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#!/usr/bin/python
import pandas as pd
import numpy as np
from statsmodels.tsa.arima_model import ARIMA
from sklearn.metrics import mean_squared_error
import warnings
warnings.simplefilter("ignore")
def get_data(start):
#iterate through protocols
protocols = ['dns', 'http', 'https', 'icmp', 'ntp', 'pop']
max = 0
for protocol in protocols:
try:
data = pd.read_csv('packets_' + protocol + '.csv', names=['Time','Size','Buckets'])
data = data.astype(int)
#count the number of packets in each second
data = data['Time'].value_counts()
#sort by seconds
data = data.sort_index()
#fill missing seconds
data = data.reindex(pd.RangeIndex(data.index.max() + 1)).fillna(0)
a = []
a = | np.array(a, int) | numpy.array |
import numpy as np
import os
import subprocess
import shutil
import multiprocessing
import sys
import copy
from collections import OrderedDict
from pyfoamsetup.coreLibrary import *
import pyfoamsetup.coreLibrary.CaseSetup as CaseSetup
class PropellerSimulation(CaseSetup.CaseSetup):
def __init__(self, runName, c, D, Re, J, fluid='air', rotationAxis='right', pushPull='push'):
# Default environment settings
if fluid == 'air':
rho = 1.226
nu = 1.45e-05
elif fluid == 'water':
rho = 1000
nu = 1.19e-6
self.D = D
self.r = D/2
self.J = J
self.n = Re*nu/(np.sqrt((J*D)**2 + (0.7*self.r*2*np.pi)**2)*c)
self.omega = 2*np.pi*self.n
self.U_r = 0.7*(D/2)*self.omega
U = self.J*self.n*self.D
A = np.pi*(D/2)**2
self.rotationAxis = rotationAxis
patchList = ['propeller']
# Call init from base class
self.homePath = os.path.dirname(os.path.realpath(__file__))
super().__init__(runName, patchList, c, U, A, nu, rho, 'PropellerSimulation')
# Reset reynolds number from input
self.Re = Re
# Time step settings
self.maxDegreesPrTimeStep = 2
self.numberOfRevolutions = 4
self.baseSize = 1
self.domainWake = 6
self.domainFront = 4
self.domainWidth = 4
self.rotatingCylinderRadius = 0.75
self.rotatingCylinderLength = 1
self.setMeshSettings()
self.nrLayers = 0
self.setSolver('pimpleDyMFoam')
self.adjustTimeStep = False
def setDefaultCellLengths(self):
super().setDefaultCellLengths()
self.maxBaseSize = 0.1*self.D # Ensure that the geometry is captured!
self.maxSmallestSize = 0.01*self.L
self.viscousLength = 0.02*self.D
def writeBlockMesh(self):
blockMesh = BlockMesh.Dict()
# Calculate minimum values for domain size
xBack = self.domainWake*self.D
xFront = -self.domainFront*self.D
yRight = self.domainWidth*self.D
yLeft = -self.domainWidth*self.D
zHeight = self.domainWidth*self.D
zDepth = -self.domainWidth*self.D
# Calculate number of cells in each direction
x_nrCells = np.ceil((xBack - xFront)/self.baseSize)
y_nrCells = np.ceil((yRight - yLeft)/self.baseSize)
z_nrCells = np.ceil((zHeight - zDepth)/self.baseSize)
# Readjust domain size to fit nr cells
xLength = self.baseSize*x_nrCells
yLength = self.baseSize*y_nrCells
zLength = self.baseSize*z_nrCells
wakeFraction = (self.domainWake/(self.domainWake + self.domainFront))
frontFraction = (self.domainFront/(self.domainWake + self.domainFront))
xFront = -xLength*frontFraction
xBack = xLength*wakeFraction
yRight = yLength/2
yLeft = -yLength/2
# Add data to blockmesh and write
blockMesh.addVertex([xFront, yLeft, zDepth])
blockMesh.addVertex([xBack, yLeft, zDepth])
blockMesh.addVertex([xBack, yRight, zDepth])
blockMesh.addVertex([xFront, yRight, zDepth])
blockMesh.addVertex([xFront, yLeft, zHeight])
blockMesh.addVertex([xBack, yLeft, zHeight])
blockMesh.addVertex([xBack, yRight, zHeight])
blockMesh.addVertex([xFront, yRight, zHeight])
blockMesh.addBlock([x_nrCells, y_nrCells, z_nrCells])
blockMesh.addBoundary('inlet', 'patch', [[0, 4, 7, 3],[3, 2, 6, 7], [4, 5, 6, 7], [0, 1, 5, 4], [0, 3, 2, 1]])
blockMesh.addBoundary('outlet', 'patch', [[2, 6, 5, 1]])
blockMesh.write(self.systemFolder)
def writeMesh(self):
self.calculateBaseSize()
self.writeBlockMesh()
# Add geometry
self.snappyDict.addGeometry('propeller.obj', 'triSurfaceMesh', {'name':'propeller'})
self.snappyDict.addRefinementSurface('propeller', self.maxRefinementLevel-1, self.maxRefinementLevel, self.nrLayers)
self.snappyDict.addFeature('propeller.eMesh', self.maxRefinementLevel)
self.snappyDict.addGeometry('propellerStem.obj', 'triSurfaceMesh', {'name':'propellerStem'})
self.snappyDict.addRefinementSurface('propellerStem', self.maxRefinementLevel-3, self.maxRefinementLevel-3, 0)
# Add cylinders
name = 'rotatingCylinder'
length = self.rotatingCylinderLength*self.D
radius = self.rotatingCylinderRadius*self.D
x0 = 0
level = self.maxRefinementLevel-2
point1String = '({:.6f} {:.6f} {:.6f})'.format(x0, 0, 0)
point2String = '({:.6f} {:.6f} {:.6f})'.format(x0+length, 0, 0)
radiusString = '{:.6f}'.format(radius)
extraArgumentDict = OrderedDict()
extraArgumentDict['faceType'] = 'boundary'
extraArgumentDict['cellZone'] = name
extraArgumentDict['faceZone'] = name
extraArgumentDict['cellZoneInside'] = 'inside'
self.snappyDict.addGeometry(name, 'searchableCylinder', {'point1':point1String, 'point2':point2String, 'radius':radiusString})
self.snappyDict.addRefinementSurface(name, level, level, 0, extraArgumentDict=extraArgumentDict)
self.snappyDict.addRefinementRegion(name, 'inside', np.array([1, level]))
# Set up layer settings
self.snappyDict.addLayersControls['relativeSizes'] = 'false'
self.snappyDict.addLayersControls['finalLayerThickness'] = self.t_final
self.snappyDict.addLayersControls['minThickness'] = 0.5*self.t_final
self.snappyDict.addLayersControls['expansionRatio'] = self.layerExpansion
self.snappyDict.castellatedMeshControls['locationInMesh'] = '({:.3f} {:.3f} {:.3f})'.format(-1.03*self.D, 1.04*self.D, 1.3*self.D)
self.snappyDict.castellatedMeshControls['nCellsBetweenLevels'] = int(self.nCellsBetweenLevels)
self.snappyDict.write(self.systemFolder)
self.snappyDict.writeSurfaceFeatureExtractDict(self.systemFolder, 'propeller.obj')
def writeCaseFiles(self):
# Recalculate time stepping
self.deltaT = np.round(self.maxDegreesPrTimeStep/(self.n*360), decimals=8)
self.maxDeltaT = np.round(self.maxDegreesPrTimeStep/(self.n*360), decimals=8)
self.endTime = np.round(self.numberOfRevolutions/self.n, decimals=8)
self.writeInterval = np.round(self.endTime/10, decimals = 8)
super().writeCaseFiles()
FileHandling.changeLine(self.constantFolder+'dynamicMeshDict', 'omega', '\t\tomega {:.6f};'.format(self.omega))
if self.rotationAxis == 'left':
FileHandling.changeLine(self.constantFolder+'dynamicMeshDict', 'axis', '\t\taxis (-1 0 0);')
self.writePropInfo()
createPatchDict = createPatch.Dict()
createPatchDict.addPatch('AMI1', 'rotatingCylinder', 'AMI2')
createPatchDict.addPatch('AMI2', 'rotatingCylinder_slave', 'AMI1')
createPatchDict.write(self.systemFolder)
def writeScripts(self):
# ------ Mesh --------------------
f = open(self.runFolder+'/mesh.sh', 'w')
f.write('#!/bin/bash\n\n')
if self.snappyDict.snapControls['explicitFeatureSnap'] == 'true':
f.write('surfaceFeatureExtract\n')
f.write('blockMesh\n')
f.write('mv system/decomposeParDict system/decomposeParDict.sim\n')
f.write('mv system/decomposeParDict.mesh system/decomposeParDict\n')
f.write('decomposePar\n')
f.write('mpirun -np {:.0f} snappyHexMesh -overwrite -parallel\n'.format(self.nCPUs_mesh))
f.write('reconstructParMesh -constant\n')
f.write('rm -fr processor*\n')
f.write('createPatch -overwrite\n')
f.write('mv system/decomposeParDict system/decomposeParDict.mesh\n')
f.write('mv system/decomposeParDict.sim system/decomposeParDict\n')
f.write('renumberMesh -overwrite\n')
if len(self.topoSetList) > 0:
f.write('topoSet\n')
f.close()
# ------- Simulation ---------------------
f = open(self.runFolder + '/runSim.sh', 'w')
f.write('#!/bin/bash\n\n')
f.write('decomposePar\n')
if self.vilje:
f.write('mpiexec ' + self.solver + ' -parallel\n')
else:
f.write('mpirun -np {:.0f} '.format(self.nCPUs) + self.solver + ' -parallel\n')
f.write('reconstructPar\n')
f.write('rm -fr processor*\n')
f.close()
def addViscousWake(self, x0, y0, z0, lengthFactor = 4, radiusFactor = 1.0, expansion = 2):
# Ensure that mesh size is calculated
self.turbulence = Turbulence.Properties(self.U, self.L, self.nu, self.turbulenceModel, self.turbulenceType)
self.turbulence.calculateInitialValues()
self.calculateBaseSize()
maxLevel = int(np.floor(np.log(self.baseSize/self.viscousLength)/np.log(2)))
print(maxLevel)
radius0 = radiusFactor*self.D
length0 = lengthFactor*self.D
level = maxLevel
for i in range(maxLevel):
cellLength = self.baseSize/(2**level+1)
name = 'viscWake{:.0f}'.format(i+1)
length = length0*expansion**(i)
radius = radius0*expansion**(i)
point1String = '({:.6f} {:.6f} {:.6f})'.format(x0, y0, z0)
point2String = '({:.6f} {:.6f} {:.6f})'.format(x0+length, y0, z0)
radiusString = '{:.6f}'.format(radius)
self.snappyDict.addGeometry(name, 'searchableCylinder', {'point1':point1String, 'point2':point2String, 'radius':radiusString})
self.snappyDict.addRefinementRegion(name, 'inside', np.array([1, level]))
level -= 1
def writePropInfo(self):
f = open(self.runFolder + 'propInfo.txt', 'w')
f.write('D {:.6f}\n'.format(self.D))
f.write('c {:.6f}\n'.format(self.L))
f.write('Re {:.6f}\n'.format(self.Re))
f.write('J {:.6f}\n'.format(self.J))
f.write('n {:.6f}\n'.format(self.n))
f.write('omega {:.6f}\n'.format(self.omega))
f.write('rho {:.6f}\n'.format(self.rho))
f.write('U {:.6f}\n'.format(self.U))
f.write('U_R {:.6f}\n'.format(self.U_r))
f.close()
class ActuatorDisk(CaseSetup):
def __init__(self, runName, U, D, CT, CQ=0.0, rh_factor=0.1, alpha=0, fluid='air', meshSetting='medium', vilje=False):
# Default environment settings
if fluid == 'air':
rho = 1.226
nu = 1.45e-05
elif fluid == 'water':
rho = 1000
nu = 1.19e-6
self.D = D
self.r = D/2
self.r_h = rh_factor*self.r
self.CT = CT
self.CQ = CQ
self.alpha = alpha
A = np.pi*self.r**2
patchList = []
# Call init from base class
super().__init__(runName, patchList, 0.5*self.r, U, A, nu, rho, vilje)
self.Thrust = 0.5*self.A*self.CT*self.U**2
self.Torque = 0.5*self.A*self.CQ*self.U**2*self.D
# Essential folder paths
self.foamPath = os.environ['FOAM_RUN']
self.mainRunFolder = self.foamPath + '/PropellerSimulation'
self.homePath = os.path.dirname(os.path.realpath(__file__))
self.setFolderPaths()
self.maxBaseSize = 0.5*self.D
self.maxSmallestSize = 0.01*self.D
self.actuatorDiskLength = 0.05*self.D
self.viscousLength = 0.02*self.D
# Default mesh settings
if meshSetting == 'fine':
self.maxBaseSize /= np.sqrt(2)
self.maxSmallestSize /= np.sqrt(2)
self.viscousLength /= | np.sqrt(2) | numpy.sqrt |
import numpy as np
from termcolor import colored
def solve_Newton(
R, J, u0, abs_tol=1.0e-10, rel_tol=1.0e-10, max_iters=200, debug=False
):
"""
Solve nonlinear system R=0 by Newton's method.
J is the Jacobian of R. Both R and J must be functions of x.
At input, x holds the start value. The iteration continues
until ||F|| < abs_tol or ||F|| / ||F0|| < rel_tol.
"""
# Initial Residuals
u = u0
Ru = R(u)
Ju = J(u)
Rnrm = | np.linalg.norm(Ru) | numpy.linalg.norm |
import math
import os
import sys
from pathlib import Path
from pedrec.evaluations.eval_helper import get_skel_coco, get_skel_h36m, get_skel_h36m_handfootends
from pedrec.evaluations.eval_np.eval_angular import get_angular_distances
from pedrec.evaluations.validate import get_2d_pose_pck_results, get_3d_pose_results
from pedrec.models.constants.skeleton_coco import SKELETON_COCO_JOINTS
from pedrec.models.constants.skeleton_h36m import SKELETON_H36M_JOINTS
from pedrec.models.constants.skeletons import SKELETON
from pedrec.models.validation.orientation_validation_results import FullOrientationValidationResult
from pedrec.training.experiments.experiment_path_helper import get_experiment_paths_home
from pedrec.utils.skeleton_helper import flip_lr_joints
from pedrec.utils.skeleton_helper_3d import flip_lr_joints_3d, flip_lr_orientation
print(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))))
import numpy as np
import pandas as pd
from pedrec.models.constants.skeleton_pedrec import SKELETON_PEDREC_JOINTS
def get_df(dataset_root, result_filename):
dataset_df_path = os.path.join(dataset_root, "results", result_filename)
return pd.read_pickle(dataset_df_path)
def get_skeleton2d(df):
filter_skeleton2d = [col for col in df if col.startswith("skeleton2d")]
skeleton_2ds = df[filter_skeleton2d].to_numpy(dtype=np.float32).reshape(len(df),
len(SKELETON_PEDREC_JOINTS), 5)
return df, skeleton_2ds
def get_skeleton3d(df):
filter_skeleton3d = [col for col in df if col.startswith("skeleton3d")]
skeleton_3ds = df[filter_skeleton3d].to_numpy(dtype=np.float32).reshape(len(df),
len(SKELETON_PEDREC_JOINTS), 6)
return df, skeleton_3ds
def get_orientations(df):
filter_body = [col for col in df if col.startswith("body_orientation_")]
orientation_body = df[filter_body].to_numpy(dtype=np.float32).reshape(len(df), 5)
filter_head = [col for col in df if col.startswith("head_orientation_")]
orientation_head = df[filter_head].to_numpy(dtype=np.float32).reshape(len(df), 5)
return orientation_body, orientation_head
def get_msjpe(output, target):
mask = target[:, :, 4] == 1
a = output[mask][:, :3]
b = target[mask][:, :3]
num_visible_joints = b.shape[0]
if num_visible_joints < 1:
print("NOOO")
return 0
x = np.linalg.norm(a[:, 0:3] - b[:, 0:3], axis=1)
return np.mean(x)
def get_results(experiment_name: str, flip_test: bool = False, skeleton: SKELETON = SKELETON.PEDREC):
df_full_gt = pd.read_pickle("data/datasets/Conti01/rt_conti_01_val_FIN.pkl")
skeleton2d_visibles = [col for col in df_full_gt if col.startswith('skeleton2d') and col.endswith('_visible')]
df_full_gt["visible_joints"] = df_full_gt[skeleton2d_visibles].sum(axis=1)
df_valid_filter = (df_full_gt['bb_score'] >= 1) & (df_full_gt['visible_joints'] >= 3)
df_full_gt = df_full_gt[df_valid_filter]
df_gt = get_df("data/datasets/Conti01", f"C01F_gt_df_{experiment_name}.pkl")
df = get_df("data/datasets/Conti01", f"C01F_pred_df_{experiment_name}.pkl")
# df_flipped = get_df("data/datasets/Conti01", f"C01_pred_df_{experiment_name}_flipped.pkl")
_, skeleton_3d_full_gt = get_skeleton3d(df_full_gt)
_, skeleton_3d_gt = get_skeleton3d(df_gt)
dist_3d = np.abs(skeleton_3d_full_gt[:, :, :3]-skeleton_3d_gt[:, :, :3])
assert dist_3d.max() <= 0.001 # ignore floating point errors, smaller than 0.001mm == ok
_, skeleton_3d = get_skeleton3d(df)
assert skeleton_3d_gt.shape[0] == skeleton_3d.shape[0]
if flip_test:
df_flipped_view, skeleton_3d_flipped = get_skeleton3d(df_flipped)
for i in range(0, skeleton_3d_flipped.shape[0]):
skeleton_3d_flipped[i, :, :3] = flip_lr_joints_3d(skeleton_3d_flipped[i, :, :3])
skeleton_3d += skeleton_3d_flipped
skeleton_3d /= 2
#
# skeleton_3d_h36m_gt = np.zeros((skeleton_3d.shape[0], 17, 6), dtype=np.float32)
# skeleton_3d_h36m = np.zeros((skeleton_3d.shape[0], 17, 6), dtype=np.float32)
# for idx, joint in enumerate(SKELETON_H36M_JOINTS):
# skeleton_3d_h36m[:, idx, :] = skeleton_3d[:, joint.value, :]
# skeleton_3d_h36m_gt[:, idx, :] = skeleton_3d_gt[:, joint.value, :]
msjpe = get_msjpe(skeleton_3d, skeleton_3d_gt)
_, skeleton_2d_gt = get_skeleton2d(df_gt)
_, skeleton_2d_pred = get_skeleton2d(df)
if flip_test:
_, skeleton_2d_pred_flipped = get_skeleton2d(df_flipped)
for i in range(0, skeleton_2d_pred_flipped.shape[0]):
skeleton_2d_pred_flipped[i, :, :2] = flip_lr_joints(skeleton_2d_pred_flipped[i, :, :2], 1980)
skeleton_2d_pred += skeleton_2d_pred_flipped
skeleton_2d_pred /= 2
if skeleton == SKELETON.COCO:
skeleton_2d_gt = get_skel_coco(skeleton_2d_gt)
skeleton_2d_pred = get_skel_coco(skeleton_2d_pred)
elif skeleton == SKELETON.H36M:
skeleton_2d_gt = get_skel_h36m(skeleton_2d_gt)
skeleton_2d_pred = get_skel_h36m(skeleton_2d_pred)
elif skeleton == SKELETON.H36M_HANDFOOTENDS:
skeleton_2d_gt = get_skel_h36m_handfootends(skeleton_2d_gt)
skeleton_2d_pred = get_skel_h36m_handfootends(skeleton_2d_pred)
pck_results = get_2d_pose_pck_results(skeleton_2d_gt, skeleton_2d_pred)
o_body_gt, o_head_gt = get_orientations(df_gt)
o_body_pred, o_head_pred = get_orientations(df)
# Hack, forgot to add phi vis / supported, always 1
temp = np.ones(o_body_gt.shape[0])
temp = np.array([temp, temp]).transpose(1, 0)
o_body_gt = np.concatenate((o_body_gt, temp), axis=1)
o_head_gt = np.concatenate((o_head_gt, temp), axis=1)
o_body_gt[:, 0] *= math.pi
o_body_gt[:, 1] *= 2 * math.pi
o_head_gt[:, 0] *= math.pi
o_head_gt[:, 1] *= 2 * math.pi
o_body_pred[:, 0] *= math.pi
o_body_pred[:, 1] *= 2 * math.pi
o_head_pred[:, 0] *= math.pi
o_head_pred[:, 1] *= 2 * math.pi
if flip_test:
o_body_pred_flipped, o_head_pred_flipped = get_skeleton2d(df_flipped)
for i in range(0, o_body_pred_flipped.shape[0]):
o_body_pred_flipped[i, :, :2] = flip_lr_orientation(o_body_pred_flipped[i, :, :2])
o_head_pred_flipped[i, :, :2] = flip_lr_orientation(o_head_pred_flipped[i, :, :2])
o_body_pred += o_body_pred_flipped
o_body_pred /= 2
o_head_pred += o_head_pred_flipped
o_head_pred /= 2
dist_phi_body, dist_theta_body, spherical_distance_body = get_angular_distances(o_body_gt, o_body_pred)
dist_phi_body = np.degrees(dist_phi_body)
dist_theta_body = np.degrees(dist_theta_body)
spherical_distance_body = np.degrees(spherical_distance_body)
o_body_results = FullOrientationValidationResult(
angle_error_theta_5=len(np.where(dist_theta_body <= 5)[0]) / dist_theta_body.shape[0],
angle_error_theta_15=len(np.where(dist_theta_body <= 15)[0]) / dist_theta_body.shape[0],
angle_error_theta_22_5=len(np.where(dist_theta_body <= 22.5)[0]) / dist_theta_body.shape[0],
angle_error_theta_30=len(np.where(dist_theta_body <= 30)[0]) / dist_theta_body.shape[0],
angle_error_theta_45=len(np.where(dist_theta_body <= 45)[0]) / dist_theta_body.shape[0],
angle_error_theta_mean=np.mean(dist_theta_body),
angle_error_theta_std=np.std(dist_theta_body),
angle_error_phi_5=len(np.where(dist_phi_body <= 5)[0]) / dist_phi_body.shape[0],
angle_error_phi_15=len(np.where(dist_phi_body <= 15)[0]) / dist_phi_body.shape[0],
angle_error_phi_22_5=len(np.where(dist_phi_body <= 22.5)[0]) / dist_phi_body.shape[0],
angle_error_phi_30=len(np.where(dist_phi_body <= 30)[0]) / dist_phi_body.shape[0],
angle_error_phi_45=len(np.where(dist_phi_body <= 45)[0]) / dist_phi_body.shape[0],
angle_error_phi_mean=np.mean(dist_phi_body),
angle_error_phi_std=np.std(dist_phi_body),
spherical_distance_mean=spherical_distance_body
)
dist_phi_head, dist_theta_head, spherical_distance_head = get_angular_distances(o_head_gt, o_head_pred)
dist_phi_head = np.degrees(dist_phi_head)
dist_theta_head = np.degrees(dist_theta_head)
spherical_distance_head = np.degrees(spherical_distance_head)
o_head_results = FullOrientationValidationResult(
angle_error_theta_5=len(np.where(dist_theta_head <= 5)[0]) / dist_theta_head.shape[0],
angle_error_theta_15=len(np.where(dist_theta_head <= 15)[0]) / dist_theta_head.shape[0],
angle_error_theta_22_5=len( | np.where(dist_theta_head <= 22.5) | numpy.where |
"""
@brief Script used to control the main steps of the pick of the PAF rail
and place it over the kidney target (targetk).
@author <NAME> (<EMAIL>)
@date 03 Sep 2020
"""
import numpy as np
from scipy.spatial.transform import Rotation as R
import transforms3d.euler as euler
import transforms3d.quaternions as quaternions
import time
# My imports
from dVRL_simulator.PsmEnv import PSMEnv
from dVRL_simulator.vrep.simObjects import table, rail, targetK, collisionCheck
from dVRL_simulator.vrep.vrepObject import vrepObject
def goal_distance(goal_a, goal_b):
assert goal_a.shape == goal_b.shape
return np.linalg.norm(goal_a - goal_b, axis=-1)
class PSMEnv_Position_pickplace_k(PSMEnv):
def __init__(self, psm_num, n_substeps, block_gripper,
has_object, target_in_the_air, height_offset, target_offset,
obj_range, target_range, x_range, y_range, z_range,
distance_threshold, initial_pos, initial_pos_k, reward_type,
dynamics_enabled, two_dimension_only,
randomize_initial_pos_ee, randomize_initial_pos_obj,
randomize_initial_or_obj, randomize_initial_pos_kidney,
randomize_initial_or_kidney, randomize_target_point,
randomize_grasping_site, docker_container, action_type):
"""Initializes a new signle PSM Position Controlled Environment
Args:
psm_num (int): which psm you are using (1 or 2)
n_substeps (int): number of substeps the simulation runs on every
call to step
gripper_extra_height (float): additional height above the table
when positioning the gripper
block_gripper (boolean): whether or not the gripper is blocked
(i.e. not movable) or not
has_object (boolean): whether or not the environment has an object
target_in_the_air (boolean): whether or not the target should be
in the air above the table or on the
table surface
height_offset (float): offset from the table for everything
target_offset ( array with 3 elements): offset of the target,
usually z is set to the
height of the object
obj_range (float): range of a uniform distribution for sampling
initial object positions
target_range (float): range of a uniform distribution for sampling
a target Note: target_range must be
set > obj_range
distance_threshold (float): the threshold after which a goal is
considered achieved
initial_pos (3x1 float array): The initial position for the PSM
when reseting the environment.
initial_pos_k (3x1 float array): The initial position for the
target kidney
reward_type ('sparse' or 'dense'): the reward type, i.e.
sparse or dense
dynamics_enabled (boolean): To enable dynamics or not
two_dimension_only (boolean): To only do table top or not.
target_in_the_air must be set off too.
randomize_initial_pos_obj (boolean)
docker_container (string): name of the docker container that loads
the v-rep
randomize_initial_or_obj (boolean)
randomize_initial_pos_kidney (boolean)
randomize_initial_or_kidney (boolean)
randomize_target_point (boolean) referring to the target point over
the kidney surface
randomize_grasping_site (boolean)
action_type ('continuous', 'discrete'): the action space type, i.e. continuous or discrete
"""
#self.gripper_extra_height = gripper_extra_height
self.block_gripper = block_gripper
self.has_object = has_object
self.target_in_the_air = target_in_the_air
self.height_offset = height_offset
self.target_offset = target_offset
self.obj_range = obj_range
self.target_range = target_range
self.distance_threshold = distance_threshold
self.initial_pos = initial_pos
self.initial_pos_k = initial_pos_k
self.reward_type = reward_type
self.dynamics_enabled = dynamics_enabled
self.two_dimension_only = two_dimension_only
self.randomize_initial_pos_obj = randomize_initial_pos_obj
self.randomize_initial_pos_ee = randomize_initial_pos_ee
self.randomize_initial_or_obj = randomize_initial_or_obj
self.randomize_initial_pos_kidney = randomize_initial_pos_kidney
self.randomize_initial_or_kidney = randomize_initial_or_kidney
self.x_range = x_range
self.y_range = y_range
self.z_range = z_range
self.randomize_target_point = randomize_target_point
self.randomize_grasping_site = randomize_grasping_site
self.action_type = action_type
if self.block_gripper:
self.n_actions = 3
self.n_states = 3 + self.has_object*3
else:
self.n_actions = 4
self.n_states = 4 + self.has_object*3
super(PSMEnv_Position_pickplace_k, self).__init__(
psm_num = psm_num, n_substeps=n_substeps,
n_states = self.n_states, n_goals = 3,
n_actions=self.n_actions, camera_enabled = False,
docker_container =docker_container, action_type=action_type)
self.targetK = targetK(self.clientID)
self.collisionCheck = collisionCheck(self.clientID, psm_num)
self.vrepObject=vrepObject(self.clientID)
if self.has_object:
self.rail = rail(self.clientID)
self.table = table(self.clientID)
self.prev_ee_pos = np.zeros((3,))
self.prev_ee_rot = np.zeros((3,))
self.prev_obj_pos = np.zeros((3,))
self.prev_obj_rot = np.zeros((3,))
self.prev_jaw_pos = 0
if(psm_num == 1):
self.psm = self.psm1
else:
self.psm = self.psm2
#Start the streaming from VREP for specific data:
#PSM Arms:
self.psm.getPoseAtEE(ignoreError = True, initialize = True)
self.psm.getJawAngle(ignoreError = True, initialize = True)
#Used for _sample_goal
self.targetK.getPosition(
self.psm.base_handle,
ignoreError=True,
initialize=True)
#Used for _reset_sim
self.table.getPose(
self.psm.base_handle,
ignoreError=True,
initialize=True)
# Initilization of the streaming of the dummies
if self.has_object:
self.rail.getPose(
self.rail.dummy1_rail_handle,
self.psm.base_handle,
ignoreError=True,
initialize=True) # Also used in _get_obs
self.rail.getPose(
self.rail.dummy2_rail_handle,
self.psm.base_handle,
ignoreError=True,
initialize=True) # Also used in _get_obs
self.rail.getPose(
self.rail.dummy3_rail_handle,
self.psm.base_handle,
ignoreError=True,
initialize=True) # Also used in _get_obs
self.rail.getPose(
self.rail.dummy4_rail_handle,
self.psm.base_handle,
ignoreError=True,
initialize=True) # Also used in _get_obs
self.rail.getPose(
self.rail.dummy5_rail_handle,
self.psm.base_handle,
ignoreError=True,
initialize=True) # Also used in _get_obs
self.rail.getPose(
self.rail.dummy6_rail_handle,
self.psm.base_handle,
ignoreError=True,
initialize=True) # Also used in _get_obs
self.rail.getPose(
self.rail.dummy7_rail_handle,
self.psm.base_handle,
ignoreError=True,
initialize=True) # Also used in _get_obs
self.rail.getPose(
self.rail.dummy8_rail_handle,
self.psm.base_handle,
ignoreError=True,
initialize=True) # Also used in _get_obs
# Used for _get_obs
grasp = self.rail.isGrasped(ignoreError=True, initialize=True)
self.rail.readProximity(
ignoreError=True) # for the proximity sensor
# GoalEnv methods
# ----------------------------
def compute_reward(self, achieved_goal, goal, info):
d = goal_distance(achieved_goal, goal)*self.target_range
#Need to scale it back!
if self.reward_type == 'sparse':
return -(d > self.distance_threshold).astype(np.float32)
else:
return -100*d
# PsmEnv methods
# ----------------------------
def _set_action(self, action):
'''
@details: method used to set the next action to take
Grasped=True step: get a new quaternion for the EE, closer
to the target's orientation. Set it to the new
quaternion if the orientations are not yet close enough
(threshold dictates this).
Else, set the orientation equal to the target's. This is
done because the error doesn't converge to 0, due to the
instability of setting an orientation in V-Rep.
