if supplied.
For safety purposes, always makes a copy"""
self.__do_essential_memebers_exist__()
ndim = self.InferSpatialDimension()
if ndim==2:
if self.element_type == "tri" or self.element_type == "quad":
assert self.edges is not None
elif ndim==3:
if self.element_type == "tet" or self.element_type == "hex":
assert self.faces is not None
if self.IsHighOrder is False:
if solution is not None:
return deepcopy(self), deepcopy(solution)
return deepcopy(self)
else:
if not remap:
# WORKS ONLY IF THE FIST COLUMNS CORRESPOND TO
# LINEAR CONNECTIVITY
lmesh = Mesh()
lmesh.element_type = self.element_type
lmesh.degree = 1
if self.element_type == "tri":
lmesh.elements = np.copy(self.elements[:,:3])
lmesh.edges = np.copy(self.edges[:,:2])
lmesh.nnode = int(np.max(lmesh.elements)+1)
lmesh.points = np.copy(self.points[:lmesh.nnode,:])
elif self.element_type == "tet":
lmesh.elements = np.copy(self.elements[:,:4])
lmesh.faces = np.copy(self.faces[:,:3])
lmesh.nnode = int(np.max(lmesh.elements)+1)
lmesh.points = np.copy(self.points[:lmesh.nnode,:])
elif self.element_type == "quad":
lmesh.elements = np.copy(self.elements[:,:4])
lmesh.edges = np.copy(self.edges[:,:2])
lmesh.nnode = int(np.max(lmesh.elements)+1)
lmesh.points = np.copy(self.points[:lmesh.nnode,:])
elif self.element_type == "hex":
lmesh.elements = | np.copy(self.elements[:,:8]) | numpy.copy |
import pytest
import numpy as np
import reward.utils as U
def test_lazy_array_memory_opt():
arr1 = np.arange(10)
arr2 = np.arange(10)
lazy = U.LazyArray([arr1, arr2])
arr1 += 1
np.testing.assert_equal(U.to_np(lazy), np.array([arr1, arr2]))
def test_lazy_array_lazy_transform():
arr1 = np.arange(10)
arr2 = np.arange(10)
lazy = U.LazyArray([arr1, arr2], transform=lambda x: x * 0)
np.testing.assert_equal(U.to_np(lazy), 0)
# Original data should not be modified
np.testing.assert_equal(arr1, np.arange(10))
np.testing.assert_equal(arr2, np.arange(10))
# LazyArray data should not be modified
| np.testing.assert_equal(lazy.data, [arr1, arr2]) | numpy.testing.assert_equal |
__package__ = "valkyrie_gym_env"
import scipy
import os, inspect, time
from pybullet_utils.bullet_client import BulletClient
currentdir = os.path.dirname(os.path.abspath(inspect.getfile(inspect.currentframe())))
parentdir = os.path.dirname(os.path.dirname(currentdir))
os.sys.path.insert(0, parentdir)
# from rllab.envs.pybullet.valkyrie_multi_env.utils.util import quat_to_rot, rotX, rotY, rotZ
from b3px_gym.b3px_env.parallel.util import quat_to_rot, rotX, rotY, rotZ
import gym
import copy
from gym import spaces
from gym.utils import seeding
import numpy as np
import time
import pybullet as pybullet
import math
from b3px_gym.b3px_env.singleton.valkyrie_gym_env.filter import FilterClass, KalmanFilter, BinaryFilter
from b3px_gym.b3px_env.singleton.valkyrie_gym_env.PD_controller import PDController
from b3px_gym.b3px_env.singleton.valkyrie_gym_env.sensor_signal_process import calCOP
class Valkyrie(gym.Env):
metadata = {
'render.modes': ['human', 'rgb_array'],
'video.frames_per_second': 50
}
# def __del__(self):
# self._p.disconnect()
def __init__(self,
max_time=16, # in seconds
initial_gap_time=0.01, # in seconds
isEnableSelfCollision=False,
renders=False,
Kp_scale=None,
Kd_scale=None,
planeId=None,
fixed_base=False,
time_step=0.005,
frame_skip=8,
scaling_factor = 1.0,
margin_in_degree=1000., # if > 90. then read from urdf
useFullDOF=True,
regularise_action=True
):
self.Kp_scale = dict([
("rightShoulderPitch", 1),
("rightShoulderRoll", 1),
("rightShoulderYaw", 1),
("rightElbowPitch", 1),
("leftShoulderPitch", 1),
("leftShoulderRoll", 1),
("leftShoulderYaw", 1),
("leftElbowPitch", 1),
("torsoYaw", 1),
("torsoPitch", 1),
("torsoRoll", 1),
("leftHipYaw", 1),
("leftHipRoll", 1),
("leftHipPitch", 1),
("leftKneePitch", 2),
("leftAnklePitch", 2),
("leftAnkleRoll", 1),
("rightHipYaw", 1),
("rightHipRoll", 1),
("rightHipPitch", 1),
("rightKneePitch", 2),
("rightAnklePitch", 2),
("rightAnkleRoll", 1),
]) if Kp_scale is None else Kp_scale
self.Kd_scale = dict([
("rightShoulderPitch", 1),
("rightShoulderRoll", 1),
("rightShoulderYaw", 1),
("rightElbowPitch", 1),
("leftShoulderPitch", 1),
("leftShoulderRoll", 1),
("leftShoulderYaw", 1),
("leftElbowPitch", 1),
("torsoYaw", 1),
("torsoPitch", 1),
("torsoRoll", 1),
("leftHipYaw", 1),
("leftHipRoll", 1),
("leftHipPitch", 1),
("leftKneePitch", 1),
("leftAnklePitch", 1),
("leftAnkleRoll", 1),
("rightHipYaw", 1),
("rightHipRoll", 1),
("rightHipPitch", 1),
("rightKneePitch", 1),
("rightAnklePitch", 1),
("rightAnkleRoll", 1),
]) if Kd_scale is None else Kd_scale
self.regularise_action = regularise_action
self.useFullDOF= useFullDOF
self.timestep = time_step
self.frame_skip=frame_skip
self.robot_loaded = False
self.fixed_base = fixed_base
self.planeID = planeId
self.jointIdx = {}
self.jointNameIdx = {}
self.jointLowerLimit = []
self.jointUpperLimit = []
self.total_mass = 0.0
# self._p = p
# self._seed()
self._envStepCounter = 0
self._renders = renders
self._p = BulletClient(connection_mode=pybullet.DIRECT) if not renders else BulletClient(connection_mode=pybullet.GUI)
if self.useFullDOF:
self.controlled_joints = [
"rightShoulderPitch",
"rightShoulderRoll",
"rightShoulderYaw",
"rightElbowPitch",
"leftShoulderPitch",
"leftShoulderRoll",
"leftShoulderYaw",
"leftElbowPitch",
"torsoYaw",
"torsoPitch",
"torsoRoll",
"rightHipYaw",
"rightHipRoll",
"rightHipPitch",
"rightKneePitch",
"rightAnklePitch",
"rightAnkleRoll",
"leftHipYaw",
"leftHipRoll",
"leftHipPitch",
"leftKneePitch",
"leftAnklePitch",
"leftAnkleRoll",
]
else:
self.controlled_joints = [
"rightHipPitch",
"rightKneePitch",
"rightAnklePitch",
"leftHipPitch",
"leftKneePitch",
"leftAnklePitch", ]
self.nu = len(self.controlled_joints)
self.r = -1
self.PD_freq = 1/(self.timestep*self.frame_skip)
self.Physics_freq = 1/self.timestep
self._actionRepeat = int(self.Physics_freq/self.PD_freq)
self._dt_physics = (1./ self.Physics_freq)
self._dt_PD = (1. / self.PD_freq)
self._dt = self._dt_physics # PD control loop timestep
self._dt_filter = self._dt_PD #filter time step
self.g = 9.81
self.joint_states = {}
self.u_max = dict([("torsoYaw", 190),
("torsoPitch", 150),
("torsoRoll", 150),
("rightShoulderPitch", 190),
("rightShoulderRoll", 190),
("rightShoulderYaw", 65),
("rightElbowPitch", 65),
("rightForearmYaw", 26),
("rightWristRoll", 14),
("rightWristPitch", 14),
("leftShoulderPitch", 190),
("leftShoulderRoll", 190),
("leftShoulderYaw", 65),
("leftElbowPitch", 65),
("leftForearmYaw", 26),
("leftWristRoll", 14),
("leftWristPitch", 14),
("rightHipYaw", 190),
("rightHipRoll", 350),
("rightHipPitch", 350),
("rightKneePitch", 350),
("rightAnklePitch", 205),
("rightAnkleRoll", 205),
("leftHipYaw", 190),
("leftHipRoll", 350),
("leftHipPitch", 350),
("leftKneePitch", 350),
("leftAnklePitch", 205),
("leftAnkleRoll", 205),
("lowerNeckPitch", 50),
("upperNeckPitch", 50),
("neckYaw", 50)])
self.v_max = dict([("torsoYaw", 5.89),
("torsoPitch", 9),
("torsoRoll", 9),
("rightShoulderPitch", 5.89),
("rightShoulderRoll", 5.89),
("rightShoulderYaw", 11.5),
("rightElbowPitch", 11.5),
("leftShoulderPitch", 5.89),
("leftShoulderRoll", 5.89),
("leftShoulderYaw", 11.5),
("leftElbowPitch", 11.5),
("rightHipYaw", 5.89),
("rightHipRoll", 7),
("rightHipPitch", 6.11),
("rightKneePitch", 6.11),
("rightAnklePitch", 11),
("rightAnkleRoll", 11),
("leftHipYaw", 5.89),
("leftHipRoll", 7),
("leftHipPitch", 6.11),
("leftKneePitch", 6.11),
("leftAnklePitch", 11),
("leftAnkleRoll", 11),
("lowerNeckPitch", 5),
("upperNeckPitch", 5),
("neckYaw", 5)])
# nominal joint configuration
# self.q_nom = dict([("torsoYaw", 0.0),
# ("torsoPitch", 0.0),
# ("torsoRoll", 0.0),
# ("lowerNeckPitch", 0.0),
# ("neckYaw", 0.0),
# ("upperNeckPitch", 0.0),
# ("rightShoulderPitch", 0.300196631343),
# ("rightShoulderRoll", 1.25),
# ("rightShoulderYaw", 0.0),
# ("rightElbowPitch", 0.785398163397),
# ("leftShoulderPitch", 0.300196631343),
# ("leftShoulderRoll", -1.25),
# ("leftShoulderYaw", 0.0),
# ("leftElbowPitch", -0.785398163397),
# ("rightHipYaw", 0.0),
# ("rightHipRoll", 0.0),
# ("rightAnkleRoll", 0.0),
# ("leftHipYaw", 0.0),
# ("leftHipRoll", 0.0),
# # ("rightHipPitch", -0.49), # -0.49
# # ("rightKneePitch", 1.205), # 1.205
# # ("rightAnklePitch", -0.71), # -0.71
# # ("leftHipPitch", -0.49), # -0.49
# # ("leftKneePitch", 1.205), # 1.205
# # ("leftAnklePitch", -0.71), # -0.71
# ("rightHipPitch", -0.49*0.5), # -0.49
# ("rightKneePitch", 1.205*0.5), # 1.205
# ("rightAnklePitch", -0.71*0.5), # -0.71
# ("leftHipPitch", -0.49*0.5), # -0.49
# ("leftKneePitch", 1.205*0.5), # 1.205
# ("leftAnklePitch", -0.71*0.5), # -0.71
# ("leftAnkleRoll", 0.0)])
if self.useFullDOF:
self.q_nom = dict([
("rightHipYaw", 0.0),
("rightHipRoll", -0.1),
("rightHipPitch", -0.45*1.), # -0.49
("rightKneePitch", 0.944*1.), # 1.205
("rightAnklePitch", -0.527*1.), # -0.71
("rightAnkleRoll", 0.1),
("leftHipYaw", 0.0),
("leftHipRoll", 0.1),
("leftHipPitch", -0.45*1.), # -0.49
("leftKneePitch", 0.944*1.), # 1.205
("leftAnklePitch", -0.527*1.), # -0.71
("leftAnkleRoll", -0.1),
("torsoYaw", 0.0),
("torsoPitch", 0.0),
("torsoRoll", 0.0),
("rightShoulderPitch", 0.300196631343),
("rightShoulderRoll", 1.25),
("rightShoulderYaw", 0.0),
("rightElbowPitch", 0.785398163397),
("leftShoulderPitch", 0.300196631343),
("leftShoulderRoll", -1.25),
("leftShoulderYaw", 0.0),
("leftElbowPitch", -0.785398163397),
])
else:
self.q_nom = dict([
("rightHipPitch", -0.45*1.), # -0.49 , -0.49
("rightKneePitch", 0.944*1.), # 1.205 , 1.205
("rightAnklePitch", -0.527*1.), # -0.71 , -0.8
("leftHipPitch", -0.45*1.), # -0.49 , -0.49
("leftKneePitch", 0.944*1.), # 1.205 , 1.205
("leftAnklePitch", -0.527*1.), # -0.71 , -0.8
])
margin = margin_in_degree*3.14/180
# print("MARGIN IN DEG: %.1f" % margin_in_degree)
self.margin = margin
if self.useFullDOF:
self.joint_limits_low = {
"rightHipYaw": -margin+self.q_nom["rightHipYaw"],
"rightHipRoll": -margin+self.q_nom["rightHipRoll"],
"rightHipPitch": -margin+self.q_nom["rightHipPitch"],
"rightKneePitch": -margin+self.q_nom["rightKneePitch"],
"rightAnklePitch": -margin+self.q_nom["rightAnklePitch"],
"rightAnkleRoll": -margin+self.q_nom["rightAnkleRoll"],
"leftHipYaw": -margin+self.q_nom["leftHipYaw"],
"leftHipRoll": -margin+self.q_nom["leftHipRoll"],
"leftHipPitch": -margin+self.q_nom["leftHipPitch"],
"leftKneePitch": -margin+self.q_nom["leftKneePitch"],
"leftAnklePitch": -margin+self.q_nom["leftAnklePitch"],
"leftAnkleRoll": -margin+self.q_nom["leftAnkleRoll"] }
self.joint_limits_high = {
"rightHipYaw": +margin+self.q_nom["rightHipYaw"],
"rightHipRoll": +margin+self.q_nom["rightHipRoll"],
"rightHipPitch": +margin+self.q_nom["rightHipPitch"],
"rightKneePitch": +margin+self.q_nom["rightKneePitch"],
"rightAnklePitch": +margin+self.q_nom["rightAnklePitch"],
"rightAnkleRoll": +margin+self.q_nom["rightAnkleRoll"],
"leftHipYaw": +margin+self.q_nom["leftHipYaw"],
"leftHipRoll": +margin+self.q_nom["leftHipRoll"],
"leftHipPitch": +margin+self.q_nom["leftHipPitch"],
"leftKneePitch": +margin+self.q_nom["leftKneePitch"],
"leftAnklePitch": +margin+self.q_nom["leftAnklePitch"],
"leftAnkleRoll": +margin+self.q_nom["leftAnkleRoll"]}
else:
self.joint_limits_low = {
"rightHipPitch": -margin+self.q_nom["rightHipPitch"],
"rightKneePitch": -margin+self.q_nom["rightKneePitch"],
"rightAnklePitch": -margin+self.q_nom["rightAnklePitch"],
"leftHipPitch": -margin+self.q_nom["leftHipPitch"],
"leftKneePitch": -margin+self.q_nom["leftKneePitch"],
"leftAnklePitch": -margin+self.q_nom["leftAnklePitch"],
}
self.joint_limits_high = {
"rightHipPitch": +margin+self.q_nom["rightHipPitch"],
"rightKneePitch": +margin+self.q_nom["rightKneePitch"],
"rightAnklePitch": +margin+self.q_nom["rightAnklePitch"],
"leftHipPitch": +margin+self.q_nom["leftHipPitch"],
"leftKneePitch": +margin+self.q_nom["leftKneePitch"],
"leftAnklePitch": +margin+self.q_nom["leftAnklePitch"],
}
self.linkCOMPos = {}
self.linkMass = {}
offset = 1. if self.fixed_base else 0.
self.base_pos_nom = np.array([0, 0, 1.08+offset]) # 1.175 straight #1.025 bend
self.base_orn_nom = np.array([0, 0, 0, 1]) # x,y,z,w
self.plane_pos_nom = np.array([0.,0.,0.])
self.plane_orn_nom = np.array([0.,0.,0.,1.])
self._setupSimulation()
error_for_full_torque = 10*np.pi/180.
kd_fraction = 1/100.
self.Kp = {}
self.Kd = {}
for name in self.controlled_joints:
val = self.u_max[name]/error_for_full_torque
self.Kp.update({name: val*self.Kp_scale[name]})
self.Kd.update({name: val*kd_fraction*self.Kd_scale[name]})
print("%s: %.1f" % (name, val))
self.q_nom_list = []
for jointName in self.controlled_joints:
self.q_nom_list.append(self.q_nom[jointName])
self.q_nom_list = np.array(self.q_nom_list)
self.action = self.q_nom_list
self._actionDim = len(self.controlled_joints)
observationDim = 9+self._actionDim
observation_high = np.array([np.finfo(np.float32).max] * observationDim)
self.observation_space = spaces.Box(-observation_high, observation_high)
self._observationDim = observationDim
self.action_space = spaces.Box(np.array(-self.joint_increment), np.array(self.joint_increment))
# print("Action space: ", self.action_space.low)
self.getLinkMass()
# print("observationDim", self._observationDim, "actionDim", self._actionDim)
def getLinkMass(self):
self.total_mass = 0
info = self._p.getDynamicsInfo(self.r, -1) # for base link
self.linkMass.update({"base": info[0]})
# self.linkMass.update({"pelvisBase": info[0]})
self.total_mass += info[0]
for key, value in self.jointIdx.items():
info = self._p.getDynamicsInfo(self.r, value)
self.linkMass.update({key: info[0]})
self.total_mass += info[0]
def step(self, action):
# clip action
# print("raw action", action)
action = np.clip(action, self.action_space.low, self.action_space.high)
# print("Clipped action", action)
# print("low", self.action_space.low)
# print("high", self.action_space.high)
self.action += action
self.action = np.clip(self.action, self.jointLowerLimit, self.jointUpperLimit)
# self.action = self.getJacobian([0.0, 0.2, 1.1])
# need to clip and perform jacobian here! Filter in loop
for _ in range(self._actionRepeat):
self.set_pos(self.action)
# action = self.getFilteredAction(raw_action)
# _ = self.getObservation() # filter is running in here. Thus call getObservation()
self._p.stepSimulation()
self._observation = self.getExtendedObservation()
reward = copy.copy(self.getReward())
done = copy.copy(self.checkFall())
return copy.copy(self._observation), reward, done, {}
def render(self, mode='human', close=False, distance=3, yaw=0, pitch=-30, roll=0, ):
# p.addUserDebugLine(self.COM_pos + np.array([0, 0, 2]), self.COM_pos + np.array([0, 0, -2]), [1, 0, 0], 5,
# 0.1) # TODO rendering to draw COM
# p.addUserDebugLine(self.support_polygon_center[0] + np.array([0, 0, 2]),
# self.support_polygon_center[0] + np.array([0, 0, -2]), [0, 1, 0], 5,
# 0.1) # TODO rendering to draw support polygon
# p.addUserDebugLine(self.support_polygon_center[0] + np.array([2, 0, 0]),
# self.support_polygon_center[0] + np.array([-2, 0, 0]), [0, 1, 0], 5,
# 0.1) # TODO rendering to draw support polygon
width = 1600
height = 900
base_pos, base_quat = self._p.getBasePositionAndOrientation(self.r)
base_orn = self._p.getEulerFromQuaternion(base_quat)
# yaw = base_orn[2]*180/math.pi
view_matrix = self._p.computeViewMatrixFromYawPitchRoll(
cameraTargetPosition=base_pos,
distance=distance,
yaw=yaw,
pitch=pitch,
roll=roll,
upAxisIndex=2,
)
#
# view_matrix = p.computeViewMatrix(
# cameraTargetPosition=base_pos,
# cameraEyePosition=np.array(base_pos)+np.array([3,-3,2]),
# cameraUpVector=np.array(base_pos)+np.array([0,0,1]),
# )
proj_matrix = self._p.computeProjectionMatrixFOV(
fov=60,
aspect=float(width)/height,
nearVal=0.1,
farVal=100.0,
)
# start_time = time.time()
(_, _, px, _, _) = self._p.getCameraImage(
width=width,
height=height,
viewMatrix=view_matrix,
projectionMatrix=proj_matrix,
renderer=self._p.ER_TINY_RENDERER
)
#ER_TINY_RENDERER ER_BULLET_HARDWARE_OPENGL
rgb_array = np.array(px)
rgb_array = rgb_array[:,:,:3]
# print("Time it took to get getCameraImage: %.5fs" % (time.time()-start_time))
return rgb_array
def reset(self):
return self._reset()
def _reset(self, base_pos_nom = None, base_orn_nom = None, fixed_base = False, q_nom = None):
self.action = self.q_nom_list
seed=int((time.time()*1e6)%1e9)
np.random.seed(seed=seed)
self._p.resetSimulation()
self._setupSimulation(base_pos_nom, base_orn_nom, fixed_base, q_nom)
self._envStepCounter = 0
self._observation = self.getExtendedObservation()
#self._reading = self.getReading()
return np.array(self._observation)
def get_observation(self):
return self.getExtendedObservation()
def getExtendedObservation(self):
self._observation = self.getFilteredObservation() # filtered observation
return self._observation
def getReward(self):
return self._reward()
def applyForce(self, force=[0,0,0], linkName="base"):
if linkName == 'base':
index = -1
else:
index = self.jointIdx[linkName]#
frame_flag = self._p.LINK_FRAME
pos = [0,0,0]
# if linkName is 'base':
# pos = self.base_pos
# else:
# link_state = self._p.getLinkState(self.r, self.jointIdx[linkName])
# pos = link_state[0]
self._p.applyExternalForce(self.r, index,
forceObj=force,
posObj=pos ,#[0, 0.0035, 0],
flags=frame_flag)
def _reward(self):
x_pos_err = 0 - self.base_pos[0]
y_pos_err = 0 - self.base_pos[1]
z_pos_err = 1.05868 - self.base_pos[2] #1.128
# print("Self pos: %.2f, %.2f, %.2f " % (x_pos_err, y_pos_err, z_pos_err))
# print("Base pos: ", self.base_pos)
# print("VEL: ", self.base_vel_yaw)
x_vel_err = -self.base_vel_yaw[0]
y_vel_err = -self.base_vel_yaw[1]
z_vel_err = -self.base_vel_yaw[2]
chest_link_state = self._p.getLinkState(self.r, self.jointIdx['torsoRoll'], computeLinkVelocity=1)
torso_pitch_err = 0-chest_link_state[1][1]
pelvis_pitch_err = 0-self.base_orn[1]
torso_roll_err = 0-chest_link_state[1][0]
pelvis_roll_err = 0-self.base_orn[0]
alpha = 1e-3#1e-2#1e-1
x_pos_reward = math.exp(math.log(alpha)*(x_pos_err/0.7)**2) #1.0
y_pos_reward = math.exp(math.log(alpha)*(y_pos_err/0.7)**2) #1.0
z_pos_reward = math.exp(math.log(alpha)*(z_pos_err/0.7)**2) #1.0
x_vel_reward = math.exp(math.log(alpha)*(x_vel_err/1.0)**2) #4.0
y_vel_reward = math.exp(math.log(alpha)*(y_vel_err/1.0)**2) #4.0
z_vel_reward = math.exp(math.log(alpha)*(z_vel_err/1.0)**2) #2.0
torso_pitch_reward = math.exp(math.log(alpha)*(torso_pitch_err/1.57)**2)
pelvis_pitch_reward = math.exp(math.log(alpha)*(pelvis_pitch_err/1.57)**2)
torso_roll_reward = math.exp(math.log(alpha)*(torso_roll_err/1.57)**2)
pelvis_roll_reward = math.exp(math.log(alpha)*(pelvis_roll_err/1.57)**2)
# reward = (
# 1.0 * x_pos_reward + 0.0 * y_pos_reward + 6.0 * z_pos_reward\
# +1.0 * x_vel_reward + 1.0 * y_vel_reward + 1.0 * z_vel_reward \
# +0.0 * torso_pitch_reward + 1.0 * pelvis_pitch_reward \
# +0.0 * torso_roll_reward + 1.0 * pelvis_roll_reward \
# ) \
# * 1 / (1.0 + 0.0 + 6.0 + 1.0 + 1.0 + 1.0 + 1.0 + 1.0 )
# print(self.total_mass)
force_targ = -self.total_mass*self.g/2.0
left_foot_force_err = force_targ-self.leftContactForce[2] # Z contact force
right_foot_force_err = force_targ-self.rightContactForce[2]
left_foot_force_reward = math.exp(math.log(alpha)*(left_foot_force_err/force_targ)**2)
right_foot_force_reward = math.exp(math.log(alpha)*(right_foot_force_err/force_targ)**2)
if self.regularise_action:
velocity_error = 0
torque_error = 0
for idx, key in enumerate(self.controlled_joints):
velocity_error += (self.joint_velocity[idx] / self.v_max[key])**2
torque_error += (self.joint_torques[idx]/ self.u_max[key])**2
# print("Foot contact: ", foot_contact_term, "vel: %.2f, torque: %.2f, power: %.2f" % (velocity_penalty, torque_penalty, power_penalty))
velocity_error /= len(self.controlled_joints)
torque_error /= len(self.controlled_joints)
joint_vel_reward = math.exp(math.log(alpha)*velocity_error)
joint_torque_reward = math.exp(math.log(alpha)*velocity_error)
else:
joint_vel_reward = 0
joint_torque_reward = 0
foot_contact_term = 0
fall_term = 0
if (self.leftFoot_isInContact and self.rightFoot_isInContact): # both feet lost contact
foot_contact_term = 2.0#-5 # 1 TODO increase penalty for losing contact with the ground
elif (self.leftFoot_isInContact or self.rightFoot_isInContact): # both feet lost contact
foot_contact_term = 0.5#-5 # 1 TODO increase penalty for losing contact with the ground
# if self.checkFall():
# fall_term -= 10
reward = (
1.0 * x_pos_reward + 1.0 * y_pos_reward + 4.0 * z_pos_reward\
+1.0 * x_vel_reward + 1.0 * y_vel_reward + 1.0 * z_vel_reward \
+0.5 * torso_pitch_reward + 0.5 * pelvis_pitch_reward \
# +0.5 * torso_roll_reward + 0.5 * pelvis_roll_reward \
+1.0 * left_foot_force_reward + 1.0 * right_foot_force_reward \
+1.0 * joint_vel_reward + 1.0 * joint_torque_reward + 2.0* foot_contact_term
) \
* 10 / (2.0 + 4.0 + 2.0 + 1.0 + 1.0 + 1.0 + 1.0 + 2.0 + 2.0)
# penalize reward when joint is moving too fast
# velocity_penalty = 0
# torque_penalty = 0
# power_penalty = 0
# if self.regularise_action:
# for idx, key in enumerate(self.controlled_joints):
# velocity_penalty -= (self.joint_velocity[idx] / self.v_max[key])**2
# torque_penalty -= 0.1 * abs(self.joint_torques[idx]/ self.u_max[key])
# power_penalty -= 0.1 * abs(self.joint_velocity[idx]) * abs(self.joint_torques[idx])
# # print("Foot contact: ", foot_contact_term, "vel: %.2f, torque: %.2f, power: %.2f" % (velocity_penalty, torque_penalty, power_penalty))
# reward += foot_contact_term #+fall_term+velocity_penalty+torque_penalty+power_penalty
reward_term = dict([
("x_pos_reward", x_pos_reward),
("y_pos_reward", y_pos_reward),
("z_pos_reward", z_pos_reward),
("x_vel_reward", x_vel_reward),
("y_vel_reward", y_vel_reward),
("z_vel_reward", z_vel_reward),
("torso_pitch_reward", torso_pitch_reward),
("pelvis_pitch_reward", pelvis_pitch_reward),
("torso_roll_reward", torso_roll_reward),
("pelvis_roll_reward", pelvis_roll_reward),
("left_foot_force_reward", left_foot_force_reward),
("right_foot_force_reward", right_foot_force_reward)
])
# print("Reward: %.4f" % (reward/20))
# print("Reward: ", reward_term)
return reward, reward_term
def resetJointStates(self, base_pos_nom=None, base_orn_nom=None, q_nom=None):
# if base_pos_nom is None:
# base_pos_nom = self.base_pos_nom
# if base_orn_nom is None:
# base_orn_nom = self.base_orn_nom
if q_nom is None:
q_nom = self.q_nom
else:
#replace nominal joint angle with target joint angle
temp=dict(self.q_nom)
for key, value in q_nom.items():
temp[key] = value
q_nom = dict(temp)
self.q_nom = dict(q_nom)
for jointName in q_nom:
self._p.resetJointState(self.r,
self.jointIdx[jointName],
targetValue=q_nom[jointName],
targetVelocity=0)
# print("Reset %s to %.2f" % (jointName, q_nom[jointName]))
# print(base_orn_nom)
# self._p.resetBasePositionAndOrientation(self.r, base_pos_nom, base_orn_nom)
# self._p.resetBaseVelocity(self.r, [0, 0, 0], [0, 0, 0])
def calcCOM(self):
self.linkCOMPos.update({"base": np.array(self.base_pos)}) # base position is the COM of the pelvis
self.com_pos = np.zeros((1, 3))
for key, value in self.linkMass.items():
if key != "base":
info = self._p.getLinkState(self.r, self.jointIdx[key], computeLinkVelocity=0)
self.linkCOMPos.update({key: info[0]})
# print("WTF: %.3f" % value, np.array(self.linkCOMPos[key]))
self.com_pos += np.array(self.linkCOMPos[key]) * value
# print("KEY: %s, value: %.2f" % (key, value))
self.com_pos /= self.total_mass
# self.com_pos /= self.total_mass
# update global COM position
# self.com_pos = np.array(sum)
return self.com_pos
def _setupSimulation(self, base_pos_nom=None, base_orn_nom=None, fixed_base=False, q_nom=None):
if base_pos_nom is None:
base_pos_nom = self.base_pos_nom
if base_orn_nom is None:
base_orn_nom = self.base_orn_nom
self._p.setRealTimeSimulation(0)
self._p.setGravity(0, 0, -self.g) #TODO set gravity
self._p.setTimeStep(self._dt)
self.dir_path = os.path.dirname(os.path.realpath(__file__))
self._p.configureDebugVisualizer(self._p.COV_ENABLE_RENDERING, 0)
plane_urdf = self.dir_path + "/plane/plane.urdf"
self.plane = self._p.loadURDF(plane_urdf, basePosition=[0, 0, 0], baseOrientation=[0,0,0,1], useFixedBase=True)
if self.useFullDOF:
valkyrie_urdf = self.dir_path + "/valkyrie_full_dof.urdf"
else:
valkyrie_urdf = self.dir_path + "/valkyrie_reduced_fixed.urdf"
# print("Fixed: ", self.fixed_base)
self.r = self._p.loadURDF(fileName=valkyrie_urdf,
basePosition=base_pos_nom,
baseOrientation=base_orn_nom,
flags=self._p.URDF_USE_INERTIA_FROM_FILE|self._p.URDF_USE_SELF_COLLISION_EXCLUDE_ALL_PARENTS,
useFixedBase=self.fixed_base,
)
self._p.configureDebugVisualizer(self._p.COV_ENABLE_RENDERING, 1)
jointIds = []
for j in range(self._p.getNumJoints(self.r)):
self._p.changeDynamics(self.r, j, linearDamping=0, angularDamping=0)
info = self._p.getJointInfo(self.r, j)
#print(info)
jointName = info[1].decode("utf-8")
# print(jointName)
jointType = info[2]
if (jointType == self._p.JOINT_REVOLUTE):
jointIds.append(j)
# print("Appending %s" % jointName)
self.jointIdx.update({jointName: info[0]})
self.jointNameIdx.update({info[0]: jointName})
self.jointIds = []
for name in self.controlled_joints:
_id = self.jointIdx[name]
if _id in jointIds:
self.jointIds.append(_id)
if self.margin > 90*3.14/180:
for joint in self.controlled_joints:
# print("self joint didx", self.jointIdx)
info = self._p.getJointInfo(self.r, self.jointIdx[joint])
self.joint_limits_low.update({joint: (info[8])})
self.joint_limits_high.update({joint: (info[9])})
self.jointLowerLimit = []
self.jointUpperLimit = []
for jointName in self.controlled_joints:
self.jointLowerLimit.append(self.joint_limits_low[jointName])
self.jointUpperLimit.append(self.joint_limits_high[jointName])
self.joint_increment = (np.array(self.jointUpperLimit) - np.array(self.jointLowerLimit))/ (25 * 10)
self.resetJointStates(base_pos_nom, base_orn_nom, q_nom)
def getObservation(self):
self.base_pos, self.base_quat = self._p.getBasePositionAndOrientation(self.r)
self.base_vel, self.base_orn_vel = self._p.getBaseVelocity(self.r)
# print(self.base_pos)
# for idx in self.jointNameIdx.keys():
# print("Val: ", self._p.getLinkState(self.r, idx+1)[0])
queried_links = [
"head_imu_joint",
"leftElbowPitch",
"rightElbowPitch",
"left_hand",
"right_hand",
"torsoYaw",
"leftKneePitch",
"rightKneePitch",
"leftAnklePitch",
"rightAnklePitch",
]
queried_indices = []
for link in queried_links:
queried_indices.append(self.jointIdx[link])
self.linkStates = self._p.getLinkStates(self.r, queried_indices)
self.head_pos = self.linkStates[0][0]
self.left_elbow_pos = self.linkStates[1][0]
self.right_elbow_pos = self.linkStates[2][0]
self.left_hand_pos = self.linkStates[3][0]
self.right_hand_pos = self.linkStates[4][0]
self.torso_pos = self.linkStates[5][0]
self.left_knee_pos = self.linkStates[6][0]
self.right_knee_pos = self.linkStates[7][0]
self.left_foot_pos = self.linkStates[8][0]
self.right_foot_pos = self.linkStates[9][0]
# self.left_foot_pos = self._p.getLinkState(self.r, self.jointIdx["leftAnklePitch"])[0]
# self.right_foot_pos = self._p.getLinkState(self.r, self.jointIdx["rightAnklePitch"])[0]
# ankleRollContact = self._p.getContactPoints(self.r, self.plane, self.jointIdx['leftAnkleRoll'], -1)
# anklePitchContact = self._p.getContactPoints(self.r, self.plane, self.jointIdx['leftAnklePitch'], -1)
# ankleRollContact = self._p.getContactPoints(self.r, self.plane, self.jointIdx['rightAnkleRoll'], -1)
# anklePitchContact = self._p.getContactPoints(self.r, self.plane, self.jointIdx['rightAnklePitch'], -1)
leftContactInfo = self._p.getContactPoints(self.r, self.plane, self.jointIdx["leftAnkleRoll"], -1)
rightContactInfo = self._p.getContactPoints(self.r, self.plane, self.jointIdx["rightAnkleRoll"], -1)
# print(leftContactInfo)
self.leftFoot_isInContact = (len(leftContactInfo) > 0)
self.rightFoot_isInContact = (len(rightContactInfo) > 0)
# print("LEFT: %d, RIGHT: %d" % (self.leftFoot_isInContact, self.rightFoot_isInContact))
self.leftContactForce = [0, 0, 0]
self.rightContactForce = [0, 0, 0]
if self.leftFoot_isInContact:
for info in leftContactInfo:
contactNormal = np.array(info[7]) # contact normal of foot pointing towards plane
contactNormal = -contactNormal # contact normal of plane pointing towards foot
contactNormalForce = | np.array(info[9]) | numpy.array |
import numpy as np
import matplotlib.pyplot as plt
from lmfit.lineshapes import pvoigt
from lmfit import Model
def ikeda_carpenter(t, alpha, beta, fraction, t0, norm_factor=1):
_t = t - t0
# _t = t1[np.logical_not(t1 < 0)]
_t[_t < 0] = 0 # t>=0 required
# α=vΣ
# Σ is the macroscopic neutron scattering cross-section of the moderator
# (Σ=1.6 cm-1 for polyethylene in the high energy limit) and
# v is the neutron speed
part1 = 0.5 * alpha * (alpha*_t)**2 * np.exp(-alpha*_t)
part2_1 = alpha**3 * beta / (alpha - beta)**3 # jparc uses alpha**2 instead of alpha**3 in the original function
part2_2 = np.exp(-beta*_t) - np.exp(-alpha*_t) * (1 + (alpha - beta) * _t + 0.5 * (alpha - beta)**2 * _t**2)
part2 = part2_1 * part2_2
f = ((1 - fraction) * part1 + fraction * part2) * norm_factor
return f
def ikeda_carpenter_jparc(t, alpha, beta, fraction, t0, norm_factor=1):
_t = t - t0
# _t = t1[np.logical_not(t1 < 0)]
_t[_t < 0] = 0 # t>=0 required
part1 = 0.5 * alpha * (alpha*_t)**2 * np.exp(-alpha*_t)
part2_1 = alpha**2 * beta / (alpha - beta)**3 # jparc uses alpha**2 instead of alpha**3 in the original function
part2_2 = np.exp(-beta*_t) - np.exp(-alpha*_t) * (1 + (alpha - beta) * _t + 0.5 * (alpha - beta)**2 * _t**2)
part2 = part2_1 * part2_2
f = ((1 - fraction) * part1 + fraction * part2) * norm_factor
return f
def cole_windsor(t, sig1, sig2, gamma, fraction, t0, norm_factor=1):
_t = t - t0
f = []
for each_t in _t:
# for F1
if each_t <= 0:
f1 = np.exp(-0.5 * (each_t / sig1) ** 2)
if 0 < each_t <= gamma * sig2 ** 2:
f1 = np.exp(-0.5 * (each_t / sig2) ** 2)
if gamma * sig2 ** 2 < each_t:
f1 = np.exp(0.5 * (gamma * sig2) ** 2 - gamma * each_t)
# for F2
if each_t <= 0:
f2 = np.exp(-0.5 * (each_t / sig1) ** 2)
if 0 < each_t <= gamma * sig2 ** 2:
f2 = | np.exp(0.5 * (each_t / sig2) ** 2) | numpy.exp |
'''
Extensions to Numpy, including finding array elements and smoothing data.
Highlights:
- ``sc.findinds()``: find indices of an array matching a condition
- ``sc.findnearest()``: find nearest matching value
- ``sc.smooth()``: simple smoothing of 1D or 2D arrays
- ``sc.smoothinterp()``: linear interpolation with smoothing
'''
import numpy as np
import warnings
from . import sc_utils as ut
##############################################################################
### Find and approximation functions
##############################################################################
__all__ = ['approx', 'safedivide', 'findinds', 'findfirst', 'findlast', 'findnearest', 'dataindex', 'getvalidinds', 'sanitize', 'getvaliddata', 'isprime']
def approx(val1=None, val2=None, eps=None, **kwargs):
'''
Determine whether two scalars (or an array and a scalar) approximately match.
Alias for np.isclose() and may be removed in future versions.
Args:
val1 (number or array): the first value
val2 (number): the second value
eps (float): absolute tolerance
kwargs (dict): passed to np.isclose()
**Examples**::
sc.approx(2*6, 11.9999999, eps=1e-6) # Returns True
sc.approx([3,12,11.9], 12) # Returns array([False, True, False], dtype=bool)
'''
if eps is not None:
kwargs['atol'] = eps # Rename kwarg to match np.isclose()
output = np.isclose(a=val1, b=val2, **kwargs)
return output
def safedivide(numerator=None, denominator=None, default=None, eps=None, warn=False):
'''
Handle divide-by-zero and divide-by-nan elegantly.
**Examples**::
sc.safedivide(numerator=0, denominator=0, default=1, eps=0) # Returns 1
sc.safedivide(numerator=5, denominator=2.0, default=1, eps=1e-3) # Returns 2.5
sc.safedivide(3, np.array([1,3,0]), -1, warn=True) # Returns array([ 3, 1, -1])
'''
# Set some defaults
if numerator is None: numerator = 1.0
if denominator is None: denominator = 1.0
if default is None: default = 0.0
# Handle the logic
invalid = approx(denominator, 0.0, eps=eps)
if ut.isnumber(denominator): # The denominator is a scalar
if invalid:
output = default
else:
output = numerator/denominator
elif ut.checktype(denominator, 'array'):
if not warn:
denominator[invalid] = 1.0 # Replace invalid values with 1
output = numerator/denominator
output[invalid] = default
else: # pragma: no cover # Unclear input, raise exception
errormsg = f'Input type {type(denominator)} not understood: must be number or array'
raise TypeError(errormsg)
return output
def findinds(arr, val=None, eps=1e-6, first=False, last=False, die=True, **kwargs):
'''
Little function to find matches even if two things aren't eactly equal (eg.
due to floats vs. ints). If one argument, find nonzero values. With two arguments,
check for equality using eps. Returns a tuple of arrays if val1 is multidimensional,
else returns an array. Similar to calling np.nonzero(np.isclose(arr, val))[0].