'''
assert action.shape == (self.n_actions,)
action = action.copy() # ensure that we don't change the action
# outside of this scope
if self.block_gripper:
pos_ctrl = action[0:3]
gripper_ctrl = 0
else:
pos_ctrl, gripper_ctrl = action[0:3], action[3]
gripper_ctrl = (gripper_ctrl+1.0)/2.0 #gripper_ctrl bound to 0 and 1
# Cheking if the rail object has any parents
grasped = self.rail.isGrasped()
# Get EE's pose:
pos_ee, quat_ee = self.psm.getPoseAtEE()
# Add position control:
pos_ee = pos_ee + pos_ctrl*0.001
# eta = 1mm used to avoid overshoot on real robot
# Get table information to constrain orientation and position:
pos_table, q_table = self.table.getPose(self.psm.base_handle)
# Make sure tool tip is not in the table by checking tt and which
# side of the table it is on.
# DH parameters to find tt position:
ct = np.cos(0)
st = np.sin(0)
ca = np.cos(-np.pi/2.0)
sa = | np.sin(-np.pi/2.0) | numpy.sin |
#!/usr/bin/env python
import numpy as np
import pickle
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import os
def generate_sinusoids_sum_1out (lb, ub, num_pts, y_offset, if_add_noise=True):
# generate multi-dimensional sinusoid
x1 = np.linspace(lb, ub, num_pts+1)
x2 = np.linspace(lb, ub, num_pts+1)
num_grid_pts = (num_pts+1) ** 2
X1, X2 = np.meshgrid(x1, x2)
X1 = np.reshape(X1, (num_grid_pts,1))
X2 = np.reshape(X2, (num_grid_pts,1))
X = np.hstack((X1, X2))
scale = 2 * np.pi / (ub-lb)
if if_add_noise == True:
# X += 0.1 * np.random.randn(num_grid_pts,2)
Y = np.sin(scale * X1) + np.sin(scale * X2) + y_offset + 0.1 * | np.random.randn(num_grid_pts,1) | numpy.random.randn |
import numpy as np
import matplotlib.pyplot as plt
import sympy
from sympy import *
import sys
sys.path.append(r'C:\Users\elira\Google Drive\butools2\Python')
sys.path.append('/home/d/dkrass/eliransc/Python')
from tqdm import tqdm
from butools.ph import *
from butools.map import *
from butools.queues import *
from butools.mam import *
from butools.dph import *
from scipy.linalg import expm, sinm, cosm
from sympy import *
from sympy import Symbol
from sympy.physics.quantum import TensorProduct
import pickle as pkl
import pandas as pd
from sympy import diff, sin, exp
from numpy.linalg import matrix_power
def busy(s, lam2, mu2):
return ((lam2 + mu2 + s) - ((lam2 + mu2 + s) ** 2 - 4 * lam2 * mu2) ** 0.5) / (2 * lam2)
def ser_lap(s, mu):
return mu / (s + mu)
def hyper(s, lam1, lam2, mu1, mu2):
return ser_lap(s, mu1) * lam1 / (lam1 + lam2) + ser_lap(s, mu2) * lam2 / (lam1 + lam2)
def rho(lam1, lam2, mu1, mu2):
return (lam1 + lam2) * ((lam1 / ((lam1 + lam2) * mu1)) + (lam2 / ((lam1 + lam2) * mu2)))
def w_lap(s, lam1, lam2, mu1, mu2):
return ((1 - rho(lam1, lam2, mu1, mu2)) * s) / (s - (lam1 + lam2) * (1 - hyper(s, lam1, lam2, mu1, mu2)))
def F(s, lam1, lam2, mu1, mu2):
return w_lap(s, lam1, lam2, mu1, mu2) * ser_lap(s, mu1)
def A(s, lam1, lam2, mu2):
return (lam1 / (lam1 + lam2 - lam2 * (ser_lap(s, mu2))))
def beta(s, lam1, lam2, mu1, mu2):
return (lam1 / (lam1 + lam2 + s) + ((A(s, lam1, lam2, mu2) * lam2) / (lam1 + lam2 + s)) * (
ser_lap(s, mu2) - busy(s + lam1, lam2, mu2))) / (
1 - ((lam2 * busy(s + lam1, lam2, mu2)) / (lam1 + lam2 + s)))
def tau(s, lam1, lam2, mu1, mu2):
return ser_lap(s, mu1) * (A(s, lam1, lam2, mu2) * (
1 - F(lam1 + lam2 - lam2 * busy(s + lam1, lam2, mu2), lam1, lam2, mu1, mu2)) + F(
lam1 + lam2 - lam2 * busy(s + lam1, lam2, mu2), lam1, lam2, mu1, mu2) * beta(s, lam1, lam2, mu1, mu2))
def get_var(lam1, lam2, mu1, mu2):
s = Symbol('s')
y = tau(s, lam1, lam2, mu1, mu2)
dx = diff(y, s)
dxdx = diff(dx, s)
return dxdx.subs(s, 0) - (dx.subs(s, 0)) ** 2
def get_nth_moment(lam1, lam2, mu1, mu2, n):
s = Symbol('s')
y = tau(s, lam1, lam2, mu1, mu2)
for i in range(n):
if i == 0:
dx = diff(y, s)
else:
dx = diff(dx, s)
return dx.subs(s, 0)
def get_first_n_moments(parameters, n=5):
lam1, lam2, mu1, mu2 = parameters
moments = []
for n in range(1, n + 1):
moments.append(get_nth_moment(lam1, lam2, mu1, mu2, n) * (-1) ** n)
moments = np.array([moments], dtype='float')
return moments
def kroneker_sum(G, H):
size_g = G.shape[0]
size_h = H.shape[0]
return np.kron(G, np.identity(size_h)) + np.kron(np.identity(size_g), H)
def give_boundry_probs(R, A0, A1, A, B, C0, ro):
p00, p01, p02, p100, p110, p120, p101, p111, p121 = symbols('p00 p01 p02 p100 p110 p120 p101 p111 p121')
eqns = [np.dot(np.array([p00, p01, p02]), np.ones((A0.shape[0]))) - (1 - ro)]
eq3 = np.dot(np.array([p00, p01, p02]), A0) + np.dot(np.array([p100, p110, p120, p101, p111, p121]), A1)
eq1 = np.dot(np.array([p00, p01, p02]), C0)
eq2 = np.dot(np.array([p100, p110, p120, p101, p111, p121]), B + np.dot(R, A))
for eq_ind in range(B.shape[0]):
eqns.append(eq1[0, eq_ind] + eq2[0, eq_ind])
for eq_ind in range(A0.shape[0]):
eqns.append(eq3[0, eq_ind])
A_mat, b = linear_eq_to_matrix(eqns[:-1], [p00, p01, p02, p100, p110, p120, p101, p111, p121])
return A_mat, b
def get_expect_gph_system(R, p1_arr, xm_max=5000):
expected = 0
for pi_val in range(1, xm_max):
ui = p1_arr.reshape((1, R.shape[0]))
Ri = np.linalg.matrix_power(R, pi_val - 1)
expected += np.dot(np.dot(ui, Ri), np.ones((R.shape[0], 1))) * pi_val
return expected[0, 0]
def get_expect_gph_system(R, p1_arr, xm_max=5000):
expected = 0
for pi_val in range(1, xm_max):
ui = p1_arr.reshape((1, R.shape[0]))
Ri = np.linalg.matrix_power(R, pi_val - 1)
expected += np.dot(np.dot(ui, Ri), np.ones((R.shape[0], 1))) * pi_val
return expected[0, 0]
def get_A0(Ts):
krom_sum = kroneker_sum(Ts[0], Ts[1])
if len(Ts) > 2:
for T_ind in range(2, len(Ts)):
krom_sum = kroneker_sum(krom_sum, Ts[T_ind])
return krom_sum
def get_C_first(T0s, Ts, s):
krom_sum = kroneker_sum(T0s[0], T0s[1])
if len(Ts) > 2:
for T_ind in range(2, len(Ts)):
krom_sum = kroneker_sum(krom_sum, T0s[T_ind])
return krom_sum
def get_B(Ts, s):
krom_sum = kroneker_sum(Ts[0], Ts[1])
if len(Ts) > 2:
for T_ind in range(2, len(Ts)):
krom_sum = kroneker_sum(krom_sum, Ts[T_ind])
return kroneker_sum(krom_sum, s)
def get_A(Ts, new_beta, s0):
kron_sum = kroneker_sum(np.zeros(Ts[0].shape[0]), np.zeros(Ts[1].shape[0]))
if len(Ts) > 2:
for T_ind in range(2, len(Ts)):
kron_sum = kroneker_sum(kron_sum, np.zeros(Ts[T_ind].shape[0]))
kron_sum = kroneker_sum(kron_sum, np.dot(s0, new_beta))
return kron_sum
def compute_s_beta(r, mu, num_stations=2):
s_ = np.array([])
total_arrivals_to_station = np.sum(r[:, station_ind]) + np.sum(r[station_ind, :]) - np.sum(
r[station_ind, station_ind])
beta = np.array([])
for stream_ind in range(r.shape[0]):
if r[station_ind, stream_ind] > 0:
beta = np.append(beta, r[station_ind, stream_ind] / total_arrivals_to_station)
s_ = np.append(s_, -mu[station_ind, stream_ind])
for out_station in range(num_stations):
if out_station != station_ind:
if r[out_station, station_ind] > 0:
beta = np.append(beta, r[out_station, station_ind] / total_arrivals_to_station)
s_ = np.append(s_, -mu[station_ind, station_ind])
new_beta = np.array([])
new_s_ = np.unique(s_)
for val in new_s_:
new_beta = np.append(new_beta, np.sum(beta[np.argwhere(s_ == val)]))
new_beta = new_beta.reshape((1, new_beta.shape[0]))
s = | np.identity(new_s_.shape[0]) | numpy.identity |
# coding: utf-8
"""
Defines the DEQATN class and sub-functions.
The capitalization of the sub-functions is important.
"""
from __future__ import annotations
from typing import TYPE_CHECKING
import numpy as np
from numpy import (
cos, sin, tan, log, log10, mean, exp, sqrt, square, mod, abs, sum,
arcsin as asin, arccos as acos, arctan as atan, arctan2 as atan2,
arcsinh as asinh, arccosh as acosh, arctanh as atanh)
# atan2h
from numpy.linalg import norm # type: ignore
from pyNastran.bdf.cards.base_card import BaseCard
if TYPE_CHECKING: # pragma: no cover
from pyNastran.bdf.bdf import BDF
def pi(num):
"""weird way to multiply π by a number"""
return np.pi * num
def rss(*args): # good
"""2-norm; generalized magnitude of vector for N components"""
return norm(args)
def avg(*args):
"""average"""
return np.mean(args)
def ssq(*args):
"""sum of squares"""
return | np.square(args) | numpy.square |
import numpy as np
from copy import deepcopy
from warnings import warn
import gc
from time import time
import multiprocessing as MP
from Florence.Tensor import itemfreq, makezero, unique2d, remove_duplicates_2D
import Florence.ParallelProcessing.parmap as parmap
from .GetInteriorCoordinates import GetInteriorNodesCoordinates
#--------------------------------------------------------------------------------------------------------------------------#
# SUPPLEMENTARY FUNCTIONS
def ElementLoopHex(elem,elements,points,MeshType,eps,Neval):
xycoord_higher = GetInteriorNodesCoordinates(points[elements[elem,:],:],MeshType,elem,eps,Neval)
return xycoord_higher
def HighOrderMeshHex(C, mesh, Decimals=10, equally_spaced=False, check_duplicates=True,
parallelise=False, nCPU=1, compute_boundary_info=True):
from Florence.FunctionSpace import Hex, HexES
from Florence.QuadratureRules import GaussLobattoPointsHex
from Florence.QuadratureRules.EquallySpacedPoints import EquallySpacedPoints
from Florence.MeshGeneration.NodeArrangement import NodeArrangementHex
# SWITCH OFF MULTI-PROCESSING FOR SMALLER PROBLEMS WITHOUT GIVING A MESSAGE
Parallel = parallelise
if (mesh.elements.shape[0] < 500) and (C < 5):
Parallel = False
nCPU = 1
if not equally_spaced:
eps = GaussLobattoPointsHex(C)
# COMPUTE BASES FUNCTIONS AT ALL NODAL POINTS
Neval = np.zeros((8,eps.shape[0]),dtype=np.float64)
hpBases = Hex.LagrangeGaussLobatto
for i in range(8,eps.shape[0]):
Neval[:,i] = hpBases(0,eps[i,0],eps[i,1],eps[i,2])[:,0]
else:
eps = EquallySpacedPoints(4,C)
# COMPUTE BASES FUNCTIONS AT ALL NODAL POINTS
Neval = np.zeros((8,eps.shape[0]),dtype=np.float64)
hpBases = HexES.Lagrange
for i in range(8,eps.shape[0]):
Neval[:,i] = hpBases(0,eps[i,0],eps[i,1],eps[i,2])[:,0]
# THIS IS NECESSARY FOR REMOVING DUPLICATES
makezero(Neval, tol=1e-12)
nodeperelem = mesh.elements.shape[1]
renodeperelem = int((C+2)**3)
left_over_nodes = renodeperelem - nodeperelem
reelements = -1*np.ones((mesh.elements.shape[0],renodeperelem),dtype=np.int64)
reelements[:,:8] = mesh.elements
# TOTAL NUMBER OF (INTERIOR+EDGE+FACE) NODES
iesize = renodeperelem - 8
repoints = | np.zeros((mesh.points.shape[0]+iesize*mesh.elements.shape[0],3),dtype=np.float64) | numpy.zeros |
import time
import numpy as np
import configparser
import json
from datetime import datetime
import os
import re
import logging
import pyvisa
from pydlcp import arduino_board, hotplate, errors, impedance_analyzer as ia, DLCPDataStore as dh5, bts
import platform
from typing import List, Union
# Different data type definitions
from pydlcp.DLCPDataStore import DLCPDataStore
ard_list = List[arduino_board.ArduinoBoard]
bts_list = List[bts.BTS]
hp_list = List[hotplate.Hotplate]
vcr_type = np.dtype([('V', 'd'), ('C', 'd'), ('R', 'd')])
dlcp_type = np.dtype([('osc_level', 'd'),
('bias', 'd'),
('nominal_bias', 'd'),
('V', 'd'),
('C', 'd'),
('R', 'd')])
class Controller:
"""
This class provides methods to control a DLCP experiment and save the results to a h5 data store.
"""
_dataPath: str = None
_dlcpDataStore: dh5.DLCPDataStore = None
_dlcpParams: dict = None
_fileTag: str = None
_hotPlates: hp_list = []
_impedanceAnalyzer: ia.ImpedanceAnalyzer = None
abort: bool = False
_loggingLevels = {'NOTSET': logging.NOTSET,
'DEBUG': logging.DEBUG,
'INFO': logging.INFO,
'WARNING': logging.WARNING,
'ERROR': logging.ERROR,
'CRITICAL': logging.CRITICAL}
_loggerName: str = None
_measurementConfig: configparser.ConfigParser = None
def __init__(self, config_file_url: str = None, **kwargs):
cwd = os.path.join(os.getcwd(), 'pydlcp')
if config_file_url is None:
config_file_url = os.path.join(cwd, 'dlcp_hardware_config.ini')
elif not isinstance(config_file_url, str):
raise TypeError('The first argument should be an instance of str.')
self.debug: bool = kwargs.get('debug', False)
default_sys_required_options_json = os.path.join(cwd, 'dlcp_system_config_required_options.json')
default_dlcp_meas_required_json = os.path.join(cwd, 'dlcp_measurement_config_required_options.json')
system_option_requirements_json = kwargs.get('dlcp_system_option_requirements_json',
default_sys_required_options_json)
measurement_option_requirements_json = kwargs.get('dlcp_measurement_options_requirements_json',
default_dlcp_meas_required_json)
# Load validation rules for the system configuration file
self._configSystemRequiredOptions = self._read_json_file(system_option_requirements_json)
# Load validation rules for the measurement configuration file
self._configMeasurementRequiredOptions = self._read_json_file(measurement_option_requirements_json)
# Load the system configuration file
config = configparser.ConfigParser()
config.read(config_file_url)
# If the system configuration file is valid, then store it in the object
if self._validate_config(config, self._configSystemRequiredOptions):
self._systemConfig = config
self._resourceManager: pyvisa.highlevel.ResourceManager = pyvisa.highlevel.ResourceManager()
self._availableResources = self._resourceManager.list_resources()
def load_test_config(self, config: configparser.ConfigParser):
"""
Load the acquisition settings. Follows
1. Loads the configuration object
2. Validates the configuration settings using the rules provided by the constructor (default rules are in
./dlcp_system_config_required_options.json).
3. If valid, creates the data structure for the measurement.
4. Creates a data storage object that will ouput the data to an h5 file.
Parameters
----------
config: configparser.ConfigParser
The configuration settings as read from the ini file specified on the constructor
Raises
------
TypeError:
If the config argument is not an instance of configparser.ConfigParser
"""
if not isinstance(config, configparser.ConfigParser):
raise TypeError('The argument should be an instance of configparser.ConfigParser.')
if self.debug:
self._print('Loading measurement configuration...') # No logger yet...
if self._validate_config(config, self._configMeasurementRequiredOptions):
self._measurementConfig = config
now = datetime.now()
time_stamp = now.strftime('%Y%m%d')
# iso_date = now.astimezone().isoformat()
self._dlcpParams = dict(config.items('dlcp'))
self._fileTag = config.get(section='general', option='file_tag')
base_path: str = config.get(section='general', option='base_path')
if platform.system() == 'Windows':
base_path = r'\\?\\' + base_path
base_path = self._create_path(base_path)
# Create main logger
self._create_logger(base_path, name='experiment_logger', level='DEBUG', console=True)
if self._impedanceAnalyzer is not None:
self._impedanceAnalyzer.set_logger(logger_name=self._loggerName)
if self.debug:
self._print('Created base path at {0}'.format(base_path)) # No logger yet...
self._dataPath = base_path
self._print('Loaded acquisition parameters successfully.', level='INFO')
h5_name = os.path.join(self._dataPath, '{0}_{1}.h5'.format(self._fileTag, time_stamp))
ds: DLCPDataStore = dh5.DLCPDataStore(file_path=h5_name)
metadata = self._dlcpParams
metadata['file_tag'] = self._fileTag
ds.metadata(metadata=metadata, group="/dlcp")
self._dlcpDataStore = ds
def start_dlcp(self) -> int:
"""
Starts the DLCP acquisition.
1. Loads the acquisition parameters from the _dlcpParams class property.
2. Iterates over all the nominal biases
3. Saves the data on the _dlcpDataStore
Returns
-------
int:
0 if the measurement was interrupted
1 if it was successful.
"""
ds = self._dlcpDataStore
dlcp_params = self._dlcpParams
circuit = dlcp_params['circuit']
nb_start = float(dlcp_params['nominal_bias_start'])
nb_step = float(dlcp_params['nominal_bias_step'])
nb_stop = float(dlcp_params['nominal_bias_stop'])
osc_level_start = float(dlcp_params['osc_level_start'])
osc_level_step = float(dlcp_params['osc_level_step'])
osc_level_stop = float(dlcp_params['osc_level_stop'])
freq = float(dlcp_params['frequency'])
integration_time = dlcp_params['integration_time']
noa = int(dlcp_params['number_of_averages'])
# Iterate from nominal bias start to nominal bias stop
nb_scan = | np.arange(start=nb_start, stop=nb_stop + nb_step, step=nb_step) | numpy.arange |
# 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]) | numpy.array |
# -*- coding: utf-8 -*-
"""
Created on Fri Nov 16 08:08:33 2018
Machine Learning to train model. Run each cell separately in order
Model naming convention: Model_Version_inputxoutput_YYYY-MM-DD-HH-MM-SS
e.g. Model_3-1_56x26_2018-12-02-12-07-26
Version and input & output size must match for valid model
@author: mike_k
"""
#%%
import numpy as np
import config
import os
from sys import stdout
import datetime
from matplotlib import pyplot as plt
from word_to_vector import EMBED_SIZE as INPUT_SIZE
from table_to_array import TAG_SIZE as OUTPUT_SIZE
import model
#%% build train and test sets
''' Data must be manually copied to the train & test folders.
'''
def load_nparray(fullfile):
''' load an array and add a dimension'''
npa = np.load(fullfile)
npa = np.expand_dims(npa,0)
return npa
def load_arrays(pathdata, pathlabel):
''' load arrays to single arrays to generate train and test sets
generates data, label arrays'''
tree = os.walk(pathdata)
files = list(tree)[0][2]
data = []
label = []
n = len(files)
for i,f in enumerate(files):
data.append(load_nparray(pathdata + '/' + f))
f_label = f[:-9] + '_labels.npy'
label.append(load_nparray(pathlabel + '/' + f_label))
stdout.write('\r' + str(i+1) + '/' + str(n)) # show progress
stdout.write('\n')
return | np.concatenate(data) | numpy.concatenate |
__author__ = 'stephen'
# ===============================================================================
# GLOBAL IMPORTS:
import os,sys
import numpy as np
import argparse
# ===============================================================================
# LOCAL IMPORTS:
#HK_DataMiner_Path = os.path.relpath(os.pardir)
HK_DataMiner_Path = os.path.abspath("/Users/stephen/Dropbox/projects/work-2019.1/HK_DataMiner")
print(HK_DataMiner_Path)
sys.path.append(HK_DataMiner_Path)
#from cluster.dbscan_ import DBSCAN
from sklearn.cluster import DBSCAN
from utils import XTCReader, plot_cluster
# ===============================================================================
outliers = -1
def merge_assignments(new_assignments, old_assignments, remove_outliers=False):
# Number of clusters in assignments, ignoring noise if present.
#clusters_size = len(set(old_assignments)) - (1 if -1 in old_assignments else 0)
clusters_size = np.max(old_assignments) + 1
max_clust_id = clusters_size
print("max_clust_id:", max_clust_id)
count_first = [0] * clusters_size
count_second = [0] * clusters_size
old_assignments_size = len(old_assignments)
# new_assignments_size = len(new_assignments)
for i in range(0, old_assignments_size):
if old_assignments[i] != outliers:
if new_assignments[i] != outliers:
count_first[old_assignments[i]] += 1
count_second[old_assignments[i]] += 1
# Percentage
percentage = [0.0] * clusters_size
for i in range(0, clusters_size):
if count_second[i] is 0:
percentage[i] = 0.0
else:
percentage[i] = float(count_first[i])/float(count_second[i])
# Starting assignment
assignments=np.copy(old_assignments)
for i in range(0, old_assignments_size):
if old_assignments[i] != outliers and percentage[old_assignments[i]] > 0.7:
if new_assignments[i] != outliers:
assignments[i] = new_assignments[i] + max_clust_id
# print old_assignments[i]
elif remove_outliers is True: #if want to remove outliers in the iterations
assignments[i] = outliers
return assignments
def main():
cli = argparse.ArgumentParser()
cli.add_argument('-t', '--trajListFns', default = 'trajlist',
help='List of trajectory files to read in, separated by spaces.')
cli.add_argument('-a', '--atomListFns', default='atom_indices',
help='List of atom index files to read in, separated by spaces.')
cli.add_argument('-g', '--topology', default='native.pdb', help='topology file.')
cli.add_argument('-o', '--homedir', help='Home dir.', default=".", type=str)
cli.add_argument('-e', '--iext', help='''The file extension of input trajectory
files. Must be a filetype that mdtraj.load() can recognize.''',
default="xtc", type=str)
cli.add_argument('-n', '--n_clusters', help='''n_clusters.''',
default=100, type=int)
cli.add_argument('-m', '--n_macro_states', help='''n_macro_states.''',
default=6, type=int)
cli.add_argument('-s', '--stride', help='stride.',
default=None, type=int)
args = cli.parse_args()
trajlistname = args.trajListFns
atom_indicesname = args.atomListFns
trajext = args.iext
File_TOP = args.topology
homedir = args.homedir
n_clusters = args.n_clusters
n_macro_states = args.n_macro_states
stride = args.stride
# ===========================================================================
# Reading Trajs from XTC files
#print "stride:", stride
#trajreader = XTCReader(trajlistname, atom_indicesname, homedir, trajext, File_TOP, nSubSample=stride)
#trajs = trajreader.trajs
#print(trajs)
#traj_len = trajreader.traj_len
#np.savetxt("./traj_len.txt", traj_len, fmt="%d")
if os.path.isfile("./phi_angles.txt") and os.path.isfile("./psi_angles.txt") is True:
phi_angles = np.loadtxt("./phi_angles.txt", dtype=np.float32)
psi_angles = np.loadtxt("./psi_angles.txt", dtype=np.float32)
else:
#phi_angles, psi_angles = trajreader.get_phipsi(trajs, psi=[6, 8, 14, 16], phi=[4, 6, 8, 14])
phi_angles, psi_angles = trajreader.get_phipsi(trajs, psi=[5, 7, 13, 15], phi=[3, 5, 7, 13])
np.savetxt("./phi_angles.txt", phi_angles, fmt="%f")
np.savetxt("./psi_angles.txt", psi_angles, fmt="%f")
phi_psi=np.column_stack((phi_angles, psi_angles))
n_samples = 1000
percent = 0.9
import random
whole_samples = random.sample(list(phi_psi), n_samples)
#print whole_samples
from metrics.pairwise import pairwise_distances
sample_dist_metric = pairwise_distances(whole_samples, whole_samples, metric='euclidean')
print(sample_dist_metric.shape)
sample_dist = []
for i in range(0, n_samples):
for j in range(i+1, n_samples):
sample_dist.append(sample_dist_metric[i, j])
sorted_sample_dist = np.sort(sample_dist)
print("Len of samples:", len(sorted_sample_dist), np.max(sorted_sample_dist), np.min(sorted_sample_dist))
eps_list = []
len_samples = len(sorted_sample_dist)
for percent in [0.05, 0.025, 0.008 ]: #,0.005, 0.003,
# 0.002, 0.001, 0.0008, 0.0005, 0.0003, 0.0002, 0.0001, 0.00005]:
percent /= 10.0
index = int(round(len_samples*percent))
if index == len_samples:
index -= 1
dc = sorted_sample_dist[index]
#print index, sorted_sample_dist[index]
eps_list.append(dc)
print(eps_list)
# from sklearn.neighbors import NearestNeighbors
# print len(phi_psi)
# neighborhoods_model = NearestNeighbors(n_neighbors=len(phi_psi), algorithm='kd_tree')
# neighborhoods_model.fit(phi_psi)
# #distances, indices = neighborhoods_model.kneighbors(phi_psi)
# distances, indices = neighborhoods_model.kneighbors(phi_psi, 5)
# print distances
#print phi_psi
# ===========================================================================
# do Clustering using MR -DBSCAN method
clustering_name = "mr-dbscan_iter_"
potential = True
# potential = False
#eps = eps_list[0]
eps = 9.376904
min_samples = 1
len_frames = len(phi_psi)
print("Total frames:", len_frames)
print("Running first calculation")
db = DBSCAN(eps=eps, min_samples=min_samples, algorithm='kd_tree').fit(phi_psi)
core_samples_mask = np.zeros_like(db.labels_, dtype=bool)
core_samples_mask[db.core_sample_indices_] = True
old_assignments = db.labels_
n_microstates = len(set(old_assignments)) - (1 if -1 in old_assignments else 0)
print('Estimated number of clusters: %d' % n_microstates)
# Calculating percentage of each states
frame_bincount = np.bincount(old_assignments[old_assignments>=0]) #remove outliers
frame_freq_index_sorted = np.argsort(frame_bincount)[::-1] # descending arg sort
frame_freq_percent_sorted = frame_bincount[frame_freq_index_sorted]/np.float32(len_frames)
print(frame_freq_percent_sorted[0:10])
print(frame_freq_index_sorted[0:10])
old_frame_freq_percent_sorted = frame_freq_percent_sorted
old_frame_freq_index_sorted = frame_freq_index_sorted
iter_name = clustering_name + '0' + '_eps_' + str(eps) + '_min_samples_' + str(min_samples) + '_n_states_' + str(n_microstates)
plot_cluster(labels=old_assignments, phi_angles=phi_angles, psi_angles=psi_angles, name=iter_name, potential=potential)
n_iterations = len(eps_list)
print("n_iterations:", n_iterations)
eps_list = [9.376904, 3.3741567, 0.87675905]
min_samples_list = [1, 20, 20]
#min_samples_list = [50, 30, 20, 15, 10, 8, 5, 2]
n_min_samples = len(min_samples_list)
#eps_list = [3.0, 2.0, 1.0, 0.8, 0.5]
#min_samples_list = [3, 3, 3, 3, 3, 2, 2]
r#esults = np.zeros((n_min_samples,n_iterations,len_frames), dtype=np.int32)
results = np.zeros((n_iterations, len_frames), dtype=np.int32)
for i in range(0, n_iterations):
#for j in range(0, n_min_samples):
eps = eps_list[i]
min_samples = min_samples_list[i]
db = DBSCAN(eps=eps, min_samples=min_samples).fit(phi_psi)
'''
core_samples_mask = np.zeros_like(db.labels_, dtype=bool)
core_samples_mask[db.core_sample_indices_] = True
new_assignments = db.labels_
if i < 7:
remove_outliers = True
else:
remove_outliers = False
assignments = merge_assignments(new_assignments, old_assignments, remove_outliers=remove_outliers)
n_microstates = len(set(assignments)) - (1 if -1 in assignments else 0)
# Calculating percentage of each states
frame_bincount = np.bincount(assignments[assignments >= 0]) # remove outliers
frame_freq_index_sorted = np.argsort(frame_bincount)[::-1] # descending arg sort
frame_freq_percent_sorted = frame_bincount[frame_freq_index_sorted] / np.float32(len_frames)
frame_freq_percent_sorted = frame_freq_percent_sorted[0:10]
frame_freq_index_sorted = frame_freq_index_sorted[0:10]
print frame_freq_percent_sorted
print frame_freq_index_sorted
old_frame_freq_index_sorted = []
for j in xrange(0, 10):
index = np.argwhere(assignments==frame_freq_index_sorted[j])[0]
old_frame_freq_index_sorted.append(old_assignments[index][0])
print old_frame_freq_index_sorted
'''
core_samples_mask = np.zeros_like(db.labels_, dtype=bool)
core_samples_mask[db.core_sample_indices_] = True
assignments = db.labels_
n_microstates = len(set(assignments)) - (1 if -1 in assignments else 0)
#results[j,i, :]= np.array(assignments)
results[i, :] = np.array(assignments)
print("Iter:", i, "Running MR-DBSCAN at eps:", eps, 'min_sampes:', min_samples, 'Estimated number of clusters:', n_microstates)
#print('Estimated number of clusters: %d' % n_microstates)
iter_name = clustering_name + str(i) + '_eps_' + str(eps) + '_min_samples_' + str(min_samples) + '_n_states_' + str(n_microstates)
plot_cluster(labels=assignments, phi_angles=phi_angles, psi_angles=psi_angles, name=iter_name, potential=potential)
#old_assignments = assignments
print(results)
np.save("results.npy", results)
#np.savetxt("results.csv", results, fmt="%d", delimiter=",")
| np.savetxt("eps_list.txt", eps_list, fmt="%f", delimiter=",") | numpy.savetxt |
import math
import os
import time
import numpy as np
from paddle import fluid
from paddle.fluid import layers
from pytracking.features import augmentation
from pytracking.libs import dcf, operation, fourier
from pytracking.libs.optimization import ConjugateGradient, GaussNewtonCG, GradientDescentL2
from pytracking.libs.paddle_utils import mod, n2p, \
leaky_relu, dropout2d
from pytracking.libs.tensorlist import TensorList
from pytracking.tracker.atom.optim import FactorizedConvProblem, ConvProblem
from pytracking.tracker.base.basetracker import BaseTracker
class ATOM(BaseTracker):
def initialize_features(self):
if not getattr(self, 'features_initialized', False):
self.params.features.initialize()
self.features_initialized = True
def initialize(self, image, state, *args, **kwargs):
# Initialize some stuff
self.frame_num = 1
# TODO: for now, we don't support explictly setting up device
# if not hasattr(self.params, 'device'):
# self.params.device = 'cuda' if self.params.use_gpu else 'cpu'
# Initialize features
self.initialize_features()
# Check if image is color
self.params.features.set_is_color(image.shape[2] == 3)
# Get feature specific params
self.fparams = self.params.features.get_fparams('feature_params')
self.time = 0
tic = time.time()
# Get position and size
self.pos = np.array(
[state[1] + (state[3] - 1) / 2, state[0] + (state[2] - 1) / 2],
'float32')
self.target_sz = np.array([state[3], state[2]], 'float32')
# Set search area
self.target_scale = 1.0
search_area = np.prod(self.target_sz * self.params.search_area_scale)
if search_area > self.params.max_image_sample_size:
self.target_scale = math.sqrt(search_area /
self.params.max_image_sample_size)
elif search_area < self.params.min_image_sample_size:
self.target_scale = math.sqrt(search_area /
self.params.min_image_sample_size)
# Check if IoUNet is used
self.use_iou_net = getattr(self.params, 'use_iou_net', True)
# Target size in base scale
self.base_target_sz = self.target_sz / self.target_scale
# Use odd square search area and set sizes
feat_max_stride = max(self.params.features.stride())
if getattr(self.params, 'search_area_shape', 'square') == 'square':
self.img_sample_sz = np.ones((2, ), 'float32') * np.round(
np.sqrt(
np.prod(self.base_target_sz *
self.params.search_area_scale)))
elif self.params.search_area_shape == 'initrect':
self.img_sample_sz = np.round(self.base_target_sz *
self.params.search_area_scale)
else:
raise ValueError('Unknown search area shape')
if self.params.feature_size_odd:
self.img_sample_sz += feat_max_stride - mod(self.img_sample_sz,
(2 * feat_max_stride))
else:
self.img_sample_sz += feat_max_stride - mod(
(self.img_sample_sz + feat_max_stride), (2 * feat_max_stride))
# Set sizes
self.img_support_sz = self.img_sample_sz
self.feature_sz = self.params.features.size(self.img_sample_sz)
self.output_sz = self.params.score_upsample_factor * self.img_support_sz # Interpolated size of the output
self.kernel_size = self.fparams.attribute('kernel_size')
self.iou_img_sample_sz = self.img_sample_sz
# Optimization options
self.params.precond_learning_rate = self.fparams.attribute(
'learning_rate')
if self.params.CG_forgetting_rate is None or max(
self.params.precond_learning_rate) >= 1:
self.params.direction_forget_factor = 0
else:
self.params.direction_forget_factor = (
1 - max(self.params.precond_learning_rate)
)**self.params.CG_forgetting_rate
self.output_window = None
if getattr(self.params, 'window_output', False):
if getattr(self.params, 'use_clipped_window', False):
self.output_window = dcf.hann2d_clipped(
self.output_sz.astype('long'),
self.output_sz.astype('long') *
self.params.effective_search_area /
self.params.search_area_scale,
centered=False)
else:
self.output_window = dcf.hann2d(
self.output_sz.astype('long'), centered=False)
# Initialize some learning things
self.init_learning()
# Convert image
im = image.astype('float32')
self.im = im # For debugging only
# Setup scale bounds
self.image_sz = np.array([im.shape[0], im.shape[1]], 'float32')
self.min_scale_factor = np.max(10 / self.base_target_sz)
self.max_scale_factor = np.min(self.image_sz / self.base_target_sz)
# Extract and transform sample
x = self.generate_init_samples(im)
# Initialize iounet
if self.use_iou_net:
self.init_iou_net()
# Initialize projection matrix
self.init_projection_matrix(x)
# Transform to get the training sample
train_x = self.preprocess_sample(x)
# Generate label function
init_y = self.init_label_function(train_x)
# Init memory
self.init_memory(train_x)
# Init optimizer and do initial optimization
self.init_optimization(train_x, init_y)
self.pos_iounet = self.pos.copy()
self.time += time.time() - tic
def track(self, image):
self.frame_num += 1
# Convert image
# im = numpy_to_paddle(image)
im = image.astype('float32')
self.im = im # For debugging only
# ------- LOCALIZATION ------- #
# Get sample
sample_pos = self.pos.round()
sample_scales = self.target_scale * self.params.scale_factors
test_x = self.extract_processed_sample(im, self.pos, sample_scales,
self.img_sample_sz)
# Compute scores
scores_raw = self.apply_filter(test_x)
translation_vec, scale_ind, s, flag = self.localize_target(scores_raw)
# Update position and scale
if flag != 'not_found':
if self.use_iou_net:
update_scale_flag = getattr(self.params,
'update_scale_when_uncertain',
True) or flag != 'uncertain'
if getattr(self.params, 'use_classifier', True):
self.update_state(sample_pos + translation_vec)
self.refine_target_box(sample_pos, sample_scales[scale_ind],
scale_ind, update_scale_flag)
elif getattr(self.params, 'use_classifier', True):
self.update_state(sample_pos + translation_vec,
sample_scales[scale_ind])
# ------- UPDATE ------- #
# Check flags and set learning rate if hard negative
update_flag = flag not in ['not_found', 'uncertain']
hard_negative = (flag == 'hard_negative')
learning_rate = self.params.hard_negative_learning_rate if hard_negative else None
if update_flag:
# Get train sample
train_x = TensorList([x[scale_ind:scale_ind + 1] for x in test_x])
# Create label for sample
train_y = self.get_label_function(sample_pos,
sample_scales[scale_ind])
# Update memory
self.update_memory(train_x, train_y, learning_rate)
# Train filter
if hard_negative:
self.filter_optimizer.run(self.params.hard_negative_CG_iter)
elif (self.frame_num - 1) % self.params.train_skipping == 0:
self.filter_optimizer.run(self.params.CG_iter)
self.filter = self.filter_optimizer.x
# Set the pos of the tracker to iounet pos
if self.use_iou_net and flag != 'not_found':
self.pos = self.pos_iounet.copy()
# Return new state
yx = self.pos - (self.target_sz - 1) / 2
new_state = np.array(
[yx[1], yx[0], self.target_sz[1], self.target_sz[0]], 'float32')
return new_state.tolist()
def update_memory(self,
sample_x: TensorList,
sample_y: TensorList,
learning_rate=None):
replace_ind = self.update_sample_weights(
self.sample_weights, self.previous_replace_ind,
self.num_stored_samples, self.num_init_samples, self.fparams,
learning_rate)
self.previous_replace_ind = replace_ind
for train_samp, x, ind in zip(self.training_samples, sample_x,
replace_ind):
train_samp[ind] = x[0]
for y_memory, y, ind in zip(self.y, sample_y, replace_ind):
y_memory[ind] = y[0]
if self.hinge_mask is not None:
for m, y, ind in zip(self.hinge_mask, sample_y, replace_ind):
m[ind] = layers.cast(y >= self.params.hinge_threshold,
'float32')[0]
self.num_stored_samples += 1
def update_sample_weights(self,
sample_weights,
previous_replace_ind,
num_stored_samples,
num_init_samples,
fparams,
learning_rate=None):
# Update weights and get index to replace in memory
replace_ind = []
for sw, prev_ind, num_samp, num_init, fpar in zip(
sample_weights, previous_replace_ind, num_stored_samples,
num_init_samples, fparams):
lr = learning_rate
if lr is None:
lr = fpar.learning_rate
init_samp_weight = getattr(fpar, 'init_samples_minimum_weight',
None)
if init_samp_weight == 0:
init_samp_weight = None
s_ind = 0 if init_samp_weight is None else num_init
if num_samp == 0 or lr == 1:
sw[:] = 0
sw[0] = 1
r_ind = 0
else:
# Get index to replace
r_ind = np.argmin(sw[s_ind:], 0)
r_ind = int(r_ind + s_ind)
# Update weights
if prev_ind is None:
sw /= 1 - lr
sw[r_ind] = lr
else:
sw[r_ind] = sw[prev_ind] / (1 - lr)
sw /= sw.sum()
if init_samp_weight is not None and sw[:num_init].sum(
) < init_samp_weight:
sw /= init_samp_weight + sw[num_init:].sum()
sw[:num_init] = init_samp_weight / num_init
replace_ind.append(r_ind)
return replace_ind
def localize_target(self, scores_raw):
# Weighted sum (if multiple features) with interpolation in fourier domain
weight = self.fparams.attribute('translation_weight', 1.0)
scores_raw = weight * scores_raw
sf_weighted = fourier.cfft2(scores_raw) / (scores_raw.size(2) *
scores_raw.size(3))
for i, (sz, ksz) in enumerate(zip(self.feature_sz, self.kernel_size)):
sf_weighted[i] = fourier.shift_fs(sf_weighted[i], math.pi * (
1 - np.array([ksz[0] % 2, ksz[1] % 2]) / sz))
scores_fs = fourier.sum_fs(sf_weighted)
scores = fourier.sample_fs(scores_fs, self.output_sz)
if self.output_window is not None and not getattr(
self.params, 'perform_hn_without_windowing', False):
scores *= self.output_window
if getattr(self.params, 'advanced_localization', False):
return self.localize_advanced(scores)
# Get maximum
max_score, max_disp = dcf.max2d(scores)
scale_ind = np.argmax(max_score, axis=0)[0]
max_disp = max_disp.astype('float32')
# Convert to displacements in the base scale
output_sz = self.output_sz.copy()
disp = mod((max_disp + output_sz / 2), output_sz) - output_sz / 2
# Compute translation vector and scale change factor
translation_vec = np.reshape(
disp[scale_ind].astype('float32'), [-1]) * (
self.img_support_sz / self.output_sz) * self.target_scale
translation_vec *= self.params.scale_factors[scale_ind]
# Shift the score output for visualization purposes
if self.params.debug >= 2:
sz = scores.shape[-2:]
scores = np.concatenate(
[scores[..., sz[0] // 2:, :], scores[..., :sz[0] // 2, :]], -2)
scores = np.concatenate(
[scores[..., sz[1] // 2:], scores[..., :sz[1] // 2]], -1)
return translation_vec, scale_ind, scores, None
def update_state(self, new_pos, new_scale=None):
# Update scale
if new_scale is not None:
self.target_scale = np.clip(new_scale, self.min_scale_factor,
self.max_scale_factor)
self.target_sz = self.base_target_sz * self.target_scale
# Update pos
inside_ratio = 0.2
inside_offset = (inside_ratio - 0.5) * self.target_sz
self.pos = np.maximum(
np.minimum(new_pos,
self.image_sz.astype('float32') - inside_offset),
inside_offset)
def get_label_function(self, sample_pos, sample_scale):
# Generate label function
train_y = TensorList()
target_center_norm = (self.pos - sample_pos) / (self.img_support_sz *
sample_scale)
for sig, sz, ksz in zip(self.sigma, self.feature_sz, self.kernel_size):
center = sz * target_center_norm + 0.5 * np.array(
[(ksz[0] + 1) % 2, (ksz[1] + 1) % 2], 'float32')
train_y.append(dcf.label_function_spatial(sz, sig, center))
return train_y
def extract_sample(self,
im: np.ndarray,
pos: np.ndarray,
scales,
sz: np.ndarray,
debug_save_name):
return self.params.features.extract(im, pos, scales, sz,
debug_save_name)
def extract_processed_sample(self,
im: np.ndarray,
pos: np.ndarray,
scales,
sz: np.ndarray,
debug_save_name=None) -> (TensorList,
TensorList):
x = self.extract_sample(im, pos, scales, sz, debug_save_name)
return self.preprocess_sample(self.project_sample(x))
def apply_filter(self, sample_x: TensorList):
with fluid.dygraph.guard():
sample_x = sample_x.apply(n2p)
filter = self.filter.apply(n2p)
return operation.conv2d(sample_x, filter, mode='same').numpy()
def init_projection_matrix(self, x):
# Set if using projection matrix
self.params.use_projection_matrix = getattr(
self.params, 'use_projection_matrix', True)
if self.params.use_projection_matrix:
self.compressed_dim = self.fparams.attribute('compressed_dim', None)
proj_init_method = getattr(self.params, 'proj_init_method', 'pca')
if proj_init_method == 'pca':
raise NotImplementedError
elif proj_init_method == 'randn':
with fluid.dygraph.guard():
self.projection_matrix = TensorList([
None if cdim is None else layers.gaussian_random(
(cdim, ex.shape[1], 1, 1), 0.0,
1 / math.sqrt(ex.shape[1])).numpy()
for ex, cdim in zip(x, self.compressed_dim)
])
elif proj_init_method == 'np_randn':
rng = np.random.RandomState(0)
self.projection_matrix = TensorList([
None if cdim is None else rng.normal(
size=(cdim, ex.shape[1], 1, 1),
loc=0.0,
scale=1 / math.sqrt(ex.shape[1])).astype('float32')
for ex, cdim in zip(x, self.compressed_dim)
])
elif proj_init_method == 'ones':
self.projection_matrix = TensorList([
None if cdim is None else
np.ones((cdim, ex.shape[1], 1, 1),
'float32') / math.sqrt(ex.shape[1])
for ex, cdim in zip(x, self.compressed_dim)
])
else:
self.compressed_dim = x.size(1)
self.projection_matrix = TensorList([None] * len(x))
def preprocess_sample(self, x: TensorList) -> (TensorList, TensorList):
if getattr(self.params, '_feature_window', False):
x = x * self.feature_window
return x
def init_label_function(self, train_x):
# Allocate label function
self.y = TensorList([
np.zeros(
[self.params.sample_memory_size, 1, x.shape[2], x.shape[3]],
'float32') for x in train_x
])
# Output sigma factor
output_sigma_factor = self.fparams.attribute('output_sigma_factor')
self.sigma = output_sigma_factor * np.ones((2, ), 'float32') * (
self.feature_sz / self.img_support_sz *
self.base_target_sz).apply(np.prod).apply(np.sqrt)
# Center pos in normalized coords
target_center_norm = (self.pos - np.round(self.pos)) / (
self.target_scale * self.img_support_sz)
# Generate label functions
for y, sig, sz, ksz, x in zip(self.y, self.sigma, self.feature_sz,
self.kernel_size, train_x):
center_pos = sz * target_center_norm + 0.5 * np.array(
[(ksz[0] + 1) % 2, (ksz[1] + 1) % 2], 'float32')
for i, T in enumerate(self.transforms[:x.shape[0]]):
sample_center = center_pos + np.array(
T.shift, 'float32') / self.img_support_sz * sz
y[i] = dcf.label_function_spatial(sz, sig, sample_center)
# Return only the ones to use for initial training
return TensorList([y[:x.shape[0]] for y, x in zip(self.y, train_x)])
def init_memory(self, train_x):
# Initialize first-frame training samples
self.num_init_samples = train_x.size(0)
self.init_sample_weights = TensorList(
[np.ones(x.shape[0], 'float32') / x.shape[0] for x in train_x])
self.init_training_samples = train_x
# Sample counters and weights
self.num_stored_samples = self.num_init_samples.copy()
self.previous_replace_ind = [None] * len(self.num_stored_samples)
self.sample_weights = TensorList([
np.zeros(self.params.sample_memory_size, 'float32') for x in train_x
])
for sw, init_sw, num in zip(self.sample_weights,
self.init_sample_weights,
self.num_init_samples):
sw[:num] = init_sw
# Initialize memory
self.training_samples = TensorList(
[[np.zeros([cdim, x.shape[2], x.shape[3]], 'float32')] *
self.params.sample_memory_size
for x, cdim in zip(train_x, self.compressed_dim)])
def init_learning(self):
# Get window function
self.feature_window = TensorList(
[dcf.hann2d(sz) for sz in self.feature_sz])
# Filter regularization
self.filter_reg = self.fparams.attribute('filter_reg')
# Activation function after the projection matrix (phi_1 in the paper)
projection_activation = getattr(self.params, 'projection_activation',
'none')
if isinstance(projection_activation, tuple):
projection_activation, act_param = projection_activation
if projection_activation == 'none':
self.projection_activation = lambda x: x
elif projection_activation == 'relu':
self.projection_activation = layers.relu
elif projection_activation == 'elu':
self.projection_activation = layers.elu
elif projection_activation == 'mlu':
self.projection_activation = lambda x: layers.elu(leaky_relu(x, 1 / act_param), act_param)
else:
raise ValueError('Unknown activation')
# Activation function after the output scores (phi_2 in the paper)
response_activation = getattr(self.params, 'response_activation',
'none')
if isinstance(response_activation, tuple):
response_activation, act_param = response_activation
if response_activation == 'none':
self.response_activation = lambda x: x
elif response_activation == 'relu':
self.response_activation = layers.relu
elif response_activation == 'elu':
self.response_activation = layers.elu
elif response_activation == 'mlu':
self.response_activation = lambda x: layers.elu(leaky_relu(x, 1 / act_param), act_param)
else:
raise ValueError('Unknown activation')
def generate_init_samples(self, im: np.ndarray) -> TensorList:
"""Generate augmented initial samples."""
# Compute augmentation size
aug_expansion_factor = getattr(self.params,
'augmentation_expansion_factor', None)
aug_expansion_sz = self.img_sample_sz.copy()
aug_output_sz = None
if aug_expansion_factor is not None and aug_expansion_factor != 1:
aug_expansion_sz = (self.img_sample_sz *
aug_expansion_factor).astype('long')
aug_expansion_sz += (
aug_expansion_sz - self.img_sample_sz.astype('long')) % 2
aug_expansion_sz = aug_expansion_sz.astype('float32')
aug_output_sz = self.img_sample_sz.astype('long').tolist()
# Random shift operator
get_rand_shift = lambda: None
random_shift_factor = getattr(self.params, 'random_shift_factor', 0)
if random_shift_factor > 0:
get_rand_shift = lambda: ((np.random.uniform(size=[2]) - 0.5) * self.img_sample_sz * random_shift_factor).astype('long').tolist()
# Create transofmations
self.transforms = [augmentation.Identity(aug_output_sz)]
if 'shift' in self.params.augmentation:
self.transforms.extend([
augmentation.Translation(shift, aug_output_sz)
for shift in self.params.augmentation['shift']
])
if 'relativeshift' in self.params.augmentation:
get_absolute = lambda shift: (np.array(shift, 'float32') * self.img_sample_sz / 2).astype('long').tolist()
self.transforms.extend([
augmentation.Translation(get_absolute(shift), aug_output_sz)
for shift in self.params.augmentation['relativeshift']
])
if 'fliplr' in self.params.augmentation and self.params.augmentation[
'fliplr']:
self.transforms.append(
augmentation.FlipHorizontal(aug_output_sz, get_rand_shift()))
if 'blur' in self.params.augmentation:
self.transforms.extend([
augmentation.Blur(sigma, aug_output_sz, get_rand_shift())
for sigma in self.params.augmentation['blur']
])
if 'scale' in self.params.augmentation:
self.transforms.extend([
augmentation.Scale(scale_factor, aug_output_sz,
get_rand_shift())
for scale_factor in self.params.augmentation['scale']
])
if 'rotate' in self.params.augmentation:
self.transforms.extend([
augmentation.Rotate(angle, aug_output_sz, get_rand_shift())
for angle in self.params.augmentation['rotate']
])
# Generate initial samples
init_samples = self.params.features.extract_transformed(
im, self.pos, self.target_scale, aug_expansion_sz, self.transforms)
# Remove augmented samples for those that shall not have
for i, use_aug in enumerate(self.fparams.attribute('use_augmentation')):
if not use_aug:
init_samples[i] = init_samples[i][0:1]
# Add dropout samples
if 'dropout' in self.params.augmentation:
num, prob = self.params.augmentation['dropout']
self.transforms.extend(self.transforms[:1] * num)
with fluid.dygraph.guard():
for i, use_aug in enumerate(
self.fparams.attribute('use_augmentation')):
if use_aug:
init_samples[i] = np.concatenate([
init_samples[i], dropout2d(
layers.expand(
n2p(init_samples[i][0:1]), (num, 1, 1, 1)),
prob,
is_train=True).numpy()
])
return init_samples
def init_optimization(self, train_x, init_y):
# Initialize filter
filter_init_method = getattr(self.params, 'filter_init_method', 'zeros')
self.filter = TensorList([
np.zeros([1, cdim, sz[0], sz[1]], 'float32')
for x, cdim, sz in zip(train_x, self.compressed_dim,
self.kernel_size)
])
if filter_init_method == 'zeros':
pass
elif filter_init_method == 'ones':
for idx, f in enumerate(self.filter):
self.filter[idx] = np.ones(f.shape,
'float32') / np.prod(f.shape)
elif filter_init_method == 'np_randn':
rng = np.random.RandomState(0)
for idx, f in enumerate(self.filter):
self.filter[idx] = rng.normal(
size=f.shape, loc=0,
scale=1 / np.prod(f.shape)).astype('float32')
elif filter_init_method == 'randn':
for idx, f in enumerate(self.filter):
with fluid.dygraph.guard():
self.filter[idx] = layers.gaussian_random(
f.shape, std=1 / np.prod(f.shape)).numpy()
else:
raise ValueError('Unknown "filter_init_method"')
# Get parameters
self.params.update_projection_matrix = getattr(
self.params, 'update_projection_matrix',
True) and self.params.use_projection_matrix
optimizer = getattr(self.params, 'optimizer', 'GaussNewtonCG')
# Setup factorized joint optimization
if self.params.update_projection_matrix:
self.joint_problem = FactorizedConvProblem(
self.init_training_samples, init_y, self.filter_reg,
self.fparams.attribute('projection_reg'), self.params,
self.init_sample_weights, self.projection_activation,
self.response_activation)
# Variable containing both filter and projection matrix
joint_var = self.filter.concat(self.projection_matrix)
# Initialize optimizer
analyze_convergence = getattr(self.params, 'analyze_convergence',
False)
if optimizer == 'GaussNewtonCG':
self.joint_optimizer = GaussNewtonCG(
self.joint_problem,
joint_var,
plotting=(self.params.debug >= 3),
analyze=True,
fig_num=(12, 13, 14))
elif optimizer == 'GradientDescentL2':
self.joint_optimizer = GradientDescentL2(
self.joint_problem,
joint_var,
self.params.optimizer_step_length,
self.params.optimizer_momentum,
plotting=(self.params.debug >= 3),
debug=analyze_convergence,
fig_num=(12, 13))
# Do joint optimization
if isinstance(self.params.init_CG_iter, (list, tuple)):
self.joint_optimizer.run(self.params.init_CG_iter)
else:
self.joint_optimizer.run(self.params.init_CG_iter //
self.params.init_GN_iter,
self.params.init_GN_iter)
# Get back filter and optimizer
len_x = len(self.joint_optimizer.x)
self.filter = self.joint_optimizer.x[:len_x // 2] # w2 in paper
self.projection_matrix = self.joint_optimizer.x[len_x //
2:] # w1 in paper
if analyze_convergence:
opt_name = 'CG' if getattr(self.params, 'CG_optimizer',
True) else 'GD'
for val_name, values in zip(['loss', 'gradient'], [
self.joint_optimizer.losses,
self.joint_optimizer.gradient_mags
]):
val_str = ' '.join(
['{:.8e}'.format(v.item()) for v in values])
file_name = '{}_{}.txt'.format(opt_name, val_name)
with open(file_name, 'a') as f:
f.write(val_str + '\n')
raise RuntimeError('Exiting')
# Re-project samples with the new projection matrix
compressed_samples = self.project_sample(self.init_training_samples,
self.projection_matrix)
for train_samp, init_samp in zip(self.training_samples,
compressed_samples):
for idx in range(init_samp.shape[0]):
train_samp[idx] = init_samp[idx]
self.hinge_mask = None
# Initialize optimizer
self.conv_problem = ConvProblem(self.training_samples, self.y,
self.filter_reg, self.sample_weights,
self.response_activation)
if optimizer == 'GaussNewtonCG':
self.filter_optimizer = ConjugateGradient(
self.conv_problem,
self.filter,
fletcher_reeves=self.params.fletcher_reeves,
direction_forget_factor=self.params.direction_forget_factor,
debug=(self.params.debug >= 3),
fig_num=(12, 13))
elif optimizer == 'GradientDescentL2':
self.filter_optimizer = GradientDescentL2(
self.conv_problem,
self.filter,
self.params.optimizer_step_length,
self.params.optimizer_momentum,
debug=(self.params.debug >= 3),
fig_num=12)
# Transfer losses from previous optimization
if self.params.update_projection_matrix:
self.filter_optimizer.residuals = self.joint_optimizer.residuals
self.filter_optimizer.losses = self.joint_optimizer.losses
if not self.params.update_projection_matrix:
self.filter_optimizer.run(self.params.init_CG_iter)
# Post optimization
self.filter_optimizer.run(self.params.post_init_CG_iter)
self.filter = self.filter_optimizer.x
# Free memory
del self.init_training_samples
if self.params.use_projection_matrix:
del self.joint_problem, self.joint_optimizer
def project_sample(self, x: TensorList, proj_matrix=None):
# Apply projection matrix
if proj_matrix is None:
proj_matrix = self.projection_matrix
with fluid.dygraph.guard():
return operation.conv2d(x.apply(n2p), proj_matrix.apply(n2p)).apply(
self.projection_activation).numpy()
def get_iounet_box(self, pos, sz, sample_pos, sample_scale):
"""All inputs in original image coordinates"""
box_center = (pos - sample_pos) / sample_scale + (self.iou_img_sample_sz
- 1) / 2
box_sz = sz / sample_scale
target_ul = box_center - (box_sz - 1) / 2
return np.concatenate([np.flip(target_ul, 0), np.flip(box_sz, 0)])
def get_iou_features(self):
return self.params.features.get_unique_attribute('iounet_features')
def get_iou_backbone_features(self):
return self.params.features.get_unique_attribute(
'iounet_backbone_features')
def init_iou_net(self):
# Setup IoU net
self.iou_predictor = self.params.features.get_unique_attribute(
'iou_predictor')
# Get target boxes for the different augmentations
self.iou_target_box = self.get_iounet_box(self.pos, self.target_sz,
self.pos.round(),
self.target_scale)
target_boxes = TensorList()
if self.params.iounet_augmentation:
for T in self.transforms:
if not isinstance(
T, (augmentation.Identity, augmentation.Translation,
augmentation.FlipHorizontal,
augmentation.FlipVertical, augmentation.Blur)):
break
target_boxes.append(self.iou_target_box + np.array(
[T.shift[1], T.shift[0], 0, 0]))
else:
target_boxes.append(self.iou_target_box.copy())
target_boxes = np.concatenate(target_boxes.view(1, 4), 0)
# Get iou features
iou_backbone_features = self.get_iou_backbone_features()
# Remove other augmentations such as rotation
iou_backbone_features = TensorList(
[x[:target_boxes.shape[0], ...] for x in iou_backbone_features])
# Extract target feat
with fluid.dygraph.guard():
iou_backbone_features = iou_backbone_features.apply(n2p)
target_boxes = n2p(target_boxes)
target_feat = self.iou_predictor.get_filter(iou_backbone_features,
target_boxes)
self.target_feat = TensorList(
[layers.reduce_mean(x, 0).numpy() for x in target_feat])
if getattr(self.params, 'iounet_not_use_reference', False):
self.target_feat = TensorList([
np.full_like(tf, tf.norm() / tf.numel())
for tf in self.target_feat
])
def optimize_boxes(self, iou_features, init_boxes):
with fluid.dygraph.guard():
# Optimize iounet boxes
init_boxes = np.reshape(init_boxes, (1, -1, 4))
step_length = self.params.box_refinement_step_length
target_feat = self.target_feat.apply(n2p)
iou_features = iou_features.apply(n2p)
output_boxes = n2p(init_boxes)
for f in iou_features:
f.stop_gradient = False
for i_ in range(self.params.box_refinement_iter):
# forward pass
bb_init = output_boxes
bb_init.stop_gradient = False
outputs = self.iou_predictor.predict_iou(target_feat,
iou_features, bb_init)
if isinstance(outputs, (list, tuple)):
outputs = outputs[0]
outputs.backward()
# Update proposal
bb_init_np = bb_init.numpy()
bb_init_gd = bb_init.gradient()
output_boxes = bb_init_np + step_length * bb_init_gd * np.tile(
bb_init_np[:, :, 2:], (1, 1, 2))
output_boxes = n2p(output_boxes)
step_length *= self.params.box_refinement_step_decay
return layers.reshape(output_boxes, (
-1, 4)).numpy(), layers.reshape(outputs, (-1, )).numpy()
def refine_target_box(self,
sample_pos,
sample_scale,
scale_ind,
update_scale=True):
# Initial box for refinement
init_box = self.get_iounet_box(self.pos, self.target_sz, sample_pos,
sample_scale)
# Extract features from the relevant scale
iou_features = self.get_iou_features()
iou_features = TensorList(
[x[scale_ind:scale_ind + 1, ...] for x in iou_features])
init_boxes = np.reshape(init_box, (1, 4)).copy()
rand_fn = lambda a, b: np.random.rand(a, b).astype('float32')
if self.params.num_init_random_boxes > 0:
# Get random initial boxes
square_box_sz = np.sqrt(init_box[2:].prod())
rand_factor = square_box_sz * np.concatenate([
self.params.box_jitter_pos * np.ones(2),
self.params.box_jitter_sz * np.ones(2)
])
minimal_edge_size = init_box[2:].min() / 3
rand_bb = (rand_fn(self.params.num_init_random_boxes, 4) - 0.5
) * rand_factor
new_sz = np.clip(init_box[2:] + rand_bb[:, 2:], minimal_edge_size,
1e10)
new_center = (init_box[:2] + init_box[2:] / 2) + rand_bb[:, :2]
init_boxes = np.concatenate([new_center - new_sz / 2, new_sz], 1)
init_boxes = np.concatenate(
[np.reshape(init_box, (1, 4)), init_boxes])
# Refine boxes by maximizing iou
output_boxes, output_iou = self.optimize_boxes(iou_features, init_boxes)
# Remove weird boxes with extreme aspect ratios
output_boxes[:, 2:] = np.clip(output_boxes[:, 2:], 1, 1e10)
aspect_ratio = output_boxes[:, 2] / output_boxes[:, 3]
keep_ind = (aspect_ratio < self.params.maximal_aspect_ratio) * \
(aspect_ratio > 1 / self.params.maximal_aspect_ratio)
output_boxes = output_boxes[keep_ind, :]
output_iou = output_iou[keep_ind]
# If no box found
if output_boxes.shape[0] == 0:
return
# Take average of top k boxes
k = getattr(self.params, 'iounet_k', 5)
topk = min(k, output_boxes.shape[0])
inds = np.argsort(-output_iou)[:topk]
predicted_box = | np.mean(output_boxes[inds, :], axis=0) | numpy.mean |
"""
HMM model
"""
from hmmlearn import hmm
import numpy as np
import pandas as pd
from sklearn import preprocessing as pp
class hmmModel(object):
def __init__(self,nc = 3):
self.nc = nc
def fit_predict(self,dataSet):
"""
Fit HMM model based on data
Args:
dataSet: a data frame with Var and Gradient as columns
Returns:
feature_index: a list where the first element is the index of maximum gradient points,
the rest are the index of state changing points
"""
np.random.seed()
n = dataSet.shape[0] # total number of data
HMM_data = pp.scale(dataSet[["Var","Gradient"]])
if self.nc == 3:
# initialize transition matrix
transmat = np.zeros((3, 3))
transmat[0, 1] = 3.0/n
transmat[0, 0] = 1.0 - transmat[0, 1]
transmat[1, 2] = 3.0/n
transmat[1, 1] = 1.0 - transmat[1, 2]
transmat[2, 2] = 1.0
# Force the first point is in state 0
startprob = np.array([1, 0, 0])
# The state mean of variable
state_means = np.zeros((3, 2))
state_means[0, 0] = np.percentile(HMM_data[:10, 0],50)
state_means[2, 0] = | np.percentile(HMM_data[-10:, 0],50) | numpy.percentile |
from typing_extensions import TypeAlias
from copy import deepcopy
import numpy as np
from util.activation import sigmoid
from util.range import Range
Voltage: TypeAlias = np.ndarray
class Ranges:
weights: Range = Range(-16, 16)
biases: Range = Range(-16, 16)
time_constants: Range = Range(0.5, 10)
class Ctrnn:
def __init__(self, size: int = 2) -> None:
self.size = size
self.biases = np.zeros(self.size)
self.time_constants = np.ones(self.size)
self._inv_time_constants = 1.0 / self.time_constants
self.weights = np.zeros((self.size, self.size))
def init_voltage(self) -> Voltage:
"""Create a new voltage instance where all neurons have 0V"""
return np.zeros(self.size)
def set_bias(self, neuron: int, bias: float) -> None:
"""Set an individual neuron's bias"""
self.biases[neuron] = Ranges.biases.clip(bias)
def set_time_constant(self, neuron: int, time_constant: float) -> None:
"""Set an individual neuron's time constant"""
self.time_constants[neuron] = Ranges.time_constants.clip(time_constant)
self._inv_time_constants[neuron] = 1.0 / self.time_constants[neuron]
def set_weight(self, pre: int, post: int, weight: float) -> None:
"""Set the synaptic weight from a presynaptic to a postsynaptic neuron"""
self.weights[pre][post] = Ranges.weights.clip(weight)
def perturb(
self,
change: float,
rng: np.random.Generator,
weights: bool = True,
biases: bool = True,
) -> None:
"""Slightly modify the synaptic weights and biases of this network"""
if weights:
range = Ranges.weights
direction = rng.uniform(-1, 1, size=(self.size, self.size))
magnitude = np.sqrt(np.sum( | np.power(direction.flat, 2) | numpy.power |
"""
Module for the database cruncher which uses the 'equal quantile walk' technique.
"""
import numpy as np
from pyam import IamDataFrame
from ..stats import calc_quantiles_of_data
from .base import _DatabaseCruncher
class EqualQuantileWalk(_DatabaseCruncher):
"""
Database cruncher which uses the 'equal quantile walk' technique.
This cruncher assumes that the amount of effort going into reducing one emission set
is equal to that for another emission, therefore the lead and follow data should be
at the same quantile of all pathways in the infiller database.
It calculates the quantile of the lead infillee data in the lead infiller database,
then outputs that quantile of the follow data in the infiller database.
"""
def derive_relationship(self, variable_follower, variable_leaders):
"""
Derive the relationship between two variables from the database.
Parameters
----------
variable_follower : str
The variable for which we want to calculate timeseries (e.g.
``"Emissions|C5F12"``).
variable_leaders : list[str]
The variable we want to use in order to infer timeseries of
``variable_follower`` (e.g. ``["Emissions|CO2"]``).
Returns
-------
:obj:`func`
Function which takes a :obj:`pyam.IamDataFrame` containing
``variable_leaders`` timeseries and returns timeseries for
``variable_follower`` based on the derived relationship between the two.
Please see the source code for the exact definition (and docstring) of the
returned function.
Raises
------
ValueError
``variable_leaders`` contains more than one variable.
ValueError
There is no data for ``variable_leaders`` or ``variable_follower`` in the
database.
"""
iamdf_follower = self._get_iamdf_follower(variable_follower, variable_leaders)
follower_ts = iamdf_follower.timeseries()
data_follower_time_col = iamdf_follower.time_col
data_follower_unit = iamdf_follower["unit"].values[0]
lead_ts = self._db.filter(variable=variable_leaders).timeseries()
lead_unit = lead_ts.index.get_level_values("unit")[0]
def filler(in_iamdf):
"""
Filler function derived from :obj:`EqualQuantileWalk`.
Parameters
----------
in_iamdf : :obj:`pyam.IamDataFrame`
Input data to fill data in
Returns
-------
:obj:`pyam.IamDataFrame`
Filled in data (without original source data)
Raises
------
ValueError
Not all required timepoints are present in the database we crunched...