Args:
arr (array): the array to find values in
val (float): if provided, the value to match
eps (float): the precision for matching (default 1e-6, equivalent to np.isclose's atol)
first (bool): whether to return the first matching value
last (bool): whether to return the last matching value
die (bool): whether to raise an exception if first or last is true and no matches were found
kwargs (dict): passed to np.isclose()
**Examples**::
sc.findinds(rand(10)<0.5) # returns e.g. array([2, 4, 5, 9])
sc.findinds([2,3,6,3], 3) # returs array([1,3])
sc.findinds([2,3,6,3], 3, first=True) # returns 1
New in version 1.2.3: "die" argument
'''
# Handle first or last
if first and last: raise ValueError('Can use first or last but not both')
elif first: ind = 0
elif last: ind = -1
else: ind = None
# Handle kwargs
atol = kwargs.pop('atol', eps) # Ensure atol isn't specified twice
if 'val1' in kwargs or 'val2' in kwargs: # pragma: no cover
arr = kwargs.pop('val1', arr)
val = kwargs.pop('val2', val)
warnmsg = 'sc.findinds() arguments "val1" and "val2" have been deprecated as of v1.0.0; use "arr" and "val" instead'
warnings.warn(warnmsg, category=DeprecationWarning, stacklevel=2)
# Calculate matches
arr = ut.promotetoarray(arr)
if val is None: # Check for equality
output = np.nonzero(arr) # If not, just check the truth condition
else:
if ut.isstring(val):
output = np.nonzero(arr==val)
try: # Standard usage, use nonzero
output = np.nonzero(np.isclose(a=arr, b=val, atol=atol, **kwargs)) # If absolute difference between the two values is less than a certain amount
except Exception as E: # pragma: no cover # As a fallback, try simpler comparison
output = np.nonzero(abs(arr-val) < atol)
if kwargs: # Raise a warning if and only if special settings were passed
warnmsg = f'{str(E)}\nsc.findinds(): np.isclose() encountered an exception (above), falling back to direct comparison'
warnings.warn(warnmsg, category=RuntimeWarning, stacklevel=2)
# Process output
try:
if arr.ndim == 1: # Uni-dimensional
output = output[0] # Return an array rather than a tuple of arrays if one-dimensional
if ind is not None:
output = output[ind] # And get the first element
else:
if ind is not None:
output = [output[i][ind] for i in range(arr.ndim)]
except IndexError as E:
if die:
errormsg = 'No matching values found; use die=False to return None instead of raising an exception'
raise IndexError(errormsg) from E
else:
output = None
return output
def findfirst(*args, **kwargs):
''' Alias for findinds(..., first=True). New in version 1.0.0. '''
return findinds(*args, **kwargs, first=True)
def findlast(*args, **kwargs):
''' Alias for findinds(..., last=True). New in version 1.0.0. '''
return findinds(*args, **kwargs, last=True)
def findnearest(series=None, value=None):
'''
Return the index of the nearest match in series to value -- like findinds, but
always returns an object with the same type as value (i.e. findnearest with
a number returns a number, findnearest with an array returns an array).
**Examples**::
findnearest(rand(10), 0.5) # returns whichever index is closest to 0.5
findnearest([2,3,6,3], 6) # returns 2
findnearest([2,3,6,3], 6) # returns 2
findnearest([0,2,4,6,8,10], [3, 4, 5]) # returns array([1, 2, 2])
Version: 2017jan07
'''
series = ut.promotetoarray(series)
if ut.isnumber(value):
output = np.argmin(abs(series-value))
else:
output = []
for val in value: output.append(findnearest(series, val))
output = ut.promotetoarray(output)
return output
def dataindex(dataarray, index): # pragma: no cover
'''
Take an array of data and return either the first or last (or some other) non-NaN entry.
This function is deprecated.
'''
nrows = np.shape(dataarray)[0] # See how many rows need to be filled (either npops, nprogs, or 1).
output = np.zeros(nrows) # Create structure
for r in range(nrows):
output[r] = sanitize(dataarray[r])[index] # Return the specified index -- usually either the first [0] or last [-1]
return output
def getvalidinds(data=None, filterdata=None): # pragma: no cover
'''
Return the indices that are valid based on the validity of the input data from an arbitrary number
of 1-D vector inputs. Warning, closely related to getvaliddata().
This function is deprecated.
**Example**::
getvalidinds([3,5,8,13], [2000, nan, nan, 2004]) # Returns array([0,3])
'''
data = ut.promotetoarray(data)
if filterdata is None: filterdata = data # So it can work on a single input -- more or less replicates sanitize() then
filterdata = ut.promotetoarray(filterdata)
if filterdata.dtype=='bool': filterindices = filterdata # It's already boolean, so leave it as is
else: filterindices = findinds(~np.isnan(filterdata)) # Else, assume it's nans that need to be removed
dataindices = findinds(~np.isnan(data)) # Also check validity of data
validindices = np.intersect1d(dataindices, filterindices)
return validindices # Only return indices -- WARNING, not consistent with sanitize()
def getvaliddata(data=None, filterdata=None, defaultind=0): # pragma: no cover
'''
Return the data value indices that are valid based on the validity of the input data.
This function is deprecated.
**Example**::
getvaliddata(array([3,5,8,13]), array([2000, nan, nan, 2004])) # Returns array([3,13])
'''
data = np.array(data)
if filterdata is None: filterdata = data # So it can work on a single input -- more or less replicates sanitize() then
filterdata = np.array(filterdata)
if filterdata.dtype=='bool': validindices = filterdata # It's already boolean, so leave it as is
else: validindices = ~np.isnan(filterdata) # Else, assume it's nans that need to be removed
if validindices.any(): # There's at least one data point entered
if len(data)==len(validindices): # They're the same length: use for logical indexing
validdata = np.array(np.array(data)[validindices]) # Store each year
elif len(validindices)==1: # They're different lengths and it has length 1: it's an assumption
validdata = np.array([np.array(data)[defaultind]]) # Use the default index; usually either 0 (start) or -1 (end)
else:
errormsg = f'Array sizes are mismatched: {len(data)} vs. {len(validindices)}'
raise ValueError(errormsg)
else:
validdata = np.array([]) # No valid data, return an empty array
return validdata
def sanitize(data=None, returninds=False, replacenans=None, die=True, defaultval=None, label=None, verbose=True):
'''
Sanitize input to remove NaNs. Warning, does not work on multidimensional data!!
**Examples**::
sanitized,inds = sanitize(array([3,4,nan,8,2,nan,nan,nan,8]), returninds=True)
sanitized = sanitize(array([3,4,nan,8,2,nan,nan,nan,8]), replacenans=True)
sanitized = sanitize(array([3,4,nan,8,2,nan,nan,nan,8]), replacenans=0)
'''
try:
data = np.array(data,dtype=float) # Make sure it's an array of float type
inds = np.nonzero(~np.isnan(data))[0] # WARNING, nonzero returns tuple :(
sanitized = data[inds] # Trim data
if replacenans is not None:
newx = range(len(data)) # Create a new x array the size of the original array
if replacenans==True: replacenans = 'nearest'
if replacenans in ['nearest','linear']:
sanitized = smoothinterp(newx, inds, sanitized, method=replacenans, smoothness=0) # Replace nans with interpolated values
else:
naninds = inds = np.nonzero(np.isnan(data))[0]
sanitized = ut.dcp(data)
sanitized[naninds] = replacenans
if len(sanitized)==0:
if defaultval is not None:
sanitized = defaultval
else:
sanitized = 0.0
if verbose: # pragma: no cover
if label is None: label = 'this parameter'
print(f'sc.sanitize(): no data entered for {label}, assuming 0')
except Exception as E: # pragma: no cover
if die:
errormsg = f'Sanitization failed on array: "{repr(E)}":\n{data}'
raise RuntimeError(errormsg)
else:
sanitized = data # Give up and just return an empty array
inds = []
if returninds: return sanitized, inds
else: return sanitized
def isprime(n, verbose=False):
'''
Determine if a number is prime.
From https://stackoverflow.com/questions/15285534/isprime-function-for-python-language
**Example**::
for i in range(100): print(i) if sc.isprime(i) else None
'''
if n < 2:
if verbose: print('Not prime: n<2')
return False
if n == 2:
if verbose: print('Is prime: n=2')
return True
if n == 3:
if verbose: print('Is prime: n=3')
return True
if n%2 == 0:
if verbose: print('Not prime: divisible by 2')
return False
if n%3 == 0:
if verbose: print('Not prime: divisible by 3')
return False
if n < 9:
if verbose: print('Is prime: <9 and not divisible by 2')
return True
r = int(n**0.5)
f = 5
while f <= r:
if n%f == 0:
if verbose: print(f'Not prime: divisible by {f}')
return False
if n%(f+2) == 0:
if verbose: print(f'Not prime: divisible by {f+2}')
return False
f +=6
if verbose: print('Is prime!')
return True
##############################################################################
### Other functions
##############################################################################
__all__ += ['perturb', 'normsum', 'normalize', 'inclusiverange', 'rolling', 'smooth', 'smoothinterp', 'randround', 'cat']
def perturb(n=1, span=0.5, randseed=None, normal=False):
'''
Define an array of numbers uniformly perturbed with a mean of 1.
Args:
n (int): number of points
span (float): width of distribution on either side of 1
normal (bool): whether to use a normal distribution instead of uniform
**Example**::
sc.perturb(5, 0.3) # Returns e.g. array([0.73852362, 0.7088094 , 0.93713658, 1.13150755, 0.87183371])
'''
if randseed is not None:
np.random.seed(int(randseed)) # Optionally reset random seed
if normal:
output = 1.0 + span*np.random.randn(n)
else:
output = 1.0 + 2*span*(np.random.rand(n)-0.5)
return output
def normsum(arr, total=None):
'''
Multiply a list or array by some normalizing factor so that its sum is equal
to the total. Formerly called sc.scaleratio().
Args:
arr (array): array (or list) to normalize
total (float): amount to sum to (default 1)
**Example**::
normarr = sc.normsum([2,5,3,10], 100) # Scale so sum equals 100; returns [10.0, 25.0, 15.0, 50.0]
Renamed in version 1.0.0.
'''
if total is None: total = 1.0
origtotal = float(sum(arr))
ratio = float(total)/origtotal
out = | np.array(arr) | numpy.array |
# Distributed under the MIT License.
# See LICENSE.txt for details.
import numpy as np
# Functions for testing SmoothFlow.cpp
def rest_mass_density(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude):
return 1.0 + (density_amplitude *
np.sin(np.dot(np.asarray(wave_vector),
np.asarray(x) - np.asarray(mean_velocity) * t)))
def spatial_velocity(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude):
return np.asarray(mean_velocity)
def specific_internal_energy(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude):
return (pressure /
((adiabatic_exponent - 1.0) *
rest_mass_density(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude)))
def pressure(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude):
return pressure
def magnetic_field(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude):
return np.array([0.0,0.0,0.0])
def dt_rest_mass_density(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude):
return (-density_amplitude *
np.dot(np.asarray(wave_vector),np.asarray(mean_velocity)) *
np.cos(np.dot(np.asarray(wave_vector),
np.asarray(x) - np.asarray(mean_velocity) * t)))
def dt_spatial_velocity(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude):
return np.array([0.0,0.0,0.0])
def dt_specific_internal_energy(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude):
return (-pressure /
((adiabatic_exponent - 1.0) * rest_mass_density(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude)**2 ) *
dt_rest_mass_density(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude))
def dt_pressure(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude):
return 0.0
def dt_magnetic_field(x, t, mean_velocity, wave_vector, pressure,
adiabatic_exponent, density_amplitude):
return | np.array([0.0,0.0,0.0]) | numpy.array |
from copy import copy
from itertools import cycle, islice
import numpy as np
import pandas as pd
import pytest
from napari._tests.utils import check_layer_world_data_extent
from napari.layers import Shapes
from napari.layers.utils._text_constants import TextMode
from napari.utils.colormaps.standardize_color import transform_color
def _make_cycled_properties(values, length):
"""Helper function to make property values
Parameters
----------
values
The values to be cycled.
length : int
The length of the resulting property array
Returns
-------
cycled_properties : np.ndarray
The property array comprising the cycled values.
"""
cycled_properties = np.array(list(islice(cycle(values), 0, length)))
return cycled_properties
def test_empty_shapes():
shp = Shapes()
assert shp.ndim == 2
properties_array = {'shape_type': _make_cycled_properties(['A', 'B'], 10)}
properties_list = {'shape_type': list(_make_cycled_properties(['A', 'B'], 10))}
@pytest.mark.parametrize("properties", [properties_array, properties_list])
def test_properties(properties):
shape = (10, 4, 2)
np.random.seed(0)
data = 20 * np.random.random(shape)
layer = Shapes(data, properties=copy(properties))
np.testing.assert_equal(layer.properties, properties)
current_prop = {'shape_type': np.array(['B'])}
assert layer.current_properties == current_prop
# test removing shapes
layer.selected_data = {0, 1}
layer.remove_selected()
remove_properties = properties['shape_type'][2::]
assert len(layer.properties['shape_type']) == (shape[0] - 2)
assert np.all(layer.properties['shape_type'] == remove_properties)
# test selection of properties
layer.selected_data = {0}
selected_annotation = layer.current_properties['shape_type']
assert len(selected_annotation) == 1
assert selected_annotation[0] == 'A'
# test adding shapes with properties
new_data = np.random.random((1, 4, 2))
new_shape_type = ['rectangle']
layer.add(new_data, shape_type=new_shape_type)
add_properties = np.concatenate((remove_properties, ['A']), axis=0)
assert np.all(layer.properties['shape_type'] == add_properties)
# test copy/paste
layer.selected_data = {0, 1}
layer._copy_data()
assert np.all(layer._clipboard['properties']['shape_type'] == ['A', 'B'])
layer._paste_data()
paste_properties = np.concatenate((add_properties, ['A', 'B']), axis=0)
assert np.all(layer.properties['shape_type'] == paste_properties)
# test updating a property
layer.mode = 'select'
layer.selected_data = {0}
new_property = {'shape_type': np.array(['B'])}
layer.current_properties = new_property
updated_properties = layer.properties
assert updated_properties['shape_type'][0] == 'B'
@pytest.mark.parametrize("attribute", ['edge', 'face'])
def test_adding_properties(attribute):
"""Test adding properties to an existing layer"""
shape = (10, 4, 2)
np.random.seed(0)
data = 20 * np.random.random(shape)
layer = Shapes(data)
# add properties
properties = {'shape_type': _make_cycled_properties(['A', 'B'], shape[0])}
layer.properties = properties
np.testing.assert_equal(layer.properties, properties)
# add properties as a dataframe
properties_df = pd.DataFrame(properties)
layer.properties = properties_df
np.testing.assert_equal(layer.properties, properties)
# add properties as a dictionary with list values
properties_list = {
'shape_type': list(_make_cycled_properties(['A', 'B'], shape[0]))
}
layer.properties = properties_list
assert isinstance(layer.properties['shape_type'], np.ndarray)
# removing a property that was the _*_color_property should give a warning
setattr(layer, f'_{attribute}_color_property', 'shape_type')
properties_2 = {
'not_shape_type': _make_cycled_properties(['A', 'B'], shape[0])
}
with pytest.warns(RuntimeWarning):
layer.properties = properties_2
def test_data_setter_with_properties():
"""Test layer data on a layer with properties via the data setter"""
shape = (10, 4, 2)
np.random.seed(0)
data = 20 * np.random.random(shape)
properties = {'shape_type': _make_cycled_properties(['A', 'B'], shape[0])}
layer = Shapes(data, properties=properties)
# test setting to data with fewer shapes
n_new_shapes = 4
new_data = 20 * np.random.random((n_new_shapes, 4, 2))
layer.data = new_data
assert len(layer.properties['shape_type']) == n_new_shapes
# test setting to data with more shapes
n_new_shapes_2 = 6
new_data_2 = 20 * np.random.random((n_new_shapes_2, 4, 2))
layer.data = new_data_2
assert len(layer.properties['shape_type']) == n_new_shapes_2
# test setting to data with same shapes
new_data_3 = 20 * np.random.random((n_new_shapes_2, 4, 2))
layer.data = new_data_3
assert len(layer.properties['shape_type']) == n_new_shapes_2
def test_properties_dataframe():
"""Test if properties can be provided as a DataFrame"""
shape = (10, 4, 2)
np.random.seed(0)
data = 20 * np.random.random(shape)
properties = {'shape_type': _make_cycled_properties(['A', 'B'], shape[0])}
properties_df = pd.DataFrame(properties)
properties_df = properties_df.astype(properties['shape_type'].dtype)
layer = Shapes(data, properties=properties_df)
np.testing.assert_equal(layer.properties, properties)
def test_empty_layer_with_text_properties():
"""Test initializing an empty layer with text defined"""
default_properties = {'shape_type': np.array([1.5], dtype=float)}
text_kwargs = {'text': 'shape_type', 'color': 'red'}
layer = Shapes(
properties=default_properties,
text=text_kwargs,
)
assert layer.text._mode == TextMode.PROPERTY
assert layer.text.values.size == 0
np.testing.assert_allclose(layer.text.color, [1, 0, 0, 1])
# add a shape and check that the appropriate text value was added
layer.add(np.random.random((1, 4, 2)))
np.testing.assert_equal(layer.text.values, ['1.5'])
np.testing.assert_allclose(layer.text.color, [1, 0, 0, 1])
def test_empty_layer_with_text_formatted():
"""Test initializing an empty layer with text defined"""
default_properties = {'shape_type': np.array([1.5], dtype=float)}
layer = Shapes(
properties=default_properties,
text='shape_type: {shape_type:.2f}',
)
assert layer.text._mode == TextMode.FORMATTED
assert layer.text.values.size == 0
# add a shape and check that the appropriate text value was added
layer.add(np.random.random((1, 4, 2)))
np.testing.assert_equal(layer.text.values, ['shape_type: 1.50'])
@pytest.mark.parametrize("properties", [properties_array, properties_list])
def test_text_from_property_value(properties):
"""Test setting text from a property value"""
shape = (10, 4, 2)
np.random.seed(0)
data = 20 * np.random.random(shape)
layer = Shapes(data, properties=copy(properties), text='shape_type')
np.testing.assert_equal(layer.text.values, properties['shape_type'])
@pytest.mark.parametrize("properties", [properties_array, properties_list])
def test_text_from_property_fstring(properties):
"""Test setting text with an f-string from the property value"""
shape = (10, 4, 2)
np.random.seed(0)
data = 20 * np.random.random(shape)
layer = Shapes(
data, properties=copy(properties), text='type: {shape_type}'
)
expected_text = ['type: ' + v for v in properties['shape_type']]
np.testing.assert_equal(layer.text.values, expected_text)
# test updating the text
layer.text = 'type-ish: {shape_type}'
expected_text_2 = ['type-ish: ' + v for v in properties['shape_type']]
np.testing.assert_equal(layer.text.values, expected_text_2)
# copy/paste
layer.selected_data = {0}
layer._copy_data()
layer._paste_data()
expected_text_3 = expected_text_2 + ['type-ish: A']
np.testing.assert_equal(layer.text.values, expected_text_3)
# add shape
layer.selected_data = {0}
new_shape = np.random.random((1, 4, 2))
layer.add(new_shape)
expected_text_4 = expected_text_3 + ['type-ish: A']
np.testing.assert_equal(layer.text.values, expected_text_4)
@pytest.mark.parametrize("properties", [properties_array, properties_list])
def test_set_text_with_kwarg_dict(properties):
text_kwargs = {
'text': 'type: {shape_type}',
'color': [0, 0, 0, 1],
'rotation': 10,
'translation': [5, 5],
'anchor': 'upper_left',
'size': 10,
'visible': True,
}
shape = (10, 4, 2)
np.random.seed(0)
data = 20 * np.random.random(shape)
layer = Shapes(data, properties=copy(properties), text=text_kwargs)
expected_text = ['type: ' + v for v in properties['shape_type']]
np.testing.assert_equal(layer.text.values, expected_text)
for property, value in text_kwargs.items():
if property == 'text':
continue
layer_value = getattr(layer._text, property)
np.testing.assert_equal(layer_value, value)
@pytest.mark.parametrize("properties", [properties_array, properties_list])
def test_text_error(properties):
"""creating a layer with text as the wrong type should raise an error"""
shape = (10, 4, 2)
np.random.seed(0)
data = 20 * np.random.random(shape)
# try adding text as the wrong type
with pytest.raises(TypeError):
Shapes(data, properties=copy(properties), text=123)
def test_refresh_text():
"""Test refreshing the text after setting new properties"""
shape = (10, 4, 2)
np.random.seed(0)
data = 20 * np.random.random(shape)
properties = {'shape_type': ['A'] * shape[0]}
layer = Shapes(data, properties=copy(properties), text='shape_type')
new_properties = {'shape_type': ['B'] * shape[0]}
layer.properties = new_properties
| np.testing.assert_equal(layer.text.values, new_properties['shape_type']) | numpy.testing.assert_equal |
# ------------------------------------------------------------------------------
# Copyright (c) Microsoft
# Licensed under the MIT License.
# Some code is from https://github.com/princeton-vl/pose-ae-train/blob/454d4ba113bbb9775d4dc259ef5e6c07c2ceed54/utils/group.py
# Written by <NAME> (<EMAIL>)
# Modified by <NAME> (<EMAIL>)
# ------------------------------------------------------------------------------
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from munkres import Munkres
import numpy as np
import torch
#tags.append(tag[i, y, x]) = tags.append(tag[i, y, x])
def py_max_match(scores):
m = Munkres()
tmp = m.compute(scores)
tmp = np.array(tmp).astype(np.int32)
return tmp
class Params(object):
def __init__(self, cfg):
self.num_joints = cfg.DATASET.NUM_JOINTS
self.max_num_people = cfg.DATASET.MAX_NUM_PEOPLE
self.detection_threshold = cfg.TEST.DETECTION_THRESHOLD
self.tag_threshold = cfg.TEST.TAG_THRESHOLD
self.use_detection_val = cfg.TEST.USE_DETECTION_VAL
self.ignore_too_much = cfg.TEST.IGNORE_TOO_MUCH
'''
if cfg.DATASET.WITH_CENTER and cfg.TEST.IGNORE_CENTER:
self.num_joints -= 1
if cfg.DATASET.WITH_CENTER and not cfg.TEST.IGNORE_CENTER:
self.joint_order = [
i-1 for i in [18, 1, 2, 3, 4, 5, 6, 7, 12, 13, 8, 9, 10, 11, 14, 15, 16, 17]
]
else:
self.joint_order = [
i-1 for i in [1, 2, 3, 4, 5, 6, 7, 12, 13, 8, 9, 10, 11, 14, 15, 16, 17]
]
'''
with_hier_refine_val = False
def hierarchical_pool(heatmap):
'''
this function is copied from DEKR
:param heatmap:
:return:
'''
pool1 = torch.nn.MaxPool2d(3, 1, 1)
pool2 = torch.nn.MaxPool2d(5, 1, 2)
pool3 = torch.nn.MaxPool2d(7, 1, 3)
map_size = (heatmap.shape[1] + heatmap.shape[2]) / 2.0
if map_size > 300:
maxm = pool3(heatmap[:, :, :])
elif map_size > 200:
maxm = pool2(heatmap[:, :, :])
else:
maxm = pool1(heatmap[:, :, :])
return maxm
class HeatmapParser(object):
def __init__(self, cfg):
self.params = Params(cfg)
self.tag_per_joint = cfg.MODEL.TAG_PER_JOINT
self.pool = torch.nn.MaxPool2d(
cfg.TEST.NMS_KERNEL, 1, cfg.TEST.NMS_PADDING
)
self.detection_threshold = 0.1
self.rjg = cfg.DATASET.RJG_TAG
self.ljg_4 = cfg.DATASET.LJG_WITH_HIER
self.ljg_2 = cfg.DATASET.LJG_CENTER_ONLY
self.flip = cfg.TEST.FLIP_TEST
self.diff_thre = 70.
self.mrm_thre = 0.75
def match_by_de(self, dict, params):
'''
tag_val(1，num_joints,topk,2)
location(1,num_joints,topk,2)
heatmap_val(1,num_joints,topk)
'''
assert isinstance(params, Params), 'params should be class Params()'
tag_t = dict['tag_t'] # [len(rjg)*(thre,2)]
off_2, off_4 = dict['off_t'] # [len(ljg_2or4)*(thre,2or4)]
loc_t = dict['loc_t'] # [18*(thre,2)] vs location(1,num_joints,topk,2)
val_t = dict['val_t'] # [18*(thre)] vs heatmap_val(1,num_joints,topk)
default_ = np.zeros((params.num_joints + 1, 3 + 2))
# (30,x+y+val+4+tag+tag_flip)30*5
joint_dict = {}
tag_dict = {}
center2_key = []
other2_key = [[],[],[],[]]
# store the keys of shouler l,shoulder r, hip l, hip r
center_array = loc_t[-1]
for i,person_center_tag in enumerate(tag_t[-1]):
key = person_center_tag[0]
joint_dict.setdefault(key, np.copy(default_))[-1] = np.array([loc_t[-1][i][0], loc_t[-1][i][1], val_t[-1][i], key, person_center_tag[1]])
tag_dict[key] = [person_center_tag]
center2_key.append(key)
# center2_key = np.array(center2_key)
if center2_key == []:
return np.array([])
for idx_tag, idx in enumerate(self.rjg):
tags = tag_t[idx_tag]
joints = np.concatenate(
(loc_t[idx], val_t[idx][:, None], tags), 1
)
if joints.shape[0] == 0:
continue
grouped_keys = list(joint_dict.keys())[:params.max_num_people]
grouped_tags = [np.mean(tag_dict[i], axis=0) for i in grouped_keys]
# print('mean')
# print(np.mean(tag_dict[0], axis=0))
if params.ignore_too_much \
and len(grouped_keys) == params.max_num_people:
continue
# print('joints:', joints.shape)
# print('tags:', np.array(grouped_tags))
diff = joints[:, None, 3:] - np.array(grouped_tags)[None, :, :]
# joints：（thre，1，tag*2） tags：（1，thre，tag*2）
# print('j_tag',joints[:, None, 3:])
diff_normed = np.linalg.norm(diff, ord=2, axis=2)
diff_saved = np.copy(diff_normed)
if params.use_detection_val:
diff_normed = np.round(diff_normed) * 100 - joints[:, 2:3]
num_added = diff.shape[0]
num_grouped = diff.shape[1]
if num_added > num_grouped:
diff_normed = np.concatenate(
(
diff_normed,
np.zeros((num_added, num_added - num_grouped)) + 1e10
),
axis=1
)
pairs = py_max_match(diff_normed)
for row, col in pairs:
if (
row < num_added
and col < num_grouped
and diff_saved[row][col] < params.tag_threshold
):
key = grouped_keys[col]
joint_dict[key][idx] = joints[row]
tag_dict[key].append(tags[row])
else:
key = tags[row][0]
joint_dict.setdefault(key, np.copy(default_))[idx] = \
joints[row]
tag_dict[key] = [tags[row]]
# other2_key[idx_tag].setdefault(row, key)
if idx_tag < 4:
other2_key[idx_tag].append(key)
# print('joints_cur',joints.shape)
# print('keys after once',len(joint_dict.keys()))
for idx_off, idx in enumerate(self.ljg_2):
center_key = center2_key
center_t = center_array.copy()
center_towards = loc_t[idx] + off_2[idx_off]
joints = np.concatenate(
(loc_t[idx], val_t[idx][:, None], off_2[idx_off]), 1
)
while(center_t.shape[0] > 0 and center_towards.shape[0] > 0):
diff = np.sum(np.square(center_towards[:, None, :] - center_t[None, :, :]), axis=-1)
connection = np.where(diff == diff.min())
if diff[connection[0][0], connection[1][0]] > self.diff_thre ** 2:
break
key = center_key[connection[1][0]]
joint_dict[key][idx] = joints[connection[0][0]]
center_key = np.delete(center_key, connection[1][0], axis=0)
center_t = np.delete(center_t, connection[1][0], axis=0)
center_towards = np.delete(center_towards, connection[0][0], axis=0)
joints = np.delete(joints, connection[0][0], axis=0)
hier_pre = [[], []]
for idx_off, idx in enumerate(self.ljg_4):
ident = 0 + idx_off % 2 if idx_off < 4 else 2 + idx_off % 2
hier2_key = other2_key[ident]
hier_t = loc_t[idx - 2].copy() if idx_off in [0, 1, 4, 5] else np.array(hier_pre[0 + idx_off % 2])
hier_towards = loc_t[idx] + off_4[idx_off][:, :2]
center_towards = loc_t[idx] + off_4[idx_off][:,2:]
'''
center_key = center2_key.copy()
center_t = center_array.copy()
'''
inter_key = []
inter_loc = []
# maintain the relationship between loc with new order and their keys
# tag_used = []
joints = np.concatenate(
(loc_t[idx], val_t[idx][:, None], off_4[idx_off][:, :2]), 1
)
while(hier_t.shape[0] > 0 and hier_towards.shape[0] > 0):
diff = np.sum(np.square(hier_towards[:, None, :] - hier_t[None, :, :]), axis=-1)
connection = np.where(diff == diff.min())
key = hier2_key[connection[1][0]]
joint_dict[key][idx] = joints[connection[0][0]]
inter_key.append(key)
inter_loc.append(joints[connection[0][0]][:2])
hier2_key = np.delete(hier2_key, connection[1][0], axis=0)
hier_t = np.delete(hier_t, connection[1][0], axis=0)
hier_towards = np.delete(hier_towards, connection[0][0], axis=0)
joints = np.delete(joints, connection[0][0], axis=0)
center_towards = np.delete(center_towards, connection[0][0], axis=0)
'''
center_c = np.where(np.array(center_key) == key)
center_key = np.delete(center_key, center_c[0], axis=0)
center_t = np.delete(center_t, center_c[0], axis=0)
'''
left_key = list(set(joint_dict.keys()) ^ set(inter_key))
if not len(left_key)==0:
left_key_li = []
for key in left_key:
left_key_li.append(joint_dict[key][-1][:2])
center_t = np.stack(left_key_li, axis = 0)
while (center_t.shape[0] > 0 and center_towards.shape[0] > 0):
diff = np.sum(np.square(center_towards[:, None, :] - center_t[None, :, :]), axis=-1)
connection = np.where(diff == diff.min())
if diff[connection[0][0],connection[1][0]] > self.diff_thre ** 2:
break
key = left_key[connection[1][0]]
joint_dict[key][idx] = joints[connection[0][0]]
if with_hier_refine_val: # and joints[connection[0][0]][2] >= 0.75:
joint_dict[key][idx - 2][:2] = joints[connection[0][0]][:2] + joints[connection[0][0]][3:]
joint_dict[key][idx - 2][2] = self.params.detection_threshold
inter_key.append(key)
inter_loc.append(joints[connection[0][0]][:2])
left_key = np.delete(left_key, connection[1][0], axis=0)
center_t = np.delete(center_t, connection[1][0], axis=0)
center_towards = np.delete(center_towards, connection[0][0], axis=0)
joints = np.delete(joints, connection[0][0], axis=0)
hier_pre[0 + idx_off % 2] = inter_loc
other2_key[ident] = inter_key
ans = []
for i in joint_dict:
if np.sum(joint_dict[i][:-1, 2]) > 0:
ans.append(joint_dict[i][:-1, :])
ans = | np.array(ans) | numpy.array |
import numpy as np
from bp.Model import Model
# ANN 经典 2 -> 3 -> 6 -> 1
# x = np.linspace(-1,1,20)
x = | np.array([[1, 2], [2, 3], [3, 3], [1, 4], [-1, -2], [-1, -1], [-2, -3], [-3, -2]]) | numpy.array |
import base64
import io
import gdown
import hmmlearn
from hmmlearn import hmm
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import pickle
import streamlit as st
# load data and cache it
@st.cache
def load_data(data: str, interval: float = None):
"""Load data from csv file using pandas."""
df = pd.read_csv(data)
if interval is not None:
df["lags"] = df["lags"] * interval
return df
@st.cache
def load_model(name: str):
"""Load model from pickle."""
with open(name, "rb") as f:
model = pickle.load(f)
return model
def myround(x):
return np.around(x, 6)
def fit_alpha_d(
subset: pd.DataFrame, end1: float, end2: float, log=False
) -> pd.DataFrame:
"""Fit the alpha and D under the 3 different regimes separated by end1 and end2 values."""
subset["loglags"] = np.log10(subset["lags"].values)
if not log:
subset["logtamsd"] = np.log10(subset["tamsd"].values)
else:
subset["logtamsd"] = subset["tamsd"].values
subset = subset.dropna()
r1 = subset[subset["lags"] < end1].copy()
r2 = subset[(subset["lags"] >= end1) & (subset["lags"] <= end2)].copy()
r3 = subset[subset["lags"] > end2].copy()
(a1, d1), cov1 = np.polyfit((r1["loglags"]), (r1["logtamsd"]), 1, cov=True)
sda1, sdd1 = np.sqrt(np.diag(cov1))
(a2, d2), cov2 = np.polyfit((r2["loglags"]), (r2["logtamsd"]), 1, cov=True)
sda2, sdd2 = np.sqrt(np.diag(cov2))
(a3, d3), cov3 = np.polyfit((r3["loglags"]), (r3["logtamsd"]), 1, cov=True)
sda3, sdd3 = np.sqrt(np.diag(cov3))
minimum = np.min(r1["lags"])
maximum = np.max(r3["lags"])
regimes = [f"{minimum}-{end1}", f"{end1}-{end2}", f"{end2}-{maximum}"]
alphas = [
f"{myround(a1)} +/- {myround(sda1)}",
f"{myround(a2)} +/- {myround(sda2)}",
f"{myround(a3)} +/- {myround(sda3)}",
]
ds = [
f"{myround(10**d1)} +/- {myround(sdd1 * np.abs(10**d1) * np.log(10))}",
f"{myround(10**d2)} +/- {myround(sdd2 * np.abs(10**d2) * np.log(10))}",
f"{myround(10**d3)} +/- {myround(sdd3 * np.abs(10**d3) * np.log(10))}",
]
df = pd.DataFrame(
{
"alphas": alphas,
"Ds": ds,
"Regimes": regimes,
}
)
return df
def sample_specific_systematic_error(data: pd.DataFrame):
"""Subtract sample specific systematic error."""
for celline in data["cell_line"].unique():
subset = data[data["cell_line"] == celline].copy()
try:
systematic_error = round(
subset[
(subset["induction_time"] == "fixed")
& (subset["motion_correction_type"] == "cellIDs_corrected")
]
.groupby(["lags"])
.mean()["tamsd"]
.values[0],
4,
)
except:
systematic_error = round(
subset[(subset["induction_time"] == "fixed")]
.groupby(["lags"])
.mean()["tamsd"]
.values[0],
4,
)
data.loc[data["cell_line"] == celline, "tamsd"] = data["tamsd"].apply(
lambda x: x - systematic_error
)
data = data[~(data["induction_time"] == "fixed")]
return data
def download_plot(download_filename: str, download_link_text: str) -> str:
"""Generates a link to download a plot.
Args:
download_filename: filename and extension of file. e.g. myplot.pdf
download_link_text: Text to display for download link.
"""
file = io.BytesIO()
plt.savefig(file, format="pdf", bbox_inches="tight")
file = base64.b64encode(file.getvalue()).decode("utf-8").replace("\n", "")
return f'<a href="data:application/pdf;base64,{file}" download="{download_filename}">{download_link_text}</a>'
def download_csv(
df: pd.DataFrame, download_filename: str, download_link_text: str
) -> str:
"""Generates link to download csv of DataFrame.
Args:
df: DataFrame to download.
download_filename: filename and extension of file. e.g. myplot.pdf
download_link_text: Text to display for download link.
"""
csv = df.to_csv().encode()
b64 = base64.b64encode(csv).decode()
href = f'<a href="data:file/csv;base64,{b64}" download="{download_filename}" target="_blank">{download_link_text}</a>'
return href
def rle(inarray, full=False):
"""Run length encoding. Partial credit to R rle function.
Multi datatype arrays catered for including non Numpy
Returns: tuple (runlengths, startpositions, values)"""
ia = np.asarray(inarray) # convert to numpy array
n = len(ia)
if n == 0:
return (None, None, None)
else:
y = ia[1:] != ia[:-1] # pairwise unequal (string safe)
i = np.append( | np.where(y) | numpy.where |
import numpy as np
coef_ml_drf_0 = np.array([-0.9887517])
vcov_ml_drf_0 = np.array([0.001317148]).reshape(1,1, order='F')
cov_re_ml_drf_0 = np.array([0.2522485]).reshape(1,1, order='F')
scale_ml_drf_0 = np.array([0.2718486])
loglike_ml_drf_0 = np.array([-240.1254])
ranef_mean_ml_drf_0 = np.array([0.04977167])
ranef_condvar_ml_drf_0 = np.array([0.130841])
coef_reml_drf_0 = np.array([-0.9887533])
vcov_reml_drf_0 = np.array([0.001323559]).reshape(1,1, order='F')
cov_re_reml_drf_0 = np.array([0.2524129]).reshape(1,1, order='F')
scale_reml_drf_0 = np.array([0.2733467])
loglike_reml_drf_0 = np.array([-242.5214])
ranef_mean_reml_drf_0 = np.array([0.04964696])
ranef_condvar_reml_drf_0 = np.array([0.1312315])
coef_ml_drf_1 = np.array([-0.9115929])
vcov_ml_drf_1 = np.array([0.01340632]).reshape(1,1, order='F')
cov_re_ml_drf_1 = np.array([0]).reshape(1,1, order='F')
scale_ml_drf_1 = np.array([4.050921])
loglike_ml_drf_1 = np.array([-538.0763])
ranef_mean_ml_drf_1 = np.array([0])
ranef_condvar_ml_drf_1 = np.array([0])
coef_reml_drf_1 = np.array([-0.9115929])
vcov_reml_drf_1 = np.array([0.01345931]).reshape(1,1, order='F')
cov_re_reml_drf_1 = np.array([2.839777e-14]).reshape(1,1, order='F')
scale_reml_drf_1 = np.array([4.066932])
loglike_reml_drf_1 = np.array([-539.3124])
ranef_mean_reml_drf_1 = np.array([2.424384e-14])
ranef_condvar_reml_drf_1 = np.array([2.839777e-14])
coef_ml_drf_2 = np.array([-1.012044,0.9789052])
vcov_ml_drf_2 = np.array([0.00117849,1.458744e-05,1.458744e-05,0.001054926]).reshape(2,2, order='F')
cov_re_ml_drf_2 = np.array([0.1596058]).reshape(1,1, order='F')
scale_ml_drf_2 = np.array([0.2129146])
loglike_ml_drf_2 = np.array([-200.319])
ranef_mean_ml_drf_2 = np.array([0.3197174])
ranef_condvar_ml_drf_2 = np.array([0.09122291])
coef_reml_drf_2 = np.array([-1.012137,0.9790792])
vcov_reml_drf_2 = np.array([0.001190455,1.482666e-05,1.482666e-05,0.001066002]).reshape(2,2, order='F')
cov_re_reml_drf_2 = np.array([0.1595015]).reshape(1,1, order='F')
scale_reml_drf_2 = np.array([0.2154276])
loglike_reml_drf_2 = np.array([-205.275])
ranef_mean_reml_drf_2 = np.array([0.3172978])
ranef_condvar_reml_drf_2 = np.array([0.09164674])
coef_ml_drf_3 = np.array([-1.028053,0.8602685])
vcov_ml_drf_3 = np.array([0.01398831,0.001592619,0.001592619,0.01602274]).reshape(2,2, order='F')
cov_re_ml_drf_3 = np.array([0.8130996]).reshape(1,1, order='F')
scale_ml_drf_3 = np.array([3.100447])
loglike_ml_drf_3 = np.array([-477.1707])
ranef_mean_ml_drf_3 = np.array([-0.2641747])
ranef_condvar_ml_drf_3 = np.array([0.6441656])
coef_reml_drf_3 = np.array([-1.027583,0.8605714])
vcov_reml_drf_3 = np.array([0.01411922,0.001607343,0.001607343,0.01617574]).reshape(2,2, order='F')
cov_re_reml_drf_3 = np.array([0.8117898]).reshape(1,1, order='F')
scale_reml_drf_3 = np.array([3.13369])
loglike_reml_drf_3 = np.array([-479.5354])
ranef_mean_reml_drf_3 = np.array([-0.2614875])
ranef_condvar_reml_drf_3 = np.array([0.6447625])
coef_ml_drf_4 = np.array([-1.005151,-0.003657404,1.054786])
vcov_ml_drf_4 = np.array([0.001190639,-5.327162e-05,5.992985e-05,-5.327162e-05,0.001460303,-2.662532e-05,5.992985e-05,-2.662532e-05,0.00148609]).reshape(3,3, order='F')
cov_re_ml_drf_4 = np.array([0.1703249]).reshape(1,1, order='F')
scale_ml_drf_4 = np.array([0.251763])
loglike_ml_drf_4 = np.array([-231.6389])
ranef_mean_ml_drf_4 = np.array([-0.2063164])
ranef_condvar_ml_drf_4 = np.array([0.0459578])
coef_reml_drf_4 = np.array([-1.005067,-0.003496032,1.054666])
vcov_reml_drf_4 = np.array([0.001206925,-5.4182e-05,6.073475e-05,-5.4182e-05,0.001479871,-2.723494e-05,6.073475e-05,-2.723494e-05,0.001506198]).reshape(3,3, order='F')
cov_re_reml_drf_4 = np.array([0.1705659]).reshape(1,1, order='F')
scale_reml_drf_4 = np.array([0.2556394])
loglike_reml_drf_4 = np.array([-238.761])
ranef_mean_reml_drf_4 = np.array([-0.2055303])
ranef_condvar_reml_drf_4 = np.array([0.04649027])
coef_ml_drf_5 = np.array([-0.8949725,0.08141558,1.052529])
vcov_ml_drf_5 = np.array([0.01677563,0.0008077524,-0.001255011,0.0008077524,0.01719346,0.0009266736,-0.001255011,0.0009266736,0.01608435]).reshape(3,3, order='F')
cov_re_ml_drf_5 = np.array([0.3444677]).reshape(1,1, order='F')
scale_ml_drf_5 = np.array([4.103944])
loglike_ml_drf_5 = np.array([-579.4568])
ranef_mean_ml_drf_5 = np.array([0.08254713])
ranef_condvar_ml_drf_5 = np.array([0.3177935])
coef_reml_drf_5 = np.array([-0.8946164,0.08134261,1.052486])
vcov_reml_drf_5 = np.array([0.0169698,0.0008162714,-0.001268635,0.0008162714,0.01739219,0.0009345538,-0.001268635,0.0009345538,0.01627074]).reshape(3,3, order='F')
cov_re_reml_drf_5 = np.array([0.3420993]).reshape(1,1, order='F')
scale_reml_drf_5 = np.array([4.155737])
loglike_reml_drf_5 = np.array([-582.8377])
ranef_mean_reml_drf_5 = np.array([0.08111449])
ranef_condvar_reml_drf_5 = np.array([0.3160797])
coef_ml_drf_6 = np.array([-0.8885425])
vcov_ml_drf_6 = np.array([0.002443738]).reshape(1,1, order='F')
cov_re_ml_drf_6 = np.array([0.2595201,0.04591071,0.04591071,2.204612]).reshape(2,2, order='F')
scale_ml_drf_6 = np.array([0.243133])
loglike_ml_drf_6 = np.array([-382.551])
ranef_mean_ml_drf_6 = np.array([-0.0597406,0.6037288])
ranef_condvar_ml_drf_6 = np.array([0.2420741,0.2222169,0.2222169,0.4228908]).reshape(2,2, order='F')
coef_reml_drf_6 = np.array([-0.8883881])
vcov_reml_drf_6 = np.array([0.002461581]).reshape(1,1, order='F')
cov_re_reml_drf_6 = np.array([0.2595767,0.04590012,0.04590012,2.204822]).reshape(2,2, order='F')
scale_reml_drf_6 = np.array([0.2453537])
loglike_reml_drf_6 = np.array([-384.6373])
ranef_mean_reml_drf_6 = np.array([-0.05969892,0.6031793])
ranef_condvar_reml_drf_6 = np.array([0.2421365,0.2221108,0.2221108,0.4244443]).reshape(2,2, order='F')
coef_ml_irf_6 = np.array([-0.8874992])
vcov_ml_irf_6 = np.array([0.002445505]).reshape(1,1, order='F')
cov_re_ml_irf_6 = np.array([0.2587624,0,0,2.188653]).reshape(2,2, order='F')
scale_ml_irf_6 = np.array([0.2432694])
loglike_ml_irf_6 = np.array([-382.6581])
coef_reml_irf_6 = np.array([-0.8873394])
vcov_reml_irf_6 = np.array([0.002463375]).reshape(1,1, order='F')
cov_re_reml_irf_6 = np.array([0.2588157,0,0,2.188876]).reshape(2,2, order='F')
scale_reml_irf_6 = np.array([0.2454935])
loglike_reml_irf_6 = np.array([-384.7441])
coef_ml_drf_7 = np.array([-0.9645281])
vcov_ml_drf_7 = | np.array([0.01994]) | numpy.array |
import warnings
import numpy as np
from numpy.linalg import LinAlgError
from scipy.optimize._numdiff import approx_derivative
import scipy.stats as stats
from refnx.util import ErrorProp as EP
from refnx._lib import flatten, approx_hess2
from refnx._lib import unique as f_unique
from refnx.dataset import Data1D
from refnx.analysis import (
is_parameter,
Parameter,
possibly_create_parameter,
is_parameters,
Parameters,
Interval,
PDF,
)
class BaseObjective:
"""Don't necessarily have to use Parameters, could use np.array"""
def __init__(
self,
p,
logl,
logp=None,
fcn_args=(),
fcn_kwds=None,
name=None,
weighted=True,
):
self.name = name
self.parameters = p
self.nvary = len(p)
self._logl = logl
self._logp = logp
self.fcn_args = fcn_args
self.fcn_kwds = {}
# give the BaseObjective a default value, so that it can be used in a
# GlobalObjective
self.weighted = weighted
if fcn_kwds is not None:
self.fcn_kwds = fcn_kwds
def setp(self, pvals):
"""
Set the parameters from pvals
Parameters
----------
pvals : np.ndarray
Array containing the values to be tested.