"""
lead_in = in_iamdf.filter(variable=variable_leaders)
if not all(lead_in.variables(True)["unit"] == lead_unit):
raise ValueError(
"Units of lead variable is meant to be `{}`, found `{}`".format(
lead_unit, lead_in.variables(True)["unit"].tolist()
)
)
if data_follower_time_col != in_iamdf.time_col:
raise ValueError(
"`in_iamdf` time column must be the same as the time column used "
"to generate this filler function (`{}`)".format(
data_follower_time_col
)
)
if lead_in.data.empty:
raise ValueError(
"There is no data for {} so it cannot be infilled".format(
variable_leaders
)
)
output_ts = lead_in.timeseries()
if any(
[
(time not in lead_ts.columns) or (time not in follower_ts.columns)
for time in output_ts.columns
]
):
# We allow for cases where either lead or follow have gaps
raise ValueError(
"Not all required timepoints are present in the database we "
"crunched, we crunched \n\t{} for the lead and \n\t{} for the "
"follow \nbut you passed in \n\t{}".format(
lead_ts.columns, follower_ts.columns, output_ts.columns
)
)
for col in output_ts.columns:
output_ts[col] = self._find_same_quantile(
follower_ts[col], lead_ts[col], output_ts[col]
)
output_ts = output_ts.reset_index()
output_ts["variable"] = variable_follower
output_ts["unit"] = data_follower_unit
return IamDataFrame(output_ts)
return filler
def _get_iamdf_follower(self, variable_follower, variable_leaders):
if len(variable_leaders) > 1:
raise ValueError(
"For `EqualQuantileWalk`, ``variable_leaders`` should only "
"contain one variable"
)
self._check_follower_and_leader_in_db(variable_follower, variable_leaders)
return self._db.filter(variable=variable_follower)
def _find_same_quantile(self, follow_vals, lead_vals, lead_input):
# Dispose of nans that can cloud the calculation
follow_vals = follow_vals[~np.isnan(follow_vals)]
input_quantiles = calc_quantiles_of_data(lead_vals, lead_input)
if all( | np.isnan(input_quantiles) | numpy.isnan |
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Dec 22 16:48:57 2021
This script clean data from FastTrack analysis to crate an Xarray object that is saved inside an twin folder, in a .nc file
@author: baptistelafoux
"""
#### WARNING : TO DO - Slide light signal time basis to account for different starting time (not so important)
# %% Modules import
import numpy as np
import pandas as pd
import cv2
import os
import glob
import time as time_module
import xarray as xr
import yaml
import termplotlib as tpl
import matplotlib.pyplot as plt
from utils.data_operations import interpolate_nans
from scipy.spatial.distance import pdist, squareform
from datetime import timedelta
np.seterr(all="ignore")
# %% Main function
def generate_dataset(data_folder):
# useful file names
fasttrack_filename = glob.glob(data_folder + "/Tracking_Result*" + "/tracking.txt")
if fasttrack_filename:
fasttrack_filename = fasttrack_filename[0]
bg_filename = glob.glob(data_folder + "/Tracking_Result*" + "/background.pgm")[0]
#### Extraction of general data, metadata & BG
tic = time_module.time()
# load raw data
data = pd.read_csv(fasttrack_filename, sep="\t")
print("Successfully loaded data from the server")
# loading the background image
bg = cv2.imread(bg_filename)
# compute the mean size of fish (they are decomposed into head + tail)
global mean_BL_pxl
mean_BL_pxl = np.mean(2 * data.headMajorAxisLength +
2 * data.tailMajorAxisLength)
n_frames = np.max(data.imageNumber) + 1
n_fish = np.max(data.id) + 1
fish_by_frame = [data[data.imageNumber == i].shape[0] for i in range(n_frames)]
tank_w, tank_h = bg.shape[1], bg.shape[0]
#### Log infos
print('\n#########################')
print("Number of fish: ", n_fish)
print("Number of frames: ", n_frames,
'(' + str(timedelta(seconds=int(n_frames/fps))) + ' @ {:.0f} fps)'.format(fps))
print("Avg. body length in pxl: {:.2f} pxl \n".format(mean_BL_pxl))
print('#########################\n')
toc = time_module.time()
print("Loading file, metadata and BG \t {:.2f} s".format(toc - tic))
#### Coordinates interpolation
tic = time_module.time()
s, v, a, e, theta, vel = generate_traj(data, n_frames, n_fish)
toc = time_module.time()
print(
"Coordinates and coordinates interpolation \t {:.2f} s".format(toc - tic))
#### Distances and rotation/polarization parameters
tic = time_module.time()
ii_dist = np.array([squareform(pdist(s[t, ...])) for t in range(n_frames)])
if n_fish==1:
return None, False
else:
nn_dist = np.sort(ii_dist, axis=1)[:, 1]
center_of_mass = np.mean(s, axis=1)
if circular_arena:
center = find_arena_center(bg)
r = s - center[None, None, :] / mean_BL_pxl
else:
r = s - center_of_mass[:, None, :]
rotation_parameter = rot_param(r, v, n_fish)
polarization_parameter = pol_param(e, n_fish)
toc = time_module.time()
print(
"Distances and rotation/polarization parameters \t {:.2f} s".format(
toc - tic)
)
#### Create the dataset
attrs = {
"track_filename": fasttrack_filename,
"bg_filename": bg_filename,
"n_frames": n_frames,
"n_fish": n_fish,
"fps": fps,
"mean_BL_pxl": mean_BL_pxl,
"tank_size": pxl2BL(np.array([tank_w, tank_h]))
}
data_dict = dict(
s=(["time", "fish", "space"], s),
v=(["time", "fish", "space"], v),
a=(["time", "fish", "space"], a),
vel=(["time", "fish"], vel),
center_of_mass=(["time", "space"], center_of_mass),
ii_dist=(["time", "fish", "neighbour"], ii_dist),
nn_dist=(["time", "fish"], nn_dist),
e=(["time", "fish", "space"], e),
theta=(["time", "fish"], theta),
rot_param=(["time"], rotation_parameter),
pol_param=(["time"], polarization_parameter),
fish_by_frame=(["time"], fish_by_frame)
)
coords = {
"time": (["time"], np.arange(n_frames) / fps),
"fish": (["fish"], np.arange(n_fish)),
"neighbour": (["neighbour"], np.arange(n_fish)),
"space": (["space"], ["x", "y"]),
}
#### metadata.yaml file
# only if the file exists (should be the case for all experiments after septembre 2021)
metadata_filename = glob.glob(data_folder + "/metadata*")
if metadata_filename:
print('\n#### There is a metadata.yaml file : processing it')
metadata_filename = metadata_filename[0]
time = np.arange(n_frames) / fps
file = open(metadata_filename)
metadata = yaml.load(file, Loader=yaml.FullLoader)
file.close()
print("Successfully loaded metadata", "\n")
# we interpolate the light signal from metadata in case it is not an the same rate
light = np.interp(
np.linspace(0, len(metadata["light"]), n_frames),
np.arange(len(metadata["light"])),
metadata["light"],
)
print('Exact start time :', str(metadata['t_start']))
fig = tpl.figure()
fig.plot(time, light, width=60, height=10)
fig.show()
attrs_meta = {
"T_exp": metadata["T_exp"],
"T_settle": metadata["T_settle"],
"T_period": metadata["T_per"],
"date": str(metadata["t_start"].date()),
"t_start": str(metadata["t_start"].time()),
}
attrs.update(attrs_meta)
data_dict['light'] = (["time"], light)
ds = xr.Dataset(data_vars=data_dict, coords=coords, attrs=attrs)
print("Dataset generated without too big of a surprise")
return ds, True
# %% Utilities function
def generate_traj(data, n_frames, n_fish):
"""
A function that generates velocity and acceleration data from dirty (x,y) data.
It interpolates the data so that they are all on the same time basis, remove NaNs
All values returned in BL !!
Parameters
----------
data : DataSet
Generated from Fasttrack tracking.txt file.
n_frames : int
n_fish : int
time : np.array of int
Common time basis.
Returns
-------
s : np.array
size : (n_frames, n_fish, 2). (x, y) position for each frame for each fish.
v : np.array
(n_frames, n_fish, 2). (v_x, v_y) velocity for each frame for each fish.
a : np.array
(n_frames, n_fish, 2). (a_x, a_y) acceleration for each frame for each fish.
e : np.array
heading vector.
theta : np.array
angle with vertical (<- not sure for the with vertical part, it is an angle though).
"""
time = np.arange(n_frames)
s = np.empty((n_frames, n_fish, 2))
e = np.empty((n_frames, n_fish, 2))
theta = np.empty((n_frames, n_fish))
for focal in range(n_fish):
t = data[data.id == focal].imageNumber
x = data[data.id == focal].xHead
y = data[data.id == focal].yHead
th = data[data.id == focal].tHead
x_interp = np.interp(time, t, x)
y_interp = np.interp(time, t, y)
th_interp = np.interp(time, t, th)
s[:, focal, :] = pxl2BL(np.c_[x_interp, y_interp])
e[:, focal, :] = np.c_[np.cos(th_interp), np.sin(th_interp)]
theta[:, focal] = th_interp
v = np.gradient(s, axis=0, edge_order=2)
a = np.gradient(v, axis=0, edge_order=2)
vel = np.linalg.norm(v, axis=-1)
s = interpolate_nans(s)
v = interpolate_nans(v)
a = interpolate_nans(a)
e = interpolate_nans(e)
vel = interpolate_nans(vel)
theta = interpolate_nans(theta)
return s, v, a, e, theta, vel
def rot_param(r, v, N):
# we add an epilon to the norm of the velocity in case is it 0
rotation_parameter = np.sum(np.cross(r, v) / ( | np.linalg.norm(r, axis=2) | numpy.linalg.norm |
# ----------------------------------------------------------
# Main simulation control
#
# <NAME>, MRC Laboratory of Molecular Biology, 2013
# email: <EMAIL>
# ----------------------------------------------------------
import numpy as np
import pickle
import time
################################################################################
# Removing dependency on Brian 1 as the class used, OfflinePoissonGroup is not compatible
# with recent versions of Numpy. Using slightly modified OfflinePoissonGroup here.
# See https://github.com/OpenSourceBrain/SmithEtAl2013-L23DendriticSpikes/issues/3
#
######import brian as br
from numpy.random import exponential, randint
from numpy import ones, cumsum, sum, isscalar
## Copied from https://github.com/brian-team/brian/blob/master/brian/directcontrol.py#L450
# and changed: T * totalrate * 2 -> int(T * totalrate * 2)
class OfflinePoissonGroup(object): # This is weird, there is only an init method
def __init__(self, N, rates, T):
"""
Generates a Poisson group with N spike trains and given rates over the
time window [0,T].
"""
if isscalar(rates):
rates = rates * ones(N)
totalrate = sum(rates)
isi = exponential(1 / totalrate, int(T * totalrate * 2))
spikes = cumsum(isi)
spikes = spikes[spikes <= T]
neurons = randint(0, N, len(spikes))
self.spiketimes = zip(neurons, spikes)
################################################################################
import libcell as lb
import saveClass as sc
#----------------------------------------------------------------------------
# Functions and Classes
def initOnsetSpikes():
model.ncAMPAlist[0].event(data.st_onset)
def initSpikes():
for s in data.etimes:
model.ncAMPAlist[int(s[0])].event(float(s[1]))
if data.NMDA: model.ncNMDAlist[int(s[0])].event(float(s[1]))
if data.GABA == True:
for s in data.itimes:
model.ncGABAlist[int(s[0])].event(float(s[1]))
def storeSimOutput(data, v,vD,i,g,r,ca, vSec):
data.vdata.append(v)
data.vDdata.append(vD)
data.idata.append(i)
data.gdata.append(g)
data.rates.append(r)
data.caDdata.append(ca)
data.vsec.append(vSec)
# Synapse location functions
def genRandomLocs(data, model, nsyn):
locs = []
for s in np.arange(0,nsyn):
dend = np.random.randint(low=0, high=len(model.dends))
pos = np.random.uniform()
locs.append([dend, pos])
return locs
# Input generation functions
def genPoissonInput(nsyn, rate, duration, onset):
times = np.array([])
while times.shape[0]<2:
P = OfflinePoissonGroup(nsyn, rate, duration)
times = np.array(P.spiketimes)
times[:,1] = times[:,1] * 1000 + onset
rates = 1./np.diff(np.array(P.spiketimes)[:,1]).mean()
return times, rates
def genRandomFixedInput(nsyn, tInterval, onset):
times = np.zeros([nsyn, 2])
times[:,0] = np.arange(0, nsyn)
np.random.shuffle(times[:,0])
times[:,1] = np.arange(0, nsyn*tInterval, tInterval) + onset
return times
def addBground(data, nsyn, Snsyn, rate, sTimes):
P = OfflinePoissonGroup(nsyn, rate, data.TSTOP)
bTimes = np.array(P.spiketimes)
bTimes[:,0] = bTimes[:,0] + Snsyn
bTimes[:,1] = bTimes[:,1] * 1000
times = np.vstack((bTimes, sTimes))
return times
# Simulation functions
def sim_oneRandomInput(data, model, Ensyn, Insyn, Erate, Irate, bGround=False):
soma_v, gdata, idata, Erates, Irates, dend_v, dend_ca, vSec = [], [], [], [], [], [], [], []
data.all_Etimes, data.all_Itimes = [], []
ETIMES = np.load('./etimes.npy')
ITIMES = np.load('./itimes.npy')
for trial in np.arange(0, data.TRIALS):
# Generate input
data.etimes, erates = genPoissonInput(Ensyn, Erate, data.st_duration,
data.st_onset)
data.itimes, irates = genPoissonInput(Insyn, Irate, data.st_duration,
data.st_onset)
Erates.append(erates)
Irates.append(irates)
if bGround:
data.etimes = addBground(data, data.bEnsyn, Ensyn, data.EbGroundRate,
data.etimes)
data.itimes = addBground(data, data.bInsyn, Insyn, data.IbGroundRate,
data.itimes)
# Hack for freezing the input
# Comment out to get random times
data.etimes = ETIMES[trial]
data.itimes = ITIMES[trial]
# Run
fih = lb.h.FInitializeHandler(1, initSpikes)
taxis, v, vD, g, i, ca , vsec = lb.simulate(model, t_stop=data.TSTOP,
NMDA=data.NMDA, recDend=data.recordDend, recSec=data.recordSec)
# Store data
soma_v.append(v)
dend_v.append(vD)
dend_ca.append(ca)
vSec.append(vsec)
data.all_Etimes.append(data.etimes)
data.all_Itimes.append(data.itimes)
if data.NMDA == True:
#idata.append(np.sum(np.array(i).min(1)))
idata.append(np.array(i))
gdata.append(np.sum(np.array(g).max(1)))
return taxis, soma_v, dend_v, Erates, gdata, idata, dend_ca, vSec
def SIM_rateIteration(data, model, rRange, bGround):
for rate in rRange:
print('Running E rate %s'% rate)
print("Running rateIteration simulation with parameters:")
for k in sorted(data.__dict__.keys()):
print(" %s:\t\t%s"%(k, data.__dict__[k]))
data.taxis, v, vD, r, g, i, ca, vsec = sim_oneRandomInput(data, model, data.Ensyn, data.Insyn, Erate=rate, Irate=rate, bGround=bGround)
storeSimOutput(data, v,vD,i,g,r,ca,vsec)
def SIM_currentSteps(data, model, iRange, bGround=False):
soma_v, r, idata, gdata = [], [], [], []
if bGround:
data.etimes = addBground(data, data.bEnsyn, data.Ensyn, data.EbGroundRate,
[0,0])
data.itimes = addBground(data, data.bInsyn, data.Insyn, data.IbGroundRate,
[0,0])
fih = lb.h.FInitializeHandler(1, initSpikes)
for step in iRange:
print("Running current step simulation with parameters:")
for k in sorted(data.__dict__.keys()):
print(" %s:\t\t%s"%(k, data.__dict__[k]))
model.stim.amp = step
taxis, v, vD, g, i, ca, vsec = lb.simulate(model, t_stop=data.TSTOP,
NMDA=data.NMDA, recDend=data.recordDend)
if data.NMDA == True:
idata.append(np.sum(np.array(i).min(1)))
gdata.append(np.sum(np.array(g).max(1)))
storeSimOutput(data, v,vD,idata,gdata,r=0,ca=ca,vSec=vsec)
data.taxis = taxis
#----------------------------------------------------------------------------
# Data saving object
data = sc.emptyObject()
def main(args=None):
"""Main"""
# Simulation general parameters
data.dt = 0.1
lb.h.dt = data.dt
lb.h.steps_per_ms = 1.0/lb.h.dt
data.st_onset = 200.0
data.st_duration = 200.
data.TSTOP = 600
data.TRIALS = 5
data.Egmax = 1
data.Igmax = 1
data.Irev = -80
data.Ensyn = 100
data.Insyn = int(data.Ensyn*0.2)
data.bEnsyn = 200
data.bInsyn = int(data.bEnsyn*0.2)
# Simulation CONTROL
data.model = 'L23'
data.locType = 'fixed'
data.simType = 'rateIteration'
data.fixedINPUT = False
data.ACTIVE = True
data.ACTIVEdend = True
data.ACTIVEdendNa = True
data.ACTIVEdendCa = True
data.ACTIVEaxonSoma = True
data.ACTIVEhotSpot = True
data.SYN = True
data.SPINES = False
data.ICLAMP = False
data.NMDA = True
data.GABA = True
data.BGROUND = True
global model
# Create neuron and add mechanisms
if data.model == 'BS': model = lb.BS()
if data.model == 'L23': model = lb.L23()
if data.model == 'CELL': model = lb.CELL()
if data.SPINES: lb.addSpines(model)
if data.ACTIVE: lb.init_active(model, axon=data.ACTIVEaxonSoma,
soma=data.ACTIVEaxonSoma, dend=data.ACTIVEdend,
dendNa=data.ACTIVEdendNa, dendCa=data.ACTIVEdendCa)
if data.ACTIVEhotSpot: lb.hotSpot(model)
# Generate synapse locations
if data.locType=='random':
data.Elocs = genRandomLocs(data, model, data.Ensyn)
data.Ilocs = genRandomLocs(data, model, data.Insyn)
if data.locType=='fixed':
loadElocs = np.load('./Elocs.npy')
data.Elocs = loadElocs[0:data.Ensyn]
loadIlocs = np.load('./Ilocs.npy')
data.Ilocs = loadIlocs[0:data.Insyn]
if data.BGROUND:
data.bElocs = genRandomLocs(data, model, data.bEnsyn)
data.bIlocs = genRandomLocs(data, model, data.bInsyn)
data.Elocs = np.vstack((data.Elocs, data.bElocs))
data.Ilocs = np.vstack((data.Ilocs, data.bIlocs))
# Hack for freezing the background
# Uncomment first 2 lines and comment out last 2 for
# random background
#data.bElocs = loadElocs[data.Ensyn+1:]
#data.bIlocs = loadIlocs[data.Insyn+1:]
data.Elocs = loadElocs
data.Ilocs = loadIlocs
# Insert synapses
if data.SYN:
lb.add_AMPAsyns(model, locs=data.Elocs, gmax=data.Egmax)
if data.NMDA: lb.add_NMDAsyns(model, locs=data.Elocs, gmax=data.Egmax)
if data.GABA: lb.add_GABAsyns(model, locs=data.Ilocs, gmax=data.Igmax,
rev=data.Irev)
# Insert IClamp
data.iclampLoc = ['dend', 0.5, 28]
data.iclampOnset = 50
data.iclampDur = 250
data.iclampAmp = 0
if data.ICLAMP:
if data.iclampLoc[0]=='soma':
lb.add_somaStim(model, data.iclampLoc[1], onset=data.iclampOnset,
dur=data.iclampDur, amp=data.iclampAmp)
if data.iclampLoc[0]=='dend':
lb.add_dendStim(model, data.iclampLoc[1], data.iclampLoc[2],
onset=data.iclampOnset, dur=data.iclampDur, amp=data.iclampAmp)
#----------------------------------------------------------------------------
# Data storage lists
data.vdata, data.vDdata, data.gdata, data.idata, data.caDdata, data.vsec = [], [], [], [], [], []
data.rates = []
#----------------------------------------------------------------------------
# Run simulation
# Specific parameters
data.rateRange = | np.arange(8,9,10) | numpy.arange |
import numpy as np
class MLPData:
""" """
@staticmethod
def syn1(N):
"""data(samples, features)
:param N:
"""
data = np.empty(shape=(N,2), dtype = np.float32)
tar = np.empty(shape=(N,), dtype = np.float32)
N1 = int(N/2)
data[:N1,0] = 4 + np.random.normal(loc=.0, scale=1., size=(N1))
data[N1:,0] = -4 + np.random.normal(loc=.0, scale=1., size=(N-N1))
data[:,1] = 10*np.random.normal(loc=.0, scale=1., size=(N))
data = data / data.std(axis=0)
# Target
tar[:N1] = np.ones(shape=(N1,))
tar[N1:] = np.zeros(shape=(N-N1,))
# Rotation
theta = np.radians(30)
c, s = np.cos(theta), np.sin(theta)
R = np.array([[c,-s],[s,c]]) # rotation matrix
data = np.dot(data,R)
return data,tar
@staticmethod
def syn2(N):
"""data(samples, features)
:param N:
"""
data = np.empty(shape=(N,2), dtype = np.float32)
tar = np.empty(shape=(N,), dtype = np.float32)
N1 = int(N/2)
# Positive samples
data[:N1,:] = 0.8 + np.random.normal(loc=.0, scale=1., size=(N1,2))
# Negative samples
data[N1:,:] = -.8 + np.random.normal(loc=.0, scale=1., size=(N-N1,2))
# Target
tar[:N1] = | np.ones(shape=(N1,)) | numpy.ones |
import time
import numpy as np
import galsim
import ngmix
from cs_interpolate import interpolate_image_and_noise_cs
def test_interpolate_image_and_noise_cs_gauss_linear(show=False):
"""
test that our interpolation works decently for a linear
piece missing from a gaussian image
"""
rng = np.random.RandomState(seed=31415)
noise = 0.001
sigma = 4.0
is2 = 1.0/sigma**2
dims = 51, 51
cen = (np.array(dims)-1.0)/2.0
rows, cols = np.mgrid[
0:dims[0],
0:dims[1],
]
rows = rows - cen[0]
cols = cols - cen[1]
image_unmasked = np.exp(-0.5*(rows**2 + cols**2)*is2)
weight = image_unmasked*0 + 1.0/noise**2
noise_image = rng.normal(scale=noise, size=image_unmasked.shape)
badcol = int(cen[1]-3)
bw = 3
rr = badcol-bw, badcol+bw+1
weight[rr[0]:rr[1], badcol] = 0.0
image_masked = image_unmasked.copy()
image_masked[rr[0]:rr[1], badcol] = 0.0
bmask = np.zeros_like(image_unmasked, dtype=np.int32)
bad_flags = 0
iimage, inoise = interpolate_image_and_noise_cs(
image=image_masked,
weight=weight,
bmask=bmask,
bad_flags=bad_flags,
noise=noise_image,
rng=np.random.RandomState(seed=45),
c=1,
)
maxdiff = np.abs(image_unmasked-iimage).max()
if show:
from espy import images
images.view_mosaic([image_masked, weight])
images.compare_images(
image_unmasked,
iimage,
width=1000,
height=int(1000*2/3),
)
print('max diff:', maxdiff)
assert maxdiff < 0.5
def test_interpolate_image_and_noise_cs_gauss_circle(show=False):
"""
test that our interpolation works decently for a linear
piece missing from a gaussian image
"""
rng = np.random.RandomState(seed=31415)
noise = 0.001
sigma = 4.0
is2 = 1.0/sigma**2
dims = 51, 51
cen = (np.array(dims)-1.0)/2.0
rows, cols = np.mgrid[
0:dims[0],
0:dims[1],
]
rows = rows - cen[0]
cols = cols - cen[1]
radius2 = rows**2 + cols**2
image_unmasked = np.exp(-0.5*(radius2)*is2)
weight = image_unmasked*0 + 1.0/noise**2
noise_image = rng.normal(scale=noise, size=image_unmasked.shape)
wbad = np.where(radius2 <= 3**2)
weight[wbad] = 0.0
image_masked = image_unmasked.copy()
image_masked[wbad] = 0.0
bmask = np.zeros_like(image_unmasked, dtype=np.int32)
bad_flags = 0
iimage, inoise = interpolate_image_and_noise_cs(
image=image_masked,
weight=weight,
bmask=bmask,
bad_flags=bad_flags,
noise=noise_image,
rng=np.random.RandomState(seed=45),
# sampling_rate=0.1,
c=0.001,
)
# iimage[wbad] *= 2.75
# iimage[wbad] *= 1.5
maxdiff = np.abs(image_unmasked-iimage).max()
if show:
from espy import images
images.view_mosaic([image_masked, weight])
images.compare_images(
image_unmasked,
iimage,
width=1000,
height=int(1000*2/3),
)
print('max diff:', maxdiff)
assert maxdiff < 0.5
def test_interpolate_image_and_noise_cs_gauss_circle_many(
*,
seed,
sampling_rate=1.0,
c=0.1,
show=False):
"""
test that our interpolation works decently for a linear
piece missing from a gaussian image
"""
rng = np.random.RandomState(seed=seed)
flux_pdf = ngmix.priors.LogNormal(500, 500, rng=rng)
hlr_pdf = ngmix.priors.LogNormal(0.5, 0.5, rng=rng)
noise = 1
dims = 500, 500
imcen = (np.array(dims)-1)/2
scale = 0.2
buff = 50
shift_max = (np.array(dims)-2*buff)/2.0 * scale
nobj = 100
weight = np.zeros(dims) + 1.0/noise**2
noise_image = rng.normal(scale=noise, size=dims)
badone = nobj//2
subsize = 25
psf = galsim.Moffat(fwhm=0.7, beta=2.5)
objlist = []
for i in range(nobj):
shift_row, shift_col = rng.uniform(
low=-shift_max, high=shift_max,
size=2,
)
if i == badone:
flux = 1000
half_light_radius = 1.0e-4
else:
flux = flux_pdf.sample()
half_light_radius = hlr_pdf.sample()
obj0 = galsim.Exponential(
half_light_radius=half_light_radius,
flux=flux,
)
obj0 = obj0.shift(dx=shift_col, dy=shift_row)
obj = galsim.Convolve(obj0, psf)
objlist.append(obj)
if i == badone:
cen = imcen + (shift_row/scale, shift_col/scale)
rows, cols = np.mgrid[
0:dims[0],
0:dims[1],
]
rows = rows - cen[0]
cols = cols - cen[1]
radius2 = rows**2 + cols**2
rowmin = int(cen[0]-subsize)
rowmax = int(cen[0]+subsize) + 1
colmin = int(cen[1]-subsize)
colmax = int(cen[1]+subsize) + 1
wbad = np.where(radius2 <= 3**2)
weight[wbad] = 0.0
objects = galsim.Sum(objlist)
image_unmasked = objects.drawImage(
nx=dims[1],
ny=dims[0],
scale=scale,
).array
image_unmasked += rng.normal(scale=noise, size=image_unmasked.shape)
# nbad = int(500 * 500 / 4)
# xind = rng.choice(dims[1], size=nbad, replace=True)
# yind = rng.choice(dims[0], size=nbad, replace=True)
# weight[yind, xind] = 0.0
wbad = np.where(weight <= 0.0)
image_masked = image_unmasked.copy()
image_masked[wbad] = 0.0
bmask = np.zeros_like(image_unmasked, dtype=np.int32)
bad_flags = 0
_nlscale = np.sqrt(np.median(weight)) * 10
def _scale(__im):
return np.arcsinh(__im * _nlscale)
def _descale(__im):
return | np.sinh(__im) | numpy.sinh |
import numpy as np
from numpy.fft import fft, rfft, ifft, irfft
import gmpy
def is_prime(n):
i = 2
while i * i <= n:
if n % i == 0:
return False
i += 1
return True
def find_next_prime(n):
while True:
n += 1
if is_prime(n):
return n
primes_list = []
def get_primes(bound):
global primes_list
pos = 0
cur_mult = 1
last_num = 1000000000
while cur_mult <= bound or pos == 0:
if pos >= len(primes_list):
primes_list.append(find_next_prime(last_num))
last_num = primes_list[pos]
cur_mult *= last_num
pos += 1
return primes_list[:pos]
def multiply_fft(v1, v2, real=False):
N = 1
while N < len(v1):
N *= 2
N *= 2
if real:
f1 = rfft(v1, n=N)
f2 = rfft(v2, n=N)
else:
f1 = fft(v1, n=N)
f2 = fft(v2, n=N)
tmp_res = f1 * f2
if real:
mult_res = irfft(tmp_res, n=N)
else:
mult_res = ifft(tmp_res, n=N)
result = mult_res[:len(v1) + len(v2)]
assert len(result) == len(v1) + len(v2)
return result
def multiply_1d_modulo(v1, v2, m):
b = int(np.sqrt(m)) + 1
t1 = np.array([x % m for x in v1])
t2 = np.array([x % m for x in v2])
t11 = np.floor_divide(t1, b)
t12 = np.mod(t1, b)
a1 = t11 * 1j + t12
t21 = np.floor_divide(t2, b)
t22 = np.mod(t2, b)
a2 = t21 * 1j + t22
r = multiply_fft(a1, a2)
tmp = multiply_fft(t11, t21, True)
res = np.mod(np.floor(r.imag + 0.5).astype(np.int), m) * b + np.mod(np.floor(r.real + 0.5).astype(np.int), m) + np.mod(np.floor(tmp.real + 0.5).astype(np.int), m) * (b * b + 1)
res = np.mod(res, m)
res = [ | np.asscalar(x) | numpy.asscalar |
import time
import torch
from torch.backends import cudnn
from backbone import HybridNetsBackbone
import cv2
import numpy as np
from glob import glob
from utils.utils import letterbox, scale_coords, postprocess, BBoxTransform, ClipBoxes, restricted_float, boolean_string
from utils.plot import STANDARD_COLORS, standard_to_bgr, get_index_label, plot_one_box
import os
from torchvision import transforms
import argparse
parser = argparse.ArgumentParser('HybridNets: End-to-End Perception Network - DatVu')
parser.add_argument('-c', '--compound_coef', type=int, default=3, help='Coefficient of efficientnet backbone')
parser.add_argument('--source', type=str, default='demo/image', help='The demo image folder')
parser.add_argument('--output', type=str, default='demo_result', help='Output folder')
parser.add_argument('-w', '--load_weights', type=str, default='weights/hybridnets.pth')
parser.add_argument('--nms_thresh', type=restricted_float, default='0.25')
parser.add_argument('--iou_thresh', type=restricted_float, default='0.3')
parser.add_argument('--imshow', type=boolean_string, default=False, help="Show result onscreen (unusable on colab, jupyter...)")
parser.add_argument('--imwrite', type=boolean_string, default=True, help="Write result to output folder")
parser.add_argument('--show_det', type=boolean_string, default=False, help="Output detection result exclusively")
parser.add_argument('--show_seg', type=boolean_string, default=False, help="Output segmentation result exclusively")
parser.add_argument('--cuda', type=boolean_string, default=True)
parser.add_argument('--float16', type=boolean_string, default=True, help="Use float16 for faster inference")
args = parser.parse_args()
compound_coef = args.compound_coef
source = args.source
if source.endswith("/"):
source = source[:-1]
output = args.output
if output.endswith("/"):
output = output[:-1]
weight = args.load_weights
img_path = glob(f'{source}/*.jpg') + glob(f'{source}/*.png')
# img_path = [img_path[0]] # demo with 1 image
input_imgs = []
shapes = []
det_only_imgs = []
# replace this part with your project's anchor config
anchor_ratios = [(0.62, 1.58), (1.0, 1.0), (1.58, 0.62)]
anchor_scales = [2 ** 0, 2 ** 0.70, 2 ** 1.32]
threshold = args.nms_thresh
iou_threshold = args.iou_thresh
imshow = args.imshow
imwrite = args.imwrite
show_det = args.show_det
show_seg = args.show_seg
os.makedirs(output, exist_ok=True)
use_cuda = args.cuda
use_float16 = args.float16
cudnn.fastest = True
cudnn.benchmark = True
obj_list = ['car']
color_list = standard_to_bgr(STANDARD_COLORS)
ori_imgs = [cv2.imread(i, cv2.IMREAD_COLOR | cv2.IMREAD_IGNORE_ORIENTATION) for i in img_path]
ori_imgs = [cv2.cvtColor(i, cv2.COLOR_BGR2RGB) for i in ori_imgs]
# cv2.imwrite('ori.jpg', ori_imgs[0])
# cv2.imwrite('normalized.jpg', normalized_imgs[0]*255)
resized_shape = 640
normalize = transforms.Normalize(
mean=[0.485, 0.456, 0.406], std=[0.229, 0.224, 0.225]
)
transform = transforms.Compose([
transforms.ToTensor(),
normalize,
])
for ori_img in ori_imgs:
h0, w0 = ori_img.shape[:2] # orig hw
r = resized_shape / max(h0, w0) # resize image to img_size
input_img = cv2.resize(ori_img, (int(w0 * r), int(h0 * r)), interpolation=cv2.INTER_AREA)
h, w = input_img.shape[:2]
(input_img, _, _), ratio, pad = letterbox((input_img, input_img.copy(), input_img.copy()), resized_shape, auto=True,
scaleup=False)
input_imgs.append(input_img)
# cv2.imwrite('input.jpg', input_img * 255)
shapes.append(((h0, w0), ((h / h0, w / w0), pad))) # for COCO mAP rescaling
if use_cuda:
x = torch.stack([transform(fi).cuda() for fi in input_imgs], 0)
else:
x = torch.stack([transform(fi) for fi in input_imgs], 0)
x = x.to(torch.float32 if not use_float16 else torch.float16)
# print(x.shape)
model = HybridNetsBackbone(compound_coef=compound_coef, num_classes=len(obj_list),
ratios=anchor_ratios, scales=anchor_scales, seg_classes=2)
try:
model.load_state_dict(torch.load(weight, map_location='cuda' if use_cuda else 'cpu'))
except:
model.load_state_dict(torch.load(weight, map_location='cuda' if use_cuda else 'cpu')['model'])
model.requires_grad_(False)
model.eval()
if use_cuda:
model = model.cuda()
if use_float16:
model = model.half()
with torch.no_grad():
features, regression, classification, anchors, seg = model(x)
seg = seg[:, :, 12:372, :]
da_seg_mask = torch.nn.functional.interpolate(seg, size=[720, 1280], mode='nearest')
_, da_seg_mask = torch.max(da_seg_mask, 1)
for i in range(da_seg_mask.size(0)):
# print(i)
da_seg_mask_ = da_seg_mask[i].squeeze().cpu().numpy().round()
color_area = np.zeros((da_seg_mask_.shape[0], da_seg_mask_.shape[1], 3), dtype=np.uint8)
color_area[da_seg_mask_ == 1] = [0, 255, 0]
color_area[da_seg_mask_ == 2] = [0, 0, 255]
color_seg = color_area[..., ::-1]
# cv2.imwrite('seg_only_{}.jpg'.format(i), color_seg)
color_mask = | np.mean(color_seg, 2) | numpy.mean |
import gdb
import matplotlib.pyplot as plt
import numpy as np
# target_x_coord = 11
# target_y_coord = 80
# target_sample = 1
# target_x_coord = 10
# target_y_coord = 10
# target_sample = 1
tracking_path = False
class PathSegment:
def __init__(self):
self.depth = None
self.world_ray_origin = None
self.world_ray_direction = None
self.hit_point = None
self.hit_point_normal = None
self.local_wo = None
self.local_wi = None
self.original_bsdf = None
self.adjusted_bsdf = None
self.emission = None
self.pdf = None
self.stop_reason = None
self.returned_radiance = None
full_path = []
def DumpFullPathData():
print("-- Full path data dump BEGIN ---------------------------------------------------")
print(" Path length: " + str(len(full_path)))
for i in range(len(full_path)):
print (" -- [" + str(i) + "] - depth " + str(full_path[i].depth) + " -------------------------------------------------------------------")
if (full_path[i].world_ray_origin is not None):
print (" world ray origin: " + str(full_path[i].world_ray_origin[0]) + ", " + str(full_path[i].world_ray_origin[1]) + ", " + str(full_path[i].world_ray_origin[2]))
if (full_path[i].world_ray_direction is not None):
print (" world ray direction: " + str(full_path[i].world_ray_direction[0]) + ", " + str(full_path[i].world_ray_direction[1]) + ", " + str(full_path[i].world_ray_direction[2]))
if (full_path[i].hit_point is not None):
print (" hit point: " + str(full_path[i].hit_point[0]) + ", " + str(full_path[i].hit_point[1]) + ", " + str(full_path[i].hit_point[2]))
if (full_path[i].hit_point_normal is not None):
print (" hit point normal: " + str(full_path[i].hit_point_normal[0]) + ", " + str(full_path[i].hit_point_normal[1]) + ", " + str(full_path[i].hit_point_normal[2]))
if (full_path[i].local_wo is not None):
print (" local_wo: " + str(full_path[i].local_wo[0]) + ", " + str(full_path[i].local_wo[1]) + ", " + str(full_path[i].local_wo[2]))
if (full_path[i].local_wi is not None):
print (" local_wi: " + str(full_path[i].local_wi[0]) + ", " + str(full_path[i].local_wi[1]) + ", " + str(full_path[i].local_wi[2]))
if (full_path[i].original_bsdf is not None):
print (" original bsdf: " + str(full_path[i].original_bsdf[0]) + ", " + str(full_path[i].original_bsdf[1]) + ", " + str(full_path[i].original_bsdf[2]))
if (full_path[i].adjusted_bsdf is not None):
print (" adjusted bsdf: " + str(full_path[i].adjusted_bsdf[0]) + ", " + str(full_path[i].adjusted_bsdf[1]) + ", " + str(full_path[i].adjusted_bsdf[2]))
if (full_path[i].emission is not None):
print (" emission: " + str(full_path[i].emission[0]) + ", " + str(full_path[i].emission[1]) + ", " + str(full_path[i].emission[2]))
if (full_path[i].pdf is not None):
print (" pdf: " + str(full_path[i].pdf))
if (full_path[i].stop_reason is not None):
print (" stop reason: " + full_path[i].stop_reason)
if (full_path[i].returned_radiance is not None):
print (" returned_radiance: " + str(full_path[i].returned_radiance[0]) + ", " + str(full_path[i].returned_radiance[1]) + ", " + str(full_path[i].returned_radiance[2]))
print("-- Full path data dump END -----------------------------------------------------")
class StartTracking(gdb.Breakpoint):
def stop (self):
global target_x_coord
global target_y_coord
global target_sample
global tracking_path
x = int(gdb.parse_and_eval('x'))
y = int(gdb.parse_and_eval('y'))
sample = int(gdb.parse_and_eval('sample'))
if ((x == target_x_coord) and (y == target_y_coord) and (sample == target_sample)):
tracking_path = True;
print("")
print("================================================================================")
print("== PATH TRACKING STARTED : " + "screen coord [" + str(x) + "," + str(y) + "], sample = " + str(sample))
print("================================================================================")
else:
if (tracking_path == True):
DumpFullPathData()
print("================================================================================")
print("== PATH TRACKING FINISHED")
print("================================================================================")
tracking_path = False;
return False
class RecurringIntoNewSegment(gdb.Breakpoint):
def stop (self):
global tracking_path
global full_path
if (tracking_path == True):
depth = int(gdb.parse_and_eval('depth'))
print (" >> analysing path segment at depth: " + str(depth))
full_path.append(PathSegment())
full_path[depth].depth = depth
return False
class TerminateTrackingMaxDepth(gdb.Breakpoint):
def stop (self):
global tracking_path
if (tracking_path == True):
depth = int(gdb.parse_and_eval('depth'))
print (" Returning... max depth reached!")
full_path[depth].stop_reason = "max depth reached"
class TerminateTrackingPrimaryRayMiss(gdb.Breakpoint):
def stop (self):
global tracking_path
if (tracking_path == True):
depth = int(gdb.parse_and_eval('depth'))
print (" Returning... primary ray missed surface (background color)!")
full_path[depth].stop_reason = "primary ray missed surface (background color)"
class TerminateTrackingRayMiss(gdb.Breakpoint):
def stop (self):
global tracking_path
if (tracking_path == True):
depth = int(gdb.parse_and_eval('depth'))
print (" Returning... ray (not primary) missed surface (return zero)!")
full_path[depth].stop_reason = "ray (not primary) missed surface (return zero)"
class TerminateTrackingRR(gdb.Breakpoint):
def stop (self):
global tracking_path
if (tracking_path == True):
depth = int(gdb.parse_and_eval('depth'))
r_o_x = float(gdb.parse_and_eval('world_ray.origin_.x'))
r_o_y = float(gdb.parse_and_eval('world_ray.origin_.y'))
r_o_z = float(gdb.parse_and_eval('world_ray.origin_.z'))
full_path[depth].world_ray_origin = np.array([r_o_x, r_o_y, r_o_z])
r_d_x = float(gdb.parse_and_eval('world_ray.direction_.x'))
r_d_y = float(gdb.parse_and_eval('world_ray.direction_.y'))
r_d_z = float(gdb.parse_and_eval('world_ray.direction_.z'))
full_path[depth].world_ray_direction = np.array([r_d_x, r_d_y, r_d_z])
hp_x = float(gdb.parse_and_eval('intersection_record.position_.x'))
hp_y = float(gdb.parse_and_eval('intersection_record.position_.y'))
hp_z = float(gdb.parse_and_eval('intersection_record.position_.z'))
full_path[depth].hit_point = np.array([hp_x, hp_y, hp_z])
hpn_x = float(gdb.parse_and_eval('intersection_record.normal_.x'))
hpn_y = float(gdb.parse_and_eval('intersection_record.normal_.y'))
hpn_z = float(gdb.parse_and_eval('intersection_record.normal_.z'))
full_path[depth].hit_point_normal = np.array([hpn_x, hpn_y, hpn_z])
l_wo_x = float(gdb.parse_and_eval('local_wo.x'))
l_wo_y = float(gdb.parse_and_eval('local_wo.y'))
l_wo_z = float(gdb.parse_and_eval('local_wo.z'))
full_path[depth].local_wo = np.array([l_wo_x, l_wo_y, l_wo_z])
l_wi_x = float(gdb.parse_and_eval('local_wi.x'))
l_wi_y = float(gdb.parse_and_eval('local_wi.y'))
l_wi_z = float(gdb.parse_and_eval('local_wi.z'))
full_path[depth].local_wi = np.array([l_wi_x, l_wi_y, l_wi_z])
ob_x = float(gdb.parse_and_eval('bsdf.x'))
ob_y = float(gdb.parse_and_eval('bsdf.y'))
ob_z = float(gdb.parse_and_eval('bsdf.z'))
full_path[depth].original_bsdf = np.array([ob_x, ob_y, ob_z])
e_x = float(gdb.parse_and_eval('emission.x'))
e_y = float(gdb.parse_and_eval('emission.y'))
e_z = float(gdb.parse_and_eval('emission.z'))
full_path[depth].emission = np.array([e_x, e_y, e_z])
full_path[depth].returned_radiance = np.array([e_x, e_y, e_z])
full_path[depth].pdf = float(gdb.parse_and_eval('pdf'))
print (" Returning... russian roulette!")
full_path[depth].stop_reason = "russian roulette"
class AfterIntersectionEvaluation(gdb.Breakpoint):
def stop (self):
global tracking_path
global full_path
if (tracking_path == True):
depth = int(gdb.parse_and_eval('depth'))
r_o_x = float(gdb.parse_and_eval('world_ray.origin_.x'))
r_o_y = float(gdb.parse_and_eval('world_ray.origin_.y'))
r_o_z = float(gdb.parse_and_eval('world_ray.origin_.z'))
full_path[depth].world_ray_origin = np.array([r_o_x, r_o_y, r_o_z])
r_d_x = float(gdb.parse_and_eval('world_ray.direction_.x'))
r_d_y = float(gdb.parse_and_eval('world_ray.direction_.y'))
r_d_z = float(gdb.parse_and_eval('world_ray.direction_.z'))
full_path[depth].world_ray_direction = np.array([r_d_x, r_d_y, r_d_z])
hp_x = float(gdb.parse_and_eval('intersection_record.position_.x'))
hp_y = float(gdb.parse_and_eval('intersection_record.position_.y'))
hp_z = float(gdb.parse_and_eval('intersection_record.position_.z'))
full_path[depth].hit_point = np.array([hp_x, hp_y, hp_z])
hpn_x = float(gdb.parse_and_eval('intersection_record.normal_.x'))
hpn_y = float(gdb.parse_and_eval('intersection_record.normal_.y'))
hpn_z = float(gdb.parse_and_eval('intersection_record.normal_.z'))
full_path[depth].hit_point_normal = np.array([hpn_x, hpn_y, hpn_z])
l_wo_x = float(gdb.parse_and_eval('local_wo.x'))
l_wo_y = float(gdb.parse_and_eval('local_wo.y'))
l_wo_z = float(gdb.parse_and_eval('local_wo.z'))
full_path[depth].local_wo = np.array([l_wo_x, l_wo_y, l_wo_z])
l_wi_x = float(gdb.parse_and_eval('local_wi.x'))
l_wi_y = float(gdb.parse_and_eval('local_wi.y'))
l_wi_z = float(gdb.parse_and_eval('local_wi.z'))
full_path[depth].local_wi = np.array([l_wi_x, l_wi_y, l_wi_z])
ab_x = float(gdb.parse_and_eval('bsdf.x'))
ab_y = float(gdb.parse_and_eval('bsdf.y'))
ab_z = float(gdb.parse_and_eval('bsdf.z'))
full_path[depth].adjusted_bsdf = | np.array([ab_x, ab_y, ab_z]) | numpy.array |
#
# This software is licensed under the Apache 2 license, quoted below.
#
# Copyright 2019 Astraea, Inc.
#
# Licensed under the Apache License, Version 2.0 (the "License"); you may not
# use this file except in compliance with the License. You may obtain a copy of
# the License at
#
# [http://www.apache.org/licenses/LICENSE-2.0]
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
# License for the specific language governing permissions and limitations under
# the License.
#
# SPDX-License-Identifier: Apache-2.0
#
from unittest import skip
import pyrasterframes
from pyrasterframes.rasterfunctions import *
from pyrasterframes.rf_types import *
from pyrasterframes.utils import gdal_version
from pyspark import Row
from pyspark.sql.functions import *
import numpy as np
from deprecation import fail_if_not_removed
from numpy.testing import assert_equal, assert_allclose
from . import TestEnvironment
class RasterFunctions(TestEnvironment):
def setUp(self):
import sys
if not sys.warnoptions:
import warnings
warnings.simplefilter("ignore")
self.create_layer()
def test_setup(self):
self.assertEqual(self.spark.sparkContext.getConf().get("spark.serializer"),
"org.apache.spark.serializer.KryoSerializer")
print("GDAL version", gdal_version())
def test_identify_columns(self):
cols = self.rf.tile_columns()
self.assertEqual(len(cols), 1, '`tileColumns` did not find the proper number of columns.')
print("Tile columns: ", cols)
col = self.rf.spatial_key_column()
self.assertIsInstance(col, Column, '`spatialKeyColumn` was not found')
print("Spatial key column: ", col)
col = self.rf.temporal_key_column()
self.assertIsNone(col, '`temporalKeyColumn` should be `None`')
print("Temporal key column: ", col)
def test_tile_creation(self):
from pyrasterframes.rf_types import CellType
base = self.spark.createDataFrame([1, 2, 3, 4], 'integer')
tiles = base.select(rf_make_constant_tile(3, 3, 3, "int32"), rf_make_zeros_tile(3, 3, "int32"),
rf_make_ones_tile(3, 3, CellType.int32()))
tiles.show()
self.assertEqual(tiles.count(), 4)
def test_multi_column_operations(self):
df1 = self.rf.withColumnRenamed('tile', 't1').as_layer()
df2 = self.rf.withColumnRenamed('tile', 't2').as_layer()
df3 = df1.spatial_join(df2).as_layer()
df3 = df3.withColumn('norm_diff', rf_normalized_difference('t1', 't2'))
# df3.printSchema()
aggs = df3.agg(
rf_agg_mean('norm_diff'),
)
aggs.show()
row = aggs.first()
self.assertTrue(self.rounded_compare(row['rf_agg_mean(norm_diff)'], 0))
def test_general(self):
meta = self.rf.tile_layer_metadata()
self.assertIsNotNone(meta['bounds'])
df = self.rf.withColumn('dims', rf_dimensions('tile')) \
.withColumn('type', rf_cell_type('tile')) \
.withColumn('dCells', rf_data_cells('tile')) \
.withColumn('ndCells', rf_no_data_cells('tile')) \
.withColumn('min', rf_tile_min('tile')) \
.withColumn('max', rf_tile_max('tile')) \
.withColumn('mean', rf_tile_mean('tile')) \
.withColumn('sum', rf_tile_sum('tile')) \
.withColumn('stats', rf_tile_stats('tile')) \
.withColumn('extent', st_extent('geometry')) \
.withColumn('extent_geom1', st_geometry('extent')) \
.withColumn('ascii', rf_render_ascii('tile')) \
.withColumn('log', rf_log('tile')) \
.withColumn('exp', rf_exp('tile')) \
.withColumn('expm1', rf_expm1('tile')) \
.withColumn('sqrt', rf_sqrt('tile')) \
.withColumn('round', rf_round('tile')) \
.withColumn('abs', rf_abs('tile'))
df.first()
def test_st_geometry_from_struct(self):
from pyspark.sql import Row
from pyspark.sql.functions import struct
df = self.spark.createDataFrame([Row(xmin=0, ymin=1, xmax=2, ymax=3)])
df2 = df.select(st_geometry(struct(df.xmin, df.ymin, df.xmax, df.ymax)).alias('geom'))
actual_bounds = df2.first()['geom'].bounds
self.assertEqual((0.0, 1.0, 2.0, 3.0), actual_bounds)
def test_agg_mean(self):
mean = self.rf.agg(rf_agg_mean('tile')).first()['rf_agg_mean(tile)']
self.assertTrue(self.rounded_compare(mean, 10160))
def test_agg_local_mean(self):
from pyspark.sql import Row
from pyrasterframes.rf_types import Tile
# this is really testing the nodata propagation in the agg local summation
ct = CellType.int8().with_no_data_value(4)
df = self.spark.createDataFrame([
Row(tile=Tile(np.array([[1, 2, 3, 4, 5, 6]]), ct)),
Row(tile=Tile(np.array([[1, 2, 4, 3, 5, 6]]), ct)),
])
result = df.agg(rf_agg_local_mean('tile').alias('mean')).first().mean
expected = Tile(np.array([[1.0, 2.0, 3.0, 3.0, 5.0, 6.0]]), CellType.float64())
self.assertEqual(result, expected)
def test_aggregations(self):
aggs = self.rf.agg(
rf_agg_data_cells('tile'),
rf_agg_no_data_cells('tile'),
rf_agg_stats('tile'),
rf_agg_approx_histogram('tile')
)
row = aggs.first()
# print(row['rf_agg_data_cells(tile)'])
self.assertEqual(row['rf_agg_data_cells(tile)'], 387000)
self.assertEqual(row['rf_agg_no_data_cells(tile)'], 1000)
self.assertEqual(row['rf_agg_stats(tile)'].data_cells, row['rf_agg_data_cells(tile)'])
@fail_if_not_removed
def test_add_scalar(self):
# Trivial test to trigger the deprecation failure at the right time.
result: Row = self.rf.select(rf_local_add_double('tile', 99.9), rf_local_add_int('tile', 42)).first()
self.assertTrue(True)
def test_agg_approx_quantiles(self):
agg = self.rf.agg(rf_agg_approx_quantiles('tile', [0.1, 0.5, 0.9, 0.98]))
result = agg.first()[0]
# expected result from computing in external python process; c.f. scala tests
assert_allclose(result, np.array([7963., 10068., 12160., 14366.]))
def test_sql(self):
self.rf.createOrReplaceTempView("rf_test_sql")
arith = self.spark.sql("""SELECT tile,
rf_local_add(tile, 1) AS add_one,
rf_local_subtract(tile, 1) AS less_one,
rf_local_multiply(tile, 2) AS times_two,
rf_local_divide(
rf_convert_cell_type(tile, "float32"),
2) AS over_two
FROM rf_test_sql""")
arith.createOrReplaceTempView('rf_test_sql_1')
arith.show(truncate=False)
stats = self.spark.sql("""
SELECT rf_tile_mean(tile) as base,
rf_tile_mean(add_one) as plus_one,
rf_tile_mean(less_one) as minus_one,
rf_tile_mean(times_two) as double,
rf_tile_mean(over_two) as half,
rf_no_data_cells(tile) as nd
FROM rf_test_sql_1
ORDER BY rf_no_data_cells(tile)
""")
stats.show(truncate=False)
stats.createOrReplaceTempView('rf_test_sql_stats')
compare = self.spark.sql("""
SELECT
plus_one - 1.0 = base as add,
minus_one + 1.0 = base as subtract,
double / 2.0 = base as multiply,
half * 2.0 = base as divide,
nd
FROM rf_test_sql_stats
""")
expect_row1 = compare.orderBy('nd').first()
self.assertTrue(expect_row1.subtract)
self.assertTrue(expect_row1.multiply)
self.assertTrue(expect_row1.divide)
self.assertEqual(expect_row1.nd, 0)
self.assertTrue(expect_row1.add)
expect_row2 = compare.orderBy('nd', ascending=False).first()
self.assertTrue(expect_row2.subtract)
self.assertTrue(expect_row2.multiply)
self.assertTrue(expect_row2.divide)
self.assertTrue(expect_row2.nd > 0)
self.assertTrue(expect_row2.add) # <-- Would fail in a case where ND + 1 = 1
def test_explode(self):
import pyspark.sql.functions as F
self.rf.select('spatial_key', rf_explode_tiles('tile')).show()
# +-----------+------------+---------+-------+
# |spatial_key|column_index|row_index|tile |
# +-----------+------------+---------+-------+
# |[2,1] |4 |0 |10150.0|
cell = self.rf.select(self.rf.spatial_key_column(), rf_explode_tiles(self.rf.tile)) \
.where(F.col("spatial_key.col") == 2) \
.where(F.col("spatial_key.row") == 1) \
.where(F.col("column_index") == 4) \
.where(F.col("row_index") == 0) \
.select(F.col("tile")) \
.collect()[0][0]
self.assertEqual(cell, 10150.0)
# Test the sample version
frac = 0.01
sample_count = self.rf.select(rf_explode_tiles_sample(frac, 1872, 'tile')).count()
print('Sample count is {}'.format(sample_count))
self.assertTrue(sample_count > 0)
self.assertTrue(sample_count < (frac * 1.1) * 387000) # give some wiggle room
def test_mask_by_value(self):
from pyspark.sql.functions import lit
# create an artificial mask for values > 25000; masking value will be 4
mask_value = 4
rf1 = self.rf.select(self.rf.tile,
rf_local_multiply(
rf_convert_cell_type(
rf_local_greater(self.rf.tile, 25000),
"uint8"),
lit(mask_value)).alias('mask'))
rf2 = rf1.select(rf1.tile, rf_mask_by_value(rf1.tile, rf1.mask, lit(mask_value), False).alias('masked'))
result = rf2.agg(rf_agg_no_data_cells(rf2.tile) < rf_agg_no_data_cells(rf2.masked)) \
.collect()[0][0]
self.assertTrue(result)
# note supplying a `int` here, not a column to mask value
rf3 = rf1.select(
rf1.tile,
rf_inverse_mask_by_value(rf1.tile, rf1.mask, mask_value).alias('masked'),
rf_mask_by_value(rf1.tile, rf1.mask, mask_value, True).alias('masked2'),
)
result = rf3.agg(
rf_agg_no_data_cells(rf3.tile) < rf_agg_no_data_cells(rf3.masked),
rf_agg_no_data_cells(rf3.tile) < rf_agg_no_data_cells(rf3.masked2),
) \
.first()
self.assertTrue(result[0])
self.assertTrue(result[1]) # inverse mask arg gives equivalent result
result_equiv_tiles = rf3.select(rf_for_all(rf_local_equal(rf3.masked, rf3.masked2))).first()[0]
self.assertTrue(result_equiv_tiles) # inverse fn and inverse arg produce same Tile
def test_mask_by_values(self):
tile = Tile(np.random.randint(1, 100, (5, 5)), CellType.uint8())
mask_tile = Tile(np.array(range(1, 26), 'uint8').reshape(5, 5))
expected_diag_nd = Tile(np.ma.masked_array(tile.cells, mask=np.eye(5)))
df = self.spark.createDataFrame([Row(t=tile, m=mask_tile)]) \
.select(rf_mask_by_values('t', 'm', [0, 6, 12, 18, 24])) # values on the diagonal
result0 = df.first()
# assert_equal(result0[0].cells, expected_diag_nd)
self.assertTrue(result0[0] == expected_diag_nd)
def test_mask_bits(self):
t = Tile(42 * np.ones((4, 4), 'uint16'), CellType.uint16())
# with a varitey of known values
mask = Tile(np.array([
[1, 1, 2720, 2720],
[1, 6816, 6816, 2756],
[2720, 2720, 6900, 2720],
[2720, 6900, 6816, 1]
]), CellType('uint16raw'))
df = self.spark.createDataFrame([Row(t=t, mask=mask)])
# removes fill value 1
mask_fill_df = df.select(rf_mask_by_bit('t', 'mask', 0, True).alias('mbb'))
mask_fill_tile = mask_fill_df.first()['mbb']
self.assertTrue(mask_fill_tile.cell_type.has_no_data())
self.assertTrue(
mask_fill_df.select(rf_data_cells('mbb')).first()[0],
16 - 4
)
# mask out 6816, 6900
mask_med_hi_cir = df.withColumn('mask_cir_mh',
rf_mask_by_bits('t', 'mask', 11, 2, [2, 3])) \
.first()['mask_cir_mh'].cells
self.assertEqual(
mask_med_hi_cir.mask.sum(),
5
)
@skip('Issue #422 https://github.com/locationtech/rasterframes/issues/422')
def test_mask_and_deser(self):
# duplicates much of test_mask_bits but
t = Tile(42 * np.ones((4, 4), 'uint16'), CellType.uint16())
# with a varitey of known values
mask = Tile(np.array([
[1, 1, 2720, 2720],
[1, 6816, 6816, 2756],
[2720, 2720, 6900, 2720],
[2720, 6900, 6816, 1]
]), CellType('uint16raw'))
df = self.spark.createDataFrame([Row(t=t, mask=mask)])
# removes fill value 1
mask_fill_df = df.select(rf_mask_by_bit('t', 'mask', 0, True).alias('mbb'))
mask_fill_tile = mask_fill_df.first()['mbb']
self.assertTrue(mask_fill_tile.cell_type.has_no_data())
# Unsure why this fails. mask_fill_tile.cells is all 42 unmasked.
self.assertEqual(mask_fill_tile.cells.mask.sum(), 4,
f'Expected {16 - 4} data values but got the masked tile:'
f'{mask_fill_tile}'
)
def test_mask(self):
from pyspark.sql import Row
from pyrasterframes.rf_types import Tile, CellType
np.random.seed(999)
# importantly exclude 0 from teh range because that's the nodata value for the `data_tile`'s cell type
ma = np.ma.array(np.random.randint(1, 10, (5, 5), dtype='int8'), mask=np.random.rand(5, 5) > 0.7)
expected_data_values = ma.compressed().size
expected_no_data_values = ma.size - expected_data_values
self.assertTrue(expected_data_values > 0, "Make sure random seed is cooperative ")
self.assertTrue(expected_no_data_values > 0, "Make sure random seed is cooperative ")
data_tile = Tile( | np.ones(ma.shape, ma.dtype) | numpy.ones |
import os,sys
import bpy
import numpy as np
from random import randint
from random import random
from random import gauss
from random import uniform
from random import choice as Rchoice
from random import sample
import cv2
import yaml
import itertools
from math import radians,degrees,tan,cos
from numpy.linalg import inv
# visible vertices
import bmesh
from mathutils import Vector
from bpy_extras.object_utils import world_to_camera_view
ply_header = '''ply
format ascii 1.0
element vertex %(vert_num)d
property float x
property float y
property float z
property uchar red
property uchar green
property uchar blue
end_header
'''
pcd_header = '''VERSION 0.7
FIELDS x y z rgb
SIZE 4 4 4 4
TYPE F F F F
COUNT 1 1 1 1
WIDTH 640
HEIGHT 480
VIEWPOINT 0 0 0 1 0 0 0
POINTS 307200
DATA ascii
'''
#Height : 480 for kinect, 512 for ensenso
#Points : 307200 for kinect, 327680 for ensenso
# tless: 720x540
def getVerticesVisible(obj):
scene = bpy.context.scene
cam = bpy.data.objects['cam_R']
mesh = obj.data
mat_world = obj.matrix_world
cs, ce = cam.data.clip_start, cam.data.clip_end
# edit mode to edit meshes
scene.objects.active = obj
bpy.ops.object.mode_set(mode='EDIT')
#bpy.ops.mesh.remove_doubles(threshold=0.0001)
bm = bmesh.from_edit_mesh(mesh)
limit = 0.1
#vertices = [mat_world * v.co for v in obj.data.vertices]
#for i, v in enumerate( vertices ):
for v in bm.verts:
v.select = True # need it for vertices hidden in last iteration
vec = mat_world * v.co
co_ndc = world_to_camera_view(scene, cam, vec)
#co_ndc = world_to_camera_view(scene, cam, v)
#check wether point is inside frustum
#if (0.0 < co_ndc.x < 1.0 and
# 0.0 < co_ndc.y < 1.0 and
# cs < co_ndc.z < ce):
# ray_cast if point is visible
# results, obj, mat, location, normal = scene.ray_cast(cam.location, (vec - cam.location).normalized() )
# if location and (vec - location).length < limit:
# v.select = False
# else:
# v.select = True
#else:
# v.select = True
# limit selection to visible from certain camera view
#bpy.ops.mesh.hide(unselected=False)
#bmesh.update_edit_mesh(mesh, False, False)
bpy.ops.object.mode_set(mode='OBJECT')
def getVisibleBoundingBox(objectPassIndex):
S = bpy.context.scene
width = int( S.render.resolution_x * S.render.resolution_percentage / 100 )
height = int( S.render.resolution_y * S.render.resolution_percentage / 100 )
depth = 4
pixels = np.array( bpy.data.images['Render Result'].pixels[:] ).reshape( [height, width, depth] )
# Keep only one value for each pixel (white pixels have 1 in all RGBA channels anyway), thus converting the image to black and white
pixels = np.array( [ [ pixel[0] for pixel in row ] for row in pixels ] )
bbox = np.argwhere( pixels == objectPassIndex )
(ystart, xstart), (ystop, xstop) = bbox.min(0), bbox.max(0) + 1
bb = (xstart, xstart, height - ystart, height - ystop)
return bb, bbox
# 23.4.2018
# render image 350 of object 23
# cam_K: [1076.74064739, 0.0, 215.98264967, 0.0, 1075.17825536, 204.59181836, 0.0, 0.0, 1.0]
# depth_scale: 0.1
# elev: 45
# mode: 0
# cam_R_m2c: [0.62268218, -0.78164004, -0.03612308, -0.56354950, -0.41595975, -0.71371609, 0.54284357, 0.46477486, -0.69950372]
# cam_t_m2c: [-9.10674129, -2.47862668, 634.81667094]
# obj_bb: [120, 121, 197, 190]
# obj_id: 23
# f = 580
# b = 0.0075
base_dir = "/home/stefan/data/MMAssist/Fronius_UC_092018/CAD_models/CAD_models_processed"
back_dir = "/home/stefan/data/CAD_stl/many"
total_set = 1 #10000 set of scenes, each set has identical objects with varied poses to anchor pose (+-15)
pair_set = 1 #number of pair scene for each set, 10
sample_dir = '/home/stefan/data/rendered_data/fronius20' #directory for temporary files (cam_L, cam_R, masks..~)
target_dir = '/home/stefan/data/rendered_data/fronius20/patches'
index=0
isfile=True
while isfile:
prefix='{:08}_'.format(index)
if(os.path.exists(os.path.join(target_dir,prefix+'gt.yaml'))):
index+=1
else:
isfile=False
#create dir if not exist
#if not(os.path.exists(target_dir+"/disp")):
# os.makedirs(target_dir+"/disp")
if not(os.path.exists(target_dir+"/depth")):
os.makedirs(target_dir+"/depth")
if not(os.path.exists(target_dir+"/mask")):
os.makedirs(target_dir+"/mask")
if not(os.path.exists(target_dir+"/part")):
os.makedirs(target_dir+"/part")
model_file=[]
model_solo=[]
for root, dirs, files in os.walk(base_dir):
for file in sorted(files):
if file.endswith(".STL"):
temp_fn =os.path.join(root, file)
model_file.append(temp_fn)
model_solo.append(file)
#print(len(model_file),temp_fn)
print(model_file)
# FOR BACKGROUND OBJECTS
back_file=[]
back_solo=[]
for rootb, dirsb, filesb in os.walk(back_dir):
for file in sorted(filesb):
if file.endswith(".stl"):
temp_fn =os.path.join(rootb, file)
back_file.append(temp_fn)
back_solo.append(file)
#print(len(model_file),temp_fn)
# FOR BACKGROUND OBJECTS
for num_set in np.arange(0, total_set):
bpy.ops.object.select_all(action='DESELECT')
#scene = bpy.context.scene # blender < 2.8
scene = bpy.context.view_layer
bpy.context.view_layer.objects.active = bpy.data.objects["template"]
#scene.objects.active = bpy.data.objects["template"]
for obj in scene.objects:
if obj.type == 'MESH':
if obj.name == 'template':
obj.select_set(False)
elif obj.name == 'Desk':
obj.select_set(False)
elif obj.name[0:5] == 'Plane':
obj.select_set(False)
elif obj.name == 'Plane':
obj.select_set(False)
elif obj.name == 'InvisibleCube':
obj.select_set(False)
elif obj.name == 'Laptop':
obj.select_set(False)
elif obj.name == 'Screen':
obj.select_set(False)
elif obj.name[0:7] == 'Speaker':
obj.select_set(False)
elif obj.name == 'Mouse':
obj.select_set(False)
elif obj.name == 'Keyboard':
obj.select_set(False)
elif obj.name == 'Lamp1':
obj.select_set(False)
elif obj.name == 'Monitor2':
obj.select_set(False)
elif obj.name == 'Pot':
obj.select_set(False)
elif obj.name == 'Potplant':
obj.select_set(False)
elif obj.name == 'Basket':
obj.select_set(False)
else:
obj.select_set(True)
bpy.ops.object.delete()
bpy.ops.object.select_all(action='DESELECT')
obj_object = bpy.data.objects["template"]
obj_object.pass_index = 1
mat = obj_object.active_material
# FOR BACKGROUND OBJECTS
#drawBack = list(range(10,12))
#freqBack= np.bincount(drawBack)
#BackDraw = np.random.choice(np.arange(len(freqBack)), 1, p=freqBack / len(drawBack), replace=False)
#BackObj = list(range(1,len(back_file)))
#BackfreqObj = np.bincount(BackObj)
#BackObjDraw = np.random.choice(np.arange(len(BackfreqObj)), BackDraw, p=BackfreqObj / len(BackObj), replace=True)
#Back_object = np.asscalar(BackDraw)
Back_object = 16
#real deal here
#drawAmo = list(range(4,8))
#freqAmo = np.bincount(drawAmo)
#AmoDraw = np.random.choice(np.arange(len(freqAmo)), 1, p=freqAmo / len(drawAmo), replace=False)
#drawObj = list(range(1,len(model_file)))
#freqObj = np.bincount(drawObj)
#ObjDraw = np.random.choice(np.arange(len(freqObj)), AmoDraw, p=freqObj / len(drawObj), replace=True)
#num_object = np.asscalar(AmoDraw)
num_object = 8
object_label =[]
anchor_pose = np.zeros(((Back_object + num_object),6)) #location x,y,z, euler x,y,z
# real deal here
posesCh = [[0.3, 0.3], [0.3, 0.0], [0.3, -0.3],
[-0.3, 0.3], [-0.3, 0.0], [-0.3, -0.3],
[0.0, 0.3], [0.0, 0.0], [0.0, -0.3]]
posesSam = [[0.6, 0.6], [0.6, 0.3], [0.6, 0.0], [0.6, -0.3], [0.6, -0.6],
[-0.3, 0.6], [0.0, 0.6], [0.3, 0.6],
[-0.3, -0.6], [0.0, -0.6], [0.3, -0.6],
[-0.6, 0.6], [-0.6, 0.3], [-0.6, 0.0], [-0.6, -0.3], [-0.6, -0.6]]
idxF= list(range(len(model_file)))
print(idxF)
for i in np.arange(num_object):
#file_idx = randint(0,len(model_file)-1)
file_idx = Rchoice(idxF)
file_model = model_file[file_idx]
solo_model = model_solo[file_idx]
imported_object = bpy.ops.import_mesh.stl(filepath=file_model, filter_glob="*.stl", files=[{"name":solo_model, "name":solo_model}], directory=root)
#imported_object = bpy.ops.import_mesh.ply(filepath=file_model, filter_glob="*.ply", files=[{"name":solo_model, "name":solo_model}], directory=root)
object_label.append(file_idx)
obj_object = bpy.context.selected_objects[0]
obj_object.active_material = mat
obj_object.pass_index = i +2 # don't add?