"""
self.parameters[:] = pvals
def nll(self, pvals=None):
"""
Negative log-likelihood function
Parameters
----------
pvals : np.ndarray
Array containing the values to be tested.
Returns
-------
nll : float
negative log-likelihood
"""
vals = self.parameters
if pvals is not None:
vals = pvals
return -self.logl(vals)
def logp(self, pvals=None):
"""
Log-prior probability function
Parameters
----------
pvals : np.ndarray
Array containing the values to be tested.
Returns
-------
logp : float
log-prior probability
"""
vals = self.parameters
if pvals is not None:
vals = pvals
if callable(self._logp):
return self._logp(vals, *self.fcn_args, **self.fcn_kwds)
return 0
def logl(self, pvals=None):
"""
Log-likelihood probability function
Parameters
----------
pvals : np.ndarray
Array containing the values to be tested.
Returns
-------
logl : float
log-likelihood probability.
"""
vals = self.parameters
if pvals is not None:
vals = pvals
return self._logl(vals, *self.fcn_args, **self.fcn_kwds)
def logpost(self, pvals=None):
"""
Log-posterior probability function
Parameters
----------
pvals : np.ndarray
Array containing the values to be tested.
Returns
-------
logpost : float
log-probability.
Notes
-----
The log probability is the sum is the sum of the log-prior and
log-likelihood probabilities. Does not set the parameter attribute.
"""
vals = self.parameters
if pvals is not None:
vals = pvals
logpost = self.logp(vals)
if not np.isfinite(logpost):
return -np.inf
logpost += self.logl(vals)
return logpost
def nlpost(self, pvals=None):
"""
Negative log-posterior function
Parameters
----------
pvals : np.ndarray
Array containing the values to be tested.
Returns
-------
nlpost : float
negative log-posterior
"""
return -self.logpost(pvals)
def varying_parameters(self):
"""
Returns
-------
varying_parameters : np.ndarray
The parameters varying in this objective function.
"""
return self.parameters
def covar(self, target="nll"):
"""
Estimates a covariance matrix based on numerical differentiation
of either the negative log-likelihood or negative log-posterior
probabilities.
Parameters
----------
target : str, {"nll", "nlpost"}
Returns
-------
covar : np.ndarray
The covariance matrix for the fitting system
Notes
-----
Estimation of a covariance matrix can be susceptible to numeric
instabilities. Critically evaluate the matrix before further use.
"""
_pvals = np.array(self.varying_parameters())
if target == "nll":
fn = self.nll
elif target == "nlpost":
fn = self.nlpost
try:
# from statsmodels
# the output from this for the test in test_objective.covar
# is very similar to numdifftools.Hessian, or a chained version
# of approx_derivative
hess = approx_hess2(_pvals, fn)
covar = np.linalg.inv(hess)
except LinAlgError:
sz = np.size(_pvals, 0)
covar = np.full((sz, sz), np.inf)
finally:
self.setp(_pvals)
return covar
class Objective(BaseObjective):
"""
Objective function for using with curvefitters such as
`refnx.analysis.curvefitter.CurveFitter`.
Parameters
----------
model : refnx.analysis.Model
the generative model function. One can also provide an object that
inherits `refnx.analysis.Model`.
data : refnx.dataset.Data1D
data to be analysed.
lnsigma : float or refnx.analysis.Parameter, optional
Used if the experimental uncertainty (`data.y_err`) underestimated by
a constant fractional amount. The experimental uncertainty is modified
as:
`s_n**2 = y_err**2 + exp(lnsigma * 2) * model**2`
See `Objective.logl` for more details.
use_weights : bool
use experimental uncertainty in calculation of residuals and
logl, if available. If this is set to False, then you should also
set `self.lnsigma.vary = False`, it will have no effect on the fit.
transform : callable, optional
the model, data and data uncertainty are transformed by this
function before calculating the likelihood/residuals. Has the
signature `transform(data.x, y, y_err=None)`, returning the tuple
(`transformed_y, transformed_y_err`).
logp_extra : callable, optional
user specifiable log-probability term. This contribution is in
addition to the log-prior term of the `model` parameters, and
`model.logp`, as well as the log-likelihood of the `data`. Has
signature:
`logp_extra(model, data)`. The `model` will already possess
updated parameters. Beware of including the same log-probability
terms more than once.
auxiliary_params : {sequence, Parameters}, optional
Extra Parameter objects that are involved with curvefitting, but
aren't directly included as part of the `model`. See notes for more
details.
name : str
Name for the objective.
Notes
-----
For parallelisation `logp_extra` needs to be picklable.
`auxiliary_params` are included in calculating the `Objective.logp`
term, are present in `Objective.varying_parameters()`, and are modified by
Curvefitter during an analysis. Their main purpose is to aid in making
constraints in models.
"""
def __init__(
self,
model,
data,
lnsigma=None,
use_weights=True,
transform=None,
logp_extra=None,
auxiliary_params=(),
name=None,
):
self.model = model
# should be a Data1D instance
if isinstance(data, Data1D):
self.data = data
else:
self.data = Data1D(data=data)
self.lnsigma = lnsigma
if lnsigma is not None:
self.lnsigma = possibly_create_parameter(lnsigma, "lnsigma")
if isinstance(auxiliary_params, Parameters):
self.auxiliary_params = auxiliary_params
else:
self.auxiliary_params = Parameters(auxiliary_params)
self._use_weights = use_weights
self.transform = transform
self.logp_extra = logp_extra
self.name = name
if name is None:
self.name = id(self)
def __str__(self):
s = ["{:_>80}".format("")]
s.append("Objective - {0}".format(self.name))
# dataset name
if self.data.name is None:
s.append("Dataset = {0}".format(self.data))
else:
s.append("Dataset = {0}".format(self.data.name))
s.append("datapoints = {0}".format(self.npoints))
s.append("chi2 = {0}".format(self.chisqr()))
s.append("Weighted = {0}".format(self.weighted))
s.append("Transform = {0}".format(self.transform))
s.append(str(self.parameters))
return "\n".join(s)
def __repr__(self):
return (
"Objective({model!r}, {data!r},"
" lnsigma={lnsigma!r},"
" use_weights={_use_weights},"
" transform={transform!r},"
" logp_extra={logp_extra!r},"
" name={name!r})".format(**self.__dict__)
)
@property
def weighted(self):
"""
**bool** Does the data have weights (`data.y_err`), and is the
objective using them?
"""
return self.data.weighted and self._use_weights
@weighted.setter
def weighted(self, use_weights):
self._use_weights = bool(use_weights)
@property
def npoints(self):
"""
**int** the number of points in the dataset.
"""
return self.data.y.size
def varying_parameters(self):
"""
Returns
-------
varying_parameters : refnx.analysis.Parameters
The varying Parameter objects allowed to vary during the fit.
"""
# create and return a Parameters object because it has the
# __array__ method, which allows one to quickly get numerical values.
p = Parameters()
p.data = list(f_unique(p for p in flatten(self.parameters) if p.vary))
return p
def _data_transform(self, model=None):
"""
Returns
-------
y, y_err, model: tuple of np.ndarray
The y data, its uncertainties, and the model, all put through the
transform.
"""
x = self.data.x
y = self.data.y
y_err = 1.0
if self.weighted:
y_err = self.data.y_err
if self.transform is None:
return y, y_err, model
else:
if model is not None:
model, _ = self.transform(x, model)
y, y_err = self.transform(x, y, y_err)
if self.weighted:
return y, y_err, model
else:
return y, 1, model
def generative(self, pvals=None):
"""
Calculate the generative (dependent variable) function associated with
the model.
Parameters
----------
pvals : array-like or refnx.analysis.Parameters
values for the varying or entire set of parameters
Returns
-------
model : np.ndarray
"""
self.setp(pvals)
return self.model(self.data.x, x_err=self.data.x_err)
def residuals(self, pvals=None):
"""
Calculates the residuals for a given fitting system.
Parameters
----------
pvals : array-like or refnx.analysis.Parameters
values for the varying or entire set of parameters
Returns
-------
residuals : np.ndarray
Residuals, `(data.y - model) / y_err`.
"""
self.setp(pvals)
model = self.model(self.data.x, x_err=self.data.x_err)
# TODO add in varying parameter residuals? (z-scores...)
y, y_err, model = self._data_transform(model)
if self.lnsigma is not None:
s_n = np.sqrt(
y_err * y_err + np.exp(2 * float(self.lnsigma)) * model * model
)
else:
s_n = y_err
return (y - model) / s_n
def chisqr(self, pvals=None):
"""
Calculates the chi-squared value for a given fitting system.
Parameters
----------
pvals : array-like or refnx.analysis.Parameters
values for the varying or entire set of parameters
Returns
-------
chisqr : np.ndarray
Chi-squared value, `np.sum(residuals**2)`.
"""
# TODO reduced chisqr? include z-scores for parameters? DOF?
self.setp(pvals)
res = self.residuals(None)
return np.sum(res * res)
@property
def parameters(self):
"""
:class:`refnx.analysis.Parameters`, all the Parameters contained in the
fitting system.
"""
if is_parameter(self.lnsigma):
return self.lnsigma | self.auxiliary_params | self.model.parameters
elif len(self.auxiliary_params):
return self.auxiliary_params | self.model.parameters
else:
return self.model.parameters
def setp(self, pvals):
"""
Set the parameters from pvals.
Parameters
----------
pvals : array-like or refnx.analysis.Parameters
values for the varying or entire set of parameters
"""
if pvals is None:
return
# set here rather than delegating to a Parameters
# object, because it may not necessarily be a
# Parameters object
_varying_parameters = self.varying_parameters()
if len(pvals) == len(_varying_parameters):
for idx, param in enumerate(_varying_parameters):
param.value = pvals[idx]
return
# values supplied are enough to specify all parameter values
# even those that are repeated
flattened_parameters = list(flatten(self.parameters))
if len(pvals) == len(flattened_parameters):
for idx, param in enumerate(flattened_parameters):
param.value = pvals[idx]
return
raise ValueError(
f"Incorrect number of values supplied ({len(pvals)})"
f", supply either the full number of parameters"
f" ({len(flattened_parameters)}, or only the varying"
f" parameters ({len(_varying_parameters)})."
)
def prior_transform(self, u):
"""
Calculate the prior transform of the system.
Transforms uniform random variates in the unit hypercube,
`u ~ uniform[0.0, 1.0)`, to the parameter space of interest, according
to the priors on the varying parameters.
Parameters
----------
u : array-like
Size of the varying parameters
Returns
-------
pvals : array-like
Scaled parameter values
Notes
-----
If a parameter has bounds, `x ~ Unif[-10, 10)` then the scaling from
`u` to `x` is done as follows:
.. code-block:: python
x = 2. * u - 1. # scale and shift to [-1., 1.)
x *= 10. # scale to [-10., 10.)
"""
var_pars = self.varying_parameters()
pvals = np.empty(len(var_pars), dtype=np.float64)
for i, var_par in enumerate(var_pars):
pvals[i] = var_par.bounds.invcdf(u[i])
return pvals
def logp(self, pvals=None):
"""
Calculate the log-prior of the system
Parameters
----------
pvals : array-like or refnx.analysis.Parameters
values for the varying or entire set of parameters
Returns
-------
logp : float
log-prior probability
Notes
-----
The log-prior is calculated as:
.. code-block:: python
logp = np.sum(param.logp() for param in
self.varying_parameters())
"""
self.setp(pvals)
logp = np.sum(
[
param.logp()
for param in f_unique(
p for p in flatten(self.parameters) if p.vary
)
]
)
if not np.isfinite(logp):
return -np.inf
return logp
def logl(self, pvals=None):
"""
Calculate the log-likelhood of the system
The major component of the log-likelhood probability is from the data.
Extra potential terms are added on from the Model, `self.model.logp`,
and the user specifiable `logp_extra` function.
Parameters
----------
pvals : array-like or refnx.analysis.Parameters
values for the varying or entire set of parameters
Returns
-------
logl : float
log-likelihood probability
Notes
-----
The log-likelihood is calculated as:
.. code-block:: python
logl = -0.5 * np.sum(((y - model) / s_n)**2
+ np.log(2 * pi * s_n**2))
logp += self.model.logp()
logp += self.logp_extra(self.model, self.data)
where
.. code-block:: python
s_n**2 = y_err**2 + exp(2 * lnsigma) * model**2
"""
self.setp(pvals)
model = self.model(self.data.x, x_err=self.data.x_err)
logl = 0.0
y, y_err, model = self._data_transform(model)
if self.lnsigma is not None:
var_y = (
y_err * y_err + np.exp(2 * float(self.lnsigma)) * model * model
)
else:
var_y = y_err ** 2
# TODO do something sensible if data isn't weighted
if self.weighted:
logl += np.log(2 * np.pi * var_y)
logl += (y - model) ** 2 / var_y
# nans play havoc
if np.isnan(logl).any():
raise RuntimeError("Objective.logl encountered a NaN.")
# add on extra 'potential' terms from the model.
extra_potential = self.model.logp()
if self.logp_extra is not None:
extra_potential += self.logp_extra(self.model, self.data)
return -0.5 * np.sum(logl) + extra_potential
def nll(self, pvals=None):
"""
Negative log-likelihood function
Parameters
----------
pvals : array-like or refnx.analysis.Parameters
values for the varying or entire set of parameters
Returns
-------
nll : float
negative log-likelihood
"""
self.setp(pvals)
return -self.logl()
def logpost(self, pvals=None):
"""
Calculate the log-probability of the curvefitting system
Parameters
----------
pvals : array-like or refnx.analysis.Parameters
values for the varying or entire set of parameters
Returns
-------
logpost : float
log-probability
Notes
-----
The overall log-probability is the sum of the log-prior and
log-likelihood. The log-likelihood is not calculated if the log-prior
is impossible (`logp == -np.inf`).
"""
self.setp(pvals)
logpost = self.logp()
# only calculate the probability if the parameters have finite
# log-prior
if not np.isfinite(logpost):
return -np.inf
logpost += self.logl()
return logpost
def covar(self, target="residuals"):
"""
Estimates the covariance matrix of the Objective.
Parameters
----------
target : {"residuals", "nll", "nlpost"}
Specifies what approach should be used to estimate covariance.
Returns
-------
covar : np.ndarray
Covariance matrix
Notes
-----
For most purposes the Jacobian of the `'residuals'` should be used to
calculate the covariance matrix, estimated as J.T x J.
If an Objective cannot calculate residuals then the covariance matrix
can be estimated by inverting a Hessian matrix created from either the
`'nll'` or `'nlpost'` methods.
The default `'residuals'` approach falls back to `'nll'` if a problem
is experienced.
The default `'residuals'` setting is preferred as the other settings
can sometimes experience instabilities during Hessian estimation with
numerical differentiation.
"""
if target == "residuals":
try:
covar = self._covar_from_residuals()
except Exception:
# fallback to "nll"
target = "nll"
if target in ["nll", "nlpost"]:
covar = super().covar(target)
pvar = np.diagonal(covar).copy()
psingular = np.where(pvar == 0)[0]
if len(psingular) > 0:
var_params = self.varying_parameters()
singular_params = [var_params[ps] for ps in psingular]
raise LinAlgError(
"The following Parameters have no effect on"
" Objective.residuals, please consider fixing"
" them.\n" + repr(singular_params)
)
return covar
def _covar_from_residuals(self):
_pvals = np.array(self.varying_parameters())
used_residuals_scaler = False
def fn_scaler(vals):
return np.squeeze(self.residuals(_pvals * vals))
try:
# we should be able to calculate a Jacobian for a parameter whose
# value is zero. However, the scaling approach won't work.
# This will force Jacobian calculation by unscaled parameters
if np.any(_pvals == 0):
raise FloatingPointError()
with np.errstate(invalid="raise"):
jac = approx_derivative(fn_scaler, np.ones_like(_pvals))
used_residuals_scaler = True
except FloatingPointError:
jac = approx_derivative(self.residuals, _pvals)
finally:
# using approx_derivative changes the state of the objective
# parameters have to make sure they're set at the end
self.setp(_pvals)
# need to create this because GlobalObjective may not have
# access to all the datapoints being fitted.
n_datapoints = np.size(jac, 0)
# covar = J.T x J
# from scipy.optimize.minpack.py
# eliminates singular parameters
_, s, VT = np.linalg.svd(jac, full_matrices=False)
threshold = np.finfo(float).eps * max(jac.shape) * s[0]
s = s[s > threshold]
VT = VT[: s.size]
covar = np.dot(VT.T / s ** 2, VT)
if used_residuals_scaler:
# unwind the scaling.
covar = covar * np.atleast_2d(_pvals) * np.atleast_2d(_pvals).T
scale = 1.0
# scale by reduced chi2 if experimental uncertainties weren't used.
if not (self.weighted):
scale = self.chisqr() / (
n_datapoints - len(self.varying_parameters())
)
return covar * scale
def pgen(self, ngen=1000, nburn=0, nthin=1):
"""
Yield random parameter vectors from the MCMC samples. The objective
state is not altered.
Parameters
----------
ngen : int, optional
the number of samples to yield. The actual number of samples
yielded is `min(ngen, chain.size)`
nburn : int, optional
discard this many steps from the start of the chain
nthin : int, optional
only accept every `nthin` samples from the chain
Yields
------
pvec : np.ndarray
A randomly chosen parameter vector
"""
yield from self.parameters.pgen(ngen=ngen, nburn=nburn, nthin=nthin)
def plot(self, pvals=None, samples=0, parameter=None, fig=None):
"""
Plot the data/model.
Requires matplotlib be installed.
Parameters
----------
pvals : np.ndarray, optional
Numeric values for the Parameter's that are varying
samples: number
If the objective has been sampled, how many samples you wish to
plot on the graph.
parameter: refnx.analysis.Parameter
Creates an interactive plot for the Parameter in Jupyter. Requires
ipywidgets be installed. Use with %matplotlib notebook/qt.
fig: Figure instance, optional
If `fig` is not supplied then a new figure is created. Otherwise
the graph is created on the current axes on the supplied figure.
Returns
-------
fig, ax : :class:`matplotlib.Figure`, :class:`matplotlib.Axes`
`matplotlib` figure and axes objects.
"""
self.setp(pvals)
if fig is None:
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
else:
ax = fig.gca()
y, y_err, model = self._data_transform(model=self.generative())
# add the data (in a transformed fashion)
if self.weighted:
ax.errorbar(
self.data.x,
y,
y_err,
color="blue",
label=self.data.name,
marker="o",
ms=3,
lw=0,
elinewidth=2,
)
else:
ax.scatter(self.data.x, y, color="blue", s=3, label=self.data.name)
if samples > 0:
saved_params = np.array(self.parameters)
# Get a number of chains, chosen randomly, set the objective,
# and plot the model.
for pvec in self.pgen(ngen=samples):
y, y_err, model = self._data_transform(
model=self.generative(pvec)
)
ax.plot(self.data.x, model, color="k", alpha=0.01)
# put back saved_params
self.setp(saved_params)
# add the fit
generative_plot = ax.plot(self.data.x, model, color="red", zorder=20)
if parameter is None:
return fig, ax
# create an interactive plot in a Jupyter notebook.
def f(val):
if parameter is not None:
parameter.value = float(val)
y, y_err, model = self._data_transform(model=self.generative())
generative_plot[0].set_data(self.data.x, model)
fig.canvas.draw()
import ipywidgets
return fig, ax, ipywidgets.interact(f, val=float(parameter))
def corner(self, **kwds):
"""
Corner plot of the chains belonging to the Parameters.
Requires the `corner` and `matplotlib` packages.
Parameters
----------
kwds: dict
passed directly to the `corner.corner` function
Returns
-------
fig : :class:`matplotlib.Figure` object.
"""
import corner
var_pars = self.varying_parameters()
chain = np.array([par.chain for par in var_pars])
labels = [par.name for par in var_pars]
chain = chain.reshape(len(chain), -1).T
kwds["labels"] = labels
kwds["quantiles"] = [0.16, 0.5, 0.84]
return corner.corner(chain, **kwds)
class GlobalObjective(Objective):
"""
Global Objective function for simultaneous fitting with
`refnx.analysis.CurveFitter`
Parameters
----------
objectives : list
list of :class:`refnx.analysis.Objective` objects
"""
def __init__(self, objectives):
self.objectives = objectives
weighted = [objective.weighted for objective in objectives]
self._weighted = np.array(weighted, dtype=bool)
if len(np.unique(self._weighted)) > 1:
raise ValueError(
"All the objectives must be either weighted or"
" unweighted, you cannot have a mixture."
)
def __str__(self):
s = ["{:_>80}".format("\n")]
s.append("--Global Objective--")
for obj in self.objectives:
s.append(str(obj))
s.append("\n")
return "\n".join(s)
def __repr__(self):
return "GlobalObjective({0})".format(repr(self.objectives))
@property
def weighted(self):
"""
**bool** do all the datasets have y_err, and are all the objectives
wanting to use weights?
"""
return self._weighted.all()
@property
def npoints(self):
"""
**int** number of data points in all the objectives.
"""
npoints = 0
for objective in self.objectives:
npoints += objective.npoints
return npoints
def residuals(self, pvals=None):
"""
Concatenated residuals for each of the
:meth:`refnx.analysis.Objective.residuals`.
Parameters
----------
pvals : array-like or refnx.analysis.Parameters
values for the varying or entire set of parameters
Returns
-------
residuals : np.ndarray
Concatenated :meth:`refnx.analysis.Objective.residuals`
"""
self.setp(pvals)
residuals = []
for objective in self.objectives:
residual = objective.residuals()
residuals.append(residual)
return np.concatenate(residuals)
@property
def parameters(self):
"""
:class:`refnx.analysis.Parameters` associated with all the objectives.
"""
# TODO this is probably going to be slow.
# cache and update strategy?
p = Parameters(name="global fitting parameters")
for objective in self.objectives:
p.append(objective.parameters)
return p
def logp(self, pvals=None):
"""
Calculate the log-prior of the system
Parameters
----------
pvals : array-like or refnx.analysis.Parameters, optional
values for the varying or entire set of parameters
Returns
-------
logp : float
log-prior probability
"""
self.setp(pvals)
logp = 0.0
for objective in self.objectives:
logp += objective.logp()
# shortcut if one of the priors is impossible
if not np.isfinite(logp):
return -np.inf
return logp
def logl(self, pvals=None):
"""
Calculate the log-likelhood of the system
Parameters
----------
pvals : array-like or refnx.analysis.Parameters
values for the varying or entire set of parameters
Returns
-------
logl : float
log-likelihood probability
"""
self.setp(pvals)
logl = 0.0
for objective in self.objectives:
logl += objective.logl()
return logl
def plot(self, pvals=None, samples=0, parameter=None, fig=None):
"""
Plot the data/model for all the objectives in the GlobalObjective.
Matplotlib must be installed to use this method.
Parameters
----------
pvals : np.ndarray, optional
Numeric values for the Parameter's that are varying
samples: number, optional
If the objective has been sampled, how many samples you wish to
plot on the graph.
parameter: refnx.analysis.Parameter, optional
Creates an interactive plot for the Parameter in Jupyter. Requires
ipywidgets be installed. Use with %matplotlib notebook/qt.
fig: Figure instance, optional
If `fig` is not supplied then a new figure is created. Otherwise
the graph is created on the current axes on the supplied figure.
Returns
-------
fig, ax : :class:`matplotlib.Figure`, :class:`matplotlib.Axes`
`matplotlib` figure and axes objects.
"""
self.setp(pvals)
if fig is None:
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
else:
ax = fig.gca()
generative_plots = []
if samples > 0:
saved_params = np.array(self.parameters)
# Get a number of chains, chosen randomly, set the objectives,
# and plot the model.
for pvec in self.pgen(ngen=samples):
self.setp(pvec)
for objective in self.objectives:
y, y_err, model = objective._data_transform(
model=objective.generative()
)
ax.plot(objective.data.x, model, color="k", alpha=0.01)
# put back saved_params
self.setp(saved_params)
for objective in self.objectives:
# add the data (in a transformed fashion)
y, y_err, model = objective._data_transform(
model=objective.generative()
)
if objective.weighted:
ax.errorbar(
objective.data.x,
y,
y_err,
label=objective.data.name,
ms=3,
lw=0,
elinewidth=2,
marker="o",
)
else:
ax.scatter(objective.data.x, y, label=objective.data.name)
# add the fit
generative_plots.append(
ax.plot(objective.data.x, model, color="r", lw=1.5, zorder=20)[
0
]
)
if parameter is None:
return fig, ax
# create an interactive plot in a Jupyter notebook.
def f(val):
if parameter is not None:
parameter.value = float(val)
for i, objective in enumerate(self.objectives):
y, y_err, model = objective._data_transform(
model=objective.generative()
)
generative_plots[i].set_data(objective.data.x, model)
fig.canvas.draw()
import ipywidgets
return fig, ax, ipywidgets.interact(f, val=float(parameter))
return fig, ax
class Transform:
r"""
Mathematical transforms of numeric data.
Parameters
----------
form : None or str
One of:
- 'lin'
No transform is made
- 'logY'
log10 transform
- 'YX4'
YX**4 transform
- 'YX2'
YX**2 transform
- None
No transform is made
Notes
-----
You ask for a transform to be carried out by calling the Transform object
directly.
>>> x = np.linspace(0.01, 0.1, 11)
>>> y = np.linspace(100, 1000, 11)
>>> y_err = np.sqrt(y)
>>> t = Transform('logY')
>>> ty, te = t(x, y, y_err)
>>> ty
array([2. , 2.2787536 , 2.44715803, 2.56820172, 2.66275783,
2.74036269, 2.80617997, 2.86332286, 2.91381385, 2.95904139,
3. ])
"""
def __init__(self, form):
types = [None, "lin", "logY", "YX4", "YX2"]
self.form = None
if form in types:
self.form = form
else:
raise ValueError(
"The form parameter must be one of [None, 'lin',"
" 'logY', 'YX4', 'YX2']"
)
def __repr__(self):
return "Transform({0})".format(repr(self.form))
def __call__(self, x, y, y_err=None):
"""
Calculate the transformed data
Parameters
----------
x : array-like
x-values
y : array-like
y-values
y_err : array-like
Uncertainties in `y` (standard deviation)
Returns
-------
yt, et : tuple
The transformed data
Examples
--------
>>> x = np.linspace(0.01, 0.1, 11)
>>> y = np.linspace(100, 1000, 11)
>>> y_err = np.sqrt(y)
>>> t = Transform('logY')
>>> ty, te = t(x, y, y_err)
>>> ty
array([2. , 2.2787536 , 2.44715803, 2.56820172, 2.66275783,
2.74036269, 2.80617997, 2.86332286, 2.91381385, 2.95904139,
3. ])
"""
return self.__transform(x, y, y_err=y_err)
def __transform(self, x, y, y_err=None):
r"""
Transform the data passed in
Parameters
----------
x : array-like
y : array-like
y_err : array-like
Returns
-------
yt, et : tuple
The transformed data
"""
if y_err is None:
etemp = np.ones_like(y)
else:
etemp = y_err
if self.form in ["lin", None]:
yt = np.copy(y)
et = np.copy(etemp)
elif self.form == "logY":
yt, et = EP.EPlog10(y, etemp)
if not np.isfinite(yt).all():
warnings.warn(
"Some of the transformed data was non-finite."
" Please check your datasets for points with zero or"
" negative values.",
RuntimeWarning,
)
elif self.form == "YX4":
yt = y * np.power(x, 4)
et = etemp * | np.power(x, 4) | numpy.power |
import matplotlib.pyplot as plt
import numpy as np
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans
def fake_data(num_groups, shape):
assert len(shape) == 2
# create mean and covariance matrix for each group
means = [create_mean(shape[1]) for i in range(num_groups)]
covs = [create_cov(shape[1]) for i in range(num_groups)]
y = create_target(num_groups, shape[0])
distributions = []
for m, c in zip(means, covs):
dist = np.random.multivariate_normal(m, c, shape[0]//num_groups)
distributions.append(dist)
distributions = tuple(distributions)
final_array = np.concatenate(distributions)
names = ['group'+str(i) for i in range(num_groups)]
return {'data': final_array, 'target': y, 'names': names}
def create_target(num_groups, samples):
y = [i for i in range(num_groups) for r in range(samples//num_groups)]
y = np.array(y)
return y
def create_mean(dimension):
mean = [np.random.rand() for i in range(dimension)]
return mean
def create_cov(dimension):
cov = []
for i in range(dimension):
sub_cov = [0 for i in range(dimension)]
sub_cov[i] = | np.random.rand() | numpy.random.rand |
import numpy as np
import tensorflow as tf
from scipy.ndimage.interpolation import map_coordinates
from scipy.interpolate import interp2d
from itertools import product
from PIL import Image
from multiprocessing import cpu_count
from segmentpy.tf114.augmentation import random_aug
from segmentpy.tf114.filter import *
from segmentpy.tf114.util import load_img, check_raw_gt_pair
import os
# logging
import logging
from segmentpy.tf114 import log
logger = log.setup_custom_logger(__name__)
logger.setLevel(logging.INFO)
def inputpipeline_V2(batch_size, ncores=cpu_count(),
suffix='', augmentation=False, mode='regression',
):
"""
tensorflow tf.data input pipeline based helper that return image and label at once
input:
-------
batch_size: (int) number of images per batch before update parameters
output:
-------
inputs: (dict) output of this func, but inputs of the neural network. A dictionary of img, label and the iterator
initialization operation
"""
logger.warn('The tf.py_func() will be deprecated at TF2.0, replaced by tf.function() please change later the inputpipeline() in input.py')
is_training = True if suffix in ['train', 'cv', 'test'] else False
if is_training:
# placeholder for list fo files
with tf.name_scope('input_pipeline_' + suffix):
fnames_ph = tf.placeholder(tf.string, shape=[None], name='fnames_ph')
patch_size_ph = tf.placeholder(tf.int32, shape=[None], name='patch_size_ph')
x_coord_ph = tf.placeholder(tf.int32, shape=[None], name='x_coord_ph')
y_coord_ph = tf.placeholder(tf.int32, shape=[None], name='y_coord_ph')
correction_ph = tf.placeholder(tf.float32, shape=[None], name='correction_ph')
max_nb_cls_ph = tf.placeholder(tf.int32, shape=[None], name='max_nb_cls_ph')
stretch_ph = tf.placeholder(tf.float32, shape=[None], name='stretch_ph')
# init and shuffle list of files
batch = tf.data.Dataset.from_tensor_slices((fnames_ph, patch_size_ph, x_coord_ph, y_coord_ph,
correction_ph, max_nb_cls_ph, stretch_ph))
# batch = batch.shuffle(buffer_size=tf.shape(fnames_ph)[0])
batch = batch.shuffle(buffer_size=tf.cast(tf.shape(fnames_ph)[0], tf.int64))
# tf.print(tf.cast(tf.shape(fnames_ph)[0], tf.int64))
# batch = batch.shuffle(buffer_size=batch_size)
# note: above line is no more necessary if we shuffle pythonically the fnames at the beginning of epoch
# note: the above line raise 'buffer_size must be greater than zero.' due to the number of image greater than max of int64
# read data
if mode == 'regression':
raise NotImplementedError('The regression is no more supported')
elif mode == 'classification':
batch = batch.map(_pyfn_classification_parser_wrapper_V2, num_parallel_calls=ncores)
elif mode == 'feature_extractors':
batch = batch.map(_pyfn_classification_parser_wrapper_weka, num_parallel_calls=ncores)
raise NotImplementedError
# random augment data
if augmentation:
batch = batch.map(_pyfn_aug_wrapper, num_parallel_calls=ncores)
# shuffle and prefetch batch
batch = batch.shuffle(batch_size).batch(batch_size, drop_remainder=True).prefetch(ncores).repeat()
# todo: prefetch_to_device
# batch = batch.apply(tf.data.experimental.prefetch_to_device('/device:GPU:0'))
# construct iterator
it = tf.data.Iterator.from_structure(
batch.output_types,
batch.output_shapes
# (tf.TensorShape([None, None, None, 1]), tf.TensorShape([None, None, None, 3]))
)
iter_init_op = it.make_initializer(batch, name='iter_init_op')
# get next img and label
X_it, y_it = it.get_next()
# X_it = tf.reshape(X_it, [batch_size, patch_size, patch_size, 1])
# y_it = tf.reshape(X_it, [batch_size, patch_size, patch_size, 1])
# X_it = tf.reshape(X_it, [batch_size, patch_size, patch_size, -1])
# y_it = tf.reshape(X_it, [batch_size, patch_size, patch_size, -1])
# dict
inputs = {'img': X_it,
'label': y_it,
'iterator_init_op': iter_init_op,
'fnames_ph': fnames_ph,
'patch_size_ph': patch_size_ph,
'x_coord_ph': x_coord_ph,
'y_coord_ph': y_coord_ph,
'correction_ph': correction_ph,
'max_nb_cls_ph': max_nb_cls_ph,
'stretch_ph': stretch_ph,
}
else:
raise NotImplementedError('Inference input need to be debugged')
return inputs
def _pyfn_classification_parser_wrapper_V2(fname, patch_size, x_coord, y_coord,
correction, max_nb_cls, stretch):
"""
input:
-------
filename: (tf.data.Dataset) Tensors of strings
output:
-------
function: (function) tensorflow's pythonic function with its arguements
"""
return tf.py_func(parse_h5_one_hot_V2, #wrapped pythonic function
[fname, patch_size, x_coord, y_coord, correction, max_nb_cls, stretch], #fixme: max number of class should be automatic
[tf.float32, tf.int32] #[output, output] dtype
)
def _pyfn_classification_parser_wrapper_V3(fname, patch_size, x_coord, y_coord,
):
"""
input:
-------
filename: (tf.data.Dataset) Tensors of strings
output:
-------
function: (function) tensorflow's pythonic function with its arguements
"""
return tf.py_func(parse_h5_one_hot_V3, #wrapped pythonic function
[fname, patch_size, x_coord, y_coord],
[tf.float32, tf.int32] #[output, output] dtype
)
def _pyfn_aug_wrapper(X_img, y_img):
"""
input:
-------
filename: (tf.data.Dataset) Tensors of strings
output:
-------
function: (function) tensorflow's pythonic function with its arguements
"""
return tf.py_func(random_aug,
[X_img, y_img],
[tf.float32, tf.int32] #[output, output] dtype
)
def parse_h5_one_hot_V2(fname, window_size, x_coord, y_coord, correction=1e3, impose_nb_cls=3, stretch=2.0):
try:
img = np.asarray(Image.open(fname.decode('utf8')))
label = np.asarray(Image.open(fname.decode('utf8').replace('.tif', '_label.tif')))
except Exception as e:
img = np.asarray(Image.open(fname.decode('utf8')))
label = np.asarray(Image.open(fname.decode('utf8').replace('.tif', '_label.tiff')))
logger.debug('fn, ws, x, y: {}, {}, {}, {}'.format(fname, window_size, x_coord, y_coord))
logger.debug('crt, cls, stch: {}, {}, {}'.format(correction, impose_nb_cls, stretch))
logger.debug('img:{}, label:{}'.format(img.shape, label.shape))
assert img.shape == label.shape, 'img and label shape should be equal'
assert img.shape[0] >= x_coord + window_size, 'window is out of zone'
assert img.shape[1] >= y_coord + window_size, 'window is out of zone'
if not stretch:
X = np.expand_dims(img[x_coord: x_coord + window_size, y_coord: y_coord + window_size], axis=2)
y = np.expand_dims(label[x_coord: x_coord + window_size, y_coord: y_coord + window_size], axis=2)
y = _one_hot(y, impose_nb_cls=impose_nb_cls)
else:
X, y = stretching(img, label=label,
x_coord=x_coord, y_coord=y_coord,
window_size=window_size, stretch_max=stretch)
X = np.expand_dims(X, axis=2)
y = np.expand_dims(y, axis=2)
y = _one_hot(y, impose_nb_cls=impose_nb_cls)
logger.debug('y shape: {}, nb_class: {}'.format(y.shape, y.shape[-1])) # H, W, C
# return X, y.astype(np.int32)
# return _minmaxscalar(X), y.astype(np.int32)
# note: multiplication train more flexible network than minmaxscalar since their might be variation of grayscale
return X * correction, y.astype(np.int32)
def parse_h5_one_hot_V3(fname, window_size, x_coord, y_coord):
img = np.asarray(Image.open(fname))
label = np.asarray(Image.open(fname.decode('utf8').replace('.tif', '_label.tif')))
assert img.shape == label.shape, 'img and label shape should be equal'
assert img.shape[0] >= x_coord + window_size, 'window is out of zone'
assert img.shape[1] >= y_coord + window_size, 'window is out of zone'
logger.debug('fn, ws, x, y: {}, {}, {}, {}'.format(fname, window_size, x_coord, y_coord))
# note: the order of the following list shouldn't be changed either training or testing
l_func = [
Gaussian_Blur,
Sobel,
Hessian,
DoG,
Gabor,
# 'membrane_proj': Membrane_proj,
Anisotropic_Diffusion1, #no effect
Anisotropic_Diffusion2, #no effect
Bilateral, #no effect
Median,
]
# compute feature maps
_X = img[x_coord: x_coord + window_size, y_coord: y_coord + window_size]
X = [_X]
for func in l_func:
X.append(func(_X))
X = np.stack(X, axis=2).astype(np.float32)
# y
y = np.expand_dims(label[x_coord: x_coord + window_size, y_coord: y_coord + window_size], axis=2)
y = _one_hot(y)
# logger.debug('y shape: {}, nb_class: {}'.format(y.shape, y.shape[-1])) # B, H, W, C
return X, y.astype(np.int32)
def _minmaxscalar(ndarray, dtype=np.float32):
"""
func normalize values of a ndarray into interval of 0 to 1
input:
-------
ndarray: (numpy ndarray) input array to be normalized
dtype: (dtype of numpy) data type of the output of this function
output:
-------
scaled: (numpy ndarray) output normalized array
"""
scaled = np.array((ndarray - np.min(ndarray)) / (np.max(ndarray) - np.min(ndarray)), dtype=dtype)
return scaled
def _one_hot(tensor, impose_nb_cls=None):
''' (batch, H, W) --> one hot to --> (batch, H, W, nb_class)'''
assert isinstance(tensor, np.ndarray), 'Expect input as a np ndarray'
# logger.debug('input tensor shape:{}, unique: {}'.format(tensor.shape, np.unique(tensor)))
# get how many classes
tensor = tensor.astype(np.int32)
if impose_nb_cls is not None:
nb_classes = impose_nb_cls
else:
nb_classes = len(np.unique(tensor))
logger.debug('impose: {}, nb_cls: {}'.format(impose_nb_cls, nb_classes))
if tensor.ndim == 4:
#note: (Batch, H, W, 1)
# one hot
out = []
for i in range(nb_classes):
tmp = np.zeros_like(tensor)
tmp[np.where(tensor == i)] = 1
out.append(tmp)
# stack along the last channel
out = np.concatenate(out, axis=3)
elif tensor.ndim == 3:
#note: (H, W, C) no batch size
# one hot
out = []
for i in range(nb_classes):
tmp = np.zeros(tensor.shape)
tmp[ | np.where(tensor == i) | numpy.where |
# coding=utf-8
# Copyright 2022 The Google Research Authors.
#
# 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.
# Lint as: python3
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import os
import tempfile
from absl import logging
from absl.testing import absltest
import matplotlib.pyplot as plt
import numpy as np
from simulation_research.traffic import point_process_model
class PointProcessModelTest(absltest.TestCase):
def setUp(self):
super(PointProcessModelTest, self).setUp()
self.model = point_process_model.PointProcessModel()
np.random.seed(0)
self._output_dir = tempfile.mkdtemp(dir=absltest.get_default_test_tmpdir())
def test_generator_homogeneous_poisson(self):
lmbd = 1
time_step_size = 10
rates = np.ones(100000) * lmbd
events = self.model.generator(rates, time_step_size)
actual_mean = np.mean(events)
actual_std = np.std(events)
target_mean = lmbd * time_step_size
target_std = np.sqrt(target_mean)
self.assertAlmostEqual(
np.abs(target_mean - actual_mean) / target_mean, 0, places=2)
self.assertAlmostEqual(
np.abs(target_std - actual_std) / target_std, 0, places=2)
def test_model_fitting_homogeneous_poisson(self):
lmbd = 1
time_step_size = 10
rates = | np.ones(100000) | numpy.ones |
import numpy
import scipy.ndimage
from . import _deform_grid
def deform_random_grid(X, sigma=25, points=3, order=3, mode='constant', cval=0.0, crop=None, prefilter=True, axis=None):
"""
Elastic deformation with a random deformation grid
This generates a random, square deformation grid with displacements
sampled from from a normal distribution with standard deviation `sigma`.