choice = sample(posesCh, 1)
anchor_pose[i,0] = choice[0][0]
anchor_pose[i,1] = choice[0][1]
posesCh.remove(choice[0])
anchor_pose[i,2] = 0.1 + random()*0.2
anchor_pose[i,3] = 0.0
anchor_pose[i,4] = 0.0
anchor_pose[i,5] =radians(random()*360.0)
idxF.remove(file_idx)
#anchor_pose[i+1,0] = random()-0.5
#anchor_pose[i+1,1] = random()*0.5-0.25
#anchor_pose[i+1,2] = 0.1 + random()*0.2
#anchor_pose[i+1,3] =radians(random()*360.0) #0-360 degree
#anchor_pose[i+1,4] =radians(random()*360.0)
#anchor_pose[i,3] = 0.0
#anchor_pose[i,4] = 0.0
#anchor_pose[i+1,5] =radians(random()*360.0)
print("FOREGROUND IMPORTED")
# Background objects
for i in np.arange(Back_object):
file_idx = randint(0,len(back_file)-1)
file_model = back_file[file_idx]
solo_model = back_solo[file_idx]
imported_object = bpy.ops.import_mesh.stl(filepath=file_model, filter_glob="*.stl", files=[{"name":solo_model, "name":solo_model}], directory=rootb)
#imported_object = bpy.ops.import_mesh.ply(filepath=file_model, filter_glob="*.ply", files=[{"name":solo_model, "name":solo_model}], directory=root)
object_label.append(file_idx + num_object)
obj_object = bpy.context.selected_objects[0]
obj_object.active_material = mat
obj_object.pass_index = i+ num_object+2
#draw = uniform(-1, 1)*0.4
#if draw < 0:
# anchor_pose[i+num_object+1,0] = - 0.35 + draw
#else:
# anchor_pose[i+num_object+1,0] = 0.35 + draw
#draw = uniform(-1, 1) * 0.2
#if draw < 0:
# anchor_pose[i+num_object+1,1] = draw
#else:
# anchor_pose[i+num_object+1,1] = 0.25 + draw
#anchor_pose[i+num_object+1,2] =0.3 + 0.2*float(i)
##anchor_pose[i,2] = 0.1 + random()*0.2
#anchor_pose[i+num_object+1,3] =radians(random()*360.0) #0-360 degree
#anchor_pose[i+num_object+1,4] =radians(random()*360.0)
#anchor_pose[i+num_object+1,5] =radians(random()*360.0)
choice = sample(posesSam, 1)
anchor_pose[i+num_object,0] = choice[0][0]
anchor_pose[i+num_object,1] = choice[0][1]
posesSam.remove(choice[0])
anchor_pose[i+num_object,2] =0.1 + 0.2*float(i)
#anchor_pose[i,2] = 0.1 + random()*0.2
anchor_pose[i+num_object,3] =radians(random()*360.0) #0-360 degree
anchor_pose[i+num_object,4] =radians(random()*360.0)
anchor_pose[i+num_object,5] =radians(random()*360.0)
# FOR BACKGROUND OBJECTS
print("BACKGROUND IMPORTED")
#Set object physics
#scene = bpy.context.scene # blender < 2.8
scene = bpy.context.view_layer
bpy.context.view_layer.objects.active = bpy.data.objects["template"]
#scene.objects.active = bpy.data.objects["template"]
for obj in scene.objects:
if obj.type == 'MESH':
if obj.name == 'template':
obj.select_set(False)
elif obj.name == 'Desk':
obj.select_set(False)
elif obj.name[0:5] == 'Plane':
obj.select_set(False)
elif obj.name == 'Plane':
obj.select_set(False)
elif obj.name == 'InvisibleCube':
obj.select_set(False)
elif obj.name == 'Laptop':
obj.select_set(False)
elif obj.name == 'Screen':
obj.select_set(False)
elif obj.name[0:7] == 'Speaker':
obj.select_set(False)
elif obj.name == 'Mouse':
obj.select_set(False)
elif obj.name == 'Keyboard':
obj.select_set(False)
elif obj.name == 'Lamp1':
obj.select_set(False)
elif obj.name == 'Monitor2':
obj.select_set(False)
elif obj.name == 'Pot':
obj.select_set(False)
elif obj.name == 'Potplant':
obj.select_set(False)
elif obj.name == 'Basket':
obj.select_set(False)
else:
obj.select_set(True)
print("BACKGROUND objects set to inactive for physics")
bpy.ops.rigidbody.object_settings_copy()
scene = bpy.context.scene
#Define Object position&rotation
for iii in np.arange(pair_set):
scene.frame_set(0)
for obj in scene.objects:
if obj.type == 'MESH':
obj_object= bpy.data.objects[obj.name]
if obj_object.pass_index>1 and obj_object.pass_index <= (num_object+1):
idx = obj_object.pass_index -2
obj_object.location.x=anchor_pose[idx,0]
obj_object.location.y=anchor_pose[idx,1]
obj_object.location.z=anchor_pose[idx,2]
#obj_object.rotation_euler.x= radians(random()*360.0) #anchor_pose[idx,3] + radians(random()*30.0-15.0)
#obj_object.rotation_euler.y= radians(random()*360.0) #anchor_pose[idx,4] + radians(random()*30.0-15.0)
obj_object.rotation_euler.x= radians(random()*360.0)
obj_object.rotation_euler.y= radians(random()*360.0)
obj_object.rotation_euler.z= radians(random()*360.0)
shape_rnd = np.random.random_integers(0,1)
if shape_rnd == 0:
obj_object.rigid_body.collision_shape = 'SPHERE'
else:
obj_object.rigid_body.collision_shape = 'CONVEX_HULL'
# assign different color
#rand_color = (random(), random(), random()) # blender < 2.8
rand_color = (random(), random(), random(), random())
obj_object.active_material.diffuse_color = rand_color
if obj_object.pass_index > (num_object + 1):
obj_object.pass_index = 0
if obj_object.pass_index > (num_object+1):
idx = obj_object.pass_index -2
obj_object.location.x=anchor_pose[idx,0]
obj_object.location.y=anchor_pose[idx,1]
obj_object.location.z=anchor_pose[idx,2]
obj_object.rotation_euler.x= radians(random()*360.0) #anchor_pose[idx,3] + radians(random()*30.0-15.0)
obj_object.rotation_euler.y= radians(random()*360.0) #anchor_pose[idx,4] + radians(random()*30.0-15.0)
obj_object.rotation_euler.z= radians(random()*360.0)
# assign different color
#rand_color = (random(), random(), random()) # blender < 2.8
rand_color = (random(), random(), random(), random())
obj_object.active_material.diffuse_color = rand_color
if obj_object.pass_index > (num_object + 1):
obj_object.pass_index = 0
if obj.name == 'InvisibleCube':
obj_object.rotation_euler.x=radians(random()*62.5+10.0) #0~90
#obj_object.rotation_euler.y=radians(random()*90.0-45.0) #-45-45
obj_object.rotation_euler.y = 0.0
#obj_object.rotation_euler.z=radians(75.0 - random()*150.0) #0-360
obj_object.rotation_euler.z=radians(15.0-random()*30.0)
if obj.type == 'CAMERA' and obj.name=='cam_L':
obj_object = bpy.data.objects[obj.name]
obj_object.location.z = random()*0.3+1.0 #1.0-2.5
print("start running physics")
#Run physics
count = 60
scene.frame_start = 1
scene.frame_end = count + 1
print("Start physics")
for f in range(1,scene.frame_end+1):
print("scene iteration: ", f, "/60")
scene.frame_set(f)
if f <= 1:
continue
#print("pyshics ran")
tree = bpy.context.scene.node_tree
nodes = tree.nodes
print("render images")
#When Rander cam_L, render mask together
prefix='{:08}_'.format(index)
index+=1
# render individual object mask
scene = bpy.context.view_layer
bpy.context.view_layer.objects.active = bpy.data.objects["template"]
#scene.objects.active = bpy.data.objects["template"]
for obj in scene.objects:
if obj.type == 'MESH':
if obj.name == 'template':
obj.select_set(False)
elif obj.name == 'Desk':
obj.select_set(False)
elif obj.name[0:5] == 'Plane':
obj.select_set(False)
elif obj.name == 'Plane':
obj.select_set(False)
elif obj.name == 'InvisibleCube':
obj.select_set(False)
elif obj.name == 'Laptop':
obj.select_set(False)
elif obj.name == 'Screen':
obj.select_set(False)
elif obj.name[0:7] == 'Speaker':
obj.select_set(False)
elif obj.name == 'Mouse':
obj.select_set(False)
elif obj.name == 'Keyboard':
obj.select_set(False)
elif obj.name == 'Lamp1':
obj.select_set(False)
elif obj.name == 'Monitor2':
obj.select_set(False)
elif obj.name == 'Pot':
obj.select_set(False)
elif obj.name == 'Potplant':
obj.select_set(False)
elif obj.name == 'Basket':
obj.select_set(False)
else:
obj.select_set(True)
# individual visibility mask intermezzo
ind_obj_counter = 0
scene = bpy.context.scene
scene.cycles.samples=1
for nr, obj in enumerate(bpy.context.selected_objects):
for ijui9, o_hide in enumerate(bpy.context.selected_objects):
o_hide.hide_render = True
if obj.pass_index>1 and obj.pass_index <= (num_object+1):
obj.hide_render = False
img_name = obj.name + '.png'
ind_mask_file = os.path.join(sample_dir, img_name)
for ob in scene.objects:
if ob.type == 'CAMERA':
if ob.name=='cam_L': #ob.name =='mask':
#Render IR image and Mask
print('Render individual mask for objects: ', obj.name)
bpy.context.scene.camera = ob
file_L = os.path.join(sample_dir , ob.name )
img_name = str(ind_obj_counter) + '.png'
auto_file = os.path.join(sample_dir, ob.name+'0061.png')
node= nodes['maskout']
node.file_slots[0].path = ob.name
node_mix = nodes['ColorRamp']
link_mask= tree.links.new(node_mix.outputs["Image"], node.inputs[0])
node.base_path=sample_dir
scene.render.filepath = file_L
bpy.ops.render.render( write_still=False )
os.rename(auto_file, ind_mask_file)
tree.links.remove(link_mask)
ind_obj_counter += 1
for ijui9, o_hide in enumerate(bpy.context.selected_objects):
o_hide.hide_render = False
scene.cycles.samples=20
# individual visibility mask intermezzo
maskfile = os.path.join(target_dir+'/mask' , 'mask.png')
depthfile = os.path.join(target_dir+'/depth', prefix+'depth.exr')
partfile= os.path.join(target_dir+"/part", prefix+'part.png')
#for ob in scene.objects:
# if ob.type == 'MESH':
# if ob.name == 'InvisibleCube' or ob.name == 'template':
# continue
# obj_object= bpy.data.objects[ob.name]
# #if obj_object.pass_index>1:
# print("starting visibilty check for: ")
# print(ob)
# getVerticesVisible(ob)
for ob in scene.objects:
if ob.type == 'CAMERA':
if ob.name=='cam_L': #ob.name =='mask':
#Render IR image and Mask
bpy.context.scene.camera = ob
print('Set camera %s for IR' % ob.name )
file_L = os.path.join(sample_dir , ob.name )
auto_file = os.path.join(sample_dir, ob.name+'0061.png')
node= nodes['maskout']
node.file_slots[0].path = ob.name
node_mix = nodes['ColorRamp']
link_mask= tree.links.new(node_mix.outputs["Image"], node.inputs[0])
node.base_path=sample_dir
auto_file_depth = os.path.join(sample_dir+'/temp/', ob.name+'0061.exr')
node= nodes['depthout']
node.file_slots[0].path = ob.name
node_mix = nodes['Render Layers']
#link_depth = tree.links.new(node_mix.outputs["Z"], node.inputs[0])
link_depth = tree.links.new(node_mix.outputs["Depth"], node.inputs[0])
node.base_path=sample_dir+'/temp/'
auto_file_part = os.path.join(sample_dir+'/temp/', ob.name+'0061.png')
node= nodes['rgbout']
node.file_slots[0].path = ob.name
node_mix = nodes['Render Layers']
#link_part = tree.links.new(node_mix.outputs["Diffuse Color"], node.inputs[0])
link_part = tree.links.new(node_mix.outputs["DiffCol"], node.inputs[0])
link_part = tree.links.new(node_mix.outputs["Image"], node.inputs[0])
node.base_path=sample_dir+'/temp/'
scene.render.filepath = file_L
bpy.ops.render.render( write_still=True )
tree.links.remove(link_mask)
tree.links.remove(link_depth)
tree.links.remove(link_part)
os.rename(auto_file, maskfile)
os.rename(auto_file_depth, depthfile)
os.rename(auto_file_part, partfile)
mask = cv2.imread(maskfile)
minmax_vu = np.zeros((num_object,4),dtype=np.int) #min v, min u, max v, max u
label_vu = np.zeros((mask.shape[0],mask.shape[1]),dtype=np.int8) #min v, min u, max v, max u
colors = np.zeros((num_object,3),dtype=mask.dtype)
n_label=0
color_index=np.array([ [ 0, 0, 0],
[ 0, 100, 0],
[ 0, 139, 0],
[ 0, 167, 0],
[ 0, 190, 0],
[ 0, 210, 0],
[ 0, 228, 0],
[ 0, 244, 0],
[ 0, 252, 50],
[ 0, 236, 112],
[ 0, 220, 147],
[ 0, 201, 173],
[ 0, 179, 196],
[ 0, 154, 215],
[ 0, 122, 232],
[ 0, 72, 248],
[ 72, 0, 248],
[122, 0, 232],
[154, 0, 215],
[179, 0, 196],
[201, 0, 173],
[220, 0, 147],
[236, 0, 112],
[252, 0, 50],
[255, 87, 87],
[255, 131, 131],
[255, 161, 161],
[255, 185, 185],
[255, 206, 206],
[255, 224, 224],
[255, 240, 240],
[255, 255, 255]])
for v in np.arange(mask.shape[0]):
for u in np.arange(mask.shape[1]):
has_color = False
if not(mask[v,u,0] ==0 and mask[v,u,1] ==0 and mask[v,u,2] ==0):
for ob_index in np.arange(n_label):
if colors[ob_index,0]== mask[v,u,0] and colors[ob_index,1]== mask[v,u,1] and colors[ob_index,2]== mask[v,u,2]:
has_color = True
minmax_vu[ob_index,0] = min(minmax_vu[ob_index,0], v)
minmax_vu[ob_index,1] = min(minmax_vu[ob_index,1], u)
minmax_vu[ob_index,2] = max(minmax_vu[ob_index,2], v)
minmax_vu[ob_index,3] = max(minmax_vu[ob_index,3], u)
label_vu[v,u]=ob_index+1
continue
if has_color ==False: #new label
colors[n_label] = mask[v,u]
label_vu[v,u]=n_label+1 #identical to object_index in blender
minmax_vu[n_label,0] = v
minmax_vu[n_label,1] = u
minmax_vu[n_label,2] = v
minmax_vu[n_label,3] = u
n_label=n_label+1
else:
label_vu[v,u]=0
bbox_refined = mask
color_map= | np.zeros(n_label) | numpy.zeros |
import numpy as np
from menpo.transform import Rotation, Translation
from menpo3d.camera import PerspectiveProjection, PerspectiveCamera
# For now we mirror these here - should migrate to menpo conv. constructors
# after https://github.com/menpo/menpo/pull/777 comes in.
def rotation_from_3d_ccw_angle_around_y(theta, degrees=True):
r"""
Convenience constructor for 3D CCW rotations around the y axis
Parameters
----------
theta : `float`
The angle of rotation about the origin
degrees : `bool`, optional
If ``True`` theta is interpreted as a degree. If ``False``, theta is
interpreted as radians.
Returns
-------
rotation : :map:`Rotation`
A 3D rotation transform.
"""
if degrees:
# convert to radians
theta = theta * np.pi / 180.0
return Rotation(np.array([[np.cos(theta), 0, np.sin(theta)],
[0, 1, 0],
[-np.sin(theta), 0, np.cos(theta)]]),
skip_checks=True)
def rotation_from_3d_ccw_angle_around_z(theta, degrees=True):
r"""
Convenience constructor for 3D CCW rotations around the z axis
Parameters
----------
theta : `float`
The angle of rotation about the origin
degrees : `bool`, optional
If ``True`` theta is interpreted as a degree. If ``False``, theta is
interpreted as radians.
Returns
-------
rotation : :map:`Rotation`
A 3D rotation transform.
"""
if degrees:
# convert to radians
theta = theta * np.pi / 180.0
return Rotation(np.array([[ | np.cos(theta) | numpy.cos |
# You are at the top. If you attempt to go any higher
# you will go beyond the known limits of the code
# universe where there are most certainly monsters
# might be able to get a speedup where I'm appending move and -move
# to do:
# use point raycaster to make a cloth_wrap option
# self colisions
# maybe do dynamic margins for when cloth is moving fast
# object collisions
# collisions need to properly exclude pinned and vertex pinned
# add bending springs
# add curl by shortening bending springs on one axis or diagonal
# independantly scale bending springs and structural to create buckling
# option to cache animation?
# Custom Source shape option for animated shapes
# collisions:
# Only need to check one of the edges for groups connected to a vertex
# for edge to face intersections...
# figure out where the edge hit the face
# figure out which end of the edge is inside the face
# move along the face normal to the surface for the point inside.
# if I reflect by flipping the vel around the face normal
# if it collides on the bounce it will get caught on the next iteration
# Sewing
# Could create super sewing that doesn't use edges but uses scalars along the edge to place virtual points
# sort of a barycentric virtual spring. Could even use it to sew to faces if I can think of a ui for where on the face.
# On an all triangle mesh, where sew edges come together there are long strait lines. This probably causes those edges to fold.
# in other words... creating diagonal springs between these edges will not solve the fold problem. Bend spring could do this.
# Bend springs:
# need to speed things up
# When faces have various sizes, the forces don't add up
# self collision
# where points are pinned, stuff is all jittery
'''??? Would it make sense to do self collisions with virtual edges ???'''
'''??? Could do dynamic collision margins for stuff moving fast ???'''
bl_info = {
"name": "Modeling Cloth",
"author": "<NAME> (<EMAIL>.com), <NAME> (@ucupumar)",
"version": (1, 0),
"blender": (2, 79, 0),
"location": "View3D > Extended Tools > Modeling Cloth",
"description": "Maintains the surface area of an object so it behaves like cloth",
"warning": "There might be an angry rhinoceros behind you",
"wiki_url": "",
"category": '3D View'}
import bpy
import bmesh
import numpy as np
from numpy import newaxis as nax
from bpy_extras import view3d_utils
from bpy.props import *
from bpy.app.handlers import persistent
from mathutils import *
import time, sys
#enable_numexpr = True
enable_numexpr = False
if enable_numexpr:
import numexpr as ne
you_have_a_sense_of_humor = False
#you_have_a_sense_of_humor = True
if you_have_a_sense_of_humor:
import antigravity
def get_co(ob, arr=None, key=None): # key
"""Returns vertex coords as N x 3"""
c = len(ob.data.vertices)
if arr is None:
arr = np.zeros(c * 3, dtype=np.float32)
if key is not None:
ob.data.shape_keys.key_blocks[key].data.foreach_get('co', arr.ravel())
arr.shape = (c, 3)
return arr
ob.data.vertices.foreach_get('co', arr.ravel())
arr.shape = (c, 3)
return arr
def get_proxy_co(ob, arr, me):
"""Returns vertex coords with modifier effects as N x 3"""
if arr is None:
arr = np.zeros(len(me.vertices) * 3, dtype=np.float32)
arr.shape = (arr.shape[0] //3, 3)
c = arr.shape[0]
me.vertices.foreach_get('co', arr.ravel())
arr.shape = (c, 3)
return arr
def triangulate(me, ob=None):
"""Requires a mesh. Returns an index array for viewing co as triangles"""
obm = bmesh.new()
obm.from_mesh(me)
bmesh.ops.triangulate(obm, faces=obm.faces)
#obm.to_mesh(me)
count = len(obm.faces)
#tri_idx = np.zeros(count * 3, dtype=np.int32)
#me.polygons.foreach_get('vertices', tri_idx)
tri_idx = np.array([[v.index for v in f.verts] for f in obm.faces])
# Identify bend spring groups. Each edge gets paired with two points on tips of tris around edge
# Restricted to edges with two linked faces on a triangulated version of the mesh
if ob is not None:
link_ed = [e for e in obm.edges if len(e.link_faces) == 2]
ob.bend_eidx = np.array([[e.verts[0].index, e.verts[1].index] for e in link_ed])
fv = np.array([[[v.index for v in f.verts] for f in e.link_faces] for e in link_ed])
fv.shape = (fv.shape[0],6)
ob.bend_tips = np.array([[idx for idx in fvidx if idx not in e] for e, fvidx in zip(ob.bend_eidx, fv)])
obm.free()
return tri_idx#.reshape(count, 3)
def tri_normals_in_place(col, tri_co):
"""Takes N x 3 x 3 set of 3d triangles and
returns non-unit normals and origins"""
col.origins = tri_co[:,0]
col.cross_vecs = tri_co[:,1:] - col.origins[:, nax]
col.normals = np.cross(col.cross_vecs[:,0], col.cross_vecs[:,1])
col.nor_dots = np.einsum("ij, ij->i", col.normals, col.normals)
col.normals /= np.sqrt(col.nor_dots)[:, nax]
def get_tri_normals(tr_co):
"""Takes N x 3 x 3 set of 3d triangles and
returns non-unit normals and origins"""
origins = tr_co[:,0]
cross_vecs = tr_co[:,1:] - origins[:, nax]
return cross_vecs, np.cross(cross_vecs[:,0], cross_vecs[:,1]), origins
def closest_points_edge(vec, origin, p):
'''Returns the location of the point on the edge'''
vec2 = p - origin
d = (vec2 @ vec) / (vec @ vec)
cp = vec * d[:, nax]
return cp, d
def proxy_in_place(col, me):
"""Overwrite vert coords with modifiers in world space"""
me.vertices.foreach_get('co', col.co.ravel())
col.co = apply_transforms(col.ob, col.co)
def apply_rotation(col):
"""When applying vectors such as normals we only need
to rotate"""
m = np.array(col.ob.matrix_world)
mat = m[:3, :3].T
col.v_normals = col.v_normals @ mat
def proxy_v_normals_in_place(col, world=True, me=None):
"""Overwrite vert coords with modifiers in world space"""
me.vertices.foreach_get('normal', col.v_normals.ravel())
if world:
apply_rotation(col)
def proxy_v_normals(ob, me):
"""Overwrite vert coords with modifiers in world space"""
arr = np.zeros(len(me.vertices) * 3, dtype=np.float32)
me.vertices.foreach_get('normal', arr)
arr.shape = (arr.shape[0] //3, 3)
m = np.array(ob.matrix_world, dtype=np.float32)
mat = m[:3, :3].T # rotates backwards without T
return arr @ mat
def apply_transforms(ob, co):
"""Get vert coords in world space"""
m = np.array(ob.matrix_world, dtype=np.float32)
mat = m[:3, :3].T # rotates backwards without T
loc = m[:3, 3]
return co @ mat + loc
def apply_in_place(ob, arr, cloth):
"""Overwrite vert coords in world space"""
m = np.array(ob.matrix_world, dtype=np.float32)
mat = m[:3, :3].T # rotates backwards without T
loc = m[:3, 3]
arr[:] = arr @ mat + loc
#cloth.co = cloth.co @ mat + loc
def applied_key_co(ob, arr=None, key=None):
"""Get vert coords in world space"""
c = len(ob.data.vertices)
if arr is None:
arr = np.zeros(c * 3, dtype=np.float32)
ob.data.shape_keys.key_blocks[key].data.foreach_get('co', arr)
arr.shape = (c, 3)
m = np.array(ob.matrix_world)
mat = m[:3, :3].T # rotates backwards without T
loc = m[:3, 3]
return co @ mat + loc
def revert_transforms(ob, co):
"""Set world coords on object.
Run before setting coords to deal with object transforms
if using apply_transforms()"""
m = np.linalg.inv(ob.matrix_world)
mat = m[:3, :3].T # rotates backwards without T
loc = m[:3, 3]
return co @ mat + loc
def revert_in_place(ob, co):
"""Revert world coords to object coords in place."""
m = np.linalg.inv(ob.matrix_world)
mat = m[:3, :3].T # rotates backwards without T
loc = m[:3, 3]
co[:] = co @ mat + loc
def revert_rotation(ob, co):
"""When reverting vectors such as normals we only need
to rotate"""
#m = np.linalg.inv(ob.matrix_world)
m = np.array(ob.matrix_world)
mat = m[:3, :3] # rotates backwards without T
return co @ mat
def get_last_object():
"""Finds cloth objects for keeping settings active
while selecting other objects like pins"""
cloths = [i for i in bpy.data.objects if i.mclo.enable] # so we can select an empty and keep the settings menu up
if bpy.context.object.mclo.enable:
return cloths, bpy.context.object
if len(cloths) > 0:
ob = bpy.context.scene.mclo.last_object
return cloths, ob
return None, None
def get_poly_centers(ob, type=np.float32, mesh=None):
mod = False
m_count = len(ob.modifiers)
if m_count > 0:
show = np.zeros(m_count, dtype=np.bool)
ren_set = np.copy(show)
ob.modifiers.foreach_get('show_render', show)
ob.modifiers.foreach_set('show_render', ren_set)
mod = True
p_count = len(mesh.polygons)
center = np.zeros(p_count * 3, dtype=type)
mesh.polygons.foreach_get('center', center)
center.shape = (p_count, 3)
if mod:
ob.modifiers.foreach_set('show_render', show)
return center
def simple_poly_centers(ob, key=None):
if key is not None:
s_key = ob.data.shape_keys.key_blocks[key].data
return np.squeeze([[np.mean([ob.data.vertices[i].co for i in p.vertices], axis=0)] for p in ob.data.polygons])
def get_poly_normals(ob, type=np.float32, mesh=None):
mod = False
m_count = len(ob.modifiers)
if m_count > 0:
show = np.zeros(m_count, dtype=np.bool)
ren_set = np.copy(show)
ob.modifiers.foreach_get('show_render', show)
ob.modifiers.foreach_set('show_render', ren_set)
mod = True
p_count = len(mesh.polygons)
normal = np.zeros(p_count * 3, dtype=type)
mesh.polygons.foreach_get('normal', normal)
normal.shape = (p_count, 3)
if mod:
ob.modifiers.foreach_set('show_render', show)
return normal
def get_v_normals(ob, arr, mesh):
"""Since we're reading from a shape key we have to use
a proxy mesh."""
mod = False
m_count = len(ob.modifiers)
if m_count > 0:
show = np.zeros(m_count, dtype=np.bool)
ren_set = np.copy(show)
ob.modifiers.foreach_get('show_render', show)
ob.modifiers.foreach_set('show_render', ren_set)
mod = True
#v_count = len(mesh.vertices)
#normal = np.zeros(v_count * 3)#, dtype=type)
mesh.vertices.foreach_get('normal', arr.ravel())
#normal.shape = (v_count, 3)
if mod:
ob.modifiers.foreach_set('show_render', show)
def get_v_nor(ob, nor_arr):
ob.data.vertices.foreach_get('normal', nor_arr.ravel())
return nor_arr
def closest_point_edge(e1, e2, p):
'''Returns the location of the point on the edge'''
vec1 = e2 - e1
vec2 = p - e1
d = np.dot(vec2, vec1) / np.dot(vec1, vec1)
cp = e1 + vec1 * d
return cp
def create_vertex_groups(groups=['common', 'not_used'], weights=[0.0, 0.0], ob=None):
'''Creates vertex groups and sets weights. "groups" is a list of strings
for the names of the groups. "weights" is a list of weights corresponding
to the strings. Each vertex is assigned a weight for each vertex group to
avoid calling vertex weights that are not assigned. If the groups are
already present, the previous weights will be preserved. To reset weights
delete the created groups'''
if ob is None:
ob = bpy.context.object
vg = ob.vertex_groups
for g in range(0, len(groups)):
if groups[g] not in vg.keys(): # Don't create groups if there are already there
vg.new(groups[g])
vg[groups[g]].add(range(0,len(ob.data.vertices)), weights[g], 'REPLACE')
else:
vg[groups[g]].add(range(0,len(ob.data.vertices)), 0, 'ADD') # This way we avoid resetting the weights for existing groups.
def get_bmesh(obj=None):
ob = get_last_object()[1]
if ob is None:
ob = obj
obm = bmesh.new()
if ob.mode == 'OBJECT':
obm.from_mesh(ob.data)
elif ob.mode == 'EDIT':
obm = bmesh.from_edit_mesh(ob.data)
return obm
def get_minimal_edges(ob):
obm = get_bmesh(ob)
obm.edges.ensure_lookup_table()
obm.verts.ensure_lookup_table()
obm.faces.ensure_lookup_table()
# get sew edges:
sew = [i.index for i in obm.edges if len(i.link_faces)==0]
# so if I have a vertex with one or more sew edges attached
# I need to get the mean location of all verts shared by those edges
# every one of those verts needs to move towards the total mean
# get linear edges
e_count = len(obm.edges)
eidx = np.zeros(e_count * 2, dtype=np.int32)
e_bool = np.zeros(e_count, dtype=np.bool)
e_bool[sew] = True
ob.data.edges.foreach_get('vertices', eidx)
eidx.shape = (e_count, 2)
# get diagonal edges:
diag_eidx = []
start = 0
stop = 0
step_size = [len(i.verts) for i in obm.faces]
p_v_count = np.sum(step_size)
p_verts = np.ones(p_v_count, dtype=np.int32)
ob.data.polygons.foreach_get('vertices', p_verts)
# can only be understood on a good day when the coffee flows (uses rolling and slicing)
# creates uniqe diagonal edge sets
for f in obm.faces:
fv_count = len(f.verts)
stop += fv_count
if fv_count > 3: # triangles are already connected by linear springs
skip = 2
f_verts = p_verts[start:stop]
for fv in range(len(f_verts)):
if fv > 1: # as we go around the loop of verts in face we start overlapping
skip = fv + 1 # this lets us skip the overlap so we don't have mirror duplicates
roller = np.roll(f_verts, fv)
for r in roller[skip:-1]:
diag_eidx.append([roller[0], r])
start += fv_count
# eidx groups
sew_eidx = eidx[e_bool]
lin_eidx = eidx[~e_bool]
diag_eidx = np.array(diag_eidx)
# deal with sew verts connected to more than one edge
s_t_rav = sew_eidx.T.ravel()
s_uni, s_inv, s_counts = np.unique(s_t_rav,return_inverse=True, return_counts=True)
s_multi = s_counts > 1
multi_groups = None
if np.any(s_counts):
multi_groups = []
ls = sew_eidx[:,0]
rs = sew_eidx[:,1]
for i in s_uni[s_multi]:
gr = np.array([i])
gr = np.append(gr, ls[rs==i])
gr = np.append(gr, rs[ls==i])
multi_groups.append(gr)
return lin_eidx, diag_eidx, sew_eidx, multi_groups
def add_remove_virtual_springs(remove=False):
ob = get_last_object()[1]
cloth = get_cloth_data(ob)
obm = get_bmesh()
obm.verts.ensure_lookup_table()
count = len(obm.verts)
idxer = np.arange(count, dtype=np.int32)
sel = np.array([v.select for v in obm.verts])
selected = idxer[sel]
virtual_springs = np.array([[vs.vertex_id_1, vs.vertex_id_2] for vs in ob.mclo.virtual_springs])
if virtual_springs.shape[0] == 0:
virtual_springs.shape = (0, 2)
if remove:
ls = virtual_springs[:, 0]
in_sel = np.in1d(ls, idxer[sel])
deleter = np.arange(ls.shape[0], dtype=np.int32)[in_sel]
for i in reversed(deleter):
ob.mclo.virtual_springs.remove(i)
return
existing = np.append(cloth.eidx, virtual_springs, axis=0)
flip = existing[:, ::-1]
existing = np.append(existing, flip, axis=0)
ls = existing[:,0]
#springs = []
for i in idxer[sel]:
# to avoid duplicates:
# where this vert occurs on the left side of the existing spring list
v_in = existing[i == ls]
v_in_r = v_in[:,1]
not_in = selected[~np.in1d(selected, v_in_r)]
idx_set = not_in[not_in != i]
for sv in idx_set:
#springs.append([i, sv])
new_vs = ob.mclo.virtual_springs.add()
new_vs.vertex_id_1 = i
new_vs.vertex_id_2 = sv
# gets appended to eidx in the cloth_init function after calling get connected polys in case geometry changes
def generate_guide_mesh():
"""Makes the arrow that appears when creating pins"""
verts = [[0.0, 0.0, 0.0], [-0.01, -0.01, 0.1], [-0.01, 0.01, 0.1], [0.01, -0.01, 0.1], [0.01, 0.01, 0.1], [-0.03, -0.03, 0.1], [-0.03, 0.03, 0.1], [0.03, 0.03, 0.1], [0.03, -0.03, 0.1], [-0.01, -0.01, 0.2], [-0.01, 0.01, 0.2], [0.01, -0.01, 0.2], [0.01, 0.01, 0.2]]
edges = [[0, 5], [5, 6], [6, 7], [7, 8], [8, 5], [1, 2], [2, 4], [4, 3], [3, 1], [5, 1], [2, 6], [4, 7], [3, 8], [9, 10], [10, 12], [12, 11], [11, 9], [3, 11], [9, 1], [2, 10], [12, 4], [6, 0], [7, 0], [8, 0]]
faces = [[0, 5, 6], [0, 6, 7], [0, 7, 8], [0, 8, 5], [1, 3, 11, 9], [1, 2, 6, 5], [2, 4, 7, 6], [4, 3, 8, 7], [3, 1, 5, 8], [12, 10, 9, 11], [4, 2, 10, 12], [3, 4, 12, 11], [2, 1, 9, 10]]
name = 'ModelingClothPinGuide'
if 'ModelingClothPinGuide' in bpy.data.objects:
mesh_ob = bpy.data.objects['ModelingClothPinGuide']
else:
mesh = bpy.data.meshes.new('ModelingClothPinGuide')
mesh.from_pydata(verts, edges, faces)
mesh.update()
mesh_ob = bpy.data.objects.new(name, mesh)
bpy.context.scene.objects.link(mesh_ob)
mesh_ob.show_x_ray = True
return mesh_ob
def create_guide():
"""Spawns the guide"""
if 'ModelingClothPinGuide' in bpy.data.objects:
mesh_ob = bpy.data.objects['ModelingClothPinGuide']
return mesh_ob
mesh_ob = generate_guide_mesh()
bpy.context.scene.objects.active = mesh_ob
bpy.ops.object.material_slot_add()
if 'ModelingClothPinGuide' in bpy.data.materials:
mat = bpy.data.materials['ModelingClothPinGuide']
else:
mat = bpy.data.materials.new(name='ModelingClothPinGuide')
mat.use_transparency = True
mat.alpha = 0.35
mat.emit = 2
mat.game_settings.alpha_blend = 'ALPHA_ANTIALIASING'
mat.diffuse_color = (1, 1, 0)
mesh_ob.material_slots[0].material = mat
return mesh_ob
def delete_guide():
"""Deletes the arrow"""
if 'ModelingClothPinGuide' in bpy.data.objects:
bpy.data.objects.remove(bpy.data.objects['ModelingClothPinGuide'])
if 'ModelingClothPinGuide' in bpy.data.meshes:
guide_mesh = bpy.data.meshes['ModelingClothPinGuide']
guide_mesh.user_clear()
bpy.data.meshes.remove(guide_mesh)
def scale_source(multiplier):
"""grow or shrink the source shape"""
ob = get_last_object()[1]
if ob is not None:
if ob.mclo.enable:
count = len(ob.data.vertices)
co = np.zeros(count*3, dtype=np.float32)
ob.data.shape_keys.key_blocks['modeling cloth source key'].data.foreach_get('co', co)
co.shape = (count, 3)
mean = np.mean(co, axis=0)
co -= mean
co *= multiplier
co += mean
ob.data.shape_keys.key_blocks['modeling cloth source key'].data.foreach_set('co', co.ravel())
cloth = get_cloth_data(ob)
if hasattr(cloth, 'cy_dists'):
cloth.cy_dists *= multiplier
def reset_shapes(ob=None):
"""Sets the modeling cloth key to match the source key.
Will regenerate shape keys if they are missing"""
if ob is None:
if bpy.context.object.mclo.enable:
ob = bpy.context.object
else:
ob = bpy.context.scene.mclo.last_object
if ob.data.shape_keys == None:
ob.shape_key_add('Basis')
if 'modeling cloth source key' not in ob.data.shape_keys.key_blocks:
ob.shape_key_add('modeling cloth source key')
if 'modeling cloth key' not in ob.data.shape_keys.key_blocks:
ob.shape_key_add('modeling cloth key')
ob.data.shape_keys.key_blocks['modeling cloth key'].value=1
keys = ob.data.shape_keys.key_blocks
count = len(ob.data.vertices)
co = np.zeros(count * 3, dtype=np.float32)
keys['Basis'].data.foreach_get('co', co)
#co = applied_key_co(ob, None, 'modeling cloth source key')
#keys['modeling cloth source key'].data.foreach_set('co', co)
keys['modeling cloth key'].data.foreach_set('co', co)
# reset the data stored in the class
cloth = get_cloth_data(ob)
cloth.vel[:] = 0
co.shape = (co.shape[0]//3, 3)
cloth.co = co
keys['modeling cloth key'].mute = True
keys['modeling cloth key'].mute = False
def get_spring_mix(ob, eidx):
rs = []
ls = []
minrl = []
for i in eidx:
r = eidx[eidx == i[1]].shape[0]
l = eidx[eidx == i[0]].shape[0]
rs.append (min(r,l))
ls.append (min(r,l))
mix = 1 / np.array(rs + ls, dtype=np.float32) ** 1.2
return mix
def collision_data_update(self, context):
ob = self.id_data
if ob.mclo.self_collision:
create_cloth_data(ob)
def refresh_noise(self, context):
ob = self.id_data
cloth = get_cloth_data(ob)
if cloth:
zeros = np.zeros(cloth.count, dtype=np.float32)
random = np.random.random(cloth.count)
zeros[:] = random
cloth.noise = ((zeros + -0.5) * ob.mclo.noise * 0.1)[:, nax]
def generate_wind(wind_vec, ob, cloth):
"""Maintains a wind array and adds it to the cloth vel"""
tri_nor = cloth.normals # non-unit calculated by tri_normals_in_place() per each triangle
w_vec = revert_rotation(ob, wind_vec)
turb = ob.mclo.turbulence
if turb != 0:
w_vec += np.random.random(3).astype(np.float32) * turb * np.mean(w_vec) * 4
# only blow on verts facing the wind
perp = np.abs(tri_nor @ w_vec)
cloth.wind += w_vec
cloth.wind *= perp[:, nax][:, nax]
# reshape for add.at
shape = cloth.wind.shape
cloth.wind.shape = (shape[0] * 3, 3)
cloth.wind *= cloth.tri_mix
np.add.at(cloth.vel, cloth.tridex.ravel(), cloth.wind)
cloth.wind.shape = shape
def generate_inflate(ob, cloth):
"""Blow it up baby!"""
tri_nor = cloth.normals #* ob.mclo.inflate # non-unit calculated by tri_normals_in_place() per each triangle
#tri_nor /= np.einsum("ij, ij->i", tri_nor, tri_nor)[:, nax]
# reshape for add.at
shape = cloth.inflate.shape
cloth.inflate += tri_nor[:, nax] * ob.mclo.inflate# * cloth.tri_mix
cloth.inflate.shape = (shape[0] * 3, 3)
cloth.inflate *= cloth.tri_mix
np.add.at(cloth.vel, cloth.tridex.ravel(), cloth.inflate)
cloth.inflate.shape = shape
cloth.inflate *= 0
def get_quat(rad, axis):
theta = (rad * 0.5)
w = np.cos(theta)
q_axis = axis * np.sin(theta)[:, nax]
return w, q_axis
def q_rotate(co, w, axis):
"""Takes an N x 3 numpy array and returns that array rotated around
the axis by the angle in radians w. (standard quaternion)"""
move1 = np.cross(axis, co)
move2 = np.cross(axis, move1)
move1 *= w[:, nax]
return co + (move1 + move2) * 2
def bend_springs(cloth, co, measure=None):
bend_eidx, tips = cloth.bend_eidx, cloth.bend_tips
tips_co = co[tips]
bls, brs = bend_eidx[:,0], bend_eidx[:, 1]
b_oris = co[bls]
be_vecs = co[brs] - b_oris
te_vecs = tips_co - b_oris[:, nax]
bcp_dots = np.einsum('ij,ikj->ik', be_vecs, te_vecs)
be_dots = np.einsum('ij,ij->i', be_vecs, be_vecs)
b_div = np.nan_to_num(bcp_dots / be_dots[:, nax])
tcp = be_vecs[:, nax] * b_div[:, :, nax]
# tip vecs from cp
tcp_vecs = te_vecs - tcp
tcp_dots = np.einsum('ijk,ijk->ij',tcp_vecs, tcp_vecs)
u_tcp_vecs = tcp_vecs / np.sqrt(tcp_dots)[:, :, nax]
u_tcp_ls = u_tcp_vecs[:, 0]
u_tcp_rs = u_tcp_vecs[:, 1]
# dot of unit tri tips around axis
angle_dot = np.einsum('ij,ij->i', u_tcp_ls, u_tcp_rs)
#paralell = angle_dot < -.9999999
angle = np.arccos(np.clip(angle_dot, -1, 1)) # values outside and arccos gives nan
#angle = np.arccos(angle_dot) # values outside and arccos gives nan
# get the angle sign
tcp_cross = np.cross(u_tcp_vecs[:, 0], u_tcp_vecs[:, 1])
sign = np.sign(np.einsum('ij,ij->i', be_vecs, tcp_cross))
if measure is None:
s = np.arccos(angle_dot)
s *= sign
s[angle_dot < -.9999999] = np.pi
return s
angle *= sign
# rotate edges with quaternypoos
u_be_vecs = be_vecs / np.sqrt(be_dots)[:, nax]
b_dif = angle - measure
l_ws, l_axes = get_quat(b_dif, u_be_vecs)
r_ws, r_axes = l_ws, -l_axes
# move tcp vecs so their origin is in the middle:
#u_tcp_vecs *= 0.5
# should I rotate the unit vecs or the source?
# rotating the unit vecs here.
#stiff = cloth.ob.modeling_cloth_bend_stiff * 0.0057
stiff = cloth.ob.mclo.bend_stiff * 0.0057
rot_ls = q_rotate(u_tcp_ls, l_ws, l_axes)
l_force = (rot_ls - u_tcp_ls) * stiff
rot_rs = q_rotate(u_tcp_rs, r_ws, r_axes)
r_force = (rot_rs - u_tcp_rs) * stiff
np.add.at(cloth.co, tips[:, 0], l_force)
np.add.at(cloth.co, tips[:, 1], r_force)
np.subtract.at(cloth.co, bend_eidx.ravel(), np.tile(r_force * .5, 2).reshape(r_force.shape[0] * 2, 3))
np.subtract.at(cloth.co, bend_eidx.ravel(), np.tile(l_force * .5, 2).reshape(l_force.shape[0] * 2, 3))
return
cloth.co[tips[:, 0]] += l_force
cloth.co[tips[:, 1]] += r_force
#cloth.co[bend_eidx] -= l_force
cloth.co[bend_eidx] -= r_force[:, nax]
cloth.co[bend_eidx] -= l_force[:, nax]
#cloth.co[brs] -= r_force
#print("bend here")
# will need to read bend springs continuously when using
# a dynamic source shape. Guess I should do that now...
# need the angle at each edge
# need to get the tips of each tri around each edge
# should be a pair everywhere there is a link face in
# the tri bmesh
"""
With no sign I just get the dot in radians.
Rotation should move towards the shortest distance
to the same dot in radians.
Without getting the sign at all, it will always rotate
in the same direction to go back to the target.
By multiplying the dif by the sign, I can make it spin
the other way to go back to the target dot in rads
"""
# sewing functions ---------------->>>
def create_sew_edges():
bpy.ops.mesh.bridge_edge_loops()
bpy.ops.mesh.delete(type='ONLY_FACE')
return
#highlight a sew edge
#compare vertex counts
#subdivide to match counts
#distribute and smooth back into mesh
#create sew lines
# sewing functions ---------------->>>
def check_and_get_pins_and_hooks(ob):
scene = bpy.context.scene
pins = []
hooks = []
cull_ids = []
for i, pin in enumerate(ob.mclo.pins):
# Check if hook object still exists
if not pin.hook or (pin.hook and not scene.objects.get(pin.hook.name)):
cull_ids.append(i)
else:
#vert = ob.data.vertices[pin.vertex_id]
pins.append(pin.vertex_id)
hooks.append(pin.hook)
# Delete missing hooks pointers
for i in reversed(cull_ids):
pin = ob.mclo.pins[i]
if pin.hook:
bpy.data.objects.remove(pin.hook)
ob.mclo.pins.remove(i)
return pins, hooks
class ClothData:
pass
def create_cloth_data(ob):
"""Creates instance of cloth object with attributes needed for engine"""
scene = bpy.context.scene
data = scene.modeling_cloth_data_set
# Try to get the cloth data first
try:
cloth = data[ob.name]
except:
# Search for possible name changes
cloth = None
for ob_name, c in data.items():
if c.ob == ob:
# Rename the key
data[ob.name] = data.pop(ob_name)
cloth = data[ob.name]
break
# If cloth still not found
if not cloth:
cloth = ClothData()
data[ob.name] = cloth
cloth.ob = ob
# get proxy object
#proxy = ob.to_mesh(bpy.context.scene, False, 'PREVIEW')
# ----------------
scene.objects.active = ob
cloth.idxer = np.arange(len(ob.data.vertices), dtype=np.int32)
# data only accesible through object mode
mode = ob.mode
if mode == 'EDIT':
bpy.ops.object.mode_set(mode='OBJECT')
# data is read from a source shape and written to the display shape so we can change the target springs by changing the source shape
#cloth.name = ob.name
if ob.data.shape_keys == None:
ob.shape_key_add('Basis')
if 'modeling cloth source key' not in ob.data.shape_keys.key_blocks:
ob.shape_key_add('modeling cloth source key')
if 'modeling cloth key' not in ob.data.shape_keys.key_blocks:
ob.shape_key_add('modeling cloth key')
ob.data.shape_keys.key_blocks['modeling cloth key'].value=1
cloth.count = len(ob.data.vertices)
# we can set a large group's pin state using the vertex group. No hooks are used here
if 'modeling_cloth_pin' not in ob.vertex_groups:
cloth.pin_group = create_vertex_groups(groups=['modeling_cloth_pin'], weights=[0.0], ob=None)
for i in range(cloth.count):
try:
ob.vertex_groups['modeling_cloth_pin'].weight(i)
except RuntimeError:
# assign a weight of zero
ob.vertex_groups['modeling_cloth_pin'].add(range(0,len(ob.data.vertices)), 0.0, 'REPLACE')
cloth.pin_bool = ~np.array([ob.vertex_groups['modeling_cloth_pin'].weight(i) for i in range(cloth.count)], dtype=np.bool)
# unique edges------------>>>
uni_edges = get_minimal_edges(ob)
if len(uni_edges[1]) > 0:
cloth.eidx = np.append(uni_edges[0], uni_edges[1], axis=0)
else:
cloth.eidx = uni_edges[0]
#cloth.eidx = uni_edges[0][0]
if len(ob.mclo.virtual_springs) > 0:
virtual_springs = np.array([[vs.vertex_id_1, vs.vertex_id_2] for vs in ob.mclo.virtual_springs])
cloth.eidx = np.append(cloth.eidx, virtual_springs, axis=0)
cloth.eidx_tiler = cloth.eidx.T.ravel()
mixology = get_spring_mix(ob, cloth.eidx)
#eidx1 = np.copy(cloth.eidx)
cloth.pindexer = np.arange(cloth.count, dtype=np.int32)[cloth.pin_bool]
cloth.unpinned = np.in1d(cloth.eidx_tiler, cloth.pindexer)
cloth.eidx_tiler = cloth.eidx_tiler[cloth.unpinned]
cloth.sew_edges = uni_edges[2]
cloth.multi_sew = uni_edges[3]
# unique edges------------>>>
#cloth.pcount = pindexer.shape[0]
cloth.sco = np.zeros(cloth.count * 3, dtype=np.float32)
ob.data.shape_keys.key_blocks['modeling cloth source key'].data.foreach_get('co', cloth.sco)
cloth.sco.shape = (cloth.count, 3)
cloth.co = np.zeros(cloth.count * 3, dtype=np.float32)
ob.data.shape_keys.key_blocks['modeling cloth key'].data.foreach_get('co', cloth.co)
cloth.co.shape = (cloth.count, 3)
co = cloth.co
cloth.vel = np.zeros(cloth.count * 3, dtype=np.float32)
cloth.vel.shape = (cloth.count, 3)
cloth.vel_start = np.zeros(cloth.count * 3, dtype=np.float32)
cloth.vel_start.shape = (cloth.count, 3)
cloth.self_col_vel = np.copy(co)
cloth.v_normals = np.zeros(co.shape, dtype=np.float32)
#get_v_normals(ob, cloth.v_normals, proxy)
#noise---
noise_zeros = np.zeros(cloth.count, dtype=np.float32)
random = np.random.random(cloth.count).astype(np.float32)
noise_zeros[:] = random
cloth.noise = ((noise_zeros + -0.5) * ob.mclo.noise * 0.1)[:, nax]
#cloth.waiting = False
#cloth.clicked = False # for the grab tool
# this helps with extra springs behaving as if they had more mass---->>>
cloth.mix = mixology[cloth.unpinned][:, nax]
# -------------->>>
# new self collisions:
cloth.tridex = triangulate(ob.data, cloth)
cloth.tridexer = np.arange(cloth.tridex.shape[0], dtype=np.int32)
cloth.tri_co = cloth.co[cloth.tridex]
tri_normals_in_place(cloth, cloth.tri_co) # non-unit normals
# -------------->>>
tri_uni, tri_inv, tri_counts = np.unique(cloth.tridex, return_inverse=True, return_counts=True)
cloth.tri_mix = (1 / tri_counts[tri_inv])[:, nax]
cloth.wind = np.zeros(cloth.tri_co.shape, dtype=np.float32)
cloth.inflate = np.zeros(cloth.tri_co.shape, dtype=np.float32)
bpy.ops.object.mode_set(mode=mode)
# for use with a static source shape:
cloth.source_angles = bend_springs(cloth, cloth.sco, None)
svecs = cloth.sco[cloth.eidx[:, 1]] - cloth.sco[cloth.eidx[:, 0]]
cloth.sdots = np.einsum('ij,ij->i', svecs, svecs)
# for doing static cling
# cloth.col_idx = np.array([], dtype=np.int32)
# cloth.re_col = np.empty((0,3), dtype=np.float32)
print('INFO: Cloth data for', ob.name, 'is created!')
return cloth
def run_handler(ob, cloth):
T = time.time()
scene = bpy.context.scene
extra_data = scene.modeling_cloth_data_set_extra
col_data = scene.modeling_cloth_data_set_colliders
if not ob.mclo.waiting and ob.mode != 'OBJECT':
ob.mclo.waiting = True
if ob.mclo.waiting:
if ob.mode == 'OBJECT':
create_cloth_data(ob)
ob.mclo.waiting = False
if not ob.mclo.waiting:
eidx = cloth.eidx # world's most important variable
ob.data.shape_keys.key_blocks['modeling cloth source key'].data.foreach_get('co', cloth.sco.ravel())
sco = cloth.sco
co = cloth.co
co[cloth.pindexer] += cloth.noise[cloth.pindexer]
#co += cloth.noise
cloth.noise *= ob.mclo.noise_decay
# mix in vel before collisions and sewing
co[cloth.pindexer] += cloth.vel[cloth.pindexer]
cloth.vel_start[:] = co
# measure source -------------------------->>>
dynamic = True # can store for speedup if source shape is static
# bend spring calculations:
if ob.mclo.bend_stiff != 0:
# measure bend source if using dynamic source:
source_angles = cloth.source_angles
if dynamic:
source_angles = bend_springs(cloth, sco, None)
# linear spring measure
sdots = cloth.sdots
if dynamic:
ob.data.shape_keys.key_blocks['modeling cloth source key'].data.foreach_get('co', sco.ravel())
svecs = sco[eidx[:, 1]] - sco[eidx[:, 0]]
sdots = np.einsum('ij,ij->i', svecs, svecs)
# ----------------------------------------->>>
force = ob.mclo.spring_force
mix = cloth.mix * force
pin_list = []
if len(ob.mclo.pins) > 0:
pin_list, hook_list = check_and_get_pins_and_hooks(ob)
hook_co = np.array([ob.matrix_world.inverted() * hook.matrix_world.to_translation()
for hook in hook_list])
ers = eidx[:, 1]
els = eidx[:, 0]
for x in range(ob.mclo.iterations):
# bend spring calculations:
if ob.mclo.bend_stiff != 0:
bend_springs(cloth, co, source_angles)
# add pull
vecs = co[eidx[:, 1]] - co[eidx[:, 0]]
dots = np.einsum('ij,ij->i', vecs, vecs)
div = | np.nan_to_num(sdots / dots) | numpy.nan_to_num |
# Copyright 2018 Google LLC
#
# 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.
"""Minimal data reader for GQN TFRecord datasets."""
import collections
import os
import tensorflow as tf
import numpy as np
from PIL import Image
DatasetInfo = collections.namedtuple(
'DatasetInfo',
['basepath', 'train_size', 'test_size', 'frame_size', 'sequence_size']
)
Context = collections.namedtuple('Context', ['frames', 'cameras'])
Query = collections.namedtuple('Query', ['context', 'query_camera'])
TaskData = collections.namedtuple('TaskData', ['query', 'target'])
_DATASETS = dict(
jaco=DatasetInfo(
basepath='jaco',
train_size=3600,
test_size=400,
frame_size=64,
sequence_size=11),
mazes=DatasetInfo(
basepath='mazes',
train_size=1080,
test_size=120,
frame_size=84,
sequence_size=300),
rooms_free_camera_with_object_rotations=DatasetInfo(
basepath='rooms_free_camera_with_object_rotations',
train_size=2034,
test_size=226,
frame_size=128,
sequence_size=10),
rooms_ring_camera=DatasetInfo(
basepath='rooms_ring_camera',
train_size=2160,
test_size=240,
frame_size=64,
sequence_size=10),
rooms_free_camera_no_object_rotations=DatasetInfo(
basepath='rooms_free_camera_no_object_rotations',
train_size=2160,
test_size=240,
frame_size=64,
sequence_size=10),
shepard_metzler_5_parts=DatasetInfo(
basepath='shepard_metzler_5_parts',
train_size=900,
test_size=100,
frame_size=64,
sequence_size=15),
shepard_metzler_7_parts=DatasetInfo(
basepath='shepard_metzler_7_parts',
train_size=900,
test_size=100,
frame_size=64,
sequence_size=15)
)
_NUM_CHANNELS = 3
_NUM_RAW_CAMERA_PARAMS = 5
def _get_dataset_files(dateset_info, mode, root):
"""Generates lists of files for a given dataset version."""
basepath = dateset_info.basepath
base = os.path.join(root, basepath, mode)
if mode == 'train':
num_files = dateset_info.train_size
else:
num_files = dateset_info.test_size
length = len(str(num_files))
template = '{:0%d}-of-{:0%d}.tfrecord' % (length, length)
return [os.path.join(base, template.format(i + 1, num_files))
for i in range(num_files)]
def _convert_frame_data(jpeg_data):
decoded_frames = tf.image.decode_jpeg(jpeg_data)
return tf.image.convert_image_dtype(decoded_frames, dtype=tf.float32)
def _get_randomized_indices(dataset_info, example_size):
"""Generates randomized indices into a sequence of a specific length."""
indices = tf.range(0, dataset_info.sequence_size)
indices = tf.random_shuffle(indices)
indices = tf.slice(indices, begin=[0], size=[example_size])
return indices
def _preprocess_frames(example, indices, dataset_info, example_size, custom_frame_size):
"""Instantiates the ops used to preprocess the frames data."""
frames = tf.concat(example['frames'], axis=0)
frames = tf.gather(frames, indices, axis=0)
frames = tf.map_fn(
_convert_frame_data, tf.reshape(frames, [-1]),
dtype=tf.float32, back_prop=False)
dataset_image_dimensions = tuple(
[dataset_info.frame_size] * 2 + [_NUM_CHANNELS])
# tf.Print(tf.shape(frames), [tf.shape(frames)], "Shape: ")
frames = tf.reshape(
frames, (-1, example_size) + dataset_image_dimensions)
# tf.Print(tf.shape(frames), [tf.shape(frames)], "Shape: ")
if (custom_frame_size and
custom_frame_size != dataset_info.frame_size):
frames = tf.reshape(frames, (-1,) + dataset_image_dimensions)
new_frame_dimensions = (custom_frame_size,) * 2 + (_NUM_CHANNELS,)
frames = tf.image.resize_bilinear(
frames, new_frame_dimensions[:2], align_corners=True)
frames = tf.reshape(
frames, (-1, example_size) + new_frame_dimensions)
return frames
def _preprocess_cameras(example, indices, dataset_info):
"""Instantiates the ops used to preprocess the cameras data."""
raw_pose_params = example['cameras']
raw_pose_params = tf.reshape(
raw_pose_params,
[-1, dataset_info.sequence_size, _NUM_RAW_CAMERA_PARAMS])
raw_pose_params = tf.gather(raw_pose_params, indices, axis=1)
pos = raw_pose_params[:, :, 0:3]
yaw = raw_pose_params[:, :, 3:4]
pitch = raw_pose_params[:, :, 4:5]
cameras = tf.concat(
[pos, yaw, pitch], axis=2)
return cameras
def _parse_function(example_proto, dataset_info, example_size, custom_frame_size):
feature_map = {
'frames': tf.FixedLenFeature(
shape=dataset_info.sequence_size, dtype=tf.string),
'cameras': tf.FixedLenFeature(
shape=[dataset_info.sequence_size * _NUM_RAW_CAMERA_PARAMS],
dtype=tf.float32)
}
example = tf.parse_single_example(example_proto, feature_map)
indices = _get_randomized_indices(dataset_info, example_size)
frames = _preprocess_frames(example, indices, dataset_info, example_size, custom_frame_size)
cameras = _preprocess_cameras(example, indices, dataset_info)
return frames, cameras
def make_dataset(dataset, root, context_size=5, mode='train', custom_frame_size=None, load_all=False):
dataset_info = _DATASETS[dataset]
file_names = _get_dataset_files(dataset_info, mode, root)
dataset = tf.data.TFRecordDataset(file_names)
if load_all:
context_size = dataset_info.sequence_size - 1
def parse_func(example_proto):
return _parse_function(example_proto, dataset_info=dataset_info, example_size=context_size + 1, custom_frame_size=custom_frame_size)
dataset = dataset.map(parse_func)
dataset = dataset.repeat(1)
return dataset
class DatasetWriter:
def __init__(self, dataset, mode, root):
"""
Writes images to files, and camera info csv
"""
self.dataset_info = _DATASETS[dataset]
self.mode = mode
self.root = root
self.counter = 0
# csv_header = "scene,view,x,y,z,yaw,pitch"
path = os.path.join(self.root, self.dataset_info.basepath, self.mode)
os.makedirs(path, exist_ok=True)
self.meta_file = os.path.join(path, "info.meta")
# self.csv = os.path.join(path, "info.csv")
# with open(self.csv, 'w+') as f:
# f.write(csv_header)
def save_multiple(self, records):
img_dir = os.path.join(self.root, self.dataset_info.basepath, self.mode)
frames = []
cameras = []
for rec_frames, rec_cameras in records:
rec_frames = np.squeeze(rec_frames)
rec_cameras = | np.squeeze(rec_cameras) | numpy.squeeze |
#kuang@master /home/cpuff/UNRESPForecastingSystem/vis/20220605
#$ cat ../../Python/mxNC
#!/usr/bin/python
import numpy as np
import netCDF4
import os,sys,subprocess
if not sys.warnoptions:
import warnings
warnings.simplefilter("ignore")
fname=['calpuff.con.S.grd02.nc']
rw=['r','r+']
nc0=netCDF4.Dataset(fname[0],rw[0])
V=[list(filter(lambda x:nc0.variables[x].ndim==j, [i for i in nc0.variables])) for j in [1,2,3,4]]
if len(V[3])>0:
tt=nc0.variables[V[3][0]].dimensions[0]
else:
tt=nc0.variables[V[2][0]].dimensions[0]
mxv={}
if len(V[3])>0:
for v in V[3]:
mxv.update({v:np.max((np.mean(nc0[v][:,:,:,:],axis=0)+np.max(nc0[v][:,:,:,:],axis=0))/2)})
fname='../../CALPUFF_INP/PM25.cfg'
with open(fname,'r') as f:
lines=[i for i in f]
line7=lines[7]
line50=lines[50]
line38=lines[38] #footer_line_1 value
date=subprocess.check_output('date -d "-1 day" +"%Y-%m-%d"',shell=True).decode('utf8').strip('\n')
if 'footer1' not in line38:
sys.exit(line38)
line38=line38.replace('footer1','Based on '+date+' Operation Rate%')
for spec in ['PMF','SO2','SO4','NOX']:
ss=spec
if spec=='PMF':ss='PM10'
fname=ss+'.cfg'
lines[7]=line7.replace('max=\"0.1\"','max=\"'+str(mxv[ss])+'\"')
#min=0.01
dc=( | np.log10(mxv[ss]) | numpy.log10 |
from unittest.mock import patch, Mock
import pytest
import numpy as np
import tensorflow as tf
from pathlib import Path
import ramjet.photometric_database.light_curve_database
import ramjet.photometric_database.standard_and_injected_light_curve_database as database_module
from ramjet.photometric_database.derived.toy_database import ToyDatabaseWithAuxiliary, ToyDatabaseWithFlatValueAsLabel
from ramjet.photometric_database.light_curve_collection import LightCurveCollection
from ramjet.photometric_database.standard_and_injected_light_curve_database import \
StandardAndInjectedLightCurveDatabase, OutOfBoundsInjectionHandlingMethod
class TestStandardAndInjectedLightCurveDatabase:
@pytest.fixture
def database(self) -> StandardAndInjectedLightCurveDatabase:
"""A fixture of a blank database."""
return StandardAndInjectedLightCurveDatabase()
@pytest.fixture
def database_with_collections(self) -> StandardAndInjectedLightCurveDatabase:
"""A fixture of the database with light_curve collections pre-prepared"""
database = StandardAndInjectedLightCurveDatabase()
# Setup mock light_curve collections.
standard_light_curve_collection0 = LightCurveCollection()
standard_light_curve_collection0.get_paths = lambda: [Path('standard_path0.ext')]
standard_light_curve_collection0.load_times_and_fluxes_from_path = lambda path: (np.array([10, 20, 30]),
np.array([0, 1, 2]))
standard_light_curve_collection0.label = 0
standard_light_curve_collection1 = LightCurveCollection()
standard_light_curve_collection1.get_paths = lambda: [Path('standard_path1.ext')]
standard_light_curve_collection1.load_times_and_fluxes_from_path = lambda path: (np.array([20, 30, 40]),
np.array([1, 2, 3]))
standard_light_curve_collection1.label = 1
injectee_light_curve_collection = LightCurveCollection()
injectee_light_curve_collection.get_paths = lambda: [Path('injectee_path.ext')]
injectee_light_curve_collection.load_times_and_fluxes_from_path = lambda path: (np.array([30, 40, 50]),
np.array([2, 3, 4]))
injectee_light_curve_collection.label = 0
injectable_light_curve_collection0 = LightCurveCollection()
injectable_light_curve_collection0.get_paths = lambda: [Path('injectable_path0.ext')]
injectable_light_curve_collection0.load_times_and_magnifications_from_path = lambda path: (
np.array([0, 10, 20]), np.array([0.5, 1, 1.5]))
injectable_light_curve_collection0.label = 0
injectable_light_curve_collection1 = LightCurveCollection()
injectable_light_curve_collection1.get_paths = lambda: [Path('injectable_path1.ext')]
injectable_light_curve_collection1.load_times_and_magnifications_from_path = lambda path: (
np.array([0, 10, 20, 30]), np.array([0, 1, 1, 0]))
injectable_light_curve_collection1.label = 1
database.training_standard_light_curve_collections = [standard_light_curve_collection0,
standard_light_curve_collection1]
database.training_injectee_light_curve_collection = injectee_light_curve_collection
database.training_injectable_light_curve_collections = [injectable_light_curve_collection0,
injectable_light_curve_collection1]
database.validation_standard_light_curve_collections = [standard_light_curve_collection1]
database.validation_injectee_light_curve_collection = injectee_light_curve_collection
database.validation_injectable_light_curve_collections = [injectable_light_curve_collection1]
# Setup simplified database settings
database.batch_size = 4
database.time_steps_per_example = 3
database.number_of_parallel_processes_per_map = 1
def mock_window(dataset, batch_size, window_shift):
return dataset.batch(batch_size)
database.window_dataset_for_zipped_example_and_label_dataset = mock_window # Disable windowing.
database.normalize_on_percentiles = lambda fluxes: fluxes # Don't normalize values to keep it simple.
return database
@pytest.fixture
def deterministic_database(self, database_with_collections) -> StandardAndInjectedLightCurveDatabase:
"""A fixture of a deterministic database with light_curve collections pre-prepared."""
database_with_collections.remove_random_elements = lambda x: x
database_with_collections.randomly_roll_elements = lambda x: x
return database_with_collections
def test_database_has_light_curve_collection_properties(self):
database = StandardAndInjectedLightCurveDatabase()
assert hasattr(database, 'training_standard_light_curve_collections')
assert hasattr(database, 'training_injectee_light_curve_collection')
assert hasattr(database, 'training_injectable_light_curve_collections')
assert hasattr(database, 'validation_standard_light_curve_collections')
assert hasattr(database, 'validation_injectee_light_curve_collection')
assert hasattr(database, 'validation_injectable_light_curve_collections')
@pytest.mark.slow
@pytest.mark.functional
@patch.object(database_module.np.random, 'random', return_value=0)
@patch.object(ramjet.photometric_database.light_curve_database.np.random, 'randint', return_value=0)
def test_database_can_generate_training_and_validation_datasets(self, mock_randint, mock_random,
database_with_collections):
training_dataset, validation_dataset = database_with_collections.generate_datasets()
training_batch = next(iter(training_dataset))
training_batch_examples = training_batch[0]
training_batch_labels = training_batch[1]
assert training_batch_examples.shape == (database_with_collections.batch_size, 3, 1)
assert training_batch_labels.shape == (database_with_collections.batch_size, 1)
assert np.array_equal(training_batch_examples[0].numpy(), [[0], [1], [2]]) # Standard light_curve 0.
assert np.array_equal(training_batch_labels[0].numpy(), [0]) # Standard label 0.
assert np.array_equal(training_batch_examples[1].numpy(), [[1], [2], [3]]) # Standard light_curve 1.
assert np.array_equal(training_batch_labels[1].numpy(), [1]) # Standard label 1.
assert np.array_equal(training_batch_examples[2].numpy(), [[0.5], [3], [5.5]]) # Injected light_curve 0.
assert np.array_equal(training_batch_examples[3].numpy(), [[-1], [3], [4]]) # Injected light_curve 1.
validation_batch = next(iter(validation_dataset))
validation_batch_examples = validation_batch[0]
validation_batch_labels = validation_batch[1]
assert validation_batch_examples.shape == (database_with_collections.batch_size, 3, 1)
assert validation_batch_labels.shape == (database_with_collections.batch_size, 1)
assert np.array_equal(validation_batch_examples[0].numpy(), [[1], [2], [3]]) # Standard light_curve 1.
assert np.array_equal(validation_batch_labels[0].numpy(), [1]) # Standard label 1.
assert np.array_equal(validation_batch_examples[1].numpy(), [[-1], [3], [4]]) # Injected light_curve 1.
assert np.array_equal(validation_batch_labels[1].numpy(), [1]) # Injected label 1.
assert np.array_equal(validation_batch_examples[2].numpy(), [[1], [2], [3]]) # Standard light_curve 1.
assert np.array_equal(validation_batch_examples[3].numpy(), [[-1], [3], [4]]) # Injected light_curve 1.