The deformation is then applied to the image or list of images,
See ``deform_grid`` for a full description of the parameters.
Parameters
----------
X : numpy array or list of arrays
image, or list of images of the same size
sigma : float
standard deviation of the normal distribution
points : array
number of points of the deformation grid
See Also
--------
deform_grid : for a full description of the parameters.
"""
# prepare inputs and axis selection
Xs = _normalize_inputs(X)
axis, deform_shape = _normalize_axis_list(axis, Xs)
if not isinstance(points, (list, tuple)):
points = [points] * len(deform_shape)
displacement = numpy.random.randn(len(deform_shape), *points) * sigma
return deform_grid(X, displacement, order, mode, cval, crop, prefilter, axis)
def deform_grid(X, displacement, order=3, mode='constant', cval=0.0, crop=None, prefilter=True, axis=None):
"""
Elastic deformation with a deformation grid
The procedure generates a coarse displacement grid with a random displacement
for each grid point. This grid is then interpolated to compute a displacement for
each pixel in the input image. The input image is then deformed using the
displacement vectors and a spline interpolation.
Parameters
----------
X : numpy array or list of arrays
image, or list of images of the same size
If X is a list of images, the values for order, mode and cval can be lists
to specify a different value for every image in X.
displacement : numpy array
displacement vectors for each control point
displacement is a NumPy array with displacement vectors for each
control points. For example, to deform a 2D image with 3 x 5 control
points, provide a displacement matrix of shape 2 x 3 x 5.
order : {0, 1, 2, 3, 4}
interpolation order
mode : ({nearest, wrap, reflect, mirror, constant})
border mode
cval : float
constant value to be used if mode == 'constant'
crop : None or list
None, or a list of slice() objects to crop the output
crop can be a list of slice() objects to crop the output with.
Only very simple slicing is supported: the slice start and stop values must
be positive and should not be larger than the output. Note that this parameter
is dependent of the axis parameter: if an axis list is given, crop must only
contain slice() objects for the dimensions in axis.
prefilter : bool
if True the input X will be pre-filtered with a spline filter
axis : None, int, a list of ints, or a list of lists of ints
the axes to deform over
axis indicates the axes on which the deformation should be applied.
The default (None) is to apply a deformation to all dimensions of the input.
Giving a single axis (int) or a tuple of axes will apply the deformation only
to those axes. The shape of the displacement must match this number of axes.
If multiple inputs are given, axis should be None or a list of tuples with
the axes for each input.
Returns
-------
numpy array or list of arrays
The deformed image, or a list of deformed images if a list of inputs is given.
Notes
-----
See the SciPy documentation for scipy.ndimage.interpolation.map_coordinates
for more details on some of the parameters.
The elastic deformation approach is found in
* Ronneberger, Fischer, and Brox, "U-Net: Convolutional Networks for Biomedical
Image Segmentation" https://arxiv.org/abs/1505.04597
* Cicek et al., "3D U-Net: Learning Dense Volumetric
Segmentation from Sparse Annotation" https://arxiv.org/abs/1606.06650
Based on a Python implementation by <NAME>.
"""
# prepare inputs and axis selection
Xs = _normalize_inputs(X)
axis, deform_shape = _normalize_axis_list(axis, Xs)
# prepare output cropping
output_shapes, output_offset = _compute_output_shapes(Xs, axis, deform_shape, crop)
# prepare other parameters
displacement = _normalize_displacement(displacement, Xs, axis)
order = _normalize_order(order, Xs)
mode = _normalize_mode(mode, Xs)
cval = _normalize_cval(cval, Xs)
# prefilter inputs
Xs_f = []
for i, x in enumerate(Xs):
if prefilter and order[i] > 1:
x_f = numpy.zeros_like(x)
for d in axis[i]:
scipy.ndimage.spline_filter1d(x, axis=d, order=order[i], output=x_f)
x = x_f
Xs_f.append(x_f)
else:
Xs_f.append(x)
# prefilter displacement
displacement_f = numpy.zeros_like(displacement)
for d in range(1, displacement.ndim):
scipy.ndimage.spline_filter1d(displacement, axis=d, order=3, output=displacement_f)
displacement = displacement_f
# prepare output arrays
outputs = [numpy.zeros(os, dtype=x.dtype) for os, x in zip(output_shapes, Xs)]
_deform_grid.deform_grid(Xs_f, displacement_f, output_offset, outputs, axis, order, mode, cval)
if isinstance(X, list):
return outputs
else:
return outputs[0]
def deform_grid_gradient(dY, displacement, order=3, mode='constant', cval=0.0, crop=None, prefilter=True, axis=None, X_shape=None):
"""
Gradient for deform_grid.
This method performs the backward operation that returns the gradient of deform_grid
with respect to the input. This is similar to performing an inverse deformation on
the gradient, but not exactly the same: this function gives an exact gradient that
also takes the interpolation into account.
The X_shape parameter specifices the shape of the original inputs, and is only
necessary if the crop parameter is used. Otherwise, the input shape is the same as
the shape of the gradient dY.
See the documentation for ``deform_grid``.
Parameters
----------
dY : numpy array
the input gradient, or list of gradients of the same size
displacement : numpy array
displacement vectors for each control point
order : {0, 1, 2, 3, 4}
interpolation order
mode : ({nearest, wrap, reflect, mirror, constant})
border mode
cval : float
constant value to be used if mode == 'constant'
crop : None or list
None, or a list of slice() objects to crop the output
prefilter : bool
if True the input X will be pre-filtered with a spline filter
axis : None, int, a list of ints, or a list of lists of ints
the axes to deform over
X_shape: tuple with the shape of the input, or a list of tuples
Returns
-------
numpy array
Returns the gradient with respect to X.
"""
# prepare inputs
dYs = _normalize_inputs(dY)
# find input shape
if isinstance(X_shape, tuple):
X_shape = [X_shape]
elif X_shape is None:
if crop is not None:
raise ValueError("X_shape is required if the crop parameter is given.")
X_shape = [dy.shape for dy in dYs]
# initialize gradient outputs
dXs = [numpy.zeros(s, dy.dtype) for s, dy in zip(X_shape, dYs)]
# prepare axis selection
axis, deform_shape = _normalize_axis_list(axis, dXs)
# prepare cropping
output_shapes, output_offset = _compute_output_shapes(dXs, axis, deform_shape, crop)
if [tuple(s) for s in output_shapes] != [dy.shape for dy in dYs]:
raise ValueError("X_shape does not match output shape and cropping. "
"Expected output shape is %s, but %s given."
% (str(output_shapes), str([dy.shape for dy in dYs])))
# prepare other parameters
displacement = _normalize_displacement(displacement, dYs, axis)
order = _normalize_order(order, dYs)
mode = _normalize_mode(mode, dYs)
cval = _normalize_cval(cval, dYs)
# prefilter displacement
displacement_f = numpy.zeros_like(displacement)
for d in range(1, displacement.ndim):
scipy.ndimage.spline_filter1d(displacement, axis=d, order=3, output=displacement_f)
displacement = displacement_f
_deform_grid.deform_grid_grad(dXs, displacement_f, output_offset, dYs, axis, order, mode, cval)
# compute gradient of prefilter operation
dXs_f = []
for i, x in enumerate(dXs):
if prefilter and order[i] > 1:
x_f = numpy.zeros_like(x)
for d in axis[i]:
_deform_grid.spline_filter1d_grad(x, x_f, d, order[i])
x = x_f
dXs_f.append(x_f)
else:
dXs_f.append(x)
if isinstance(dY, list):
return dXs_f
else:
return dXs_f[0]
def _normalize_inputs(X):
if isinstance(X, numpy.ndarray):
Xs = [X]
elif isinstance(X, list):
Xs = X
else:
raise Exception('X should be a numpy.ndarray or a list of numpy.ndarrays.')
# check X inputs
assert len(Xs) > 0, 'You must provide at least one image.'
assert all(isinstance(x, numpy.ndarray) for x in Xs), 'All elements of X should be numpy.ndarrays.'
return Xs
def _normalize_axis_list(axis, Xs):
if axis is None:
axis = [tuple(range(x.ndim)) for x in Xs]
elif isinstance(axis, int):
axis = (axis,)
if isinstance(axis, tuple):
axis = [axis] * len(Xs)
assert len(axis) == len(Xs), 'Number of axis tuples should match number of inputs.'
input_shapes = []
for x, ax in zip(Xs, axis):
assert isinstance(ax, tuple), 'axis should be given as a tuple'
assert all(isinstance(a, int) for a in ax), 'axis must contain ints'
assert len(ax) == len(axis[0]), 'All axis tuples should have the same length.'
assert ax == tuple(set(ax)), 'axis must be sorted and unique'
assert all(0 <= a < x.ndim for a in ax), 'invalid axis for input'
input_shapes.append(tuple(x.shape[d] for d in ax))
assert len(set(input_shapes)) == 1, 'All inputs should have the same shape.'
deform_shape = input_shapes[0]
return axis, deform_shape
def _compute_output_shapes(Xs, axis, deform_shape, crop):
if crop is not None:
assert isinstance(crop, (tuple, list)), "crop must be a tuple or a list."
assert len(crop) == len(deform_shape)
output_shapes = [list(x.shape) for x in Xs]
output_offset = [0 for d in range(len(axis[0]))]
for d in range(len(axis[0])):
if isinstance(crop[d], slice):
assert crop[d].step is None
start = (crop[d].start or 0)
stop = (crop[d].stop or deform_shape[d])
assert start >= 0
assert start < stop and stop <= deform_shape[d]
for i in range(len(Xs)):
output_shapes[i][axis[i][d]] = stop - start
if start > 0:
output_offset[d] = start
else:
raise Exception('Crop must be a slice.')
if any(o > 0 for o in output_offset):
output_offset = numpy.array(output_offset).astype('int64')
else:
output_offset = None
else:
output_shapes = [x.shape for x in Xs]
output_offset = None
return output_shapes, output_offset
def _normalize_displacement(displacement, Xs, axis):
assert isinstance(displacement, numpy.ndarray), 'Displacement matrix should be a numpy.ndarray.'
assert displacement.ndim == len(axis[0]) + 1, 'Number of dimensions of displacement does not match input.'
assert displacement.shape[0] == len(axis[0]), 'First dimension of displacement should match number of input dimensions.'
return displacement
def _normalize_order(order, Xs):
if not isinstance(order, (tuple, list)):
order = [order] * len(Xs)
assert len(Xs) == len(order), 'Number of order parameters should be equal to number of inputs.'
assert all(0 <= o and o <= 5 for o in order), 'order should be 0, 1, 2, 3, 4 or 5.'
return numpy.array(order).astype('int64')
def _normalize_mode(mode, Xs):
if not isinstance(mode, (tuple, list)):
mode = [mode] * len(Xs)
mode = [_extend_mode_to_code(o) for o in mode]
assert len(Xs) == len(mode), 'Number of mode parameters should be equal to number of inputs.'
return | numpy.array(mode) | numpy.array |
import numpy as np
def _get_angle(a, b, c):
"""
Get angle between vector ba and bc
"""
ba = a - b
bc = c - b
cosine_angle = np.dot(ba, bc) / (np.linalg.norm(ba) * | np.linalg.norm(bc) | numpy.linalg.norm |
import numpy as np
from matplotlib import pyplot as plt
from scipy.stats import uniform
from scipy.stats import multivariate_normal as mvnorm
class MCMC:
def __init__(self, target, step):
self.target = target
self.step = step
self.dim = None
self.samples = None
self.weights = None
self.norms = None
def sampling(self, size, initial):
self.dim = len(initial)
samples = [initial]
weights = [1]
while len(weights) < size + 2:
new = samples[-1] + mvnorm.rvs(mean=np.zeros(self.dim), cov=self.step ** 2)
if uniform.rvs() <= self.target(new) / self.target(samples[-1]):
samples.append(new)
weights.append(1)
else:
weights[-1] += 1
self.samples = np.array(samples[1:-1])
self.weights = np.array(weights[1:-1])
print('ESS/size/niter: {:.0f}/{}/{}'
.format(1 / ((self.weights / self.weights.sum()) ** 2).sum(), size, self.weights.sum()))
def dist(self, xi, k):
distances = np.abs(np.abs(xi) - self.norms)
return np.argsort(distances)[:k]
def draw(self, x, k):
self.norms = np.sqrt(np.sum(self.samples ** 2, axis=1))
min_norm = self.norms.min()
num = np.int64((x[1] - x[0]) / min_norm)
print('Number: {}'.format(num))
x = np.linspace(x[0], x[1], num + 1)
X = np.zeros([x.size, self.dim])
X[:, 0] = x
proposal = self.target(self.samples) / (self.weights / self.weights.mean())
proposalX = np.zeros_like(x)
for i, xi in enumerate(x):
index = self.dist(xi, k)
proposalX[i] = proposal[index].mean()
fig, ax = plt.subplots()
ax.plot(x, proposalX, c='r', label='proposal')
ax.plot(x, self.target(X), c='b', label='target')
ax.legend()
ax.set_title('{}-D target and MCMC proposal (averaging)'.format(self.dim))
plt.show()
def main(dim, step, size):
target = mvnorm(mean=np.zeros(dim)).pdf
mcmc = MCMC(target, step=step)
mcmc.sampling(size=size, initial= | np.zeros(dim) | numpy.zeros |
import numpy as np
from scipy.special import gamma
import matplotlib.pyplot as plt
# Define patient arrival rate function
def arr_int(time, num_pats, peak_time):
# num_pats determines the magnitude of the event (i.e. the number of patients)
# peak_time controls when the peak arrival time will be
t = time/60
peak_time /= 60
out = num_pats / 60 * (t)**(peak_time-1)*np.exp(-t)/(gamma(peak_time))
return out
def generate_times_opt(rate_function, max_t, delta):
t = np.arange(delta, max_t, delta)
avg_rate = (rate_function(t) + rate_function(t + delta)) / 2.0
avg_prob = 1 - np.exp(-avg_rate * delta)
rand_throws = np.random.uniform(size=t.shape[0])
return t[avg_prob >= rand_throws]
def sim_walkthrough():
numPatients = 30 # Total number of patients on average
odds = 1/3 # Ratio of IMMEDIATE patients to DELAYED patients
peakI = 270 # This parameter controls when the peak of arrivals is for IMMEDIATE patients
peakD = 150 # This parameter controls when the peak of arrivals is for DELAYED patients
# Probabilities of surviving the trip to another hospital
probI = .4
probD = .8
# Compute parameters for functions"
ratio = odds/(1+odds)
cI = numPatients * odds
cD = numPatients - cI
tp = np.linspace(0, 720, num=1000)
def yI(t): return arr_int(t, cI, peakI)
def yD(t): return arr_int(t, cD, peakD)
red_ind = np.random.binomial(1, ratio)
ppI_times = generate_times_opt(yI, 720, .1)
ppD_times = generate_times_opt(yD, 720, .1)
imm_ind = np.random.binomial(1, ratio)
if imm_ind == 1:
time = np.random.choice(ppI_times)/720 * 120
col = 'ORANGE'
survive = np.random.binomial(1, probI)
else:
time = np.random.choice(ppD_times)/720 * 120
col = 'BLUE'
survive = np.random.binomial(1, probD)
print('Grab a ' + col + ' index card from the front and write '
+ str(np.round(time, 1)) + ' on the front and ' + str(survive) + ' on the back.')
def plot_arr_int(num_pat, peak):
# Lets plot a sample of the arrival rate function
tp = np.linspace(0, 720, num=1000)
plt.plot(tp, arr_int(tp, num_pat, peak), color='black')
plt.ylim(0, np.maximum(.5, np.ndarray.max(arr_int(tp, num_pat, peak))))
plt.xlabel('Elapsed Time (min)')
plt.ylabel('Intensity of Arrivals (patients/min)')
plt.show()
def plot_arr_ints(numPatients, odds, peakI, peakD):
# Compute parameters for functions
ratio = odds/(1+odds)
cI = numPatients * odds
cD = numPatients - cI
# Lets plot the arrival rate functions for both classes of patients
tp = np.linspace(0, 720, num=1000)
plt.plot(tp, arr_int(tp, cI, peakI), label='IMMEDIATE Patients',
color='orange') # First plot for IMMEDIATE patients
plt.plot(tp, arr_int(tp, cD, peakD), label='DELAYED Patients',
color='blue') # First plot for DELAYED patients
plt.ylim(0, np.maximum(.3, np.ndarray.max(
np.array([arr_int(tp, cI, peakI), arr_int(tp, cD, peakD)], dtype=float))))
plt.xlabel('Elapsed Time (min)')
plt.ylabel('Intensity of Arrivals (patients/min)')
plt.legend()
plt.show()
def plot_arrivals(numPatients, odds, peakI, peakD):
tp = np.linspace(0, 720, num=1000)
ratio = odds/(1+odds)
cI = numPatients * odds
cD = numPatients - cI
def yI(t): return arr_int(t, cI, peakI)
def yD(t): return arr_int(t, cD, peakD)
red_ind = np.random.binomial(1, ratio/(1+ratio))
ppI_times = generate_times_opt(yI, 720, .1)
ppD_times = generate_times_opt(yD, 720, .1)
plt.plot(tp, arr_int(tp, cI, peakI), label='IMMEDIATE Patients',
color='orange') # First plot for red patients
plt.plot(tp, arr_int(tp, cD, peakD), label='DELAYED Patients',
color='blue') # First plot for green patients
plt.plot(ppI_times, arr_int(ppI_times, cI, peakI), color='orange', marker='x', linestyle='none')
plt.plot(ppD_times, arr_int(ppD_times, cD, peakD), color='blue', marker='x', linestyle='none')
plt.ylim(0, np.maximum(.3, np.ndarray.max(
np.array([arr_int(tp, cI, peakI), arr_int(tp, cD, peakD)], dtype=float))))
plt.xlabel('Elapsed Time (min)')
plt.ylabel('Intensity of Arrivals (patients/min)')
plt.legend()
plt.show()
def simulate(reps, numBeds, numPatients, odds, peakI, peakD, probI, probD):
# Compute parameters for functions"
ratio = odds/(1+odds)
cI = numPatients * odds
cD = numPatients - cI
tp = np.linspace(0, 720, num=1000)
def yI(t): return arr_int(t, cI, peakI)
def yD(t): return arr_int(t, cD, peakD)
died_FCFS = np.zeros(reps)
survived_FCFS = np.zeros(reps)
final_beds_FCFS = np.zeros(reps)
died_IO = np.zeros(reps)
survived_IO = np.zeros(reps)
final_beds_IO = np.zeros(reps)
for i in range(reps):
timesI = generate_times_opt(yI, 720, .1)
timesD = generate_times_opt(yD, 720, .1)
total_patients = len(timesI) + len(timesD)
bedsRemaining_FCFS = numBeds
bedsRemaining_IO = numBeds
while len(timesI) + len(timesD) > 0:
if len(timesI) == 0:
t = timesD[0]
timesD = timesD[1:]
is_I = 0
elif len(timesD) == 0:
t = timesI[0]
timesI = timesI[1:]
is_I = 1
else:
t = np.minimum(timesI[0], timesD[0])
if t == timesI[0]:
timesI = timesI[1:]
is_I = 1
else:
timesD = timesD[1:]
is_I = 0
# Handle FCFS
if bedsRemaining_FCFS > 0:
bedsRemaining_FCFS += -1
survived_FCFS[i] += 1
else:
if is_I == 1:
survived_FCFS[i] += np.random.binomial(1, probI)
else:
survived_FCFS[i] += | np.random.binomial(1, probD) | numpy.random.binomial |
import cv2
import numpy as np
import math
import random
def __rotateImage(image, angle):
rot_mat = cv2.getRotationMatrix2D((image.shape[1]/2,image.shape[0]/2),angle,1)
result = cv2.warpAffine(image, rot_mat, (image.shape[1], image.shape[0]),flags=cv2.INTER_LINEAR)
return result, rot_mat
def rotate(img, gt, angle):
img, mat = __rotateImage(img,angle)
gt = gt.astype(np.float64)
for a in range(0,4):
gt[a] = np.dot(mat[...,0:2], gt[a]) + mat[...,2]
a=float(angle) * math.pi / 180
# gt[0,0] = gt[3,0] = img.shape[1]*math.sin(float(angle)*math.pi/180)*cos(a)
# gt[0,1] = gt[1,1] = R2 math.sin(a) - W*(sin(a)**2)
# gt[1,0] = gt[2,0] = gt[0,0]+H
# gt[2,1] = gt[3,1] = gt[1,1] + W
# gt = gt.astype(np.int32)
return img, gt
def random_crop(img, gt):
ptr1 = (min(gt[0][0], gt[1][0], gt[2][0], gt[3][0]),
min(gt[0][1], gt[1][1], gt[2][1], gt[3][1]))
ptr2 = ((max(gt[0][0], gt[1][0], gt[2][0], gt[3][0]),
max(gt[0][1], gt[1][1], gt[2][1], gt[3][1])))
start_x = np.random.randint(0, int(max(ptr1[0] - 1,1)))
start_y = np.random.randint(0, int(max(ptr1[1] - 1,1)))
end_x = np.random.randint(int(min(ptr2[0] + 1,img.shape[1]-1)), img.shape[1])
end_y = np.random.randint(int(min(ptr2[1] + 1,img.shape[0]-1)), img.shape[0])
myGt = gt - (start_x, start_y)
sum_array = myGt.sum(axis=1)
tl_index = | np.argmin(sum_array) | numpy.argmin |
# -*- coding: utf-8 -*-
# @Time : 2017/7/13 下午8:23
# @Author : play4fun
# @File : 47.2-使用SVM进行-手写数据OCR.py
# @Software: PyCharm
"""
47.2-使用SVM进行-手写数据OCR.py:
"""
import cv2
import numpy as np
SZ = 20
bin_n = 16 # Number of bins
affine_flags = cv2.WARP_INVERSE_MAP | cv2.INTER_LINEAR
# 使用方向梯度直方图Histogram of Oriented Gradients HOG 作为特征向量
def deskew(img):
m = cv2.moments(img)
if abs(m['mu02']) < 1e-2:
return img.copy()
skew = m['mu11'] / m['mu02']
M = np.float32([[1, skew, -0.5 * SZ * skew], [0, 1, 0]])
img = cv2.warpAffine(img, M, (SZ, SZ), flags=affine_flags)
return img
# 计算图像 X 方向和 Y 方向的 Sobel 导数
def hog(img):
gx = cv2.Sobel(img, cv2.CV_32F, 1, 0)
gy = cv2.Sobel(img, cv2.CV_32F, 0, 1)
mag, ang = cv2.cartToPolar(gx, gy)
bins = np.int32(bin_n * ang / (2 * np.pi)) # quantizing binvalues in (0...16)
bin_cells = bins[:10, :10], bins[10:, :10], bins[:10, 10:], bins[10:, 10:]
mag_cells = mag[:10, :10], mag[10:, :10], mag[:10, 10:], mag[10:, 10:]
hists = [np.bincount(b.ravel(), m.ravel(), bin_n) for b, m in zip(bin_cells, mag_cells)]
hist = np.hstack(hists) # hist is a 64 bit vector
return hist
# 最后 和前 一样 我们将大图分割成小图。使用每个数字的前 250 个作 为训练数据
# 后 250 个作为测试数据
img = cv2.imread('../data/digits.png', 0)
cells = [np.hsplit(row, 100) for row in np.vsplit(img, 50)]
# First half is trainData, remaining is testData
train_cells = [i[:50] for i in cells]
test_cells = [i[50:] for i in cells]
deskewed = [map(deskew, row) for row in train_cells]
# deskewed = [deskew(row) for row in train_cells]
# deskewed = map(deskew, train_cells)
hogdata = [map(hog, row) for row in deskewed]
# hogdata = [hog(row) for row in deskewed]
# hogdata = map(hog, deskewed)
trainData = np.float32(hogdata).reshape(-1, 64)
responses = np.float32(np.repeat(np.arange(10), 250)[:, np.newaxis])
svm = cv2.ml.SVM_create()
svm.setKernel(cv2.ml.SVM_LINEAR)
svm.setType(cv2.ml.SVM_C_SVC)
svm.setC(2.67)
svm.setGamma(5.383)
svm.train(trainData, cv2.ml.ROW_SAMPLE, responses)
svm.save('svm_data.dat')
deskewed = [map(deskew, row) for row in test_cells]
hogdata = [map(hog, row) for row in deskewed]
testData = | np.float32(hogdata) | numpy.float32 |
from __future__ import division
from __future__ import print_function
import os
import networkx as nx
import sys
import glob
import time
import random
import argparse
import scipy.sparse as sp
from scipy.sparse import coo_matrix
import numpy as np
from sklearn.metrics import recall_score
from sklearn.metrics import precision_score
from sklearn.metrics import f1_score
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torch.autograd import Variable
from utils import load_data, accuracy, normalize_adj
from models import GAT, SpGAT
from plot_confusion_matrix import plot_confusion_matrix
def spy_sparse2torch_sparse(coo):
"""
:param data: a scipy sparse coo matrix
:return: a sparse torch tensor
"""
values=coo.data
indices=np.vstack((coo.row,coo.col))
i = torch.LongTensor(indices)
v = torch.FloatTensor(values)
shape = coo.shape
t = torch.sparse.FloatTensor(i, v, torch.Size(shape))
return t
# Training settings
parser = argparse.ArgumentParser()
parser.add_argument('--no-cuda', action='store_true', default=False, help='Disables CUDA training.')
parser.add_argument('--fastmode', action='store_true', default=False, help='Validate during training pass.')
parser.add_argument('--sparse', action='store_false', default=True, help='GAT with sparse version or not.')
parser.add_argument('--seed', type=int, default=72, help='Random seed.')
parser.add_argument('--epochs', type=int, default=10000, help='Number of epochs to train.')
parser.add_argument('--lr', type=float, default=0.01, help='Initial learning rate.')
parser.add_argument('--weight_decay', type=float, default=5e-4, help='Weight decay (L2 loss on parameters).')
parser.add_argument('--hidden', type=int, default=15, help='Number of hidden units.')
parser.add_argument('--nb_heads', type=int, default=8, help='Number of head attentions.')
parser.add_argument('--dropout', type=float, default=0.6, help='Dropout rate (1 - keep probability).')
parser.add_argument('--alpha', type=float, default=0.2, help='Alpha for the leaky_relu.')
parser.add_argument('--patience', type=int, default=20, help='Patience')
args = parser.parse_args()
args.cuda = not args.no_cuda and torch.cuda.is_available()
random.seed(args.seed)
| np.random.seed(args.seed) | numpy.random.seed |
#!/usr/bin/env python
#
# Author: <NAME> <<EMAIL>>
#
'''Density expansion on plane waves'''
import copy
import numpy
from pyscf import lib
from pyscf import gto
from pyscf import dft
from pyscf.lib import logger
from pyscf.pbc import tools
from pyscf.pbc.gto import pseudo, estimate_ke_cutoff, error_for_ke_cutoff
from pyscf.pbc.df import ft_ao
from pyscf.pbc.df import fft_ao2mo
from pyscf.pbc.lib.kpt_misc import is_zero, gamma_point
def get_nuc(mydf, kpts=None):
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1,3))
else:
kpts_lst = numpy.reshape(kpts, (-1,3))
gs = mydf.gs
charge = -cell.atom_charges()
Gv = cell.get_Gv(gs)
SI = cell.get_SI(Gv)
rhoG = numpy.dot(charge, SI)
coulG = tools.get_coulG(cell, gs=gs, Gv=Gv)
vneG = rhoG * coulG
vneR = tools.ifft(vneG, mydf.gs).real
vne = [lib.dot(aoR.T.conj()*vneR, aoR)
for k, aoR in mydf.aoR_loop(gs, kpts_lst)]
if kpts is None or numpy.shape(kpts) == (3,):
vne = vne[0]
return numpy.asarray(vne)
def get_pp(mydf, kpts=None):
'''Get the periodic pseudotential nuc-el AO matrix, with G=0 removed.
'''
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1,3))
else:
kpts_lst = numpy.reshape(kpts, (-1,3))
gs = mydf.gs
SI = cell.get_SI()
Gv = cell.get_Gv(gs)
vpplocG = pseudo.get_vlocG(cell, Gv)
vpplocG = -numpy.einsum('ij,ij->j', SI, vpplocG)
vpplocG[0] = numpy.sum(pseudo.get_alphas(cell)) # from get_jvloc_G0 function
ngs = len(vpplocG)
# vpploc evaluated in real-space
vpplocR = tools.ifft(vpplocG, cell.gs).real
vpp = [lib.dot(aoR.T.conj()*vpplocR, aoR)
for k, aoR in mydf.aoR_loop(gs, kpts_lst)]
# vppnonloc evaluated in reciprocal space
fakemol = gto.Mole()
fakemol._atm = numpy.zeros((1,gto.ATM_SLOTS), dtype=numpy.int32)
fakemol._bas = numpy.zeros((1,gto.BAS_SLOTS), dtype=numpy.int32)
ptr = gto.PTR_ENV_START
fakemol._env = numpy.zeros(ptr+10)
fakemol._bas[0,gto.NPRIM_OF ] = 1
fakemol._bas[0,gto.NCTR_OF ] = 1
fakemol._bas[0,gto.PTR_EXP ] = ptr+3
fakemol._bas[0,gto.PTR_COEFF] = ptr+4
# buf for SPG_lmi upto l=0..3 and nl=3
buf = numpy.empty((48,ngs), dtype=numpy.complex128)
def vppnl_by_k(kpt):
Gk = Gv + kpt
G_rad = lib.norm(Gk, axis=1)
aokG = ft_ao.ft_ao(cell, Gv, kpt=kpt) * (ngs/cell.vol)
vppnl = 0
for ia in range(cell.natm):
symb = cell.atom_symbol(ia)
if symb not in cell._pseudo:
continue
pp = cell._pseudo[symb]
p1 = 0
for l, proj in enumerate(pp[5:]):
rl, nl, hl = proj
if nl > 0:
fakemol._bas[0,gto.ANG_OF] = l
fakemol._env[ptr+3] = .5*rl**2
fakemol._env[ptr+4] = rl**(l+1.5)*numpy.pi**1.25
pYlm_part = dft.numint.eval_ao(fakemol, Gk, deriv=0)
p0, p1 = p1, p1+nl*(l*2+1)
# pYlm is real, SI[ia] is complex
pYlm = numpy.ndarray((nl,l*2+1,ngs), dtype=numpy.complex128, buffer=buf[p0:p1])
for k in range(nl):
qkl = pseudo.pp._qli(G_rad*rl, l, k)
pYlm[k] = pYlm_part.T * qkl
#:SPG_lmi = numpy.einsum('g,nmg->nmg', SI[ia].conj(), pYlm)
#:SPG_lm_aoG = numpy.einsum('nmg,gp->nmp', SPG_lmi, aokG)
#:tmp = numpy.einsum('ij,jmp->imp', hl, SPG_lm_aoG)
#:vppnl += numpy.einsum('imp,imq->pq', SPG_lm_aoG.conj(), tmp)
if p1 > 0:
SPG_lmi = buf[:p1]
SPG_lmi *= SI[ia].conj()
SPG_lm_aoGs = lib.zdot(SPG_lmi, aokG)
p1 = 0
for l, proj in enumerate(pp[5:]):
rl, nl, hl = proj
if nl > 0:
p0, p1 = p1, p1+nl*(l*2+1)
hl = numpy.asarray(hl)
SPG_lm_aoG = SPG_lm_aoGs[p0:p1].reshape(nl,l*2+1,-1)
tmp = numpy.einsum('ij,jmp->imp', hl, SPG_lm_aoG)
vppnl += numpy.einsum('imp,imq->pq', SPG_lm_aoG.conj(), tmp)
return vppnl * (1./ngs**2)
for k, kpt in enumerate(kpts_lst):
vppnl = vppnl_by_k(kpt)
if gamma_point(kpt):
vpp[k] = vpp[k].real + vppnl.real
else:
vpp[k] += vppnl
if kpts is None or numpy.shape(kpts) == (3,):
vpp = vpp[0]
return numpy.asarray(vpp)
class FFTDF(lib.StreamObject):
'''Density expansion on plane waves
'''
def __init__(self, cell, kpts=numpy.zeros((1,3))):
from pyscf.pbc.dft import numint
self.cell = cell
self.stdout = cell.stdout
self.verbose = cell.verbose
self.max_memory = cell.max_memory
self.kpts = kpts
self.gs = cell.gs
self.blockdim = 240 # to mimic molecular DF object
self.non0tab = None
# Not input options
self.exxdiv = None # to mimic KRHF/KUHF object in function get_coulG
self._numint = numint._KNumInt()
self._keys = set(self.__dict__.keys())
def dump_flags(self):
logger.info(self, '\n')
logger.info(self, '******** %s flags ********', self.__class__)
logger.info(self, 'gs = %s', self.gs)
logger.info(self, 'len(kpts) = %d', len(self.kpts))
logger.debug1(self, ' kpts = %s', self.kpts)
return self
def check_sanity(self):
lib.StreamObject.check_sanity(self)
cell = self.cell
if cell.dimension < 3:
raise RuntimeError('FFTDF method does not support low-dimension '
'PBC system. DF, MDF or AFTDF methods should '
'be used.\nSee also examples/pbc/31-low_dimensional_pbc.py')
if not cell.has_ecp():
logger.warn(self, 'FFTDF integrals are found in all-electron '
'calculation. It often causes huge error.\n'
'Recommended methods are DF or MDF. In SCF calculation, '
'they can be initialized as\n'
' mf = mf.density_fit()\nor\n'
' mf = mf.mix_density_fit()')
if cell.ke_cutoff is None:
ke_cutoff = tools.gs_to_cutoff(cell.lattice_vectors(), self.gs).min()
else:
ke_cutoff = numpy.min(cell.ke_cutoff)
ke_guess = estimate_ke_cutoff(cell, cell.precision)
if ke_cutoff < ke_guess*.8:
gs_guess = tools.cutoff_to_gs(cell.lattice_vectors(), ke_guess)
logger.warn(self, 'ke_cutoff/gs (%g / %s) is not enough for FFTDF '
'to get integral accuracy %g.\nCoulomb integral error '
'is ~ %.2g Eh.\nRecomended ke_cutoff/gs are %g / %s.',
ke_cutoff, self.gs, cell.precision,
error_for_ke_cutoff(cell, ke_cutoff), ke_guess, gs_guess)
return self
def aoR_loop(self, gs=None, kpts=None, kpts_band=None):
cell = self.cell
if cell.dimension < 3:
raise RuntimeError('FFTDF method does not support low-dimension '
'PBC system. DF, MDF or AFTDF methods should '
'be used.\nSee also examples/pbc/31-low_dimensional_pbc.py')
if kpts is None: kpts = self.kpts
kpts = numpy.asarray(kpts)
if gs is None:
gs = numpy.asarray(self.gs)
else:
gs = numpy.asarray(gs)
if any(gs != self.gs):
self.non0tab = None
self.gs = gs
ni = self._numint
coords = cell.gen_uniform_grids(gs)
if self.non0tab is None:
self.non0tab = ni.make_mask(cell, coords)
if kpts_band is None:
aoR = ni.eval_ao(cell, coords, kpts, non0tab=self.non0tab)
for k in range(len(kpts)):
yield k, aoR[k]
else:
aoR = ni.eval_ao(cell, coords, kpts_band, non0tab=self.non0tab)
if kpts_band.ndim == 1:
yield 0, aoR
else:
for k in range(len(kpts_band)):
yield k, aoR[k]
get_pp = get_pp
get_nuc = get_nuc
def get_jk(self, dm, hermi=1, kpts=None, kpts_band=None,
with_j=True, with_k=True, exxdiv='ewald'):
from pyscf.pbc.df import fft_jk
if kpts is None:
if numpy.all(self.kpts == 0):
# Gamma-point calculation by default
kpts = numpy.zeros(3)
else:
kpts = self.kpts
else:
kpts = numpy.asarray(kpts)
vj = vk = None
if kpts.shape == (3,):
vj, vk = fft_jk.get_jk(self, dm, hermi, kpts, kpts_band,
with_j, with_k, exxdiv)
else:
if with_k:
vk = fft_jk.get_k_kpts(self, dm, hermi, kpts, kpts_band, exxdiv)
if with_j:
vj = fft_jk.get_j_kpts(self, dm, hermi, kpts, kpts_band)
return vj, vk
get_eri = get_ao_eri = fft_ao2mo.get_eri
ao2mo = get_mo_eri = fft_ao2mo.general
get_ao_pairs_G = get_ao_pairs = fft_ao2mo.get_ao_pairs_G
get_mo_pairs_G = get_mo_pairs = fft_ao2mo.get_mo_pairs_G
def update_mf(self, mf):
mf = copy.copy(mf)
mf.with_df = self
return mf
################################################################################
# With this function to mimic the molecular DF.loop function, the pbc gamma
# point DF object can be used in the molecular code
def loop(self):
kpts0 = numpy.zeros((2,3))
coulG = tools.get_coulG(self.cell, numpy.zeros(3), gs=self.gs)
ngs = len(coulG)
ao_pairs_G = self.get_ao_pairs_G(kpts0, compact=True)
ao_pairs_G *= numpy.sqrt(coulG*(self.cell.vol/ngs**2)).reshape(-1,1)
Lpq = | numpy.empty((self.blockdim, ao_pairs_G.shape[1])) | numpy.empty |
import os, sys
from collections import OrderedDict
import numpy as np
import paddle
# paddle.enable_static()
import paddle.fluid as fluid
import torch
from paddle import ParamAttr
import paddle.nn as nn
import paddle.nn.functional as F
SEED = 666
INPUT_SIZE = (1, 3, 488, 488)
IN_CHANNELS = INPUT_SIZE[1]
OUT_CHANNELS = 16
MODEL_NAME = 'large'
SCALE = 1.0
NAME = 'table_mobilenet_v3'
DISABLE_SE = True
tmp_save_name = '{}.npy'.format(NAME)
def print_cmp(inp, name=None):
print('{}: shape-{}, sum: {}, mean: {}, max: {}, min: {}'.format(name, inp.shape,
np.sum(inp), np.mean(inp),
| np.max(inp) | numpy.max |
import numpy as np
import math
import torch
import torch.nn as nn
import torch.optim as optim
import torch.autograd as autograd
import torch.nn.functional as F
import pickle
from lib.model import *
from lib.zfilter import ZFilter
from lib.util import *
from lib.trpo import trpo_step
from lib.data import *
import scipy.optimize
def trpo_learn(args):
#env params
env_name, batch_size, vv, als, ex_path, fig_path = args.env_id, args.batch_size, args.vv, args.als, args.ex_path, args.fig_path
#trpo params
max_kl, cr_lr, cg_step_size, damping = args.max_kl, args.cr_lr, args.cg_step_size, args.damping
#data
data_n_steps, max_genert_num, gamma, lambd = args.data_n_steps, args.max_genert_num, args.gamma, args.lambd
#set up
env = gym.make(env_name)
env.seed(args.seed)
np.random.seed(args.seed)
torch.manual_seed(args.seed)
device = torch.device("cuda" if args.use_cuda and torch.cuda.is_available() else "cpu")
#device = torch.device("cpu")
zflt = ZFilter((env.observation_space.shape[0],), clip=5)
dtype = torch.float64
torch.set_default_dtype(dtype)
#model and optim
policy_model =ModelActor(env.observation_space.shape[0],env.action_space.shape[0]).to(device)
print(env.observation_space.shape[0])
critic_model =ModelCritic(env.observation_space.shape[0]).to(device)
#opt_policy = optim.Adam(policy_model.parameters(), lr = args.lr_policy)
opt_critic = optim.Adam(critic_model.parameters(), lr = args.lr_critic)
# data generate
gene = generate(policy_model, env, env_name, als, device, data_n_steps, ex_path, fig_path, vv, max_genert_num, zflt)
#train ...
V_loss, P_loss = [], []
for trj in gene:
states, actions, rewards, dones =trj['states'],trj['actions'],trj['rewards'],trj['dones']
states = torch.from_numpy(np.stack(states)).to(dtype).to(device)
actions = torch.from_numpy(np.stack(actions)).to(dtype).to(device)
rewards = torch.from_numpy(np.stack(rewards)).to(dtype).to(device)
dones = torch.from_numpy(np.stack(dones)).to(dtype).to(device)
with torch.no_grad():
values = critic_model(states)
old_logprob = policy_model.get_log_prob(states, actions)
adv, ref = cal_adv_ref(rewards, dones, values, gamma, lambd, device)
opt_iter = int(math.ceil(states.shape[0]/batch_size))
V_loss_, P_loss_ = [], []
#for epoch in range(args.ppo_epoches):
perm = np.arange(states.shape[0])
| np.random.shuffle(perm) | numpy.random.shuffle |
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
import bead_util as bu
from scipy.optimize import curve_fit
import dill as pickle
cpath = "/data/20180927/bead1/spinning/1k_valve_of"
filesc = bu.find_all_fnames(cpath)
freqs = np.fft.rfftfreq(50000, d = 1./5000)
def get_dir_data(files, drive_range = [1., 1500.], drive_amp = 5000.):
nf = len(files)
ns = 50000
nfreq = len(freqs)
d_ave = np.zeros((nf, nfreq), dtype = complex)
pb = []
pc = []
pp = []
t = []
xs = np.zeros((nf, nfreq), dtype = complex)
ys = np.zeros((nf, nfreq), dtype = complex)
zs = np.zeros((nf, nfreq), dtype = complex)
for i, f in enumerate(files):
df = bu.DataFile()
df.load(f)
df.load_other_data()
drive = df.other_data[2]
dbool = (np.abs(np.fft.rfft(drive))>drive_amp)*(freqs>drive_range[0])*(freqs<drive_range[1])
if not np.sum(dbool):
plt.loglog(freqs, np.abs( | np.fft.rfft(drive) | numpy.fft.rfft |
"""Generating templates of ECG and PPG complexes"""
import numpy as np
from scipy.special import erf
from sklearn.preprocessing import MinMaxScaler
from scipy import signal
import scipy
from scipy.signal import argrelextrema
from scipy.integrate import solve_ivp
from vital_sqi.preprocess.preprocess_signal import squeeze_template
def ppg_dual_double_frequency_template(width):
"""
EXPOSE
Generate a PPG template by using 2 sine waveforms.
The first waveform double the second waveform frequency
:param width: the sample size of the generated waveform
:return: a 1-D numpy array of PPG waveform
having diastolic peak at the low position
"""
t = np.linspace(0, 1, width, False) # 1 second
sig = np.sin(2 * np.pi * 2 * t - np.pi / 2) + \
np.sin(2 * np.pi * 1 * t - np.pi / 6)
sig_scale = MinMaxScaler().fit_transform(np.array(sig).reshape(-1, 1))
return sig_scale.reshape(-1)
def skew_func(x, e=0, w=1, a=0):
"""
handy
:param x: input sequence of time points
:param e: location
:param w: scale
:param a: the order
:return: a 1-D numpy array of a skewness distribution
"""
t = (x - e) / w
omega = (1 + erf((a * t) / np.sqrt(2))) / 2
gaussian_dist = 1 / (np.sqrt(2 * np.pi)) * np.exp(-(t ** 2) / 2)
return 2 / w * gaussian_dist * omega
def ppg_absolute_dual_skewness_template(width, e_1=1,
w_1=2.5, e_2=3,
w_2=3, a=4):
"""
EXPOSE
Generate a PPG template by using 2 skewness distribution.
:param width: the sample size of the generated waveform
:param e_1: the epsilon location of the first skew distribution
:param w_1: the scale of the first skew distribution
:param e_2: the epsilon location of the second skew distribution
:param w_2: the scale of the second skew distribution
:param a: the order
:return: a 1-D numpy array of PPG waveform
having diastolic peak at the high position
"""
x = np.linspace(0, 11, width, False)
p_1 = skew_func(x, e_1, w_1, a)
p_2 = skew_func(x, e_2, w_2, a)
p_ = np.max([p_1, p_2], axis=0)
sig_scale = MinMaxScaler().fit_transform(np.array(p_).reshape(-1, 1))
return sig_scale.reshape(-1)
def ppg_nonlinear_dynamic_system_template(width):
"""
EXPOSE
:param width:
:return:
"""
x1 = 0.15
x2 = 0.15
u = 0.5
beta = 1
gamma1 = -0.25
gamma2 = 0.25
x1_list = [x1]
x2_list = [x2]
dt = 0.1
for t in np.arange(1, 100, dt):
y1 = 0.5 * (np.abs(x1 + 1) - np.abs(x1 - 1))
y2 = 0.5 * (np.abs(x2 + 1) - np.abs(x2 - 1))
dx1 = -x1 + (1 + u) * y1 - beta * y2 + gamma1
dx2 = -x2 + (1 + u) * y2 + beta * y1 + gamma2
x1 = x1 + dx1 * dt
x2 = x2 + dx2 * dt
x1_list.append(x1)
x2_list.append(x2)
local_minima = argrelextrema(np.array(x2_list), np.less)[0]
s = np.array(x2_list[local_minima[-2]:local_minima[-1] + 1])
rescale_signal = squeeze_template(s, width)
window = signal.windows.cosine(len(rescale_signal), 0.5)
signal_data_tapered = np.array(window) * \
(rescale_signal - min(rescale_signal))
out_scale = MinMaxScaler().fit_transform(
np.array(signal_data_tapered).reshape(-1, 1))
return out_scale.reshape(-1)
def interp(ys, mul):
"""
handy func
:param ys:
:param mul:
:return:
"""
# linear extrapolation for last (mul - 1) points
ys = list(ys)
ys.append(2 * ys[-1] - ys[-2])
# make interpolation function
xs = np.arange(len(ys))
fn = scipy.interpolate.interp1d(xs, ys, kind="cubic")
# call it on desired data points
new_xs = np.arange(len(ys) - 1, step=1. / mul)
return fn(new_xs)
"""
Equation (3) from the paper
A dynamical model for generating synthetic electrocardiogram signals
"""
def ecg_dynamic_template(width, sfecg=256, N=256, Anoise=0, hrmean=60,
hrstd=1, lfhfratio=0.5, sfint=512,
ti=np.array([-70, -15, 0, 15, 100]),
ai=np.array([1.2, -5, 30, -7.5, 0.75]),
bi=np.array([0.25, 0.1, 0.1, 0.1, 0.4])
):
"""
EXPOSE
:param width:
:param sfecg:
:param N:
:param Anoise:
:param hrmean:
:param hrstd:
:param lfhfratio:
:param sfint:
:param ti:
:param ai:
:param bi:
:return:
"""
# convert to radians
ti = ti * np.pi / 180
# adjust extrema parameters for mean heart rate
hrfact = np.sqrt(hrmean / 60)
hrfact2 = np.sqrt(hrfact)
bi = hrfact * bi
ti = np.multiply([hrfact2, hrfact, 1, hrfact, hrfact2], ti)
flo = 0.1
fhi = 0.25
flostd = 0.01
fhistd = 0.01
# calculate time scales for rr and total output
sampfreqrr = 1
trr = 1 / sampfreqrr
rrmean = (60 / hrmean)
Nrr = 2 ** (np.ceil(np.log2(N * rrmean / trr)))
rr0 = rr_process(flo, fhi, flostd, fhistd,
lfhfratio, hrmean, hrstd, sampfreqrr, Nrr)
# upsample rr time series from 1 Hz to sfint Hz
rr = interp(rr0, sfint)
dt = 1 / sfint
rrn = np.zeros(len(rr))
tecg = 0
i = 0
while i < len(rr):
tecg = tecg + rr[i]
ip = int(np.round(tecg / dt))
rrn[i: ip + 1] = rr[i]
i = ip + 1
Nt = ip
x0 = [1, 0, 0.04]
tspan = np.arange(0, (Nt - 1) * dt, dt)
args = (rrn, sfint, ti, ai, bi)
solv_ode = solve_ivp(ordinary_differential_equation, [tspan[0], tspan[-1]],
x0, t_eval=np.arange(20.5, 21.5, 0.00001), args=args)
Y = (solv_ode.y)[2]
# if len(Y) > width:
# z = squeeze_template(Y,125)
return Y
def ordinary_differential_equation(t, x_equations, rr=None,
sfint=None, ti=None, ai=None, bi=None):
"""
handy
:param t:
:param x_equations:
:param rr:
:param sfint:
:param ti:
:param ai:
:param bi:
:return:
"""
x = x_equations[0]
y = x_equations[1]
z = x_equations[2]
ta = np.arctan2(y, x)
r0 = 1
a0 = 1.0 - np.sqrt(x ** 2 + y ** 2) / r0
ip = int(1 + | np.floor(t * sfint) | numpy.floor |
from pathlib import Path
import numpy as np
import gym
from gym import spaces, logger
from gym.utils import seeding
import matplotlib.pyplot as plt
from pycel import ExcelCompiler
class Parameters:
# (Avoid sampling random variables here: they would not be resampled upon reset())
# problem-specific parameters
techs = 3 # number of technologies (Offshore wind power, blue hydrogen, green hydrogen)
# fmt: off
reward_types = 6 # capital expenditure (capex), operating expenditure (opex), revenue, carbon emissions, total jobs supported, total economic impact
steps_per_episode = 20 # number of years in the planning horizon (2031 -> 2050 = 20)
# fmt: on
# This 'Pathways to Net Zero' environment manipulates a spreadsheet loaded in memory. The following 20 columns correspond to years 2031 to 2050 in tabs named 'Outputs' and 'CCUS':
# fmt: off
pathways2Net0ColumnInds = np.array(['P','Q','R','S','T','U','V','W','X','Y','Z','AA','AB','AC','AD','AE','AF','AG','AH','AI'])
# fmt: on
# The following 20 rows correspond to years 2031 to 2050 in tabs named 'BREEZE', 'GALE', and 'STORM':
pathways2Net0RowInds = np.arange(36, 36 + steps_per_episode)
# pathways2Net0ColumnInds[state.step_count] and pathways2Net0RowInds[state.step_count] will locate the current year's column / row respectively
# Multiplicative noise is applied to all costs. The parameters of this randomisation are:
noise_mu = 1.0
noise_sigma = 0.1
noise_clipping = 0.5 # (i.e., costs are reduced by 50% at the most)
noise_sigma_factor = np.sqrt(0.1) # this factor is applied to make CCUS capex & opex less volatile than other costs
# The costs in the Carbon capture utilisation and storage (CCUS) tab to be randomised are capex, opex, and carbon price, with these row numbers:
pathways2Net0RandomRowInds_CCUS = np.array([23, 24, 26])
# The costs in the 'Outputs' tab to be randomised are Offshore wind - Devex, Capex, and Opex, Green Hydrogen - Capex, Fixed Opex, and Variable Opex, Blue Hydrogen - price, Gas feedstock price, Capex, Fixed opex, Variable opex, and Natural gas cost, with these row numbers:
# fmt: off
pathways2Net0RandomRowInds_Outputs = np.array([148, 149, 150, 153, 154, 155, 158, 159, 163, 164, 165, 166])
# fmt: on
# multiplicative noise's mu and sigma, and clipping point:
noise_mu = 1.0
noise_sigma = 0.1 # or try 0.1, 0.0, np.sqrt(0.001), 0.02, np.sqrt(0.0003), 0.015, 0.01, np.sqrt(0.00001), 0.001
noise_clipping = 0.5 # or try 0.001, 0.1, 0.5 (i.e., original costs are reduced by 50% at the most)
noise_sigma_factor = np.sqrt(0.1) # as in https://github.com/rangl-labs/netzerotc/issues/36, CCUS capex & opex (CCUS row 23 and 24) should have smaller standard deviations
stochastic_sigma = False # set to False to use one single noise_sigma; set to True to randomly switch between two different std:
# noise_sigma_low = 0.001
# noise_sigma_high = np.sqrt(0.00001)
# OR, sample a sigma from a uniform distribution centered at noise_sigma with total 2-side range of noise_sigma_range:
noise_sigma_range = 0.002
noise_observability = False # set to True to make the observation_space contain randomized costs/prices; set to False to restrict the observation_space to contain only the state.step_count
class State:
def __init__(self, seed=None, param=Parameters()):
np.random.seed(seed=seed)
self.initialise_state(param)
def initialise_state(self, param):
# create local copy of spreadsheet model to be manipulated
self.pathways2Net0 = param.pathways2Net0
# create an array of costs for the current year and populate with 2030 costs (column 'O' in 'CCUS' and 'Outputs' tabs):
self.randomized_costs = np.ones(
len(param.pathways2Net0RandomRowInds_CCUS)
+ len(param.pathways2Net0RandomRowInds_Outputs)
)
for costRowID in np.arange(len(param.pathways2Net0RandomRowInds_CCUS)):
self.randomized_costs[costRowID] = param.pathways2Net0.evaluate(
"CCUS!O" + str(param.pathways2Net0RandomRowInds_CCUS[costRowID])
)
for costRowID in np.arange(len(param.pathways2Net0RandomRowInds_Outputs)):
self.randomized_costs[
len(param.pathways2Net0RandomRowInds_CCUS) + costRowID
] = param.pathways2Net0.evaluate(
"Outputs!O" + str(param.pathways2Net0RandomRowInds_Outputs[costRowID])
)
self.noise_observability = param.noise_observability
# time variables
# NOTE: our convention is to update step_count at the beginning of the gym step() function
self.step_count = -1
self.steps_per_episode = param.steps_per_episode
# initial jobs supported in 2030
self.jobs = np.float32(
110484
)
# variable to record jobs created each year
self.jobs_increment = np.zeros(1, dtype=np.float32) # initialized as 0
# fmt: off
# initial economic impact in 2030
self.econoImpact = np.float32(49938.9809739566)
# initial technology deployments in 2030
self.deployments = np.array([param.pathways2Net0.evaluate('GALE!P35'),
param.pathways2Net0.evaluate('GALE!X35'),
param.pathways2Net0.evaluate('GALE!Y35')],
dtype=np.float32)
# initial CO2 emissions in 2030
self.emission_amount = np.float32(param.pathways2Net0.evaluate('CCUS!O63'))
# fmt: on
# histories
self.observations_all = []
self.actions_all = []
self.rewards_all = []
self.weightedRewardComponents_all = []
self.deployments_all = []
self.emission_amount_all = []
def to_observation(self):
observation = (self.step_count,) + tuple(
self.randomized_costs
)
if self.noise_observability == False:
observation = (self.step_count,)
return observation
def is_done(self):
done = bool(self.step_count >= self.steps_per_episode - 1)
return done
def record(state, action, reward, weightedRewardComponents):
state.observations_all.append(state.to_observation())
state.actions_all.append(action)
state.rewards_all.append(reward)
state.weightedRewardComponents_all.append(weightedRewardComponents)
state.deployments_all.append(state.deployments)
state.emission_amount_all.append(state.emission_amount)
def observation_space(self):
obs_low = np.full_like(self.state.to_observation(), 0, dtype=np.float32)
obs_low[0] = -1 # first entry of obervation is the timestep
obs_high = np.full_like(self.state.to_observation(), 1e5, dtype=np.float32)
obs_high[0] = self.param.steps_per_episode # first entry of obervation is the timestep
if self.state.noise_observability == True:
obs_high[5] = 1e6
obs_high[7] = 1e6
result = spaces.Box(obs_low, obs_high, dtype=np.float32)
return result
def action_space(self):
# action specifies yearly increments in offshore wind power, blue hydrogen, and green hydrogen respectively
# lower limit on increments is zero
act_low = np.zeros(self.param.techs, dtype=np.float32)
# upper limits on increments depend on the technology
act_high = np.float32([27, 25, 24])
result = spaces.Box(act_low, act_high, dtype=np.float32)
return result
def apply_action(action, state, param):
# copy model from state to param
param.pathways2Net0 = state.pathways2Net0
# each technology gives rewards of various types (ie costs and revenues)
# create an array to hold the reward components (aggregated over all technologies):
weightedRewardComponents = np.zeros(
param.reward_types
)
# read in the current deployment for offshore wind power
offshoreWind = param.pathways2Net0.evaluate(
# "GALE!P" + str(param.pathways2Net0RowInds[state.step_count] - 1)
"GALE!S" + str(param.pathways2Net0RowInds[state.step_count] - 1)
)
# add the increment of offshore wind for this timestep (specified by the action), imposing a maximum deployment
offshoreWind = np.clip(offshoreWind + action[0], offshoreWind, 380)
# similarly for blue and green hydrogen
blueHydrogen = param.pathways2Net0.evaluate(
"GALE!X" + str(param.pathways2Net0RowInds[state.step_count] - 1)
)
blueHydrogen = np.clip(blueHydrogen + action[1], blueHydrogen, 270)
greenHydrogen = param.pathways2Net0.evaluate(
"GALE!Y" + str(param.pathways2Net0RowInds[state.step_count] - 1)
)
greenHydrogen = | np.clip(greenHydrogen + action[2], greenHydrogen, 253) | numpy.clip |
# MIT License - Copyright <NAME> and contributors
# See the LICENSE.md file included in this source code package
"""The one-line interface to this library.
Do not import this module directly, but rather import the main ennemi module.
"""
from __future__ import annotations
import concurrent.futures
from typing import Callable, Iterable, Optional, Sequence, Tuple, Type, TypeVar, Union
import itertools
import math
import numpy as np
from os import cpu_count
import sys
from ._entropy_estimators import _estimate_single_mi, _estimate_conditional_mi,\
_estimate_discrete_mi, _estimate_conditional_discrete_mi,\
_estimate_semidiscrete_mi, _estimate_conditional_semidiscrete_mi,\
_estimate_single_entropy, _estimate_discrete_entropy
try:
import numpy.typing as npt
FloatArray = npt.NDArray[np.float64]
ArrayLike = npt.ArrayLike
except:
# Just stop supporting annotations altogether on NumPy 1.20 and below
FloatArray = np.ndarray # type: ignore
ArrayLike = np.ndarray # type: ignore
GenArrayLike = TypeVar("GenArrayLike", Sequence[float], Sequence[Sequence[float]], FloatArray)
T = TypeVar("T")
def normalize_mi(mi: Union[float, GenArrayLike]) -> GenArrayLike:
"""Normalize mutual information values to the unit interval.
Equivalent to passing `normalize=True` to the estimation methods.
The return value matches the correlation coefficient between two Gaussian
random variables with unit variance. This coefficient is preserved by all
monotonic transformations, including scaling. The value is positive regardless
of the sign of the correlation.
Negative values are kept as-is. This is because mutual information is always
non-negative, but `estimate_mi` may produce negative values.
The normalization is not applicable to discrete variables:
it is not possible to get coefficient 1.0 even when the variables are completely
determined by each other. The formula assumes that the both variables have
an infinite amount of entropy.
Parameters:
---
mi : array_like or float
One or more mutual information values (in nats).
If this is a Pandas `DataFrame` or `Series`, the columns and indices
are preserved.
"""
# If the parameter is a pandas type, preserve the columns and indices
if "pandas" in sys.modules:
import pandas
if isinstance(mi, (pandas.DataFrame, pandas.Series)):
return mi.applymap(_normalize)
return np.vectorize(_normalize, otypes=[float])(mi)
def _normalize(mi: float) -> float:
if mi <= 0.0:
return mi
else:
return np.sqrt(1 - np.exp(-2 * mi))
def estimate_entropy(x: ArrayLike,
*, k: int = 3,
multidim: bool = False,
discrete: bool = False,
mask: Optional[ArrayLike] = None,
cond: Optional[ArrayLike] = None,
drop_nan: bool = False) -> FloatArray:
"""Estimate the entropy of one or more continuous random variables.
Returns the estimated entropy in nats. If `x` is two-dimensional, each
marginal variable is estimated separately by default. If the `multidim`
parameter is set to True, the array is interpreted as a single n-dimensional
random variable. If `x` is a pandas `DataFrame` or `Series`, the result is
a `DataFrame`.
If the `mask` parameter is set, only those `x` observations with the
matching mask element set to `True` are used for estimation.
The calculation is described in Kraskov et al. (2004): Estimating mutual
information. Physical Review E 69. doi:10.1103/PhysRevE.69.066138
Positional or keyword parameters:
---
x : array_like
A 1D or 2D array of observations. The interpretation of columns
depends on the `multidim` parameter.
Optional keyword parameters:
---
k : int, default 3
The number of neighbors to consider.
multidim : bool, default False
If False (the default), each column of `x` is considered a separate variable.
If True, the (n x m) array is considered a single m-dimensional variable.
discrete : bool, default False
If True, the variable and the optional conditioning variable are interpreted
as discrete variables. The result will be calculated using the mathematical
definition of entropy.
mask : array_like or None
If specified, an array of booleans that gives the input elements to use for
estimation. Use this to exclude some observations from consideration.
Currently, the mask must be one-dimensional.
cond : array_like or None
Optional 1D or 2D array of observations used for conditioning.
All variables in a 2D array are used together.
The calculation uses the chain rule H(X|Y) = H(X,Y) - H(Y) without
any correction for potential estimation bias.
drop_nan : bool, default False
If True, all NaN (not a number) values in `x` and `cond` are masked out.
Not applied to discrete data.
"""
x_arr = np.asarray(x)
# Validate the parameters
# Post-masking validation is done just before going to the algorithm
if mask is not None:
mask = np.asarray(mask)
_validate_mask(mask, x_arr.shape[0])
if not 1 <= x_arr.ndim <= 2:
raise ValueError("x must be one- or two-dimensional")
_validate_k_type(k)
if cond is None:
result = _estimate_entropy(x_arr, k, multidim, mask, discrete, drop_nan)
else:
cond_arr = np.asarray(cond)
_validate_cond(cond_arr, x_arr.shape[0])
result = _estimate_conditional_entropy(x_arr, cond_arr, k, multidim, mask, discrete, drop_nan)
# If the original x array was a pandas data type, return a DataFrame
# As an exception, if multidim=True, we still return a NumPy scalar
if not multidim and "pandas" in sys.modules:
import pandas
if isinstance(x, pandas.DataFrame):
return pandas.DataFrame(np.atleast_2d(result), columns=x.columns)
elif isinstance(x, pandas.Series):
return pandas.DataFrame(np.atleast_2d(result), columns=[x.name])
return result
def _estimate_entropy(x: FloatArray, k: int, multidim: bool,
mask: Optional[ArrayLike], discrete: bool, drop_nan: bool) -> FloatArray:
"""Strongly typed estimate_entropy()."""
if multidim or x.ndim == 1:
x = _mask_and_validate_entropy(x, mask, drop_nan, discrete, k)
return np.asarray(_call_entropy_func(x, k, discrete))
else:
nvar = x.shape[1]
result = np.empty(nvar)
for i in range(nvar):
xs = _mask_and_validate_entropy(x[:,i], mask, drop_nan, discrete, k)
result[i] = _call_entropy_func(xs, k, discrete)
return result
def _mask_and_validate_entropy(x: FloatArray, mask: Optional[ArrayLike],
drop_nan: bool, discrete: bool, k: int) -> FloatArray:
# Apply the mask and drop NaNs
# TODO: Support 2D masks (https://github.com/polsys/ennemi/issues/37)
if mask is not None:
x = x[mask]
if drop_nan and not discrete:
if x.ndim > 1:
x = x[~np.max(np.isnan(x), axis=1)]
else:
x = x[~np.isnan(x)]
# Validate the x array
if k >= x.shape[0]:
raise ValueError("k must be smaller than number of observations (after lag and mask)")
if not discrete and np.any(np.isnan(x)):
raise ValueError("input contains NaNs (after applying the mask), pass drop_nan=True to ignore")
return x
def _estimate_conditional_entropy(x: FloatArray, cond: FloatArray, k: int, multidim: bool,
mask: Optional[ArrayLike], discrete: bool, drop_nan: bool) -> FloatArray:
"""Conditional entropy by the chain rule: H(X|Y) = H(X,Y) - H(Y)."""
# Estimate the entropy of cond by the method above (multidim=True)
marginal = _estimate_entropy(cond, k, True, mask, discrete, drop_nan)
# The joint entropy depends on multidim and number of dimensions:
# In the latter case, the joint entropy is calculated for each x variable
if multidim or x.ndim == 1:
xs = _mask_and_validate_entropy(np.column_stack((x, cond)), mask, drop_nan, discrete, k)
return np.asarray(_call_entropy_func(xs, k, discrete) - marginal)
else:
nvar = x.shape[1]
joint = np.empty(nvar) # type: npt.NDArray[np.float64]
for i in range(nvar):
xs = _mask_and_validate_entropy(np.column_stack((x[:,i], cond)), mask, drop_nan, discrete, k)
joint[i] = _call_entropy_func(xs, k, discrete)
return joint - marginal
def _call_entropy_func(xs: FloatArray, k: int, discrete: bool) -> float:
if discrete:
return _estimate_discrete_entropy(xs, k)
else:
return _estimate_single_entropy(xs, k)
def estimate_mi(y: ArrayLike, x: ArrayLike,
lag: Union[Sequence[int], ArrayLike, int] = 0,
*, k: int = 3,
cond: Optional[ArrayLike] = None,
cond_lag: Union[Sequence[int], Sequence[Sequence[int]], ArrayLike, int] = 0,
mask: Optional[ArrayLike] = None,
discrete_y: bool = False,
discrete_x: bool = False,
preprocess: bool = True,
drop_nan: bool = False,
normalize: bool = False,
max_threads: Optional[int] = None,
callback: Optional[Callable[[int, int], None]] = None) -> FloatArray:
"""Estimate the mutual information between y and each x variable.
- Unconditional MI: the default.
- Conditional MI: pass a `cond` array.
- Discrete-continuous MI: set `discrete_y` to True.
Returns the estimated mutual information (in nats) for continuous
variables. The result is a 2D `ndarray` where the first index represents `lag` values
and the second index represents `x` columns. If `x` is a pandas
`DataFrame` or `Series`, the result is a `DataFrame`.
The time lag is interpreted as `y(t) ~ x(t - lag) | z(t - cond_lag)`.
The time lags are applied to the `x` and `cond` arrays such that the `y`
array stays the same every time.
This means that `y` is cropped to `y[max(max_lag,0) : N+min(min_lag,0)]`.
The `cond_lag` parameter specifies the lag for the `cond` array separately
from the `x` lag.
If the `mask` parameter is set, only those `y` observations with the
matching mask element set to `True` are used for estimation.
For accurate results, the variables should be transformed to roughly
symmetrical distributions. If `preprocess==True`, the variables are
automatically scaled to unit variance.
The calculation is based on "Kraskov et al. (2004): Estimating mutual
information. Physical Review E 69. doi:10.1103/PhysRevE.69.066138" and
derivatives by (Frenzel and Pompe 2007) and (Ross 2014).
Positional or keyword parameters:
---
y : array_like
A 1D array of observations. If `discrete_y` is True, the values may be
of any type. Otherwise the values must be numeric.
x : array_like
A 1D or 2D array where the columns are one or more variables and the
rows are observations. The number of rows must be the same as in y.
lag : int or array_like, default 0
A time lag or 1D array of time lags to apply. A positive lag means that
`y` depends on earlier `x` values and vice versa.
Optional keyword parameters:
---
k : int, default 3
The number of neighbors to consider.
Ignored if both variables are discrete.
cond : array_like or None
Optional 1D or 2D array of observations used for conditioning.
Must have as many observations as y.
All variables in a 2D array are used together.
If both `discrete_x` and `discrete_y` are set, this is interpreted as a
discrete variable. (In future versions, this might be set explicitly.)
cond_lag : int or array_like, default 0
Lag applied to the cond array. Must be broadcastable to the size of `lag`.
Can be two-dimensional to lag each conditioning variable separately.
mask : array_like or None
If specified, an array of booleans that gives the `y` elements to use for
estimation. Use this to exclude some observations from consideration
while preserving the time series structure of the data. Elements of
`x` and `cond` are masked with the lags applied.
discrete_x : bool, default False
discrete_y : bool, default False
If True, the respective variable is interpreted as a discrete variable.
Values of the variable may be non-numeric.
preprocess : bool, default True
By default, continuous variables are scaled to unit variance and
added with low-amplitude noise. The noise uses a fixed random seed.
drop_nan : bool, default False
If True, all NaN (not a number) values are masked out.
normalize : bool, default False
If True, the results will be normalized to correlation coefficient scale.
Same as calling `normalize_mi` on the results.
The results are sensible only if both variables are continuous.
max_threads : int or None
The maximum number of threads to use for estimation.
By default, the number of CPU cores is used.
callback : method or None
A method to call when each estimation task is completed. The method
must take two integer parameters: `x` variable index and lag value.
This method should be very short. Because Python code is not executed
concurrently, the callback may slow down other estimation tasks.
"""
# Convert parameters to consistent types
# Keep the original x parameter around for the Pandas data frame check
x_arr = np.asarray(x)
y_arr = np.asarray(y)
if cond is not None:
# Make cond 2D
cond_arr = np.column_stack((np.asarray(cond),))
ncond = cond_arr.shape[1]
else:
cond_arr = None
ncond = 1
mask_arr = None # type: Optional[npt.NDArray[np.float64]]
if mask is not None: mask_arr = np.asarray(mask)
# Broadcast cond_lag to be (#lags, #cond vars) in shape
lag_arr = np.atleast_1d(lag)
cond_lag_arr = np.broadcast_to(np.column_stack((cond_lag,)), (lag_arr.shape[0], ncond))
# Check the parameters and run the estimation
result = _estimate_mi(y_arr, x_arr, lag_arr, k, cond_arr,
cond_lag_arr, mask_arr, discrete_x, discrete_y, preprocess, drop_nan, max_threads, callback)
# Normalize if requested
if normalize:
result = normalize_mi(result)
# If the input was a pandas data frame, set the column names
if "pandas" in sys.modules:
import pandas
if isinstance(x, pandas.DataFrame):
return pandas.DataFrame(result, index=lag_arr, columns=x.columns)
elif isinstance(x, pandas.Series):
return pandas.DataFrame(result, index=lag_arr, columns=[x.name])
return result
def _estimate_mi(y: FloatArray, x: FloatArray, lag: FloatArray, k: int,
cond: Optional[FloatArray], cond_lag: FloatArray,
mask: Optional[FloatArray], discrete_x: bool, discrete_y: bool,
preprocess: bool, drop_nan: bool,
max_threads: Optional[int],
callback: Optional[Callable[[int, int], None]]) -> FloatArray:
"""This method is strongly typed, estimate_mi() does necessary conversion."""
_check_parameters(x, y, k, cond, mask)
# These are used for determining the y range to use
min_lag = min(np.min(lag), np.min(cond_lag))
max_lag = max(np.max(lag), np.max(cond_lag))
# Validate that the lag is not too large
if max_lag - min_lag >= y.size or max_lag >= y.size or min_lag <= -y.size:
raise ValueError("lag is too large, no observations left")
if x.ndim == 1:
nvar = 1
else:
_, nvar = x.shape
# Create a list of all variable, time lag combinations
# The params map contains tuples for simpler passing into worker function
indices = list(itertools.product(range(len(lag)), range(nvar)))
if x.ndim == 1:
params = list(map(lambda i: (x, y, lag[i[0]], max_lag, min_lag, k,
mask, cond, cond_lag[i[0]], discrete_x, discrete_y, preprocess, drop_nan), indices))
else:
params = list(map(lambda i: (x[:,i[1]], y, lag[i[0]], max_lag, min_lag, k,
mask, cond, cond_lag[i[0]], discrete_x, discrete_y, preprocess, drop_nan), indices))
# Run the estimation, possibly in parallel
def wrapped_callback(i: int) -> None:
if callback is not None:
lag_index, var_index = indices[i]
callback(var_index, lag[lag_index])
time_estimate = _get_mi_time_estimate(len(y), cond, k)
conc_result = _map_maybe_parallel(_lagged_mi, params, max_threads, time_estimate, wrapped_callback)
# Collect the results to a 2D array
result = np.empty((len(lag), nvar))
for index, res in zip(indices, conc_result):
result[index] = res
return result
def _check_parameters(x: FloatArray, y: Optional[FloatArray], k: int,
cond: Optional[FloatArray], mask: Optional[FloatArray]) -> None:
"""Does most of parameter checking, but some is still left to _lagged_mi."""
_validate_k_type(k)
# Validate the array shapes and lengths
if not 1 <= len(x.shape) <= 2:
raise ValueError("x must be one- or two-dimensional")
if y is not None:
if len(y.shape) > 1:
raise ValueError("y must be one-dimensional")
if (x.shape[0] != y.shape[0]):
raise ValueError("x and y must have same length")
# Validate the mask and condition
if mask is not None: _validate_mask(mask, x.shape[0])
if cond is not None: _validate_cond(cond, x.shape[0])
def _validate_k_type(k: int) -> None:
if not isinstance(k, int):
raise TypeError("k must be int")
if k <= 0:
raise ValueError("k must be greater than zero")
def _validate_mask(mask: FloatArray, input_len: int) -> None:
if len(mask.shape) > 1:
raise ValueError("mask must be one-dimensional")
if len(mask) != input_len:
raise ValueError("mask length does not match input length")
if mask.dtype != bool:
raise TypeError("mask must contain only booleans")
def _validate_cond(cond: FloatArray, input_len: int) -> None:
if not 1 <= cond.ndim <= 2:
raise ValueError("cond must be one- or two-dimensional")
if input_len != len(cond):
raise ValueError("x and cond must have same length")
def pairwise_mi(data: ArrayLike,
*, k: int = 3,
cond: Optional[ArrayLike] = None,
mask: Optional[ArrayLike] = None,
discrete: ArrayLike = False,
preprocess: bool = True,
drop_nan: bool = False,
normalize: bool = False,
max_threads: Optional[int] = None,
callback: Optional[Callable[[int, int], None]] = None) -> FloatArray:
"""Estimate the pairwise MI between each variable.
Returns a matrix where the (i,j)'th element is the mutual information
between the i'th and j'th columns in the data. The values are in nats or
in the normalized scale depending on the `normalize` parameter. The diagonal
contains NaNs (for better visualization, as the auto-MI should be infinite).
Positional or keyword parameters:
---
data : array_like
A 2D array where the columns represent variables.
Optional keyword parameters:
---
k : int, default 3
The number of neighbors to consider.
Ignored if both variables are discrete.
cond : array_like or None
Optional 1D or 2D array of observations used for conditioning.
Must have as many observations as the data.
All variables in a 2D array are used together.
mask : array_like or None
If specified, an array of booleans that gives the data elements to use for
estimation. Use this to exclude some observations from consideration.
discrete : bool or array_like, default False
Specifies the columns that contain discrete data. Conditioning can be
used only if the data is all-continuous or all-discrete (in which case
the condition is interpreted as discrete).
preprocess : bool, default True
By default, continuous variables are scaled to unit variance and
added with low-amplitude noise. The noise uses a fixed random seed.
drop_nan : bool, default False
If True, all NaN (not a number) values in `x` and `cond` are masked out.
normalize : bool, default False
If True, the MI values will be normalized to correlation coefficient scale.
Same as calling `normalize_mi` on the results.
The results are sensible only if both variables are continuous.
max_threads : int or None
The maximum number of threads to use for estimation.
By default, the number of CPU cores is used.
callback : method or None
A method to call when each estimation task is completed. The method
must take two integer parameters, representing the variable indices.
This method should be very short. Because Python code is not executed
concurrently, the callback may slow down other estimation tasks.
"""
# Convert arrays to consistent type; _lagged_mi assumes cond to be 2D
data_arr = np.asarray(data)
cond_arr = None # type: Optional[npt.NDArray[np.float64]]
mask_arr = None # type: Optional[npt.NDArray[np.float64]]
if cond is not None: cond_arr = np.column_stack((np.asarray(cond),))
if mask is not None: mask_arr = np.asarray(mask)
# If there is just one variable, return the trivial result
if data_arr.ndim == 1 or data_arr.shape[1] == 1:
return np.full((1,1), np.nan)
discrete_arr = np.broadcast_to(discrete, data_arr.shape[1])
result = _pairwise_mi(data_arr, k, cond_arr, preprocess, drop_nan, mask_arr,
discrete_arr, max_threads, callback)
# Normalize if asked for
if normalize:
result = normalize_mi(result)
# If data was a pandas DataFrame, return a DataFrame with matching names
if "pandas" in sys.modules:
import pandas
if isinstance(data, pandas.DataFrame):
return pandas.DataFrame(result, index=data.columns, columns=data.columns)
return result
def _pairwise_mi(data: FloatArray, k: int, cond: Optional[FloatArray], preprocess: bool,
drop_nan: bool, mask: Optional[FloatArray], discrete: FloatArray, max_threads: Optional[int],
callback: Optional[Callable[[int, int], None]]) -> FloatArray:
"""Strongly typed pairwise MI. The data array is at least 2D."""
_check_parameters(data, None, k, cond, mask)
if (not (np.all(discrete) or np.all(~discrete))) and (cond is not None):
raise ValueError("Conditioning is not supported with mixed discrete and continuous data. " +
"This is a limitation that can be lifted in the future (see " +
"https://github.com/polsys/ennemi/issues/87).")
nobs, nvar = data.shape
# Fake a cond_lag of correct shape for _lagged_mi
# TODO: Actually support cond lag (https://github.com/polsys/ennemi/issues/61)
if cond is not None:
cond_lag = np.full(cond.shape[1], 0)
else: cond_lag = np.asarray(0)
# Create a list of variable pairs
# By symmetry, it suffices to consider a triangular matrix
indices = []
params = []
for i in range(nvar):
for j in range(i+1, nvar):
indices.append((i, j))
params.append((data[:,i], data[:,j], 0, 0, 0, k, mask, cond, cond_lag,
discrete[i], discrete[j], preprocess, drop_nan))
# Run the MI estimation for each pair, possibly in parallel
def wrapped_callback(i: int) -> None:
if callback is not None:
callback(*indices[i])
time_estimate = _get_mi_time_estimate(nobs, cond, k)
conc_result = _map_maybe_parallel(_lagged_mi, params, max_threads, time_estimate, wrapped_callback)
# Collect the results, creating a symmetric matrix now
result = np.full((nvar, nvar), np.nan)
for (i,j), res in zip(indices, conc_result):
result[i,j] = res
result[j,i] = res
return result
def _get_mi_time_estimate(n: int, cond: Optional[FloatArray], k: int) -> float:
if cond is None:
n_cond = 0
else:
# cond is guaranteed to be two-dimensional
n_cond = cond.shape[1]
# These are determined pretty experimentally on a laptop computer
return n**(1.0 + 0.05*n_cond) * (0.9 + 0.1*math.sqrt(k)) * 1e-5
def _map_maybe_parallel(func: Callable[[T], float], params: Sequence[T],
max_threads: Optional[int], time_estimate: float,
callback: Callable[[int], None]) -> Iterable[float]:
# If there is benefit in doing so, and the user has not overridden the
# heuristic, execute the estimation in multiple parallel threads.
# Multithreading is fine, because the estimator code releases the
# Global Interpreter Lock for most of the time. Because the threads are
# CPU bound, we should use at most as many threads as there are cores.
# If the total execution time is very small, do not bother with threading
if len(params) * time_estimate < 0.2:
num_threads = 1
else:
num_threads = cpu_count() or 1
if max_threads is not None:
num_threads = min(num_threads, max_threads)
if num_threads > 1:
# Submit the individual tasks to thread pool
result = [ np.nan ] * len(params)
with concurrent.futures.ThreadPoolExecutor(num_threads, "ennemi-work") as executor:
tasks = []
# Do some work that would be done by executor.map() so that we can
# implement callbacks. The result list must be in the same order
# as the params list.
# Type comments because type info for Future comes from typeshed;
# the class itself is not subscriptable
def get_callback(i): # type: (int) -> Callable[[concurrent.futures.Future[float]], None]
def done(future): # type: (concurrent.futures.Future[float]) -> None
result[i] = future.result()
callback(i)
return done
for (i, p) in enumerate(params):
task = executor.submit(func, p)
task.add_done_callback(get_callback(i))
tasks.append(task)
concurrent.futures.wait(tasks)
return result
else:
# Run the tasks sequentially
# To support callbacks, we reimplement map() here too
result = []
for (i, p) in enumerate(params):
result.append(func(p))
callback(i)
return result
def _lagged_mi(param_tuple: Tuple[FloatArray, FloatArray, int, int, int, int,
Optional[FloatArray], Optional[FloatArray], FloatArray, bool, bool, bool, bool]) -> float:
# Unpack the param tuple used for possible cross-thread transfer
x, y, lag, max_lag, min_lag, k, mask, cond, cond_lag,\
discrete_x, discrete_y, preprocess, drop_nan = param_tuple
# Handle negative lags correctly
min_lag = min(min_lag, 0)
max_lag = max(max_lag, 0)
# The x observations start from max_lag - lag
xs = x[max_lag-lag : len(x)-lag+min_lag]
# The y observations always start from max_lag
ys = y[max_lag : len(y)+min_lag]
# The cond observations have their own lag terms
if cond is not None:
zs = np.column_stack([cond[max_lag-cond_lag[i] : len(cond)-cond_lag[i]+min_lag, i]\
for i in range(len(cond_lag))])
else: zs = None
# Apply masks, validate and preprocess the data
xs, ys, zs = _apply_masks(xs, ys, zs, mask, min_lag, max_lag, drop_nan)
_validate_masked_data(xs, ys, zs, k, discrete_x, discrete_y)
if preprocess:
xs, ys, zs = _rescale_data(xs, ys, zs, discrete_x, discrete_y)
# Apply the relevant estimation method
if cond is None:
if discrete_x and discrete_y:
return _estimate_discrete_mi(xs, ys)
elif discrete_x:
return _estimate_semidiscrete_mi(ys, xs, k)
if discrete_y:
return _estimate_semidiscrete_mi(xs, ys, k)
else:
return _estimate_single_mi(xs, ys, k)
else:
if discrete_x and discrete_y:
return _estimate_conditional_discrete_mi(xs, ys, zs)
elif discrete_x:
return _estimate_conditional_semidiscrete_mi(ys, xs, zs, k)
if discrete_y:
return _estimate_conditional_semidiscrete_mi(xs, ys, zs, k)
else:
return _estimate_conditional_mi(xs, ys, zs, k)
def _apply_masks(xs: FloatArray, ys: FloatArray, zs: Optional[FloatArray],
mask: Optional[FloatArray], min_lag: int, max_lag: int, drop_nan: bool)\
-> Tuple[FloatArray, FloatArray, Optional[FloatArray]]:
# Apply the mask
if mask is not None:
mask_subset = mask[max_lag : len(mask)+min_lag]
xs = xs[mask_subset]
ys = ys[mask_subset]
if zs is not None:
zs = zs[mask_subset]
# Drop NaNs
if drop_nan:
notna = ~( | np.isnan(xs) | numpy.isnan |
import torch
from torch import nn
from torch import distributions
import numpy as np
import pfrl
from pfrl import explorers
from pfrl.replay_buffer import high_level_batch_experiences_with_goal
from pfrl.agents import HIROHighLevelGoalConditionedTD3, GoalConditionedTD3
from pfrl.nn import ConstantsMult
from pfrl.nn.lmbda import Lambda
class HRLControllerBase():
def __init__(
self,
state_dim,
goal_dim,
action_dim,
scale,
replay_buffer,
actor_lr,
critic_lr,
expl_noise,
policy_noise,
noise_clip,
gamma,
policy_freq,
tau,
is_low_level,
buffer_freq,
minibatch_size,
gpu,
add_entropy,
burnin_action_func=None,
replay_start_size=2500):
self.scale = scale
# parameters
self.expl_noise = expl_noise
self.policy_noise = policy_noise
self.noise_clip = noise_clip
self.gamma = gamma
self.policy_freq = policy_freq
self.tau = tau
self.is_low_level = is_low_level
self.minibatch_size = minibatch_size
self.add_entropy = add_entropy
# create td3 agent
self.device = torch.device(f'cuda:{gpu}')
if self.add_entropy:
def squashed_diagonal_gaussian_head(x):
mean, log_scale = torch.chunk(x, 2, dim=-1)
log_scale = torch.clamp(log_scale, -20.0, 2.0)
var = torch.exp(log_scale * 2)
base_distribution = distributions.Independent(
distributions.Normal(loc=mean, scale=torch.sqrt(var)), 1
)
return base_distribution
policy = nn.Sequential(
nn.Linear(state_dim + goal_dim, 300),
nn.ReLU(),
nn.Linear(300, 300),
nn.ReLU(),
nn.Linear(300, action_dim * 2),
nn.Tanh(),
ConstantsMult(torch.cat((torch.tensor(self.scale), torch.ones(self.scale.size))).float().to(self.device)),
# pfrl.policies.DeterministicHead(),
Lambda(squashed_diagonal_gaussian_head),
)
else:
policy = nn.Sequential(
nn.Linear(state_dim + goal_dim, 300),
nn.ReLU(),
nn.Linear(300, 300),
nn.ReLU(),
nn.Linear(300, action_dim),
nn.Tanh(),
ConstantsMult(torch.tensor(self.scale).float().to(self.device)),
pfrl.policies.DeterministicHead(),
)
policy_optimizer = torch.optim.Adam(policy.parameters(), lr=actor_lr)
def make_q_func_with_optimizer():
q_func = nn.Sequential(
pfrl.nn.ConcatObsAndAction(),
nn.Linear(state_dim + goal_dim + action_dim, 300),
nn.ReLU(),
nn.Linear(300, 300),
nn.ReLU(),
nn.Linear(300, 1),
)
q_func_optimizer = torch.optim.Adam(q_func.parameters(), lr=critic_lr)
return q_func, q_func_optimizer
q_func1, q_func1_optimizer = make_q_func_with_optimizer()
q_func2, q_func2_optimizer = make_q_func_with_optimizer()
# TODO - have proper low and high values from action space.
# from the hiro paper, the scale is 1.0
explorer = explorers.AdditiveGaussian(
scale=self.expl_noise*1.0,
low=-self.scale,
high=self.scale
)
def default_target_policy_smoothing_func(batch_action):
"""Add noises to actions for target policy smoothing."""
noise = torch.clamp(self.policy_noise * torch.randn_like(batch_action), -self.noise_clip, self.noise_clip)
smoothed_action = batch_action + noise
smoothed_action = torch.min(smoothed_action, torch.tensor(self.scale).to(self.device).float())
smoothed_action = torch.max(smoothed_action, torch.tensor(-self.scale).to(self.device).float())
return smoothed_action
if self.is_low_level:
# standard goal conditioned td3
self.agent = GoalConditionedTD3(
policy,
q_func1,
q_func2,
policy_optimizer,
q_func1_optimizer,
q_func2_optimizer,
replay_buffer,
gamma=gamma,
soft_update_tau=tau,
explorer=explorer,
update_interval=1,
policy_update_delay=policy_freq,
replay_start_size=replay_start_size,
buffer_freq=buffer_freq,
minibatch_size=minibatch_size,
gpu=gpu,
add_entropy=self.add_entropy,
burnin_action_func=burnin_action_func,
target_policy_smoothing_func=default_target_policy_smoothing_func
)
else:
self.agent = HIROHighLevelGoalConditionedTD3(
policy,
q_func1,
q_func2,
policy_optimizer,
q_func1_optimizer,
q_func2_optimizer,
replay_buffer,
gamma=gamma,
soft_update_tau=tau,
explorer=explorer,
update_interval=1,
policy_update_delay=policy_freq,
replay_start_size=replay_start_size/buffer_freq,
buffer_freq=buffer_freq,
minibatch_size=minibatch_size,
gpu=gpu,
add_entropy=self.add_entropy,
burnin_action_func=burnin_action_func,
target_policy_smoothing_func=default_target_policy_smoothing_func
)
self.device = self.agent.device
def save(self, directory):
"""
save the internal state of the TD3 agent.
"""
self.agent.save(directory)
def load(self, directory):
"""
load the internal state of the TD3 agent.
"""
self.agent.load(directory)
def policy(self, state, goal):
"""
run the policy (actor).
"""
action = self.agent.act_with_goal(torch.FloatTensor(state), torch.FloatTensor(goal))
return np.clip(action, a_min=-self.scale, a_max=self.scale)
def _observe(self, states, goals, rewards, done, state_arr=None, action_arr=None):
"""
observe, and train (if we can sample from the replay buffer)
"""
self.agent.observe_with_goal(torch.FloatTensor(states), torch.FloatTensor(goals), rewards, done, None)
def observe(self, states, goals, rewards, done, iterations=1):
"""
get data from the replay buffer, and train.
"""
return self._observe(states, goals, rewards, goals, done)
# lower controller
class LowerController(HRLControllerBase):
def __init__(
self,
state_dim,
goal_dim,
action_dim,
scale,
replay_buffer,
add_entropy,
actor_lr=0.0001,
critic_lr=0.001,
expl_noise=0.1,
policy_noise=0.2,
noise_clip=0.5,
gamma=0.99,
policy_freq=2,
tau=0.005,
is_low_level=True,
buffer_freq=10,
minibatch_size=100,
gpu=None,
burnin_action_func=None):
super(LowerController, self).__init__(
state_dim=state_dim,
goal_dim=goal_dim,
action_dim=action_dim,
scale=scale,
replay_buffer=replay_buffer,
actor_lr=actor_lr,
critic_lr=critic_lr,
expl_noise=expl_noise,
policy_noise=policy_noise,
noise_clip=noise_clip,
gamma=gamma,
policy_freq=policy_freq,
tau=tau,
is_low_level=is_low_level,
buffer_freq=buffer_freq,
minibatch_size=minibatch_size,
gpu=gpu,
add_entropy=add_entropy,
burnin_action_func=burnin_action_func)
def observe(self, n_s, g, r, done):
return self._observe(n_s, g, r, done)
# higher controller
class HigherController(HRLControllerBase):
def __init__(
self,
state_dim,
goal_dim,
action_dim,
scale,
replay_buffer,
add_entropy,
actor_lr=0.0001,
critic_lr=0.001,
expl_noise=0.1,
policy_noise=0.2,
noise_clip=0.5,
gamma=0.99,
policy_freq=2,
tau=0.005,
is_low_level=False,
buffer_freq=10,
minibatch_size=100,
gpu=None,
burnin_action_func=None):
super(HigherController, self).__init__(
state_dim=state_dim,
goal_dim=goal_dim,
action_dim=action_dim,
scale=scale,
replay_buffer=replay_buffer,
actor_lr=actor_lr,
critic_lr=critic_lr,
expl_noise=expl_noise,
policy_noise=policy_noise,
noise_clip=noise_clip,
gamma=gamma,
policy_freq=policy_freq,
tau=tau,
is_low_level=is_low_level,
buffer_freq=buffer_freq,
minibatch_size=minibatch_size,
gpu=gpu,
add_entropy=add_entropy,
burnin_action_func=burnin_action_func)
self.action_dim = action_dim
def _off_policy_corrections(self, low_con, batch_size, sgoals, states, actions, candidate_goals=8):
"""
implementation of the novel off policy correction in the HIRO paper.
"""
first_s = [s[0] for s in states] # First x
last_s = [s[-1] for s in states] # Last x
# Shape: (batch_size, 1, subgoal_dim)
# diff = 1
# different in goals
diff_goal = (np.array(last_s) -
np.array(first_s))[:, np.newaxis, :self.action_dim]
# Shape: (batch_size, 1, subgoal_dim)
# original = 1
# random = candidate_goals
original_goal = np.array(sgoals)[:, np.newaxis, :]
# select random goals
random_goals = np.random.normal(loc=diff_goal, scale=.5*self.scale[None, None, :],
size=(batch_size, candidate_goals, original_goal.shape[-1]))
random_goals = random_goals.clip(-self.scale, self.scale)
# Shape: (batch_size, 10, subgoal_dim)
candidates = np.concatenate([original_goal, diff_goal, random_goals], axis=1)
# states = np.array(states)[:, :-1, :]
actions = np.array(actions)
seq_len = len(states[0])
# For ease
new_batch_sz = seq_len * batch_size
action_dim = actions[0][0].shape
obs_dim = states[0][0].shape
ncands = candidates.shape[1]
true_actions = actions.reshape((new_batch_sz,) + action_dim)
observations = states.reshape((new_batch_sz,) + obs_dim)
goal_shape = (new_batch_sz, self.action_dim)
# observations = get_obs_tensor(observations, sg_corrections=True)
# batched_candidates = np.tile(candidates, [seq_len, 1, 1])
# batched_candidates = batched_candidates.transpose(1, 0, 2)
policy_actions = np.zeros((ncands, new_batch_sz) + action_dim)
low_con.agent.training = False
for c in range(ncands):
subgoal = candidates[:,c]
candidate = (subgoal + states[:, 0, :self.action_dim])[:, None] - states[:, :, :self.action_dim]
candidate = candidate.reshape(*goal_shape)
policy_actions[c] = low_con.policy(torch.tensor(observations).float(), torch.tensor(candidate).float())
low_con.agent.training = True
difference = (policy_actions - true_actions)
difference = | np.where(difference != -np.inf, difference, 0) | numpy.where |
from ..panels import boxPanel
import numpy as np
NAME = 'Threshold'
DESCRIPTION = 'Identify the CP by thresholding it'
DOI = ''
import numpy as np
class CP(boxPanel): # Threshold
def create(self):
self.addParameter('Athreshold','float','Align Threshold [nN]',10.0)
self.addParameter('deltaX','float','Align left step [nm]',2000.0)
self.addParameter('Fthreshold','float','AVG area [nm]',100.0)
self.addParameter('shift','float','shift CP [nm]',0)
def calculate(self, x,y):
yth = self.getValue('Athreshold')*1e-9
if yth > np.max(y) or yth < | np.min(y) | numpy.min |
import numpy as np
import networkx as nx
from networkx.algorithms.traversal.breadth_first_search import bfs_edges
from osgeo import gdal, osr
from shapely.geometry import Polygon, Point
def get_sea_level(year: int, slr_intensity: str = 'low', event_freq: int = None) -> np.float:
# Get sea level return period associated with tides, surges, and tsunamis
if event_freq is None:
sl = 0.951
elif event_freq == 5:
sl = 8.2 / 3.281
elif event_freq == 10:
sl = 8.4 / 3.281
elif event_freq == 50:
sl = 8.9 / 3.281
elif event_freq == 100:
sl = 9.2 / 3.281
elif event_freq == 500:
sl = 9.7 / 3.281
else:
raise NotImplementedError
# Add sea level rise.
if year == 2000:
sl += 0. # Reference year.
elif year == 2022:
if slr_intensity == 'low':
sl += 2 / 39.37 # 2 in
elif slr_intensity == 'medium':
sl += 4 / 39.37 # 4 in
elif slr_intensity == 'high':
sl += 7 / 39.37 # 7 in
elif year == 2035:
if slr_intensity == 'low':
sl += 3 / 39.37 # 3 in
elif slr_intensity == 'medium':
sl += 7 / 39.37 # 7 in
elif slr_intensity == 'high':
sl += 13 / 39.37 # 13 in
elif year == 2050:
if slr_intensity == 'low':
sl += 4.5 / 39.37 # 4.5 in
elif slr_intensity == 'medium':
sl += 11.0 / 39.37 # 11 in
elif slr_intensity == 'high':
sl += 23.8 / 39.37 # 23.8 in
elif year == 2070:
if slr_intensity == 'low':
sl += 8.4 / 39.37 # 8.4 in
elif slr_intensity == 'medium':
sl += 18.6 / 39.37 # 18.5 in
elif slr_intensity == 'high':
sl += 38.5 / 39.37 # 38.5 in
elif year == 2100:
if slr_intensity == 'low':
sl += 16.5 / 39.37 # 16.5 in
elif slr_intensity == 'medium':
sl += 36.0 / 39.37 # 36 in
elif slr_intensity == 'high':
sl += 66.0 / 39.37 # 66 in
else:
raise NotImplementedError
return sl
class WaterBarrier:
def __init__(self, boundary_points: list, z: float, r: float = 3.):
self.boundary_points = boundary_points
self.z = z
self.r = r
self.polygon = Polygon(boundary_points)
self.minx, self.miny, self.maxx, self.maxy = self.polygon.bounds
def gaussian_elev(self, d: float, d_max: float = 5) -> float:
if abs(d) > abs(d_max):
return 0.
else:
sig = self.r / 3
return self.z * np.exp(-0.5 * (d / sig) ** 2)
class ElevatedPad(WaterBarrier):
def calculate_elevation(self, point: tuple) -> float:
pt = Point(point)
if (pt.x < self.minx - 1.5 * self.r or pt.x > self.maxx + 1.5 * self.r or
pt.y < self.miny - 1.5 * self.r or pt.y > self.maxy + 1.5 * self.r):
elev = 0.
elif pt.within(self.polygon):
elev = self.z
else:
d = self.polygon.boundary.distance(pt)
elev = self.gaussian_elev(d, d_max=1.5 * self.r)
return elev
class Berm(WaterBarrier):
def calculate_elevation(self, point: tuple) -> float:
pt = Point(point)
if (pt.x < self.minx - 1.5 * self.r or pt.x > self.maxx + 1.5 * self.r or
pt.y < self.miny - 1.5 * self.r or pt.y > self.maxy + 1.5 * self.r):
elev = 0.
elif pt.within(self.polygon):
d = self.polygon.exterior.distance(pt)
elev = self.gaussian_elev(d, d_max=1.5 * self.r)
else:
d = self.polygon.boundary.distance(pt)
elev = self.gaussian_elev(d, d_max=1.5 * self.r)
return elev
class Island:
def __init__(self, elev: np.ndarray, x: np.ndarray, y: np.ndarray, epsg: str, sea_ref_level: float, sea_ref_point: tuple):
self.elev = elev
self.x = x
self.y = y
self.epsg = epsg
self.sea_ref_level = sea_ref_level
self.sea_ref_point = sea_ref_point
self.land_mask = ~self.calculate_sea_mask(sea_ref_level)
self.elev_orig = | np.copy(elev) | numpy.copy |
# Runtime on 2.3GHz MacBook Pro with 8 Gb of RAM: ~10 minutes
# Requires: a file with limb darkening fit information that includes the intensity values
# Outputs: a .npy file with locations and values of the lowest I(mu) / I_1
# and the lowest I'(mu) / I_1 for every (T, g, lambda)
# Notes: to obtain the required file, run calc_limbdark with the -s option
import numpy as np
import pickle
import pa.lib.limbdark as limbdark
import pa.lib.fit as ft
import matplotlib.pyplot as plt
from matplotlib import rc
# real roots of a polynomial within bounds
# input: coefficients, lower bound, upper bound
def rts(a, b1, b2):
r = np.roots(a)
r = np.real(r[ np.isreal(r) ])
r = r[ (b1 <= r) & (r <= b2) ]
return r
# minimum of a polynomial: (location, value)
# inputs: polynomial's coefficients, locations of local suprema and boundary points
def minim(a, s, b1, b2):
pts = np.concatenate( (np.array([b1, b2]), s) )
val = np.polyval(a, pts)
i = | np.argmin(val) | numpy.argmin |
# encoding: utf-8
#
# @Author: <NAME>, <NAME>
# @Date: Nov 15, 2021
# @Filename: ism.py
# @License: BSD 3-Clause
# @Copyright: <NAME>, <NAME>
import os.path
from astropy import units as u
from astropy import constants as c
import numpy as np
from astropy.io import fits, ascii
from astropy.table import Table
from scipy.special import sph_harm
from astropy.wcs import WCS
from astropy.wcs.utils import proj_plane_pixel_scales
from astropy.coordinates import SkyCoord
from astropy.modeling.models import Sersic2D
from dataclasses import dataclass
import sys
if (sys.version_info[0]+sys.version_info[1]/10.) < 3.8:
from backports.cached_property import cached_property
else:
from functools import cached_property
from scipy.ndimage.interpolation import map_coordinates
from scipy.interpolate import interp1d, interp2d
import lvmdatasimulator
from lvmdatasimulator import log
import progressbar
from joblib import Parallel, delayed
from astropy.convolution import convolve_fft, kernels
from lvmdatasimulator.utils import calc_circular_mask, convolve_array, set_default_dict_values, \
ism_extinction, check_overlap, assign_units
fluxunit = u.erg / (u.cm ** 2 * u.s * u.arcsec ** 2)
velunit = u.km / u.s
def brightness_inhomogeneities_sphere(harm_amplitudes, ll, phi_cur, theta_cur, rho, med, radius, thickness):
"""
Auxiliary function producing the inhomogeneities on the brightness distribution for the Cloud of Bubble objects
using the spherical harmonics.
"""
brt = theta_cur * 0
for m in np.arange(-ll, ll + 1):
brt += (harm_amplitudes[m + ll * (ll + 1) - 1] * sph_harm(m, ll, phi_cur, theta_cur).real * med *
(1 - np.sqrt(abs(rho.value ** 2 / radius.value ** 2 - (1 - thickness / 2) ** 2))))
return brt
def sphere_brt_in_line(brt_3d, rad_3d, rad_model, flux_model):
"""
Auxiliary function computing the brightness of the Cloud or Bubble at given radii and in given line
according to the Cloudy models
"""
p = interp1d(rad_model, flux_model, fill_value='extrapolate', assume_sorted=True)
return p(rad_3d) * brt_3d
def interpolate_sphere_to_cartesian(spherical_array, x_grid=None, y_grid=None, z_grid=None,
rad_grid=None, theta_grid=None, phi_grid=None, pxscale=1. * u.pc):
"""
Auxiliary function to project the brightness or velocities from the spherical to cartesian coordinates
"""
x, y, z = np.meshgrid(x_grid, y_grid, z_grid, indexing='ij')
phi_c, theta_c, rad_c = xyz_to_sphere(x, y, z, pxscale=pxscale)
ir = interp1d(rad_grid, np.arange(len(rad_grid)), bounds_error=False)
ith = interp1d(theta_grid, np.arange(len(theta_grid)))
iphi = interp1d(phi_grid, np.arange(len(phi_grid)))
new_ir = ir(rad_c.ravel())
new_ith = ith(theta_c.ravel())
new_iphi = iphi(phi_c.ravel())
cart_data = map_coordinates(spherical_array, np.vstack([new_ir, new_ith, new_iphi]),
order=1, mode='constant', cval=0)
return cart_data.reshape([len(x_grid), len(y_grid), len(z_grid)]).T
def limit_angle(value, bottom_limit=0, top_limit=np.pi):
"""
Auxiliary function to limit the angle values to the range of [0, pi]
"""
value[value < bottom_limit] += (top_limit - bottom_limit)
value[value > top_limit] -= (top_limit - bottom_limit)
return value
def xyz_to_sphere(x, y, z, pxscale=1. * u.pc):
"""
Auxiliary function to map the coordinates from cartesian to spherical system
"""
phi_c = np.arctan2(y, x)
rad_c = (np.sqrt(x ** 2 + y ** 2 + z ** 2))
rad_c[rad_c == 0 * u.pc] = 1e-3 * pxscale
theta_c = (np.arccos(z / rad_c))
phi_c = limit_angle(phi_c, 0 * u.radian, 2 * np.pi * u.radian)
theta_c = limit_angle(theta_c, 0 * u.radian, np.pi * u.radian)
return phi_c, theta_c, rad_c
def find_model_id(file=lvmdatasimulator.CLOUDY_MODELS,
check_id=None, params=lvmdatasimulator.CLOUDY_SPEC_DEFAULTS['id']):
"""
Checks the input parameters of the pre-computed Cloudy model and return corresponding index in the grid
"""
with fits.open(file) as hdu:
if check_id is None:
if params is None:
check_id = lvmdatasimulator.CLOUDY_SPEC_DEFAULTS['id']
log.warning(f'Default Cloudy model will be used (id = {check_id})')
else:
summary_table = Table(hdu['Summary'].data)
indexes = np.arange(len(summary_table)).astype(int)
rec_table = np.ones(shape=len(summary_table), dtype=bool)
def closest(rec, prop, val):
unique_col = np.unique(summary_table[prop][rec])
if isinstance(val, str):
res = unique_col[unique_col == val]
if len(res) == 0:
return ""
return res
else:
return unique_col[np.argsort(np.abs(unique_col - val))[0]]
for p in params:
if p not in summary_table.colnames or params[p] is None or \
((isinstance(params[p], float) or isinstance(params[p], int)) and ~np.isfinite(params[p])):
continue
rec_table = rec_table & (summary_table[p] == closest(indexes, p, params[p]))
indexes = np.flatnonzero(rec_table)
if len(indexes) == 0:
break
if len(indexes) == 0 or len(indexes) == len(summary_table):
check_id = lvmdatasimulator.CLOUDY_SPEC_DEFAULTS['id']
log.warning('Input parameters do not correspond to any pre-computed Cloudy model.'
'Default Cloudy model will be used (id = {0})'.format(check_id))
elif len(indexes) == 1:
check_id = summary_table['Model_ID'][indexes[0]]
for p in params:
if p not in summary_table.colnames or params[p] is None or \
((isinstance(params[p], float) or
isinstance(params[p], int)) and ~np.isfinite(params[p])):
continue
if params[p] != summary_table[p][indexes[0]]:
log.warning(f'Use the closest pre-computed Cloudy model with id = {check_id}')
break
else:
check_id = summary_table['Model_ID'][indexes[0]]
log.warning(f'Select one of the closest pre-computed Cloudy model with id = {check_id}')
#
# for cur_ext in range(len(hdu)):
# if cur_ext == 0:
# continue
# found = False
# for p in params:
# if p == 'id':
# continue
# precision = 1
# if p == 'Z':
# precision = 2
# if np.round(params[p], precision) != np.round(hdu[cur_ext].header[p], precision):
# break
# else:
# found = True
# if found:
# return cur_ext, check_id
# check_id = lvmdatasimulator.CLOUDY_SPEC_DEFAULTS['id']
# log.warning('Input parameters do not correspond to any pre-computed Cloudy model.'
# 'Default Cloudy model will be used (id = {0})'.format(check_id))
extension_index = None
while extension_index is None:
extension_index = [cur_ext for cur_ext in range(len(hdu)) if (
check_id == hdu[cur_ext].header.get('MODEL_ID'))]
if len(extension_index) == 0:
if check_id == lvmdatasimulator.CLOUDY_SPEC_DEFAULTS['id']:
log.warning('Model_ID = {0} is not found in the Cloudy models grid. '
'Use the first one in the grid instead'.format(check_id))
extension_index = 1
else:
log.warning('Model_ID = {0} is not found in the Cloudy models grid. '
'Use default ({1}) instead'.format(check_id,
lvmdatasimulator.CLOUDY_SPEC_DEFAULTS['id']))
check_id = lvmdatasimulator.CLOUDY_SPEC_DEFAULTS['id']
extension_index = None
else:
extension_index = extension_index[0]
return extension_index, check_id
@dataclass
class Nebula:
"""
Base class defining properties of every nebula type.
By itself it describes the rectangular nebula (e.g. DIG)
Constructed nebula has 4 dimensions, where 4th derive its appearance in different lines
(if spectrum_id is None, or if it is dark nebula => only one line)
"""
xc: int = None # Center of the region in the field of view, pix
yc: int = None # Center of the region in the field of view, pix
x0: int = 0 # Coordinates of the bottom-left corner in the field of view, pix
y0: int = 0 # Coordinates of the bottom-left corner in the field of view, pix
pix_width: int = None # full width of cartesian grid, pix (should be odd)
pix_height: int = None # full height of cartesian grid, pix (should be odd)
width: u.pc = 0 * u.pc # width of the nebula in pc (not used if pix_width is set up)
height: u.pc = 0 * u.pc # height of the nebula in pc (not used if pix_height is set up)
pxscale: u.pc = 0.01 * u.pc # pixel size in pc
spectrum_id: int = None # ID of a template Cloudy emission spectrum for this nebula
n_brightest_lines: int = None # limit the number of the lines to the first N brightest
sys_velocity: velunit = 0 * velunit # Systemic velocity
turbulent_sigma: velunit = 10 * velunit # Velocity dispersion due to turbulence; included in calculations of LSF
max_brightness: fluxunit = 1e-15 * fluxunit
max_extinction: u.mag = 0 * u.mag
perturb_scale: int = 0 * u.pc # Spatial scale of correlated perturbations
perturb_amplitude: float = 0.1 # Maximal amplitude of perturbations
_npix_los: int = 1 # full size along line of sight in pixels
nchunks: int = -1 # number of chuncks to use for the convolution. If negative, select automatically
vel_gradient: (velunit / u.pc) = 0 # velocity gradient along the nebula
vel_pa: u.degree = 0 # Position angle of the kinematical axis (for the velocity gradient or rotation velocity)
def __post_init__(self):
self._assign_all_units()
self._assign_position_params()
self._ref_line_id = 0
self.linerat_constant = True # True if the ratio of line fluxes shouldn't change across the nebula
def _assign_all_units(self):
whole_list_properties = ['pxscale', 'sys_velocity', 'turbulent_sigma', 'max_brightness', 'max_extinction',
'perturb_scale', 'radius', 'PA', 'length', 'width', 'vel_gradient', 'r_eff',
'vel_rot', 'expansion_velocity', 'spectral_axis', 'vel_pa']
whole_list_units = [u.pc, velunit, velunit, fluxunit, u.mag, u.pc, u.pc, u.degree, u.pc, u.pc,
(velunit / u.pc), u.kpc, velunit, velunit, velunit, u.degree]
cur_list_properties = []
cur_list_units = []
for prp, unit in zip(whole_list_properties, whole_list_units):
if hasattr(self, prp):
cur_list_properties.append(prp)
cur_list_units.append(unit)
assign_units(self, cur_list_properties, cur_list_units)
def _assign_position_params(self, conversion_type='rect'):
if conversion_type == 'rect':
for v in ['height', 'width']:
if self.__getattribute__(f'pix_{v}') is None:
val = np.round((self.__getattribute__(v) / self.pxscale).value / 2.).astype(int) * 2 + 1
else:
val = np.round(self.__getattribute__(f'pix_{v}') / 2.).astype(int) * 2 + 1
setattr(self, f'pix_{v}', val)
elif conversion_type == 'ellipse':
self.pix_width = (np.round(np.abs(self.radius / self.pxscale * np.sin(self.PA)) +
np.abs(self.radius / self.pxscale *
self.ax_ratio * np.cos(self.PA))).astype(int) * 2 + 1).value
self.pix_height = (np.round(np.abs(self.radius / self.pxscale * np.cos(self.PA)) +
np.abs(self.radius / self.pxscale *
self.ax_ratio * np.sin(self.PA))).astype(int) * 2 + 1).value
elif conversion_type == 'galaxy':
self.pix_width = (np.round(np.abs(self.r_max * np.sin(self.PA)) +
np.abs(self.r_max * self.ax_ratio * np.cos(self.PA))).astype(int) * 2 + 1).value
self.pix_height = (np.round(np.abs(self.r_max * np.cos(self.PA)) +
np.abs(self.r_max * self.ax_ratio * np.sin(self.PA))).astype(int) * 2 + 1).value
elif conversion_type == 'cylinder':
self.pix_width = (np.ceil((self.length * np.abs(np.sin(self.PA)) +
self.width * np.abs(np.cos(self.PA))) / self.pxscale / 2.
).astype(int) * 2 + 1).value
self.pix_height = (np.ceil((self.length * np.abs(np.cos(self.PA)) +
self.width * np.abs(np.sin(self.PA))) / self.pxscale / 2.
).astype(int) * 2 + 1).value
if (self.xc is not None) and (self.yc is not None):
self.x0 = self.xc - np.round((self.pix_width - 1) / 2).astype(int)
self.y0 = self.yc - np.round((self.pix_height - 1) / 2).astype(int)
elif (self.x0 is not None) and (self.y0 is not None):
self.xc = self.x0 + np.round((self.pix_width - 1) / 2).astype(int)
self.yc = self.y0 + np.round((self.pix_height - 1) / 2).astype(int)
@cached_property
def _cartesian_x_grid(self):
return np.arange(self.pix_width) * self.pxscale
@cached_property
def _cartesian_y_grid(self):
return np.arange(self.pix_height) * self.pxscale
@cached_property
def _cartesian_z_grid(self):
return np.arange(self._npix_los) * self.pxscale
@cached_property
def _max_density(self):
return self.max_extinction * (1.8e21 / (u.cm ** 2 * u.mag))
@cached_property
def _brightness_3d_cartesian(self):
"""
Method to obtain the brightness (or density) distribution of the nebula in cartesian coordinates
"""
brt = np.ones(shape=(self.pix_height, self.pix_width, self._npix_los), dtype=float) / self._npix_los
if (self.perturb_scale > 0) and (self.perturb_amplitude > 0):
pertscale = (self.perturb_scale / self.pxscale).value
perturb = np.random.uniform(-1, 1, (self.pix_height, self.pix_width)
) * self.perturb_amplitude / self._npix_los
xx, yy = np.meshgrid(np.arange(self.pix_width), np.arange(self.pix_height))
f = np.exp(-2 * (xx ** 2 + yy ** 2) / pertscale)
perturb = 4 / np.sqrt(np.pi) / pertscale * np.fft.ifft2(np.fft.fft2(perturb) * np.fft.fft2(f)).real
brt += (perturb[:, :, None] - np.median(perturb))
return brt
@cached_property
def _brightness_4d_cartesian(self):
"""
Derive the brightness (or density) distribution of the nebula for each emission line in cartesian coordinates
"""
if self.spectrum_id is None or self.linerat_constant:
flux_ratios = np.array([1.])
else:
with fits.open(lvmdatasimulator.CLOUDY_MODELS) as hdu:
flux_ratios = hdu[self.spectrum_id].data[1:, 1]
index_ha = np.flatnonzero(hdu[self.spectrum_id].data[1:, 0] == 6562.81)
if self.n_brightest_lines is not None and \
(self.n_brightest_lines > 0) and (self.n_brightest_lines < len(flux_ratios)):
indexes_sorted = np.argsort(flux_ratios)[::-1]
flux_ratios = flux_ratios[indexes_sorted[: self.n_brightest_lines]]
index_ha = np.flatnonzero(hdu[self.spectrum_id].data[1:, 0][indexes_sorted] == 6562.81)
if len(index_ha) == 1:
self._ref_line_id = index_ha[0]
return self._brightness_3d_cartesian[None, :, :, :] * flux_ratios[:, None, None, None]
@cached_property
def brightness_skyplane(self):
"""
Project the 3D nebula onto sky plane (for emission or continuum sources)
"""
if self.max_brightness > 0:
norm_max = self.max_brightness
else:
norm_max = 1
map2d = np.nansum(self._brightness_3d_cartesian, 2)
return map2d / np.nanmax(map2d) * norm_max
@cached_property
def brightness_skyplane_lines(self):
"""
Project the 3D emission nebula line onto sky plane (return images in each emission line)
"""
if self.max_brightness > 0:
map2d = np.nansum(self._brightness_4d_cartesian, 3)
return map2d / np.nanmax(map2d[self._ref_line_id, :, :]) * self.max_brightness
else:
return None
@cached_property
def extinction_skyplane(self):
"""
Project the 3D nebula onto sky plane (for dark clouds)
"""
if self.max_extinction > 0:
map2d = np.nansum(self._brightness_3d_cartesian, 2)
return map2d / np.nanmax(map2d) * self._max_density / (1.8e21 / (u.cm ** 2 * u.mag))
else:
return None
@cached_property
def vel_field(self):
return self._get_2d_velocity()
# if vel_field is None:
# return np.atleast_1d(self.sys_velocity)
# else:
# return vel_field + self.sys_velocity
def _get_2d_velocity(self):
if hasattr(self, 'vel_gradient') and (self.vel_gradient is not None) and (self.vel_gradient != 0):
xx, yy = np.meshgrid(np.arange(self.pix_width), np.arange(self.pix_height))
vel_field = (- (xx - (self.pix_width - 1) / 2) * np.sin(self.vel_pa) +
(yy - (self.pix_height - 1) / 2) * np.cos(self.vel_pa)) * self.pxscale * self.vel_gradient
return vel_field
else:
return None
# @cached_property
# def line_profile(self):
# lprf = np.zeros(shape=len(self.los_velocity), dtype=float)
# lprf[np.floor(len(lprf) / 2.).astype(int)] = 1.
# return lprf
@dataclass
class Rectangle(Nebula):
"""
Class defining a simple rectangular component.
This is equal to Nebula, but no perturbations and turbulence by default
"""
perturb_amplitude: float = 0.0 # Maximal amplitude of perturbations
turbulent_sigma: velunit = 0 * velunit # Velocity dispersion due to turbulence; included in calculations of LSF
def __post_init__(self):
self._assign_all_units()
self._assign_position_params()
self._ref_line_id = 0
self.linerat_constant = True # True if the ratio of line fluxes shouldn't change across the nebula
@dataclass
class Ellipse(Nebula):
"""
Class defining a simple elliptical component.
No perturbations and turbulence by default
"""
perturb_amplitude: float = 0.0 # Maximal amplitude of perturbations
turbulent_sigma: velunit = 0 * velunit # Velocity dispersion due to turbulence; included in calculations of LSF
radius: u.pc = 1.0 * u.pc # Radius along the major axis of the ellipse (or radius of the circle)
PA: u.degree = 90 * u.degree # position angle of the major axis
ax_ratio: float = 1. # ratio of minor/major axes
def __post_init__(self):
self._assign_all_units()
self._npix_los = 1
self._assign_position_params(conversion_type='ellipse')
self._ref_line_id = 0
self.linerat_constant = True # True if the ratio of line fluxes shouldn't change across the nebula
@cached_property
def _brightness_3d_cartesian(self):
"""
Method to obtain the brightness (or density) distribution of the nebula in cartesian coordinates
"""
xx, yy = np.meshgrid(np.arange(self.pix_width), np.arange(self.pix_height))
brt = np.ones(shape=(self.pix_height, self.pix_width), dtype=np.float32)
angle = (self.PA + 90 * u.degree).to(u.radian).value
xct = (xx - (self.pix_width - 1) / 2) * np.cos(angle) + \
(yy - (self.pix_height - 1) / 2) * np.sin(angle)
yct = (xx - (self.pix_width - 1) / 2) * np.sin(angle) - \
(yy - (self.pix_height - 1) / 2) * np.cos(angle)
rmaj = (self.radius.to(u.pc) / self.pxscale.to(u.pc)).value
rmin = (self.radius.to(u.pc) / self.pxscale.to(u.pc)).value * self.ax_ratio
rec = (xct ** 2 / rmaj ** 2) + (yct ** 2 / rmin ** 2) >= 1
brt[rec] = 0
brt = brt.reshape((self.pix_height, self.pix_width, 1))
return brt
@dataclass
class Circle(Ellipse):
"""
Class defining a simple circular component.
"""
def __post_init__(self):
self._assign_all_units()
self.ax_ratio = 1.
self._npix_los = 1
self._assign_position_params(conversion_type='ellipse')
self._ref_line_id = 0
self.linerat_constant = True # True if the ratio of line fluxes shouldn't change across the nebula
@dataclass
class Filament(Nebula):
"""
Class of an isotropic cylindrical shape filament.
Defined by its position, length, PA, radius, maximal optical depth.
If it is emission-type filament, then also maximal brightness is required.
Velocity gradient also can be set up
"""
PA: u.degree = 90 * u.degree # position angle of the filament
length: u.pc = 10 * u.pc # full length of the filament
width: u.pc = 0.1 * u.pc # full width (diameter) of the filament
def __post_init__(self):
self._assign_all_units()
self._assign_position_params(conversion_type='cylinder')
self._npix_los = 1
self._ref_line_id = 0
self.linerat_constant = True # True if the ratio of line fluxes shouldn't change across the nebula
@cached_property
def _brightness_3d_cartesian(self):
"""
Method to obtain the brightness (or density) distribution of the nebula in cartesian coordinates
"""
xx, yy = np.meshgrid(np.arange(self.pix_width), np.arange(self.pix_height))
brt = np.zeros_like(xx, dtype=np.float32)
xct = (xx - (self.pix_width - 1) / 2) * np.cos(self.PA + 90 * u.degree) + \
(yy - (self.pix_height - 1) / 2) * np.sin(self.PA + 90 * u.degree)
yct = (xx - (self.pix_width - 1) / 2) * np.sin(self.PA + 90 * u.degree) - \
(yy - (self.pix_height - 1) / 2) * np.cos(self.PA + 90 * u.degree)
rad = ((self.width / self.pxscale).value / 2.)
len_px = ((self.length / self.pxscale).value / 2.)
rec = (np.abs(yct) <= rad) & (np.abs(xct) <= len_px)
brt[rec] = np.sqrt(1. - (yct[rec] / rad) ** 2)
brt = brt.reshape((self.pix_height, self.pix_width, 1))
return brt
@dataclass
class _ObsoleteFilament(Nebula):
"""
Class of an isotropic cylindrical shape filament.
Defined by its position, length, PA, radius, maximal optical depth
if it is emission-type filament, then maximal brightness
NB: this class is obsolete, but might be considered later in case of implementation of varying line ratios
"""
PA: u.degree = 90 * u.degree # position angle of the filament
length: u.pc = 10 * u.pc # full length of the filament
width: u.pc = 0.1 * u.pc # full width (diameter) of the filament
vel_gradient: (velunit / u.pc) = 0 # velocity gradient along the filament (to be added)
_theta_bins: int = 50
_rad_bins: int = 0
_h_bins: int = 2
_npix_los: int = 101
def __post_init__(self):
self._assign_all_units()
if self._rad_bins == 0:
self._rad_bins = np.ceil(self.width.to(u.pc).value / self.pxscale.to(u.pc).value * 5).astype(int)
if (self.xc is not None) and (self.yc is not None):
self.x0 = self.xc - np.round((len(self._cartesian_y_grid) - 1) / 2).astype(int)
self.y0 = self.yc - np.round((len(self._cartesian_z_grid) - 1) / 2).astype(int)
elif (self.x0 is not None) and (self.y0 is not None):
self.xc = self.x0 + np.round((len(self._cartesian_y_grid) - 1) / 2).astype(int)
self.yc = self.y0 + np.round((len(self._cartesian_z_grid) - 1) / 2).astype(int)
self._ref_line_id = 0
self.linerat_constant = True # True if the ratio of line fluxes shouldn't change across the nebula
@cached_property
def _theta_grid(self):
return np.linspace(0, 2 * np.pi, self._theta_bins)
@cached_property
def _h_grid(self):
return np.linspace(0, self.length, self._h_bins)
@cached_property
def _rad_grid(self):
return np.linspace(0, self.width / 2, self._rad_bins)
@cached_property
def _cartesian_y_grid(self):
npix = np.ceil(1.01 * (self.length * np.abs(np.sin(self.PA)) +
self.width * np.abs(np.cos(self.PA))) / self.pxscale).astype(int)
npix_l = npix / 2 - np.ceil(self.length / 2 * np.sin(-self.PA) / self.pxscale).astype(int)
return (np.linspace(0, npix, npix + 1) - npix_l) * self.pxscale
@cached_property
def _cartesian_z_grid(self):
npix = np.ceil(1.01 * (self.length * np.abs(np.cos(self.PA)) +
self.width * np.abs(np.sin(self.PA))) / self.pxscale).astype(int)
npix_l = npix / 2 - np.ceil(self.length / 2 * np.cos(-self.PA) / self.pxscale).astype(int)
return (np.linspace(0, npix, npix + 1) - npix_l) * self.pxscale
@cached_property
def _cartesian_x_grid(self):
return np.linspace(-1.01, 1.01, self._npix_los) * self.width / 2
@cached_property
def _brightness_3d_cylindrical(self):
"""
Method to calculate brightness (or opacity) of the cloud at given theta, phi and radii
theta: float -- azimuthal angle [0, 2 * np.pi]
rad: float -- radius [0, self.width / 2]
h: float -- height [0, self.length]
Returns:
3D cube of normalized brightness in theta-rad-h grid; total brightness = 1
"""
rho, theta, h = np.meshgrid(self._rad_grid, self._theta_grid, self._h_grid, indexing='ij')
brt = np.ones_like(theta)
brt[rho > (self.width / 2)] = 0
norm = np.sum(brt)
if norm > 0:
brt = brt / np.sum(brt)
return brt
@cached_property
def _brightness_3d_cartesian(self):
x, y, z = np.meshgrid(self._cartesian_x_grid, self._cartesian_y_grid,
self._cartesian_z_grid, indexing='ij')
h_c = -y * np.sin(self.PA) + z * np.cos(self.PA)
theta_c = np.arctan2(y * np.cos(self.PA) + z * np.sin(self.PA), x)
rad_c = np.sqrt(x ** 2 + (y * np.cos(self.PA) + z * np.sin(self.PA)) ** 2)
rad_c[rad_c == 0 * u.pc] = 1e-3 * self.pxscale
theta_c = limit_angle(theta_c, 0 * u.radian, 2 * np.pi * u.radian)
ir = interp1d(self._rad_grid, np.arange(self._rad_bins), bounds_error=False)
ith = interp1d(self._theta_grid, np.arange(self._theta_bins))
ih = interp1d(self._h_grid, np.arange(self._h_bins), bounds_error=False)
new_ir = ir(rad_c.ravel())
new_ith = ith(theta_c.ravel())
new_ih = ih(h_c.ravel())
cart_data = map_coordinates(self._brightness_3d_cylindrical,
np.vstack([new_ir, new_ith, new_ih]),
order=1, mode='constant', cval=0)
return cart_data.reshape([len(self._cartesian_x_grid),
len(self._cartesian_y_grid),
len(self._cartesian_z_grid)]).T
@dataclass
class Galaxy(Nebula):
"""
Class defining the galaxy object (set up it as Sersic2D profile assuming it has continuum and emission components)
"""
PA: u.degree = 90 * u.degree # position angle of the major axis
ax_ratio: float = 0.7 # ratio of minor/major axes
r_eff: u.kpc = 1 * u.kpc # Effective radius in kpc
rad_lim: float = 3. # Maximum radius for calculations (in R_eff)
n: float = 1. # Sersic index
vel_rot: velunit = 0 * velunit # Rotational velocity (not implemented yet)
def __post_init__(self):
self._assign_all_units()
self._npix_los = 1
self.r_max = self.r_eff.to(u.pc).value / self.pxscale.to(u.pc).value * self.rad_lim
self._assign_position_params(conversion_type='galaxy')
self._ref_line_id = 0
self.linerat_constant = True # True if the ratio of line fluxes shouldn't change across the nebula
@cached_property
def _brightness_3d_cartesian(self):
"""
Method to obtain the brightness (or density) distribution of the nebula in cartesian coordinates
"""
xx, yy = np.meshgrid(np.arange(self.pix_width), np.arange(self.pix_height))
angle = (self.PA + 90 * u.degree).to(u.radian).value
mod = Sersic2D(amplitude=1, r_eff=(self.r_eff.to(u.pc) / self.pxscale.to(u.pc)).value,
n=self.n, x_0=(self.pix_width - 1) / 2, y_0=(self.pix_height - 1) / 2,
ellip=1 - self.ax_ratio, theta=angle)
brt = mod(xx, yy)
xct = (xx - (self.pix_width - 1) / 2) * np.cos(angle) + \
(yy - (self.pix_height - 1) / 2) * np.sin(angle)
yct = (xx - (self.pix_width - 1) / 2) * np.sin(angle) - \
(yy - (self.pix_height - 1) / 2) * np.cos(angle)
rmaj = self.rad_lim * (self.r_eff.to(u.pc) / self.pxscale.to(u.pc)).value
rmin = self.rad_lim * (self.r_eff.to(u.pc) / self.pxscale.to(u.pc)).value * self.ax_ratio
mask = np.ones_like(brt, dtype=np.float32)
rec = (xct ** 2 / rmaj ** 2) + (yct ** 2 / rmin ** 2) >= 1
mask[rec] = 0
mask = convolve_fft(mask, kernels.Gaussian2DKernel(3.), fill_value=0, allow_huge=True)
brt = brt * mask
brt = brt.reshape(self.pix_height, self.pix_width, 1)
return brt
def _get_2d_velocity(self):
if hasattr(self, 'vel_rot') and (self.vel_rot is not None) and (self.vel_rot != 0):
xx, yy = np.meshgrid(np.arange(self.pix_width), np.arange(self.pix_height))
angle = (self.PA + 90 * u.degree).to(u.radian).value
xct = (xx - (self.pix_width - 1) / 2) * np.cos(angle) + \
(yy - (self.pix_height - 1) / 2) * np.sin(angle)
yct = (xx - (self.pix_width - 1) / 2) * np.sin(angle) - \
(yy - (self.pix_height - 1) / 2) * np.cos(angle)
rad = np.sqrt(xct ** 2 + yct ** 2)
vel_field = np.zeros_like(xx, dtype=np.float32) * velunit
rec = rad > 0
vel_field[rec] = self.vel_rot * np.sqrt(1 - self.ax_ratio ** 2) * xct[rec] / rad[rec]
return vel_field
else:
return None
@dataclass
class DIG(Nebula):
"""
Class defining the DIG component. For now it is defined just by its brightness (constant)
"""
max_brightness: fluxunit = 1e-17 * fluxunit
vel_gradient: (velunit / u.pc) = 0
@dataclass
class Cloud(Nebula):
"""Class of an isotropic spherical gas cloud without any ionization source.
Defined by its position, radius, density, maximal optical depth"""
radius: u.pc = 1.0 * u.pc
max_brightness: fluxunit = 0 * fluxunit
max_extinction: u.mag = 2.0 * u.mag
thickness: float = 1.0
perturb_degree: int = 0 # Degree of perturbations (max. degree of spherical harmonics for cloud)
linerat_constant: bool = False # True if the ratio of line fluxes shouldn't change across the nebula
_phi_bins: int = 90
_theta_bins: int = 90
_rad_bins: int = 0
_npix_los: int = 100
def __post_init__(self):
self._assign_all_units()
if self._rad_bins == 0:
self._rad_bins = np.ceil(self.radius.to(u.pc).value / self.pxscale.to(u.pc).value * 3).astype(int)
delta = np.round((len(self._cartesian_y_grid) - 1) / 2).astype(int)
if (self.xc is not None) and (self.yc is not None):
self.x0 = self.xc - delta
self.y0 = self.yc - delta
elif (self.x0 is not None) and (self.y0 is not None):
self.xc = self.x0 + delta
self.yc = self.y0 + delta
self._ref_line_id = 0
@cached_property
def _theta_grid(self):
return np.linspace(0, np.pi, self._theta_bins)
@cached_property
def _phi_grid(self):
return np.linspace(0, 2 * np.pi, self._phi_bins)
@cached_property
def _rad_grid(self):
return np.linspace(0, self.radius, self._rad_bins)
@cached_property
def _cartesian_z_grid(self):
npix = np.ceil(1.02 * self.radius / self.pxscale).astype(int)
return np.linspace(-npix, npix, 2 * npix + 1) * self.pxscale
@cached_property
def _cartesian_y_grid(self):
return self._cartesian_z_grid.copy()
@cached_property
def _cartesian_x_grid(self):
return np.linspace(-1.02, 1.02, self._npix_los) * self.radius
@cached_property
def _brightness_3d_spherical(self):
"""
Method to calculate brightness (or opacity) of the cloud at given theta, phi and radii
theta: float -- polar angle [0, np.pi]
phi: float -- azimuthal angle [0, 2 * np.pi]
rad: float -- radius [0, self.radius]
Returns:
3D cube of normalized brightness in theta-phi-rad grid; total brightness = 1
"""
rho, theta, phi = np.meshgrid(self._rad_grid, self._theta_grid, self._phi_grid, indexing='ij')
brt = np.ones_like(theta)
brt[rho < (self.radius * (1 - self.thickness))] = 0
brt[rho > self.radius] = 0
med = np.median(brt[brt > 0])
if self.perturb_degree > 0:
phi_cur = limit_angle(phi + np.random.uniform(0, 2 * np.pi, 1), 0, 2 * np.pi)
theta_cur = limit_angle(theta + np.random.uniform(0, np.pi, 1), 0, np.pi)
harm_amplitudes = self.perturb_amplitude * np.random.randn(self.perturb_degree * (self.perturb_degree + 2))
brt += np.nansum(Parallel(n_jobs=lvmdatasimulator.n_process)(delayed(brightness_inhomogeneities_sphere)
(harm_amplitudes, ll, phi_cur, theta_cur,
rho, med, self.radius, self.thickness)
for ll in np.arange(1,
self.perturb_degree + 1)),
axis=0)
brt[brt < 0] = 0
if med > 0:
brt = brt / np.nansum(brt)
return brt
@cached_property
def _brightness_4d_spherical(self):
"""
Method to calculate brightness of the cloud at given theta, phi and radii for each line
theta: float -- polar angle [0, np.pi]
phi: float -- azimuthal angle [0, 2 * np.pi]
rad: float -- radius [0, self.radius]
Returns:
4D cube of brightness in line-theta-phi-rad grid; normalized to the total brightness in Halpha
"""
s = self._brightness_3d_spherical.shape
if self.spectrum_id is None or self.linerat_constant:
return self._brightness_3d_spherical.reshape((1, s[0], s[1], s[2]))
rho, _, _ = np.meshgrid(self._rad_grid, self._theta_grid, self._phi_grid, indexing='ij')
with fits.open(lvmdatasimulator.CLOUDY_MODELS) as hdu:
radius = hdu[self.spectrum_id].data[0, 2:] * (self.thickness * self.radius) + \
self.radius * (1 - self.thickness)
fluxes = hdu[self.spectrum_id].data[1:, 2:]
radius = np.insert(radius, 0, self.radius * (1 - self.thickness))
fluxes = np.insert(fluxes, 0, fluxes[:, 0], axis=1)
index_ha = np.flatnonzero(hdu[self.spectrum_id].data[1:, 0] == 6562.81)
if self.n_brightest_lines is not None and \
(self.n_brightest_lines > 0) and (self.n_brightest_lines < len(fluxes)):
indexes_sorted = np.argsort(hdu[self.spectrum_id].data[1:, 1])[::-1]
fluxes = fluxes[indexes_sorted[:self.n_brightest_lines], :]
index_ha = np.flatnonzero(hdu[self.spectrum_id].data[1:, 0][indexes_sorted] == 6562.81)
if len(index_ha) == 1:
self._ref_line_id = index_ha[0]
brt = np.array(Parallel(n_jobs=lvmdatasimulator.n_process)(delayed(sphere_brt_in_line)
(self._brightness_3d_spherical, rho,
radius, flux)
for flux in fluxes)).reshape((fluxes.shape[0],
s[0], s[1], s[2]))
return brt / np.nansum(brt[self._ref_line_id])
@cached_property
def _brightness_3d_cartesian(self):
return interpolate_sphere_to_cartesian(self._brightness_3d_spherical, x_grid=self._cartesian_x_grid,
y_grid=self._cartesian_y_grid, z_grid=self._cartesian_z_grid,
rad_grid=self._rad_grid, theta_grid=self._theta_grid,
phi_grid=self._phi_grid, pxscale=self.pxscale)
@cached_property
def _brightness_4d_cartesian(self):
s = self._brightness_4d_spherical.shape
return np.array(Parallel(n_jobs=lvmdatasimulator.n_process)(delayed(interpolate_sphere_to_cartesian)
(cur_line_array,
self._cartesian_x_grid, self._cartesian_y_grid,
self._cartesian_z_grid, self._rad_grid,
self._theta_grid, self._phi_grid, self.pxscale)
for cur_line_array in self._brightness_4d_spherical)
).reshape((s[0], len(self._cartesian_z_grid), len(self._cartesian_y_grid),
len(self._cartesian_x_grid)))
@dataclass
class Bubble(Cloud):
"""Class of an isotropic thin expanding bubble."""
spectral_axis: velunit = np.arange(-20, 20, 10) * velunit
expansion_velocity: velunit = 20 * velunit
max_brightness: fluxunit = 1e-15 * fluxunit
max_extinction: u.mag = 0 * u.mag
thickness: float = 0.2
@cached_property
def _velocity_3d_spherical(self) -> velunit:
"""
Calculate line of sight velocity at given radius, phi, theta
V ~ 1/brightness (given that v~1/n_e^2 and brightness~ne^2)
"""
rho, theta, phi = np.meshgrid(self._rad_grid, self._theta_grid, self._phi_grid, indexing='ij')
vel_cube = np.zeros_like(self._brightness_3d_spherical)
rec = (rho <= self.radius) & (rho >= (self.radius * (1 - self.thickness)))
vel_cube[rec] = \
| np.sin(theta[rec]) | numpy.sin |
# Food Bank Problem
import sys
import importlib
import numpy as np
from scipy.optimize import minimize
import scipy
# ## OPT - via Convex Programming
# Calculates the optimal solution for the offline problem with convex programming
def solve(W, n, k, budget, size):
# Objective function in the nash social welfare
# Note we take the negative one to turn it into a minimization problem
def objective(x, w, n, k, size):
X = np.reshape(x, (n,k))
W = np.reshape(w, (n, k))
value = np.zeros(n)
for i in range(n):
value[i] = np.log(np.dot(X[i,:], W[i,:]))
return (-1) * np.dot(size, value)
w = W.flatten()
obj = lambda x: objective(x, w, n, k, size)
# Ensures that the allocations are positive
bds = scipy.optimize.Bounds([0 for _ in range(n*k)], [np.inf for _ in range(n*k)])
B = np.zeros((k, n*k))
for i in range(n):
B[:,k*i:k*(i+1)] = size[i]*np.eye(k)
# print(B)
# Enforces the budget constraint
constr = scipy.optimize.LinearConstraint(B, np.zeros(k), budget)
x0 = np.zeros(n*k)
# Initial solution starts out with equal allocation B / S
index = 0
for i in range(n):
for j in range(k):
x0[index] = budget[j] / np.sum(size)
index += 1
sol = minimize(obj, x0, bounds=bds, constraints = constr, tol = 10e-8)
return sol.x, sol
# Calculates the optimal solution for the offline problem with convex programming
# Note that this program instead solves for the optimization problem in a different form, where now
# the histogram is used directly in the original optimization problem instead of rewriting the problem
# as maximizing over types. This was used for investigation, and not as a primary proposed heuristic in the paper.
def solve_weights(weight_matrix, weight_distribution, n, k, budget, size):
# Similar objective, but now multiplying by the probability agent i has type j
def objective(x, weight_matrix, n, k, size, weight_distribution):
num_types = weight_distribution.shape[1]
X = np.reshape(x, (n,k))
value = np.zeros(n)
for i in range(n):
value[i] = np.sum([weight_distribution[i,j] * np.log(np.dot(X[i,:], weight_matrix[j,:])) for j in range(num_types)])
return (-1) * np.dot(size, value)
obj = lambda x: objective(x, weight_matrix, n, k, size, weight_distribution)
# Constraints are the same as before, along with initial solution
bds = scipy.optimize.Bounds([0 for _ in range(n*k)], [np.inf for _ in range(n*k)])
B = np.zeros((k, n*k))
for i in range(n):
B[:,k*i:k*(i+1)] = size[i]*np.eye(k)
constr = scipy.optimize.LinearConstraint(B, np.zeros(k), budget)
x0 = np.zeros(n*k)
index = 0
for i in range(n):
for j in range(k):
x0[index] = budget[j] / np.sum(size)
index += 1
sol = minimize(obj, x0, bounds=bds, constraints = constr, tol = 10e-8)
return sol.x, sol
# proportional solution, i.e. equal allocation B / S
def proportional_alloc(n, k, budget, size):
allocations = np.zeros((n,k))
for i in range(n):
allocations[i, :] = budget / np.sum(size)
return allocations
# Calculates the offline optimal solution just utilizing the distribution and not adapting to realized types
def offline_alloc(weight_matrix, weight_distribution, n, k, budget, size):
allocations = np.zeros((n,k))
weight_dist = np.asarray([weight_distribution for i in range(n)])
alloc, _ = solve_weights(np.asarray(weight_matrix), np.asarray(weight_dist), n, k, budget, size)
allocations = np.reshape(alloc, (n,k))
return allocations
# Implements the ET - Online heuristic algorithm
def et_online(expected_weights, observed_weights, n, k, budget, size):
allocations = np.zeros((n,k))
current_budget = np.copy(budget)
for i in range(n):
if i == n-1: # Last agent gets the maximum of earlier allocations or the remaining budget
allocations[i, :] = [max(0, min(np.max(allocations[:, j]), current_budget[j] / size[i])) for j in range(k)]
current_budget -= size[i] * allocations[i,:]
else:
cur_n = n - i # Solves the eisenbergt gale program with future weights taken to be their expectation
weights = expected_weights[i:,:]
weights[0, :] = observed_weights[i, :]
alloc, _ = solve(weights, cur_n, k, current_budget, size[i:])
alloc = np.reshape(alloc, (cur_n, k))
allocations[i, :] = [max(0, min(alloc[0, j], current_budget[j] / size[i])) for j in range(k)] # solves the eisenberg gale
current_budget -= size[i]*allocations[i, :] # reduces budget for next iteration
return allocations
# Implements the ET - Full heuristic algorithm
def et_full(expected_weights, observed_weights, n, k, budget, size):
allocations = np.zeros((n,k))
current_budget = np.copy(budget)
weights = np.copy(expected_weights)
for i in range(n):
if i == n-1:
allocations[i, :] = [max(0, min(np.max(allocations[:, j]), current_budget[j] / size[i])) for j in range(k)]
current_budget -= size[i] * allocations[i,:]
else:
weights[i, :] = observed_weights[i, :] # Replaces the weights with the observed one
alloc, _ = solve(weights, n, k, budget, size) # Solves for the allocation, and makes it
alloc = np.reshape(alloc, (n,k))
allocations[i, :] = [max(0, min(current_budget[j] / size[i], alloc[i,j])) for j in range(k)]
current_budget -= size[i]*allocations[i,:] # Reduces the budget
return allocations
# Implements the Hope-Full heuristic algorithm
def hope_full(weight_matrix, weight_distribution, observed_types, n, k, budget, size):
num_types = len(weight_distribution)
allocations = np.zeros((n,k))
current_budget = np.copy(budget)
for i in range(n):
size_factors = np.zeros(num_types) # Calculates the number of types and the N_\theta terms
for m in range(n):
if m <= i:
size_factors[observed_types[m]] += size[m]
elif m > i:
size_factors += size[m] * weight_distribution
obs_type = observed_types[i]
alloc, _ = solve(weight_matrix, num_types, k, budget, size_factors) # Solves for the allocation
alloc = np.reshape(alloc, (num_types, k))
allocations[i,:] = [max(0,min(current_budget[j] / size[i], alloc[obs_type, j])) for j in range(k)]
current_budget -= size[i] * allocations[i,:] # Reduces budget
return allocations
# Implements the Hope-Online heuristic algorithm
def hope_online(weight_matrix, weight_distribution, observed_types, n, k, budget, size):
num_types = len(weight_distribution)
allocations = np.zeros((n,k))
current_budget = np.copy(budget)
for i in range(n):
if i == n-1:
allocations[i, :] = [max(0, min(np.max(allocations[:, j]), current_budget[j] / size[i])) for j in range(k)]
else:
size_factors = np.zeros(num_types)
for m in range(n):
if m == i:
size_factors[observed_types[m]] += size[m]
elif m > i:
size_factors += size[m] * weight_distribution
obs_type = observed_types[i]
alloc, _ = solve(weight_matrix, num_types, k, current_budget, size_factors)
alloc = np.reshape(alloc, (num_types, k))
allocations[i,:] = [max(0, min(current_budget[j] / size[i], alloc[obs_type, j])) for j in range(k)]
current_budget -= size[i] * allocations[i,:]
return allocations
# Implements the Hope-Full heuristic algorithm of a different form, by solving the original Eisenberg-Gale over agents
# taking the expectation of the utility with the histogram on types.
def hope_full_v2(weight_matrix, weight_distribution, observed_types, n, k, budget, size):
num_types = len(weight_distribution)
allocations = np.zeros((n,k))
current_budget = np.copy(budget)
weight_dist = np.asarray([weight_distribution for i in range(n)])
for i in range(n):
weight_dist[i, :] = np.zeros(num_types)
weight_dist[i, observed_types[i]] += 1
obs_type = observed_types[i]
alloc, _ = solve_weights(weight_matrix, weight_dist, n, k, budget, size)
alloc = np.reshape(alloc, (n,k))
allocations[i, :] = [max(0,min(current_budget[j] / size[i], alloc[i, j])) for j in range(k)]
current_budget -= size[i] * allocations[i, :]
return allocations
# Similarly for the Hope-Online heuristic algorithm.
def hope_online_v2(weight_matrix, weight_distribution, observed_types, n, k, budget, size):
num_types = len(weight_distribution)
allocations = np.zeros((n,k))
current_budget = np.copy(budget)
weight_dist = np.asarray([weight_distribution for i in range(n)])
for i in range(n):
weight_dist[i, :] = np.zeros(num_types)
weight_dist[i, observed_types[i]] += 1
cur_dist = weight_dist[i:, :]
obs_type = observed_types[i]
alloc, _ = solve_weights(weight_matrix, cur_dist, n-i, k, budget, size[i:])
alloc = np.reshape(alloc, (n-i,k))
allocations[i, :] = [max(0,min(current_budget[j] / size[i], alloc[0, j])) for j in range(k)]
current_budget -= size[i] * allocations[i, :]
return allocations
### FAIRNESS MEASURES!
# Returns the amount of excress for each resource
def excess(allocation, budget, size):
true_alloc = np.zeros(allocation.shape[1])
for i in range(allocation.shape[0]):
true_alloc += size[i] * allocation[i,:]
return (1/allocation.shape[0])*(budget-true_alloc)
# Calculates envy-ness for each agent
def envy_utility(X, W):
n = X.shape[0]
envy = np.zeros(n)
for i in range(n):
u_i = np.dot(X[i,:], W[i,:])
max_env = (-1)*np.inf
for j in range(n):
if j != i and np.dot(X[j,:], W[i,:]) - u_i > max_env:
max_env = np.dot(X[j,:], W[i,:]) - u_i
envy[i] = max_env
return envy
def utility(allocation, observed_weights):
n = allocation.shape[0]
utility_vec = np.zeros(n)
for i in range(n):
utility_vec[i] = np.dot(allocation[i,:], observed_weights[i,:])
return utility_vec
# Calculates envy to proportional for each agent
def proportionality_utility(X, W, size, budget):
n = X.shape[0]
max_prop = | np.zeros(n) | numpy.zeros |
###
# This class contains unit and integration tests for lifesci.bed_utils.
# The structure of this file is taken from an old blog post here:
# http://blog.jameskyle.org/2010/10/nose-unit-testing-quick-start/
###
import collections
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import lifesci.bed_utils as bed_utils
import pyllars.logging_utils as logging_utils
import pyllars.math_utils as math_utils
from lifesci.bed_utils import interval_overlap
from lifesci.bed_utils import transcript_overlap
from nose.tools import assert_equal
from nose.tools import assert_not_equal
from nose.tools import assert_raises
from nose.tools import raises
class TestBedUtils(object):
@classmethod
def build_a_b_bed_dfs(self):
# these are values for a set of intervals which are either independent
# (use ab_info) or grouped into transcripts (use ab_blocks)
self.a_starts = [10, 30, 40, 70, 90, 110, 130, 155]
self.a_ends = [20, 50, 60, 80, 100, 120, 140, 160]
self.a_info = [1, 2, 3, 4, 5, 6, 7, 8]
self.a_blocks = [1, 1, 2, 2, 3, 3, 3, 4]
self.b_starts = [15, 30, 40, 70, 85, 90, 95, 110, 110, 130, 130, 145]
self.b_ends = [20, 50, 60, 80, 100, 100, 115, 120, 120, 140, 140, 155]
self.b_info = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
self.b_blocks = [1, 1, 2, 3, 4, 5, 6, 5, 4, 5, 4, 7]
# now, build a bed6 data frame for a and b
a_df = pd.DataFrame()
a_df['start'] = self.a_starts
a_df['end'] = self.a_ends
a_df['id'] = self.a_blocks
a_df['seqname'] = '1'
a_df['score'] = 0
a_df['strand'] = '+'
self.a_df = a_df
# now, build a bed6 data frame for a and b
b_df = pd.DataFrame()
b_df['start'] = self.b_starts
b_df['end'] = self.b_ends
b_df['id'] = self.b_blocks
b_df['seqname'] = '1'
b_df['score'] = 0
b_df['strand'] = '+'
self.b_df = b_df
a_df['length'] = a_df['end'] - a_df['start']
b_df['length'] = b_df['end'] - b_df['start']
a_groups = self.a_df.groupby('id')
a_lengths = a_groups['length'].sum()
self.a_lengths_map = a_lengths.to_dict()
b_groups = self.b_df.groupby('id')
b_lengths = b_groups['length'].sum()
self.b_lengths_map = b_lengths.to_dict()
# now, build the bed6 data frames for testing subtraction
a_starts = np.array([10, 30, 55, 70, 90, 120])
a_ends = np.array([20, 40, 60, 80, 101, 130])
a_ids = np.array([1, 1, 2, 3, 4, 4])
b_starts = np.array([40, 65, 100])
b_ends = np.array([50, 75, 110])
b_ids = np.array([1, 1, 2])
a_bed = pd.DataFrame()
a_bed['start'] = a_starts
a_bed['end'] = a_ends
a_bed['id'] = a_ids
a_bed['seqname'] = '1'
a_bed['score'] = 0
a_bed['strand'] = '+'
b_bed = pd.DataFrame()
b_bed['start'] = b_starts
b_bed['end'] = b_ends
b_bed['id'] = b_ids
b_bed['seqname'] = '1'
b_bed['score'] = 0
b_bed['strand'] = '+'
self.a_diff_df = a_bed
self.b_diff_df = b_bed
@classmethod
def build_complex_bed_entry(self):
exon_lengths = np.array([20, 20, 70, 70, 70, 70, 30])
exon_genomic_relative_starts = np.array([0, 40, 90, 190, 290, 390, 490])
exon_lengths_str = ','.join(str(l) for l in exon_lengths)
exon_genomic_relative_starts_str = ','.join(str(l) for l in exon_genomic_relative_starts)
self.bed_entry = {
'seqname': '1',
'start': 10,
'end': 530,
'id': 'test_me',
'score': 0,
'strand': '+',
'thick_start': 120,
'thick_end': 450,
'color': 0,
'num_exons': 7,
'exon_lengths': exon_lengths_str,
'exon_genomic_relative_starts': exon_genomic_relative_starts_str
}
@classmethod
def setup_class(klass):
"""This method is run once for each class before any tests are run"""
TestBedUtils.build_a_b_bed_dfs()
TestBedUtils.build_complex_bed_entry()
@classmethod
def teardown_class(klass):
"""This method is run once for each class _after_ all tests are run"""
def setUp(self):
"""This method is run once before _each_ test method is executed"""
def teardown(self):
"""This method is run once after _each_ test method is executed"""
def test_get_interval_overlaps(self):
overlaps = bed_utils.get_interval_overlaps(
self.a_starts,
self.a_ends,
self.a_info,
self.b_starts,
self.b_ends,
self.b_info)
expected_overlaps = [
interval_overlap(a_info=1, b_info=1, overlap=5),
interval_overlap(a_info=2, b_info=2, overlap=20),
interval_overlap(a_info=2, b_info=3, overlap=10),
interval_overlap(a_info=3, b_info=2, overlap=10),
interval_overlap(a_info=3, b_info=3, overlap=20),
interval_overlap(a_info=4, b_info=4, overlap=10),
interval_overlap(a_info=5, b_info=5, overlap=10),
interval_overlap(a_info=5, b_info=6, overlap=10),
interval_overlap(a_info=5, b_info=7, overlap=5),
interval_overlap(a_info=6, b_info=7, overlap=5),
interval_overlap(a_info=6, b_info=8, overlap=10),
interval_overlap(a_info=6, b_info=9, overlap=10),
interval_overlap(a_info=7, b_info=10, overlap=10),
interval_overlap(a_info=7, b_info=11, overlap=10)
]
assert_equal(overlaps, expected_overlaps)
def test_get_transcript_overlaps(self):
overlaps = bed_utils.get_interval_overlaps(
self.a_starts,
self.a_ends,
self.a_blocks,
self.b_starts,
self.b_ends,
self.b_blocks)
transcript_overlaps = bed_utils.get_transcript_overlaps(overlaps)
expected_transcript_overlaps = {
(1, 1): 25,
(1, 2): 10,
(2, 1): 10,
(2, 2): 20,
(2, 3): 10,
(3, 4): 30,
(3, 5): 30,
(3, 6): 10
}
assert_equal(transcript_overlaps, expected_transcript_overlaps)
def test_get_transcript_overlap_fractions(self):
overlaps = bed_utils.get_interval_overlaps(
self.a_starts,
self.a_ends,
self.a_blocks,
self.b_starts,
self.b_ends,
self.b_blocks)
transcript_overlaps = bed_utils.get_transcript_overlaps(overlaps)
transcript_fractions = bed_utils.get_transcript_overlap_fractions(
transcript_overlaps,
self.a_lengths_map,
self.b_lengths_map)
expected_transcript_fractions = [
transcript_overlap(a_info=1, b_info=2, overlap=10,
a_fraction=0.33333333333333331, b_fraction=0.5),
transcript_overlap(a_info=2, b_info=3, overlap=10,
a_fraction=0.33333333333333331, b_fraction=1.0),
transcript_overlap(a_info=3, b_info=6, overlap=10,
a_fraction=0.33333333333333331, b_fraction=0.5),
transcript_overlap(a_info=2, b_info=2, overlap=20,
a_fraction=0.66666666666666663, b_fraction=1.0),
transcript_overlap(a_info=3, b_info=4, overlap=30,
a_fraction=1.0, b_fraction=0.8571428571428571),
transcript_overlap(a_info=1, b_info=1, overlap=25,
a_fraction=0.83333333333333337, b_fraction=1.0),
transcript_overlap(a_info=2, b_info=1, overlap=10,
a_fraction=0.33333333333333331, b_fraction=0.40000000000000002),
transcript_overlap(a_info=3, b_info=5, overlap=30,
a_fraction=1.0, b_fraction=1.0)
]
assert_equal(transcript_fractions, expected_transcript_fractions)
def test_get_bed_overlaps(self):
bed_overlaps = bed_utils.get_bed_overlaps(self.a_df, self.b_df, min_a_overlap=0.33, min_b_overlap=0.5)
expected_bed_overlaps = [
transcript_overlap(a_info=1, b_info=2, overlap=10,
a_fraction=0.33333333333333331, b_fraction=0.5),
transcript_overlap(a_info=2, b_info=3, overlap=10,
a_fraction=0.33333333333333331, b_fraction=1.0),
transcript_overlap(a_info=3, b_info=6, overlap=10,
a_fraction=0.33333333333333331, b_fraction=0.5),
transcript_overlap(a_info=2, b_info=2, overlap=20,
a_fraction=0.66666666666666663, b_fraction=1.0),
transcript_overlap(a_info=3, b_info=4, overlap=30,
a_fraction=1.0, b_fraction=0.8571428571428571),
transcript_overlap(a_info=1, b_info=1, overlap=25,
a_fraction=0.83333333333333337, b_fraction=1.0),
transcript_overlap(a_info=3, b_info=5, overlap=30,
a_fraction=1.0, b_fraction=1.0)
]
assert_equal(bed_overlaps, expected_bed_overlaps)
def test_retain_thick_only(self):
thick_only_bed_entry = bed_utils.retain_thick_only(self.bed_entry)
expected_exon_lengths = np.array([50, 70, 70, 50])
expected_exon_genomic_relative_starts = np.array([0, 80, 180, 280])
expected_exon_lengths_str = ','.join(str(l) for l in expected_exon_lengths)
expected_exon_genomic_relative_starts_str = ','.join(str(l)
for l in expected_exon_genomic_relative_starts)
expected_bed_entry = {
'seqname': '1',
'start': 120,
'end': 450,
'id': 'test_me',
'score': 0,
'strand': '+',
'thick_start': 120,
'thick_end': 450,
'color': 0,
'num_exons': 4,
'exon_lengths': expected_exon_lengths_str,
'exon_genomic_relative_starts': expected_exon_genomic_relative_starts_str
}
assert_equal(thick_only_bed_entry, expected_bed_entry)
def test_retain_before_thick_only(self):
before_thick_only_bed_entry = bed_utils.retain_before_thick_only(self.bed_entry)
expected_exon_lengths = np.array([20, 20, 20])
expected_exon_genomic_relative_starts = np.array([0, 40, 90])
expected_exon_lengths_str = ','.join(str(l) for l in expected_exon_lengths)
expected_exon_genomic_relative_starts_str = ','.join(str(l)
for l in expected_exon_genomic_relative_starts)
expected_bed_entry = {
'seqname': '1',
'start': 10,
'end': 120,
'id': 'test_me',
'score': 0,
'strand': '+',
'thick_start': -1,
'thick_end': -1,
'color': 0,
'num_exons': 3,
'exon_lengths': expected_exon_lengths_str,
'exon_genomic_relative_starts': expected_exon_genomic_relative_starts_str
}
assert_equal(before_thick_only_bed_entry, expected_bed_entry)
def test_retain_after_thick_only(self):
after_thick_only_bed_entry = bed_utils.retain_after_thick_only(self.bed_entry)
expected_exon_lengths = np.array([20, 30])
expected_exon_genomic_relative_starts = np.array([0, 50])
expected_exon_lengths_str = ','.join(str(l) for l in expected_exon_lengths)
expected_exon_genomic_relative_starts_str = ','.join(str(l)
for l in expected_exon_genomic_relative_starts)
expected_bed_entry = {
'seqname': '1',
'start': 450,
'end': 530,
'id': 'test_me',
'score': 0,
'strand': '+',
'thick_start': -1,
'thick_end': -1,
'color': 0,
'num_exons': 2,
'exon_lengths': expected_exon_lengths_str,
'exon_genomic_relative_starts': expected_exon_genomic_relative_starts_str
}
assert_equal(after_thick_only_bed_entry, expected_bed_entry)
def test_subtract_bed(self):
# first, check for exact overlaps
expected_result = {1, 2}
result = bed_utils.subtract_bed(self.a_diff_df, self.b_diff_df)
assert_equal(result, expected_result)
# now, test requiring some more overlap of A
expected_result = {1, 2, 4}
min_a_overlap = 0.2
result = bed_utils.subtract_bed(self.a_diff_df, self.b_diff_df, min_a_overlap=min_a_overlap)
assert_equal(result, expected_result)
# and requiring more substantial overlap of B
expected_result = {1, 2, 3, 4}
min_b_overlap = 0.3
result = bed_utils.subtract_bed(self.a_diff_df, self.b_diff_df, min_b_overlap=min_b_overlap)
assert_equal(result, expected_result)
def test_get_entries_with_upstream_overlaps(self):
# construct the data
a_starts = np.array([20, 50, 60, 65, 58, 60])
a_ends = np.array([30, 60, 70, 75, 63, 78])
a_strands = np.array(['+', '+', '-', '-', '+', '-'])
a_ids = np.array([1, 2, 3, 4, 5, 6])
b_starts = np.array([9, 9, 40, 75])
b_ends = np.array([20, 20, 55, 80])
b_strands = np.array(['+', '-', '+', '-'])
b_ids = np.array([1, 2, 3, 4])
bed_a = pd.DataFrame()
bed_a['start'] = a_starts
bed_a['end'] = a_ends
bed_a['strand'] = a_strands
bed_a['id'] = a_ids
bed_a['score'] = 0
bed_a['seqname'] = '1'
bed_b = pd.DataFrame()
bed_b['start'] = b_starts
bed_b['end'] = b_ends
bed_b['strand'] = b_strands
bed_b['id'] = b_ids
bed_b['score'] = 0
bed_b['seqname'] = '1'
upstream_window = 5
allow_overlaps = True
expected_result = [
bed_utils.transcript_overlap(a_info=1, b_info=1, overlap=5,
a_fraction=1.0, b_fraction=0.45454545454545453),
bed_utils.transcript_overlap(a_info=2, b_info=3, overlap=5,
a_fraction=1.0, b_fraction=0.33333333333333331),
bed_utils.transcript_overlap(a_info=4, b_info=4, overlap=5,
a_fraction=1.0, b_fraction=1.0),
bed_utils.transcript_overlap(a_info=5, b_info=3, overlap=2,
a_fraction=0.40000000000000002, b_fraction=0.13333333333333333),
bed_utils.transcript_overlap(a_info=6, b_info=4, overlap=2,
a_fraction=0.40000000000000002, b_fraction=0.40000000000000002)
]
result = bed_utils.get_entries_with_upstream_overlaps(bed_a, bed_b,
upstream_window, allow_overlaps=allow_overlaps)
assert_equal(expected_result, result)
upstream_window = 5
allow_overlaps = False
expected_result = [
bed_utils.transcript_overlap(a_info=1, b_info=1, overlap=5,
a_fraction=1.0, b_fraction=0.45454545454545453),
bed_utils.transcript_overlap(a_info=4, b_info=4, overlap=5,
a_fraction=1.0, b_fraction=1.0),
bed_utils.transcript_overlap(a_info=5, b_info=3, overlap=2,
a_fraction=0.40000000000000002, b_fraction=0.13333333333333333)
]
result = bed_utils.get_entries_with_upstream_overlaps(bed_a, bed_b,
upstream_window, allow_overlaps=allow_overlaps)
assert_equal(expected_result, result)
a_starts = np.array([20, 40, 45, 40])
a_ends = np.array([30, 50, 60, 50])
a_strands = | np.array(['+', '+', '-', '+']) | numpy.array |
import numpy as np
try:
import dgl
import torch.nn as nn
import torch.nn.functional as F
from dgl.nn.pytorch import GraphConv
except ImportError:
pass
from photonai_graph.NeuralNets.dgl_base import DGLRegressorBaseModel, DGLClassifierBaseModel
class GCNClassifier(nn.Module):
def __init__(self, in_dim, hidden_dim, n_classes, hidden_layers, allow_zero_in_degree):
super(GCNClassifier, self).__init__()
self.layers = nn.ModuleList()
# input layers
self.layers.append(GraphConv(in_dim, hidden_dim, allow_zero_in_degree=allow_zero_in_degree))
# hidden layers
for layer in range(1, hidden_layers):
self.layers.append(GraphConv(hidden_dim, hidden_dim, allow_zero_in_degree=allow_zero_in_degree))
self.classify = nn.Linear(hidden_dim, n_classes)
def forward(self, g):
# Use node degree as the initial node feature. For undirected graphs, the in-degree
# is the same as the out_degree.
h = g.in_degrees().view(-1, 1).float()
# Perform graph convolution and activation function.
for i, gnn in enumerate(self.layers):
h = F.relu(gnn(g, h))
g.ndata['h'] = h
# Calculate graph representation by averaging all the node representations.
hg = dgl.mean_nodes(g, 'h')
return self.classify(hg)
class GCNClassifierModel(DGLClassifierBaseModel):
def __init__(self,
in_dim: int = 1,
hidden_layers: int = 2,
hidden_dim: int = 256,
nn_epochs: int = 200,
learning_rate: float = 0.001,
batch_size: int = 32,
adjacency_axis: int = 0,
feature_axis: int = 1,
add_self_loops: bool = True,
allow_zero_in_degree: bool = False,
logs: str = ''):
"""
Graph Attention Network for graph classification. GCN Layers
from Kipf & Welling, 2017.
Implementation based on dgl & pytorch.
Parameters
----------
in_dim: int,default=1
input dimension
hidden_layers: int,default=2
number of hidden layers used by the model
hidden_dim: int,default=256
dimensions in the hidden layers
"""
super(GCNClassifierModel, self).__init__(nn_epochs=nn_epochs,
learning_rate=learning_rate,
batch_size=batch_size,
adjacency_axis=adjacency_axis,
feature_axis=feature_axis,
add_self_loops=add_self_loops,
allow_zero_in_degree=allow_zero_in_degree,
logs=logs)
self.in_dim = in_dim
self.hidden_dim = hidden_dim
self.hidden_layers = hidden_layers
def _init_model(self, X=None, y=None):
self.model = GCNClassifier(self.in_dim,
self.hidden_dim,
len( | np.unique(y) | numpy.unique |
# -*- coding: utf-8 -*-
"""
Created on Thu Mar 8 15:53:33 2018
@author: <NAME>
"""
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
# wavelenths sampled
Wavelenghts = np.linspace(300, 700, 701 - 300, dtype=float)
# vector of ratios Acdom/Anap
r = np.array([1 / 16., 1 / 8., 1 / 4., 1 / 2., 1., 2., 4., 8., 16.])
# vector of cdom 'slopes' [1/nm]
scdom = np.array([0.01, 0.001, 0.026])
# vector of nap 'slopes' [1/nm]
snap = np.array([0.008, 0.001, 0.018])
r2 = np.zeros(shape=(np.size(scdom), np.size(snap), np.size(r)))
rmse = np.zeros(shape=( | np.size(scdom) | numpy.size |
"""
==========================
Selecting multiple objects
==========================
Here we show how to select objects in the
3D world. In this example all objects to be picked are part of
a single actor.
FURY likes to bundle objects in a few actors to reduce code and
increase speed. Nonetheless the method works for multiple actors too.
The difference with the picking tutorial is that here we will
be able to select more than one object. In addition we can
select interactively many vertices or faces.
In summary, we will create an actor with thousands of cubes and
then interactively we will be moving a rectangular box by
hovering the mouse and making transparent everything that is
behind that box.
"""
import numpy as np
from fury import actor, window, utils, pick
###############################################################################
# Adding many cubes of different sizes and colors
num_cubes = 50000
centers = 10000 * (np.random.rand(num_cubes, 3) - 0.5)
colors = np.random.rand(num_cubes, 4)
colors[:, 3] = 1.0
radii = 100 * np.random.rand(num_cubes) + 0.1
###############################################################################
# Keep track of total number of triangle faces
# Note that every quad of each cube has 2 triangles
# and each cube has 6 quads in total.
num_faces = num_cubes * 6 * 2
###############################################################################
# Build scene and add an actor with many objects.
scene = window.Scene()
###############################################################################
# Build the actor containing all the cubes
cube_actor = actor.cube(centers, directions=(1, 0, 0),
colors=colors, scales=radii)
###############################################################################
# Access the memory of the vertices of all the cubes
vertices = utils.vertices_from_actor(cube_actor)
num_vertices = vertices.shape[0]
num_objects = centers.shape[0]
###############################################################################
# Access the memory of the colors of all the cubes
vcolors = utils.colors_from_actor(cube_actor, 'colors')
###############################################################################
# Create a rectangular 2d box as a texture
rgba = 255 * np.ones((100, 200, 4))
rgba[1:-1, 1:-1] = np.zeros((98, 198, 4)) + 100
texa = actor.texture_2d(rgba.astype(np.uint8))
scene.add(cube_actor)
scene.add(texa)
scene.reset_camera()
scene.zoom(3.)
###############################################################################
# Create the Selection Manager
selm = pick.SelectionManager(select='faces')
###############################################################################
# Tell Selection Manager to avoid selecting specific actors
selm.selectable_off(texa)
###############################################################################
# Let's make the callback which will be called
# when we hover the mouse
def hover_callback(_obj, _event):
event_pos = selm.event_position(showm.iren)
# updates rectangular box around mouse
texa.SetPosition(event_pos[0] - 200//2,
event_pos[1] - 100//2)
# defines selection region and returns information from selected objects
info = selm.select(event_pos, showm.scene, (200//2, 100//2))
for node in info.keys():
if info[node]['face'] is not None:
if info[node]['actor'] is cube_actor:
for face_index in info[node]['face']:
# generates an object_index to help with coloring
# by dividing by the number of faces of each cube (6 * 2)
object_index = face_index // 12
sec = int(num_vertices / num_objects)
color_change = | np.array([150, 0, 0, 255], dtype='uint8') | numpy.array |
#!/usr/bin/python
'''
Tracks colonies through time in a single imaging field
'''
import cv2
import itertools
import numpy as np
import pandas as pd
from PIE import image_properties, analysis_configuration
class SinglePhaseSinglePosCompiler(object):
'''
Compiles and analyzes results for a single experimental phase at a
single position
'''
def __init__(self, xy_position, analysis_config, postphase_analysis_config = None):
self.analysis_config = analysis_config
self.analysis_config.set_xy_position(xy_position)
self.postphase_analysis_config = postphase_analysis_config
if self.postphase_analysis_config is not None:
self.postphase_analysis_config.set_xy_position(xy_position)
def _perform_fluor_measurements(self, curr_analysis_config, image_analyzer,
timepoint):
'''
Performs fluorescence measurements using image_analyzer based on
data in analysis_config
'''
# set up background and colony masks
image_analyzer.set_up_fluor_measurements()
# loop through fluor channels and analyze each one
for fluor_row in \
curr_analysis_config.fluor_channel_df.itertuples():
# retrieve fluorescent image
fluor_im, _, _ = \
curr_analysis_config.get_image(timepoint,
fluor_row.fluor_channel_label)
# measure fluorescences
image_analyzer.measure_fluorescence(fluor_im,
fluor_row.fluor_channel_column_name,
fluor_row.fluor_threshold)
def analyze_timepoint_ims(self):
'''
Runs colony edge detection on main (brightfield/phase contrast)
images from each timepoint, measures any fluorescent data
concurrent with those timepoints, populates dataframe of colony
properties
'''
### NEEDS UNITTEST
colony_prop_across_time_list = []
for timepoint in self.analysis_config.timepoint_list:
image, image_name, image_time = \
self.analysis_config.get_image(timepoint,
self.analysis_config.main_channel_label)
if image is not None:
# check that image size is the same for all images
if image.shape[0] != self.analysis_config.im_height or \
image.shape[1] != self.analysis_config.im_width:
raise ValueError(
'It looks like not all image sizes are the same!'
'Compare ' + image_name + ' with ' +
self.analysis_config.size_ref_im)
image_analyzer = image_properties.ImageAnalyzer(image,
image_name, self.analysis_config.phase_output_path,
self.analysis_config.main_channel_imagetype,
self.analysis_config.hole_fill_area,
self.analysis_config.cleanup,
self.analysis_config.max_proportion_exposed_edge,
self.analysis_config.cell_intensity_num,
self.analysis_config.save_extra_info,
max_col_num = self.analysis_config.max_colony_num,
write_col_props_file = False)
image_analyzer.process_image()
# if there are fluorescent channels, loop through them and
# measure fluorescence of each colony
if not self.analysis_config.fluor_channel_df.empty:
self._perform_fluor_measurements(self.analysis_config,
image_analyzer, timepoint)
# if there's a postphase_analysis_config, perform
# postphase fluor measurements (at every timepoint)
if self.postphase_analysis_config is not None:
self._perform_fluor_measurements(
self.postphase_analysis_config, image_analyzer,
None)
# retrieve colony_property_df
colony_property_df = \
image_analyzer.get_colony_property_df_to_save()
# fill in info for current timepoint
colony_property_df['main_image_name'] = image_name
colony_property_df['xy_pos_idx'] = \
self.analysis_config.xy_position_idx
colony_property_df['timepoint'] = timepoint
colony_property_df['time_in_seconds'] = image_time
colony_property_df['phase_num'] = self.analysis_config.phase_num
# append current timepoint to combined info
colony_prop_across_time_list.append(colony_property_df)
# concatenate all colony property dataframes to single list
if colony_prop_across_time_list:
phase_colony_data_untracked = pd.concat(colony_prop_across_time_list)
else:
phase_colony_data_untracked = pd.DataFrame()
return(phase_colony_data_untracked)
class ColonyTracker(object):
'''
Generic class for tracking colonies based on dataframe of colony
properties in an image and the subsequent image
The details of the tracking differ from the original matlab code
when it comes to colony splintering/merging, as well as the fact
that here, image registration occurs between every consecutive
timepoint
In addition, dealing with filters by min_growth_time, appearance in
first timepoint, etc is outsourced to growth rate functions
IMPORTANT:
tracking IDs created within this class are only unique
for the colony property dataframes being passed to it (which may
be only for a single xy position, etc), NOT across the whole
experiment
'''
def __init__(self):
# initialize dictionary for time-tracked col property dfs
self.single_phase_col_prop_df_dict = dict()
# set proportion of major axis length that satellite must be
# from colony center to be considered a satellite
self._max_sat_major_axis_prop = .7
def _find_centroid_transform(self, curr_im_data, next_im_data):
'''
Takes in dataframes of data for the current image and the
following image
Returns a rigid-body affine transformation matrix M that
transforms centroid positions in curr_im_data to centroid
positions in next_im_data
'''
# make matrices of centroids
curr_centroids = np.float32(curr_im_data[['cX', 'cY']].to_numpy())
next_centroids = np.float32(next_im_data[['cX', 'cY']].to_numpy())
# initialize brute force matcher
bf = cv2.BFMatcher()
# return top two matches for each point
matches = bf.knnMatch(curr_centroids, next_centroids, k=2)
# Apply ratio test from https://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_feature2d/py_matcher/py_matcher.html
# This ensures that only those matches are used for finding the
# transformation matrix which match their #1 match much closer
# than they match their #2 match; stringency of this requirement
# can be increased by decreasing match_ratio_cutoff, at the risk
# of ending up with too few match points
match_ratio_cutoff = 0.75
good = []
if len(matches)>0 and len(matches[0])>1:
for m,n in matches:
if m.distance < match_ratio_cutoff * n.distance:
good.append(m)
if len(good) >= 3:
curr_centroids_matching = curr_centroids[[a.queryIdx for a in good]]
next_centroids_matching = next_centroids[[a.trainIdx for a in good]]
# estimateAffinePartial2D removes outliers in its default state
# and returns a mask showing which points it didn't remove, but
# we ignore this mask here
M, _ = cv2.estimateAffinePartial2D(curr_centroids_matching,
next_centroids_matching)
else:
# can't estimate affine matrix with this few points, assume
# no transformation
M = np.float64([[1, 0, 0], [0, 1, 0]])
return(M)
def _register_images(self, curr_im_data, next_im_data):
'''
Finds the rigid affine transform between the centroids from
curr_im_data to next_im_data, applies it to the centroids and
bounds of curr_im_data, and returns the transformed curr_im_data
NB: The bound transformation for rotations is not totally
correct, since the bounding box is rotated and a new bounding
box encompassing the old, transformed one is created; this is
larger (or smaller!) than if a new bounding box were calculated
on the warped image, but with low levels of rotation expected
in most images, this should not be a big problem for tracking
'''
### !!! NEEDS UNITTEST
warp_mat = self._find_centroid_transform(curr_im_data, next_im_data)
# id bounding box and centroids
data_to_warp = curr_im_data.copy()
data_to_warp['bb_x_right'] = \
data_to_warp['bb_width'] + data_to_warp['bb_x_left']
data_to_warp['bb_y_bottom'] = \
data_to_warp['bb_height'] + data_to_warp['bb_y_top']
curr_im_bb_small = \
np.float32(data_to_warp[['bb_x_left', 'bb_y_top']].to_numpy())
curr_im_bb_large = \
np.float32(data_to_warp[['bb_x_right', 'bb_y_bottom']].to_numpy())
curr_im_centroids = np.float32(data_to_warp[['cX', 'cY']].to_numpy())
# warp centroids and bb
warped_centroids = \
np.squeeze(np.float32(cv2.transform(curr_im_centroids[np.newaxis],
warp_mat)))
warped_bb_small = np.squeeze(
np.float32(cv2.transform(curr_im_bb_small[np.newaxis], warp_mat)))
warped_bb_large = np.squeeze(
np.float32(cv2.transform(curr_im_bb_large[np.newaxis], warp_mat)))
# calculate and populate warped current image df
warped_curr_im_data = curr_im_data.copy()
warped_curr_im_data[['cX', 'cY']] = warped_centroids
warped_curr_im_data[['bb_x_left', 'bb_y_top']] = \
np.round(warped_bb_small).astype(int)
warped_curr_im_data[['bb_width', 'bb_height']] = \
np.round(warped_bb_large- warped_bb_small).astype(int)
return(warped_curr_im_data)
def _get_overlap(self, curr_im_data, next_im_data):
'''
Makes overlap df of colonies between two images
Identifies pairs of colonies between images for which the
centroid of one falls inside the other's bounding box
'''
# perform image registration
if self.perform_registration:
curr_im_data_reg = \
self._register_images(curr_im_data, next_im_data)
else:
curr_im_data_reg = curr_im_data.copy()
# get matrices of absolute differences between x and y
# centroids of the colonies in the two images
cX_diff_mat = np.abs(np.subtract.outer(
curr_im_data_reg['cX'].to_numpy(),
next_im_data['cX'].to_numpy()))
cY_diff_mat = np.abs(np.subtract.outer(
curr_im_data_reg['cY'].to_numpy(),
next_im_data['cY'].to_numpy()))
# calculate whether the other image's centroid falls
# within each respective image's bounding box bounds
curr_im_cX_bbox_overlap = (cX_diff_mat.T <
curr_im_data_reg['bb_width'].to_numpy()/2).T
curr_im_cY_bbox_overlap = (cY_diff_mat.T <
curr_im_data_reg['bb_height'].to_numpy()/2).T
next_im_cX_bbox_overlap = \
cX_diff_mat < next_im_data['bb_width'].to_numpy()/2
next_im_cY_bbox_overlap = \
cY_diff_mat < next_im_data['bb_height'].to_numpy()/2
# for each image, determine whether bounding box
# encapsulates other image's centroid
curr_bbox_next_centroid_overlap = \
np.logical_and(curr_im_cX_bbox_overlap,
curr_im_cY_bbox_overlap)
next_bbox_curr_centroid_overlap = \
np.logical_and(next_im_cX_bbox_overlap,
next_im_cY_bbox_overlap)
# create matrix of overlaps between images
# overlaps occur if a colony's bounding box in either
# image includes a colony's centroid in the other
# image
# this is the incidence matrix in colonies between
# subsequent images
overlap_mat = np.logical_or(curr_bbox_next_centroid_overlap,
next_bbox_curr_centroid_overlap)
# convert to dataframe with rows (indices) and columns labeled
# with indices of colonies from original colony property df
overlap_df = pd.DataFrame(overlap_mat,
index = curr_im_data_reg.index,
columns = next_im_data.index)
return(overlap_df)
def _id_colony_match(self, curr_im_data, next_im_data):
'''
Identifies colonies from next_im_data that match to colonies in
curr_im_data
Returns df of matches (by idx in original colony property df)
'''
# get df with labeled overlap matrix between current image and
# the subsequent one
overlap_df = self._get_overlap(curr_im_data, next_im_data)
# identify all colony matches
(curr_im_idx, next_im_idx) = np.where(overlap_df)
match_df = pd.DataFrame(
{'curr_im_colony': overlap_df.index[curr_im_idx],
'next_im_colony': overlap_df.columns[next_im_idx]})
return(match_df)
def _get_matching_indices(self, df, col_name, val_to_match):
'''
Returns list of indices of df where col_name matches
val_to_match, even if val_to_match is NaN
'''
### !!! NEEDS UNITTEST
if isinstance(val_to_match, float) and np.isnan(val_to_match):
match_bool = df[col_name].isnull()
else:
match_bool = df[col_name] == val_to_match
indices = df.index[match_bool].to_list()
return(indices)
def _match_by_parent(self, match_df, curr_im_data, next_im_data):
'''
Removes any matches in which a satellite matches its parent
Adds all matches based on shared parentage (i.e. if colony
whose parent is A matches a colony whose parent is B, all
colonies whose parent is A match all colonies whose parent is B)
Returns df of matches (by idx in original colony property df)
'''
### !!! NEEDS UNITTEST
match_df_parent = pd.DataFrame(
{'curr_im_parent':
curr_im_data.loc[match_df.curr_im_colony]['parent_colony'].values,
'next_im_parent':
next_im_data.loc[match_df.next_im_colony]['parent_colony'].values})
# remove cases of colonies merging with their parents
match_df_parent = match_df_parent[
match_df_parent.curr_im_parent != match_df_parent.next_im_parent
].drop_duplicates()
# add all combos of parent-parent and parent-satellite matches
# based on parent-parent matches to match_df
match_df_list = []
for _, row in match_df_parent.iterrows():
curr_colonies = \
self._get_matching_indices(
curr_im_data,
self.tracking_col_name,
row.curr_im_parent
)
next_colonies = \
self._get_matching_indices(
next_im_data,
self.tracking_col_name,
row.next_im_parent
)
curr_match_df = pd.DataFrame(
list(itertools.product(
*[curr_colonies, next_colonies])),
columns = ['curr_im_colony', 'next_im_colony'])
match_df_list.append(curr_match_df)
if len(match_df_list) > 0:
match_df_by_parent = pd.concat(match_df_list, sort = False)
else:
match_df_by_parent = \
pd.DataFrame(columns = ['curr_im_colony', 'next_im_colony'])
return(match_df_by_parent)
def _tag_merged_colonies(self, match_df):
'''
Identifes merge events between two subsequent images
(When a single colony in subsequent image matches multiple
colonies in current image), including both parts of a
broken-up colony if one of those parts merges with another
colony
Set self.tracking_col_name in merged colonies to np.nan
This means that if a merged colony is tracked in a subsequent
image, it will inherit np.nan as its unique tracking id
As a result, merged colonies are no longer tracked, which is the
desired behavior
'''
### !!! NEEDS UNITTEST
# id colony indices that appear twice in next_im_colony_id
# column of match_df, i.e. colonies in the next image that
# match to two different colonies in the current image
[next_im_col_matching, next_match_count] = \
np.unique(match_df['next_im_colony'], return_counts=True)
merged_colonies_direct = next_im_col_matching[next_match_count > 1]
# if a colony breaks into two, and then one part of it merges
# with another colony, we want to tag both the merged and
# non-merged part as merged
colonies_that_merge = \
match_df.curr_im_colony[
match_df['next_im_colony'].isin(merged_colonies_direct)]
colonies_that_merge_bool = \
match_df['curr_im_colony'].isin(colonies_that_merge)
merged_colonies = match_df.next_im_colony[colonies_that_merge_bool]
# set self.tracking_col_name and parent_colony to NaN for merged
# colonies in self.active_col_prop_df
self.active_col_prop_df.loc[
merged_colonies, self.tracking_col_name] = np.nan
self.active_col_prop_df.loc[
merged_colonies, 'parent_colony'] = np.nan
# return a version of match_df that is missing merged colonies
match_df_nonmerging = match_df[~colonies_that_merge_bool]
return(match_df_nonmerging)
def _resolve_splits(self, match_df_nonmerging):
'''
If a single colony in the current image matches with two
colonies in the subsequent image (e.g. due to breaking up),
treat the largest of the next image colonies as the matching
colony
This step should be done *after* removing merging colonies
'''
### !!! NEEDS UNITTEST
# id colony indices that appear twice in curr_im_colony_id
# column of match_df_nonmerging, i.e. colonies in the current
# image that match to two different colonies in the next
# image
[curr_im_col_matching, curr_match_count] = \
np.unique(match_df_nonmerging['curr_im_colony'],
return_counts=True)
split_colonies = curr_im_col_matching[curr_match_count > 1]
# create a dataframe that excludes split colonies
match_df_no_splits = \
match_df_nonmerging[
~match_df_nonmerging.curr_im_colony.isin(split_colonies)]
# loop through split colonies and add the match that has
# the largest area in the next image to match_df_filtered
split_colony_match_list = [match_df_no_splits]
for curr_colony in split_colonies:
curr_match_df = \
match_df_nonmerging[match_df_nonmerging.curr_im_colony ==
curr_colony].copy()
current_match_areas = self.active_col_prop_df.loc[
curr_match_df.next_im_colony.to_list(), 'area'].to_numpy()
curr_match_df['area'] = current_match_areas
match_to_keep = \
curr_match_df[curr_match_df.area == curr_match_df.area.max()]
# in case two areas of split colonies are identical,
# keep the first
match_to_keep = match_to_keep.iloc[[0]]
split_colony_match_list.append(
match_to_keep.drop(columns = ['area']))
# combine selected split colonies with
# match_df_no_splits into single df
match_df_filtered = \
pd.concat(split_colony_match_list, sort = False)
return(match_df_filtered)
def _find_satellites_by_dist(self, parent_candidate_df, sat_candidate_df):
'''
Returns df with indices of sat_candidate_df rows in which
satellite colony is within self._max_sat_major_axis_prop of a
single colony from parent_candidate_df, and indices of
corresponding parent colonies
'''
# create distance matrix with parent colonies along columns
# and satellite colonies along rows
if parent_candidate_df.shape[0] == 0 or sat_candidate_df.shape[0] == 0:
sat_indices = []
parent_indices = []
else:
x_dist = \
parent_candidate_df.cX.to_numpy() - \
sat_candidate_df.cX.to_numpy()[np.newaxis].T
y_dist = \
parent_candidate_df.cY.to_numpy() - \
sat_candidate_df.cY.to_numpy()[np.newaxis].T
dist_mat = np.sqrt(x_dist**2 + y_dist**2)
# find positions in dist_mat within
# self._max_sat_major_axis_prop of major_axis_length of parent
cutoff_dist_array = \
parent_candidate_df.major_axis_length.to_numpy()*\
self._max_sat_major_axis_prop
within_cutoff_mat = dist_mat <= cutoff_dist_array
# find the number of 'parents' each satellite matches to
parent_colony_num = np.sum(within_cutoff_mat, axis = 1)
# only real 'satellites' are colonies that match a single parent
real_sat_pos_list = parent_colony_num == 1
# find position corresponding to parent of each real satellite
parent_pos_list = \
np.argmax(within_cutoff_mat[real_sat_pos_list,:], axis = 1)
sat_indices = sat_candidate_df.index[real_sat_pos_list]
parent_indices = parent_candidate_df.index[parent_pos_list]
parent_sat_df = pd.DataFrame(
{'satellite_idx': sat_indices,
'parent_idx': parent_indices})
return(parent_sat_df)
def _id_satellites(self, next_im_data, match_df_filtered):
'''
Identifies colonies in next_im_data that are satellites of
other colonies
Must be fone after tagging merged colonies and resolving splits
Satellites are colonies that:
- first appear in next_im_data (i.e. have no match in
match_df_filtered, and have not been removed due to merging)
- are within self._max_sat_major_axis_prop of only one other
colony
'''
# find colonies in next_im_data with no match (post-removing
# minor colony split products) in previous timepoint and that
# have not been filtered out as merge products
unmatched_colonies = next_im_data.loc[
~next_im_data.index.isin(match_df_filtered.next_im_colony) &
~pd.isnull(self.active_col_prop_df.loc[
next_im_data.index][self.tracking_col_name])
]
# for now, allow all colonies that are not satellite candidates
# to be parent candidates; afterwards, filter out parents that
# were not successfully tracked from the previous timepoint
parent_candidates = next_im_data[
~next_im_data.index.isin(unmatched_colonies.index)]
# get dataframe of parent-satellite pair indices from
# self.active_col_prop_df
parent_sat_df = \
self._find_satellites_by_dist(
parent_candidates,
unmatched_colonies
)
# remove any parent colonies that are satellites to colonies
# that weren't matched successfully to previous timepoint (e.g.
# merged colonies)
parent_sat_df_filt = parent_sat_df[
parent_sat_df.parent_idx.isin(match_df_filtered.next_im_colony)]
return(parent_sat_df_filt)
def _replace_vals_by_keydict(self, replace_keys, replace_vals,
col_to_replace):
'''
Replaces replace_keys in col_to_replace of
self.active_col_prop_df with replace_vals
'''
if len(replace_keys) > 0 and len(replace_vals) > 0:
replace_dict = pd.Series(
replace_vals,
index=replace_keys
).to_dict()
else:
replace_dict = dict()
self.active_col_prop_df.replace(
{col_to_replace: replace_dict},
inplace = True)
def _replace_tracking_col_by_match(self, match_df, curr_im_data,
next_im_data):
'''
Uses match_df to replace tracking_col_name and parent_coloy in
self.active_col_prop_df from every timepoint that have the
values in match_df.next_im_colony with values from
match_df.curr_im_colony
'''
### !!! NEEDS UNITTEST
# replace tracking id values based on match_df
replace_vals_track = \
curr_im_data.loc[match_df.curr_im_colony.values]\
[self.tracking_col_name].to_list()
replace_keys_track = \
next_im_data.loc[match_df.next_im_colony.values]\
[self.tracking_col_name].to_list()
self._replace_vals_by_keydict(
replace_keys_track, replace_vals_track, self.tracking_col_name)
# replace parent_colony values based on match_df
replace_vals_parent = \
curr_im_data.loc[match_df.curr_im_colony.values]\
['parent_colony'].to_list()
replace_keys_parent = \
next_im_data.loc[match_df.next_im_colony.values]\
['parent_colony'].to_list()
self._replace_vals_by_keydict(
replace_keys_parent, replace_vals_parent, 'parent_colony')
def _replace_parent_for_sat(self, parent_sat_df):
'''
Uses parent_sat_df to replace parent_colony in
self.active_col_prop_df from every timepoint that have the
values in parent_sat_df.satellite_idx with values from
parent_sat_df.parent_idx
'''
### !!! NEEDS UNITTEST
replace_vals = \
self.active_col_prop_df.loc[
parent_sat_df.parent_idx.values
]['parent_colony'].to_list()
replace_keys = \
self.active_col_prop_df.loc[
parent_sat_df.satellite_idx.values
]['parent_colony'].to_list()
self._replace_vals_by_keydict(
replace_keys, replace_vals, 'parent_colony')
def _track_single_im_pair(self, curr_im_data, next_im_data):
'''
Performs full tracking between curr_im_data and next_im_data,
and records results in self.active_col_prop_df
'''
# identify all matches between colonies in the two images
match_df = self._id_colony_match(curr_im_data, next_im_data)
# modify matches so that all colonies with shared parent share
# matches, and matches between colonies with same parent are
# removed
match_df_by_parent = \
self._match_by_parent(match_df, curr_im_data, next_im_data)
# set self.tracking_col_name in merged colonies to NaN, and get
# back match_df without colonies that merge into others
match_df_nonmerging = self._tag_merged_colonies(match_df_by_parent)
# for colonies that break into multiple pieces, track the
# largest piece as the main colony
match_df_filtered = self._resolve_splits(match_df_nonmerging)
# identify satellite colonies and their parents in next_im_data
parent_sat_df_filt = \
self._id_satellites(next_im_data, match_df_filtered)
# for colonies with a direct match between subsequent
# images, set self.tracking_col_name in all images to the
# self.tracking_col_name from current_im_data
self._replace_tracking_col_by_match(match_df_filtered, curr_im_data,
next_im_data)
# for colonies in next_im that are a satellite, set the
# parent_colony of every colony that shares their parent_colony
# to the matching parent value from parent_sat_df_filt
# This is important in cross-phase tracking, when a colony that
# has already been tracked independently across multiple
# timepoints turns out to be a satellite based on tracking from
# a previous phase (in this case, these satellites will not
# receive independent growth rates in the corresponding
# phase's growth rate analysis)
self._replace_parent_for_sat(parent_sat_df_filt)
def _set_up_satellite_track(self):
'''
Sets up columns necessary for tracking satellites
'''
# initialize parent_colony column
self.active_col_prop_df['parent_colony'] = \
self.active_col_prop_df[self.tracking_col_name]
def _aggregate_by_parent(self):
'''
Aggregates data in self.active_col_prop_df by parent in the
following way:
- label across all colonies sharing same parent gets joined
with semicolon
- area is summed across all colonies sharing same parent
- all other colony properties are taken from the parent
- parent_colony column is dropped
'''
# set aside parent colonies only
parent_property_df = \
self.active_col_prop_df.loc[
self.active_col_prop_df['parent_colony'] ==
self.active_col_prop_df[self.tracking_col_name]
].copy()
# remove properties to be aggregated
parent_property_df.drop(
columns=['label', 'area'],
inplace = True)
# set up df for aggregated properties
agg_property_df_group = \
self.active_col_prop_df[[
'phase_num', 'timepoint', 'parent_colony', 'xy_pos_idx',
'label', 'area']
].groupby(
['phase_num', 'timepoint', 'parent_colony', 'xy_pos_idx']
)
agg_property_df = agg_property_df_group.agg({
'label': ';'.join,
'area': np.sum
})
property_df = parent_property_df.join(agg_property_df,
on = ['phase_num', 'timepoint', 'parent_colony', 'xy_pos_idx'])
property_df.drop(columns = ['parent_colony'], inplace = True)
return(property_df)
def match_and_track_across_time(self, phase_num, colony_prop_df,
perform_registration = True):
'''
Identifies matching colonies between subsequent timepoints
Performs equivalent role to ColonyAreas_mod in original matlab
code, but with image registration; see comments on class for
differences
'''
self.perform_registration = perform_registration
### !!! NEEDS UNITTEST
# set the tracking column we'll be using to track across time
self.tracking_col_name = 'time_tracking_id'
# set active_col_prop_df to colony_prop_df
self.active_col_prop_df = colony_prop_df.copy()
# reset indices in self.active_col_prop_df to be consecutive
# integers, to make sure each row has a unique index that can be
# used as an identifier
self.active_col_prop_df.reset_index(inplace = True, drop=True)
# identify xy positions
_xy_positions = \
np.sort(np.unique(self.active_col_prop_df.xy_pos_idx))
# identify timepoints
_curr_phase_timepts = \
np.sort(np.unique(self.active_col_prop_df.timepoint))
# populate tracking column with unique IDs
self.active_col_prop_df[self.tracking_col_name] = \
["phase_{}_xy{}_col{}".format(phase_num, xy_pos, col_id) for \
phase_num, xy_pos, col_id in \
zip(self.active_col_prop_df.phase_num,
self.active_col_prop_df.xy_pos_idx,
self.active_col_prop_df.index)]
# set up columns for tracking satellites
self._set_up_satellite_track()
if len(_curr_phase_timepts) > 1:
# loop through xy positions
for curr_xy_pos in _xy_positions:
# loop through timepoints
for curr_timepoint, next_timepoint in \
zip(_curr_phase_timepts[:-1], _curr_phase_timepts[1:]):
# get df of which colony in curr_timepoint matches
# which colony in next_timepoint
###
# get colony properties at current timepoint
curr_im_data = \
self.active_col_prop_df[
(self.active_col_prop_df.timepoint ==
curr_timepoint) &
(self.active_col_prop_df.xy_pos_idx ==
curr_xy_pos)]
# get colony properties at next timepoint
next_im_data = \
self.active_col_prop_df[
(self.active_col_prop_df.timepoint ==
next_timepoint) &
(self.active_col_prop_df.xy_pos_idx ==
curr_xy_pos)]
self._track_single_im_pair(curr_im_data, next_im_data)
# convert time tracking id column to categorical
self.active_col_prop_df[self.tracking_col_name] = \
self.active_col_prop_df[self.tracking_col_name].astype(
'category')
# aggregate data by parent_colony
parent_agg_prop_df = self._aggregate_by_parent()
# add data for this phase to dict
self.single_phase_col_prop_df_dict[phase_num] = \
parent_agg_prop_df
return(parent_agg_prop_df)
def match_and_track_across_phases(self, perform_registration = True):
'''
Identifies matching colonies between last timepoint of each
phase and the first timepoint of the subsequent phase
Performs equivalent role to ColonyAreas_mod in original matlab
code, but see comments on class for differences
'''
### !!! NEEDS UNITTEST
self.perform_registration = perform_registration
# concatenate time-tracked colony property dfs to create df for
# tracking colonies across phases
indiv_phase_dfs = list(self.single_phase_col_prop_df_dict.values())
if indiv_phase_dfs:
self.active_col_prop_df = pd.concat(indiv_phase_dfs, sort = False)
# set the tracking column we'll be using to track across phases
self.tracking_col_name = 'cross_phase_tracking_id'
# reset indices in self.active_col_prop_df to be consecutive
# integers, to make sure each row has a unique index that can be
# used as an identifier
self.active_col_prop_df.reset_index(inplace = True, drop=True)
# identify xy positions
_xy_positions = \
np.sort(np.unique(self.active_col_prop_df.xy_pos_idx))
# identify phases
phase_list = \
np.sort(np.array(list(
self.single_phase_col_prop_df_dict.keys())))
# check that phases are unique
if np.unique(phase_list).size < phase_list.size:
raise IndexError('phase list contains non-unique items: ' +
| np.array_str(phase_list) | numpy.array_str |
# Copyrighrt 2020, by the California Institute of Technology.
# ALL RIGHTS RESERVED. United States Government Sponsorship acknowledged.
# Any commercial use must be negotiated with the Office of Technology Transfer at the California Institute of Technology.
# This software may be subject to U.S. export control laws.
# By accepting this software, the user agrees to comply with all applicable U.S. export laws and regulations.
# User has the responsibility to obtain export licenses, or other export authority as may be required before exporting
# such information to foreign countries or providing access to foreign persons.
# Codes last tested 05 April 2020 by MW and IF
import uuid
import urllib3
import os
import xarray as xr
import numpy as np
import netCDF4 as nc4
import imp
import datetime
import swath_references as ref
from bs4 import BeautifulSoup
########################################################################################################################
# these are some tools to help generate the metadata
########################################################################################################################
#step 1: read in the variables from the regridded file
def read_regridded_swath(filePath):
print(' Opening ' + str(filePath))
if filePath.exists():
data = xr.open_dataset(str(filePath))
else:
print(' regridded swath file not found! aborting!')
exit()
variables = []
variableNames = []
coordinates = []
coordinateNames = []
for data_var in data.data_vars.keys():
if np.size(np.array(data[data_var])) > 1:
variables.append(np.array(data[data_var]))
variableNames.append(data_var)
for coord in data.coords.keys():
coordinates.append(np.array(data[coord]))
coordinateNames.append(coord)
projection = data['projection'].attrs['EPSG']
return(variables,variableNames,coordinates,coordinateNames,projection)
########################################################################################################################
#step 2: generate a new swath with the variable and coordinates
def generate_new_dataset(variables,variableNames,coordinates,coordinateNames,projection,addGeoid):
data_vars = {}
coords = {}
for vv in range(len(variables)):
if variableNames[vv] == 'elevation':
elevation = variables[vv]
elevation[np.isnan(elevation)] = nc4.default_fillvals['f8']
data_vars['elevation'] = (['y', 'x'], elevation)
for vv in range(len(variables)):
if variableNames[vv] == 'count':
count = variables[vv]
data_vars['elevation_count'] = (['y', 'x'], count)
if variableNames[vv] == 'standard_deviation':
standard_deviation = variables[vv]
standard_deviation[np.isnan(standard_deviation)] = nc4.default_fillvals['f8']
standard_deviation[elevation == nc4.default_fillvals['f8']] = nc4.default_fillvals['f8']
data_vars['elevation_standardDeviation'] = (['y', 'x'], standard_deviation)
if variableNames[vv] == 'longitude':
longitude = variables[vv]
data_vars['longitude'] = (['y', 'x'], longitude)
if variableNames[vv] == 'latitude':
latitude = variables[vv]
data_vars['latitude'] = (['y', 'x'], latitude)
if variableNames[vv] == 'geoid':
if addGeoid:
geoid = variables[vv]
data_vars['geoid'] = (['y', 'x'], geoid)
if addGeoid:
quality_flag = np.zeros_like(elevation, dtype=np.int8)
indices1=np.logical_and(elevation-geoid>-5,standard_deviation>20)
quality_flag[indices1] = 1
indices2 = np.logical_and(elevation - geoid < -5, standard_deviation < 20)
quality_flag[indices2] = 2
indices3 = np.logical_and(elevation - geoid < -5, standard_deviation > 20)
quality_flag[indices3] = 3
quality_flag[count==0] = 4
else:
quality_flag = np.zeros_like(elevation, dtype=np.int8)
quality_flag[standard_deviation>20]=1
quality_flag[count==0]=2
# quality_flag = quality_flag.astype(np.int8)
data_vars['elevation_qualityFlag'] = (['y', 'x'], quality_flag)
data_vars['projection'] = chr(0)
for cc in range(len(coordinates)):
if coordinateNames[cc] in ['x']:
x = coordinates[cc]
coords[coordinateNames[cc]] = x
if coordinateNames[cc] in ['y']:
y = coordinates[cc]
coords[coordinateNames[cc]] = y
dataset = xr.Dataset(data_vars=data_vars, coords=coords)
return(dataset)
########################################################################################################################
#step 3: add in the global metadata values
def read_timespan_from_metadata(dataFolder,fileID):
swathID=ref.fileNameToSwathID(fileID)
year='20'+swathID.split('_')[2][:2]
metadataFile=os.path.join(dataFolder,'Raw',year,'Metadata',swathID+'_metadata.txt')
f=open(metadataFile)
lines=f.read()
f.close()
lines=lines.split('\n')
for line in lines:
if 'Start Time of Acquisition' in line:
date=line.split()[-3]
yr=date.split('-')[2]
mo = date.split('-')[1]
if mo=='Mar':
mo='03'
if mo=='Apr':
mo='04'
dy = date.split('-')[0]
dy = '{:02d}'.format(int(dy))
time=line.split()[-2]
minTime=yr+'-'+mo+'-'+dy+'T'+time+'Z'
if 'Stop Time of Acquisition' in line:
date = line.split()[-3]
yr = date.split('-')[2]
mo = date.split('-')[1]
if mo == 'Mar':
mo = '03'
if mo == 'Apr':
mo = '04'
dy = date.split('-')[0]
dy = '{:02d}'.format(int(dy))
time = line.split()[-2]
maxTime = yr + '-' + mo + '-' + dy + 'T' + time + 'Z'
ymd = minTime.split('T')[0]
hms = minTime.split('T')[1][:-1]
startTime = datetime.datetime(int(ymd.split('-')[0]), int(ymd.split('-')[1]), int(ymd.split('-')[2]),
int(hms.split(':')[0]), int(hms.split(':')[1]), int(hms.split(':')[2]))
ymd = maxTime.split('T')[0]
hms = maxTime.split('T')[1][:-1]
endTime = datetime.datetime(int(ymd.split('-')[0]), int(ymd.split('-')[1]), int(ymd.split('-')[2]),
int(hms.split(':')[0]), int(hms.split(':')[1]), int(hms.split(':')[2]))
duration = endTime - startTime
duration_in_s = duration.total_seconds()
days = divmod(duration_in_s, 86400)
hours = divmod(days[1], 3600)
minutes = divmod(hours[1], 60)
seconds = divmod(minutes[1], 1)
durationString = 'P0Y0M0DT' + str(int(hours[0])) + 'H' + str(int(minutes[0])) + 'M' + str(int(seconds[0])) + 'S'
return(minTime,maxTime,durationString)
def main_attribute_dictionary(dataFolder,regridded_filepath,resolution,elevation,longitude,latitude,projection):
minLon = float(np.min( | np.min(longitude) | numpy.min |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.