@pytest.mark.slow
@pytest.mark.functional
def test_can_generate_standard_light_curve_and_label_dataset_from_paths_dataset_and_label(self,
deterministic_database):
database = deterministic_database
light_curve_collection = database.training_standard_light_curve_collections[0]
paths_dataset = database.generate_paths_dataset_from_light_curve_collection(light_curve_collection)
light_curve_and_label_dataset = database.generate_standard_light_curve_and_label_dataset(paths_dataset,
light_curve_collection.load_times_fluxes_and_flux_errors_from_path,
light_curve_collection.load_auxiliary_information_for_path,
light_curve_collection.load_label_from_path)
light_curve_and_label = next(iter(light_curve_and_label_dataset))
assert light_curve_and_label[0].numpy().shape == (3, 1)
assert np.array_equal(light_curve_and_label[0].numpy(), [[0], [1], [2]]) # Standard light_curve 0.
assert np.array_equal(light_curve_and_label[1].numpy(), [0]) # Standard label 0.
def test_can_preprocess_standard_light_curve(self, deterministic_database):
database = deterministic_database
light_curve_collection = database.training_standard_light_curve_collections[0]
# noinspection PyUnresolvedReferences
light_curve_path = light_curve_collection.get_paths()[0]
load_label_from_path_function = light_curve_collection.load_label_from_path
expected_label = load_label_from_path_function(Path())
load_from_path_function = light_curve_collection.load_times_fluxes_and_flux_errors_from_path
light_curve, label = database.preprocess_standard_light_curve(load_from_path_function,
light_curve_collection.load_auxiliary_information_for_path,
load_label_from_path_function,
tf.convert_to_tensor(str(light_curve_path)))
assert light_curve.shape == (3, 1)
assert np.array_equal(light_curve, [[0], [1], [2]]) # Standard light_curve 0.
assert np.array_equal(label, [expected_label]) # Standard label 0.
def test_can_preprocess_standard_light_curve_with_passed_functions(self):
database = StandardAndInjectedLightCurveDatabase()
stub_load_times_fluxes_flux_errors_function = Mock(
return_value=(np.array([0, -1, -2]), np.array([0, 1, 2]), None))
mock_load_label_function = Mock(return_value=3)
path_tensor = tf.constant('stub_path.fits')
database.preprocess_light_curve = lambda identity, *args, **kwargs: identity
# noinspection PyTypeChecker
example, label = database.preprocess_standard_light_curve(
load_times_fluxes_and_flux_errors_from_path_function=stub_load_times_fluxes_flux_errors_function,
load_auxiliary_information_for_path_function=lambda path: np.array([], dtype=np.float32),
load_label_from_path_function=mock_load_label_function, light_curve_path_tensor=path_tensor)
assert np.array_equal(example, [[0], [1], [2]])
assert np.array_equal(label, [3])
def test_can_preprocess_injected_light_curve_with_passed_functions(self):
database = StandardAndInjectedLightCurveDatabase()
stub_load_function = Mock(return_value=(np.array([0, -1, -2]), np.array([0, 1, 2]), None))
mock_load_label_function = Mock(return_value=3)
path_tensor = tf.constant('stub_path.fits')
database.preprocess_light_curve = lambda identity, *args, **kwargs: identity
database.inject_signal_into_light_curve = lambda identity, *args, **kwargs: identity
# noinspection PyTypeChecker
example, label = database.preprocess_injected_light_curve(
injectee_load_times_fluxes_and_flux_errors_from_path_function=stub_load_function,
injectable_load_times_magnifications_and_magnification_errors_from_path_function=stub_load_function,
load_label_from_path_function=mock_load_label_function, injectee_light_curve_path_tensor=path_tensor,
injectable_light_curve_path_tensor=path_tensor)
assert np.array_equal(example, [[0], [1], [2]])
assert np.array_equal(label, [3])
@pytest.mark.slow
@pytest.mark.functional
@patch.object(database_module.np.random, 'random', return_value=0)
@patch.object(ramjet.photometric_database.light_curve_database.np.random, 'randint', return_value=0)
def test_can_generate_injected_light_curve_and_label_dataset_from_paths_dataset_and_label(self, mock_randint,
mock_random,
database_with_collections):
injectee_light_curve_collection = database_with_collections.training_injectee_light_curve_collection
injectable_light_curve_collection = database_with_collections.training_injectable_light_curve_collections[0]
injectee_paths_dataset = database_with_collections.generate_paths_dataset_from_light_curve_collection(
injectee_light_curve_collection)
injectable_paths_dataset = database_with_collections.generate_paths_dataset_from_light_curve_collection(
injectable_light_curve_collection)
light_curve_and_label_dataset = database_with_collections.generate_injected_light_curve_and_label_dataset(
injectee_paths_dataset, injectee_light_curve_collection.load_times_fluxes_and_flux_errors_from_path,
injectable_paths_dataset,
injectable_light_curve_collection.load_times_magnifications_and_magnification_errors_from_path,
injectable_light_curve_collection.load_label_from_path)
light_curve_and_label = next(iter(light_curve_and_label_dataset))
assert light_curve_and_label[0].numpy().shape == (3, 1)
assert np.array_equal(light_curve_and_label[0].numpy(), [[0.5], [3], [5.5]]) # Injected light_curve 0
assert np.array_equal(light_curve_and_label[1].numpy(), [0]) # Injected label 0.
def test_can_preprocess_injected_light_curve(self, deterministic_database):
database = deterministic_database
injectee_light_curve_collection = database.training_injectee_light_curve_collection
injectable_light_curve_collection = database.training_injectable_light_curve_collections[0]
# noinspection PyUnresolvedReferences
injectee_light_curve_path = injectee_light_curve_collection.get_paths()[0]
injectee_load_from_path_function = injectee_light_curve_collection.load_times_fluxes_and_flux_errors_from_path
# noinspection PyUnresolvedReferences
injectable_light_curve_path = injectable_light_curve_collection.get_paths()[0]
load_label_from_path_function = injectable_light_curve_collection.load_label_from_path
expected_label = load_label_from_path_function(Path())
injectable_load_from_path_function = \
injectable_light_curve_collection.load_times_magnifications_and_magnification_errors_from_path
light_curve, label = database.preprocess_injected_light_curve(injectee_load_from_path_function,
injectable_load_from_path_function,
load_label_from_path_function,
tf.convert_to_tensor(
str(injectee_light_curve_path)),
tf.convert_to_tensor(
str(injectable_light_curve_path)))
assert light_curve.shape == (3, 1)
assert np.array_equal(light_curve, [[0.5], [3], [5.5]]) # Injected light_curve 0.
assert np.array_equal(label, [expected_label]) # Injected label 0.
def test_can_create_tensorflow_dataset_for_light_curve_collection_paths(self, database_with_collections):
injectee_paths_dataset = database_with_collections.generate_paths_dataset_from_light_curve_collection(
database_with_collections.training_injectee_light_curve_collection)
assert next(iter(injectee_paths_dataset)).numpy() == b'injectee_path.ext'
def test_light_curve_collection_paths_dataset_is_repeated(self, database_with_collections):
with patch.object(database_module.tf.data.Dataset, 'repeat',
side_effect=lambda dataset: dataset, autospec=True) as mock_repeat:
_ = database_with_collections.generate_paths_dataset_from_light_curve_collection(
database_with_collections.training_injectee_light_curve_collection)
assert mock_repeat.called
def test_light_curve_collection_paths_dataset_is_shuffled(self, database_with_collections):
with patch.object(database_module.tf.data.Dataset, 'shuffle',
side_effect=lambda dataset, buffer_size: dataset, autospec=True) as mock_shuffle:
_ = database_with_collections.generate_paths_dataset_from_light_curve_collection(
database_with_collections.training_injectee_light_curve_collection)
assert mock_shuffle.called
assert mock_shuffle.call_args[0][1] == database_with_collections.shuffle_buffer_size
def test_can_create_tensorflow_datasets_for_multiple_light_curve_collections_paths(self, database_with_collections):
standard_paths_datasets = database_with_collections.generate_paths_datasets_from_light_curve_collection_list(
database_with_collections.training_standard_light_curve_collections)
assert next(iter(standard_paths_datasets[0])).numpy() == b'standard_path0.ext'
assert next(iter(standard_paths_datasets[1])).numpy() == b'standard_path1.ext'
def test_can_inject_signal_into_fluxes(self, database_with_collections):
light_curve_fluxes = np.array([1, 2, 3, 4, 5])
light_curve_times = | np.array([10, 20, 30, 40, 50]) | numpy.array |
from datetime import datetime, timezone
import numpy as np
import xarray as xr
import carbonplan_trace.v1.utils as utils
from carbonplan_trace.v0.data import cat
from carbonplan_trace.v1.glas_height_metrics import HEIGHT_METRICS_MAP, get_all_height_metrics
ECOREGIONS_GROUPINGS = {
'afrotropic': np.arange(1, 117),
'tropical_asia': np.concatenate(
(
np.arange(135, 142),
np.arange(143, 147),
np.arange(151, 167),
np.arange(217, 324),
np.array([148, 149, 188, 195, 618, 621, 622, 626, 627, 634, 635, 637, 638]),
),
axis=None,
),
'tropical_neotropic': np.concatenate(
(
np.arange(439, 561),
np.arange(564, 575),
np.arange(579, 585),
np.arange(587, 618),
np.arange(622, 626),
# 634 showed up in both tropical asia and here, determined to be more suitable for tropical asia
np.arange(628, 634),
np.arange(639, 642),
np.array([562, 619, 620, 636]),
),
axis=None,
),
'extratropical_neotropic': np.concatenate(
(
np.arange(575, 579),
np.array([561, 563, 585, 586]),
),
axis=None,
),
'alaska': np.concatenate(
(
np.arange(404, 412),
np.array([369, 371, 372, 375, 416, 420]),
),
axis=None,
),
'western_canada': np.concatenate(
(
np.arange(376, 382),
np.arange(412, 416),
np.array([383, 419]),
),
axis=None,
),
'eastern_canada': np.array([370, 373, 374, 382, 421]),
'conus': np.concatenate(
(
np.arange(328, 369),
np.arange(384, 404),
np.arange(422, 426),
np.array([325, 429, 430, 433, 434, 438]),
),
axis=None,
),
'mexico_north': np.array([324, 326, 327, 426, 428, 431, 432, 435, 436, 437]),
'mexico_south': np.array([427]),
'western_boreal_eurasia': np.array([691, 708, 711, 717, 729, 774, 776, 778, 780]),
'eastern_boreal_eurasia': np.concatenate(
(
np.arange(712, 717),
np.arange(718, 721),
| np.arange(771, 774) | numpy.arange |
# coding=utf-8
"""Implement Part Affinity Fields
:param centerA: int with shape (2,), centerA will pointed by centerB.
:param centerB: int with shape (2,), centerB will point to centerA.
:param accumulate_vec_map: one channel of paf.
:param count: store how many pafs overlaped in one coordinate of accumulate_vec_map.
:param params_transform: store the value of stride and crop_szie_y, crop_size_x
"""
import random
import sys
import cv2
import matplotlib.pyplot as plt
import numpy as np
from scipy import misc, ndimage
from mpl_toolkits.mplot3d import Axes3D
def putVecMaps(centerA, centerB, accumulate_vec_map, count, grid_y, grid_x, stride):
centerA = centerA.astype(float)
centerB = centerB.astype(float)
thre = 3 # limb width
# centerB = (centerB - 3.5) / stride
# centerA = (centerA -3.5 ) / stride
centerB = centerB / stride
centerA = centerA / stride
limb_vec = centerB - centerA
norm = np.linalg.norm(limb_vec)
if (norm == 0.0):
# print 'limb is too short, ignore it...'
return accumulate_vec_map, count
limb_vec_unit = limb_vec / norm
# print 'limb unit vector: {}'.format(limb_vec_unit)
# To make sure not beyond the border of this two points
min_x = max(int(round(min(centerA[0], centerB[0]) - thre)), 0)
max_x = min(int(round(max(centerA[0], centerB[0]) + thre)), grid_x)
min_y = max(int(round(min(centerA[1], centerB[1]) - thre)), 0)
max_y = min(int(round(max(centerA[1], centerB[1]) + thre)), grid_y)
range_x = list(range(int(min_x), int(max_x), 1))
range_y = list(range(int(min_y), int(max_y), 1))
xx, yy = np.meshgrid(range_x, range_y)
ba_x = xx - centerA[0] # the vector from (x,y) to centerA
ba_y = yy - centerA[1]
limb_width = np.abs(ba_x * limb_vec_unit[1] - ba_y * limb_vec_unit[0])
mask = limb_width < thre # mask is 2D
vec_map = np.copy(accumulate_vec_map) * 0.0
vec_map[yy, xx] = np.repeat(mask[:, :, np.newaxis], 2, axis=2)
vec_map[yy, xx] *= limb_vec_unit[np.newaxis, np.newaxis, :]
mask = np.logical_or.reduce(
(np.abs(vec_map[:, :, 0]) > 0, np.abs(vec_map[:, :, 1]) > 0))
accumulate_vec_map = np.multiply(
accumulate_vec_map, count[:, :, np.newaxis])
accumulate_vec_map += vec_map
count[mask == True] += 1
mask = count == 0
count[mask == True] = 1
accumulate_vec_map = np.divide(accumulate_vec_map, count[:, :, np.newaxis])
count[mask == True] = 0
return accumulate_vec_map, count
def putVecMasks(centerA, centerB, accumulate_vec_map, grid_y, grid_x, stride):
start = stride / 2.0 - 0.5 #3.5
y_range = [i for i in range(int(grid_y))] #46
x_range = [i for i in range(int(grid_x))] #46
xx, yy = np.meshgrid(x_range, y_range)
xx = xx * stride + start
yy = yy * stride + start
d2 = (xx - centerA[0]) ** 2 + (yy - centerA[1]) ** 2
# d21= (xx1 - center[0]) ** 2 + (yy1 - center[1]) ** 2
# exponent1 = d21 / 2.0 / sigma / sigma
exponent = d2 / 2.0 / 7 / 7
mask = exponent <= 4.6052
# mask1 = exponent1 <= 4.6052
cofid_map = np.exp(-exponent)
cofid_map = np.multiply(mask, cofid_map)
accumulate_vec_map = np.where(accumulate_vec_map > cofid_map,accumulate_vec_map,cofid_map)
d2 = (xx - centerB[0]) ** 2 + (yy - centerB[1]) ** 2
# d21= (xx1 - center[0]) ** 2 + (yy1 - center[1]) ** 2
# exponent1 = d21 / 2.0 / sigma / sigma
exponent = d2 / 2.0 / 7 / 7
mask = exponent <= 4.6052
# mask1 = exponent1 <= 4.6052
cofid_map = np.exp(-exponent)
cofid_map = np.multiply(mask, cofid_map)
accumulate_vec_map = np.where(accumulate_vec_map > cofid_map,accumulate_vec_map,cofid_map)
centerA = centerA.astype(float)
centerB = centerB.astype(float)
thre = 1 # limb width
centerB = (centerB - 3.5) / stride
centerA = (centerA - 3.5 ) / stride
limb_vec = centerB - centerA
norm = np.linalg.norm(limb_vec)
# if (norm == 0.0):
# # print 'limb is too short, ignore it...'
# return accumulate_vec_map, count
limb_vec_unit = limb_vec / norm
# print 'limb unit vector: {}'.format(limb_vec_unit)
# To make sure not beyond the border of this two points
min_x = max(int(round(min(centerA[0], centerB[0]) - thre)), 0)
max_x = min(int(round(max(centerA[0], centerB[0]) + thre)), grid_x)
min_y = max(int(round(min(centerA[1], centerB[1]) - thre)), 0)
max_y = min(int(round(max(centerA[1], centerB[1]) + thre)), grid_y)
distancex = max_x- min_x
distancey = max_y -min_y
if distancey >= distancex:
distancex += 1
max_x += 1
else:
distancey += 1
range_x = list(range(int(min_x), int(max_x), 1))
range_y = list(range(int(min_y), int(max_y), 1))
range_x1 = list(range(0, int(distancex), 1))
range_y1 = list(range(0, int(distancey), 1))
xx1,yy1 = np.meshgrid(range_x1,range_y1)
xx, yy = np.meshgrid(range_x, range_y)
ba_x = xx - centerA[0] # the vector from (x,y) to centerA
ba_y = yy - centerA[1]
limb_width = np.abs(ba_x * limb_vec_unit[1] - ba_y * limb_vec_unit[0])
sigma = 1
exponent = limb_width ** 2 / (2 * sigma * sigma)
mask_paf_mask = exponent <= 4.6052
mask_paf = np.exp(-exponent)
mask_paf = np.multiply(mask_paf,mask_paf_mask)
vec_map = np.copy(accumulate_vec_map) * 0.0
vec_map[yy, xx] = mask_paf[yy1,xx1]
accumulate_vec_map = np.where(accumulate_vec_map > vec_map,accumulate_vec_map,vec_map)
# mask = limb_width < thre # mask is 2D
# vec_map = np.copy(accumulate_vec_map) * 0.0
# vec_map[yy, xx] = mask_paf[yy1,xx1]
# vec_map = vec_map[np.newaxis,:,:]
#vec_map[yy, xx] = np.repeat(mask[:, :, np.newaxis], 2, axis=2)
# vec_map[yy, xx] *= limb_vec_unit[np.newaxis, np.newaxis, :]
# mask = np.logical_or.reduce(
# (np.abs(vec_map[:, :, 0]) > 0, np.abs(vec_map[:, :, 1]) > 0))
# accumulate_vec_map = np.multiply(
# accumulate_vec_map, count[:, :, np.newaxis])
# accumulate_vec_map += vec_map
# count[mask == True] += 1
# mask = count == 0
# count[mask == True] = 1
# accumulate_vec_map = np.divide(accumulate_vec_map, count[:, :, np.newaxis])
# count[mask == True] = 0
return accumulate_vec_map#accumulate_vec_map, count
if __name__ == "__main__":
centerA = np.array((186,100))
centerB = np.array((215,145))
paf_mask = np.zeros([38,46,46])
paf_check = np.zeros([46,46,38])
i = 0
count = np.zeros((46,46),dtype=float)
paf_mask[i,:,:] = putVecMasks(centerA,centerB,paf_mask[i,:,:],46,46,8)
paf_check[:,:,i+1:i+3],count= putVecMaps(centerA,centerB,paf_check[:,:,i+1:i+3],count,46,46,8)
# center = [108,108]
# heatmap[i,:,:],heatmap[i+1,:,:] = putGaussianMaps(center,heatmap[i,:,:],heatmap[i+1,:,:],7,46,46,8)
#x,y = np.meshgrid(x,y)
a = plt.figure()
ax =Axes3D(a)
x = np.arange(0,46,1)
y = | np.arange(0,46,1) | numpy.arange |
# import sys
# sys.path.append('..')
# sys.path.append('../..')
import numpy as np
from pulse2percept import electrode2currentmap as e2cm
from pulse2percept import effectivecurrent2brightness as ec2b
from pulse2percept import utils
from pulse2percept import files as n2sf
# import npy2savedformats as n2sf
import matplotlib.pyplot as plt
import importlib as imp
#imp.reload(n2sf)
# Recreation of the Dorn 2013 paper, where subjects had to guess the direction of motion of a moving bar
# Surgeons were instructed to place the array centered over the macula (0, 0).
# Each of the 60 electrodes (in a 6 × 10 grid) were 200 μm in diameter
# The array (along the diagonal) covered an area of retina corresponding to
#about 20° in visual angle assuming 293 μm on the retina equates to 1° of
#visual angle. a=1.72, sqrt((a*6)^2+(a*10)^2)=20 so the 10 side is 17.2 degrees,
#the 6 side is 10.32 degrees
# Create electrode array for the Argus 2
# 293 μm equals 1 degree, electrode spacing is done in microns
# when you include the radius of the electrode the electrode centers span +/- 2362 and +/- 1312
# based on Ahuja et al 2013. Factors affecting perceptual thresholds in Argus ii retinal prosthesis subjects
# (figure 4, pdf is in retina folder) the mean height from the array should be 179.6 μm
# with a range of ~50-750μm
modelver='Nanduri' # this is the standard model based on the Nanduri 2012 paper.
# Alternative model is currently the 'Krishnan' model which assumes that charge accumulation
# occurs at the electrode, not neurally. The models are in fact metamers of each other,
xlist=[]
ylist=[]
rlist=[] #electrode radius, microns
hlist=[] # lift of electrode from retinal surface, microns
e_spacing=525 # spacing in microns
for x in np.arange(-2362, 2364, e_spacing):
for y in np.arange(-1312, 1314, e_spacing):
xlist.append(x)
ylist.append(y)
rlist.append(100) # electrode radiues
hlist.append(179.6)
# electrode lift from retinal surface,
# epiretinal array - distance to the ganglion layer
# subretinal array - distance to the bipolar layer
layers=['INL', 'NFL']
e_all = e2cm.ElectrodeArray(rlist,xlist,ylist,hlist, ptype='subretinal')
del xlist, ylist, rlist, hlist
# create retina, input variables include the sampling and how much of the retina is simulated, in microns
# (0,0 represents the fovea)
retinaname='1700by2900L80S150'
r = e2cm.Retina(axon_map=None,
sampling=150, ylo=-1700, yhi=1700, xlo=-2900, xhi=2900, axon_lambda=8)
e_rf=[]
for e in e_all.electrodes:
e_rf.append(e2cm.receptive_field(e, r.gridx, r.gridy,e_spacing))
[ecs, cs] = r.electrode_ecs(e_all, integrationtype='maxrule')
tm = ec2b.TemporalModel()
# create movie
# original screen was [52.74, 63.32] visual angle, res=[768 ,1024] # resolution of screen
# pixperdeg=degscreen/res
# no need to simulate the whole movie, just match it to the electrode array, xhi+xlo/294 (microns per degree)
degscreen=[10.32+5, 17.2+5] # match to array visual angle,
res=[e_rf[0].shape[0],e_rf[1].shape[1]] # resolution of screen
fps=30
# the bar is 1.4 inches in width at 12 inches,
# corresponds to 6.67 degrees visual angle
bar_width=6.77
[X,Y]=np.meshgrid(np.linspace(-degscreen[1]/2, degscreen[1]/2, res[1]),
np.linspace(-degscreen[0]/2, degscreen[0]/2, res[0]));
for o in np.arange(0, 2*np.pi,2): #DEBUG 2*np.pi/4): # each orientation
M=np.cos(o)*X +np.sin(o)*Y
# for sp in range (32:32): # DEBUG each speed, eventually 8:32
for sp in np.arange(32, 33, 1): #(7.9, 31.6, 3):
movie=np.zeros((res[0],res[1], int(np.ceil((70/5)*30))))
st=np.min(M)
fm_ct=1
while (st< | np.max(M) | numpy.max |
# -*- coding: utf-8 -*-
def read_poscar(poscar_file_path, suppress_atom_number_ortho = True):
'''
Description:
Read information from POSCAR file
Args:
@.poscar_file_path: String format. The directory of the POSCAR file. It can either be full path or relative path
Return:
poscar_dict
l_arr: Numpy float array(np.float). Dimension is 3*3
elmtindx_arr': Numpy integer array(np.int). Element index. Start from 0
elmt_num_arr': Numpy integer array(np.int). Number of atoms for each element species
elmt_species_arr': Numpy string array. element name in the periodic for each element species
elmt_start_indx_arr': Numpy integer array(np.int). staring index for each element species in the atom_indxArr
coord_system': String type. String value of either 'Direct' or 'Cartesian'
uni_scale_fac': Float type. Universal scale factor(latice constant)
slet_dyn_on': Logic type. Selective dynamics on or off? True or False
num_header': Number of header lines. i.e. the number of lines before atomic positions
'''
args_dict = locals()
import os
import numpy as np
import sys
import time
from .. import funcs
from .. import default_params
defaults_dict = default_params.default_params()
logfile = defaults_dict['logfile']
output_dir = os.path.join(os.getcwd(), defaults_dict['output_dir_name'])
poscar_file_path = os.path.abspath(poscar_file_path)
poscar_dict = {}
file_status = funcs.file_status(poscar_file_path)
poscar_dict['file_status'] = file_status
poscar_dict['file_path'] = poscar_file_path
if file_status != 1:
print('#WARNING #20120304 (from read_poscar): The file ' + poscar_file_path + ' does not exist or is empty, please check this file.')
else:
with open(poscar_file_path) as f:
lines = f.readlines()
poscar_dict['comment'] = lines[0].strip('\n').rstrip()
poscar_dict['uni_scale_fac'] = float(funcs.split_line(lines[1])[0])
box_len_arr = np.array([0.0] * 3 * 3,dtype = np.float)
box_len_arr.shape = 3, 3
l_arr = np.array([0.0] * 3 * 3,dtype = np.float)
l_arr.shape = 3, 3
box_len_arr[0,0] = float(funcs.split_line(lines[2])[0]);box_len_arr[0,1] = float(funcs.split_line(lines[2])[1]);box_len_arr[0,2] = float(funcs.split_line(lines[2])[2])
box_len_arr[1,0] = float(funcs.split_line(lines[3])[0]);box_len_arr[1,1] = float(funcs.split_line(lines[3])[1]);box_len_arr[1,2] = float(funcs.split_line(lines[3])[2])
box_len_arr[2,0] = float(funcs.split_line(lines[4])[0]);box_len_arr[2,1] = float(funcs.split_line(lines[4])[1]);box_len_arr[2,2] = float(funcs.split_line(lines[4])[2])
poscar_dict['box_len_arr'] = box_len_arr
l_arr = box_len_arr * poscar_dict['uni_scale_fac']
# get the basis length and angle
vec_a = l_arr[0,:]
vec_b = l_arr[1,:]
vec_c = l_arr[2,:]
poscar_dict['vec_a'] = vec_a
poscar_dict['vec_b'] = vec_b
poscar_dict['vec_c'] = vec_c
#basis_vector_dict = funcs.basis_vector_info(vec_a, vec_b, vec_c)
cell_arr = np.vstack((poscar_dict['vec_a'], poscar_dict['vec_b'], poscar_dict['vec_c']))
basis_vector_dict = funcs.basis_vector_info(cell_arr)
poscar_dict['len_vec_a'] = basis_vector_dict['len_vec_a']
poscar_dict['len_vec_b'] = basis_vector_dict['len_vec_b']
poscar_dict['len_vec_c'] = basis_vector_dict['len_vec_c']
poscar_dict['a_times_b'] = np.cross(poscar_dict['vec_a'], poscar_dict['vec_b'])
poscar_dict['b_times_c'] = np.cross(poscar_dict['vec_b'], poscar_dict['vec_c'])
poscar_dict['c_times_a'] = np.cross(poscar_dict['vec_c'], poscar_dict['vec_a'])
poscar_dict['b_times_a'] = - poscar_dict['a_times_b']
poscar_dict['c_times_b'] = - poscar_dict['b_times_c']
poscar_dict['a_times_c'] = - poscar_dict['c_times_a']
poscar_dict['area_ab'] = np.linalg.norm(poscar_dict['a_times_b'])
poscar_dict['area_bc'] = np.linalg.norm(poscar_dict['b_times_c'])
poscar_dict['area_ca'] = np.linalg.norm(poscar_dict['c_times_a'])
poscar_dict['area_ba'] = poscar_dict['area_ab']
poscar_dict['area_cb'] = poscar_dict['area_bc']
poscar_dict['area_ac'] = poscar_dict['area_ca']
sorted_arg_arr = np.argsort([poscar_dict['vec_a'], poscar_dict['vec_b'], poscar_dict['vec_c']])
if all([x in sorted_arg_arr[0:2] for x in [0,1]]):
poscar_dict['area_star'] = poscar_dict['area_ab']
elif all([x in sorted_arg_arr[0:2] for x in [1,2]]):
poscar_dict['area_star'] = poscar_dict['area_bc']
elif all([x in sorted_arg_arr[0:2] for x in [2,0]]):
poscar_dict['area_star'] = poscar_dict['area_ca']
poscar_dict['angle_alpha_radian'] = basis_vector_dict['angle_alpha_radian']
poscar_dict['angle_beta_radian'] = basis_vector_dict['angle_beta_radian']
poscar_dict['angle_gamma_radian'] = basis_vector_dict['angle_gamma_radian']
poscar_dict['angle_alpha_degree'] = basis_vector_dict['angle_alpha_degree']
poscar_dict['angle_beta_degree'] = basis_vector_dict['angle_beta_degree']
poscar_dict['angle_gamma_degree'] = basis_vector_dict['angle_gamma_degree']
poscar_dict['volume'] = basis_vector_dict['volume']
poscar_dict['reciprocal_arr'] = basis_vector_dict['reciprocal_arr']
poscar_dict['car2fra_matrix_arr'] = basis_vector_dict['car2fra_matrix_arr']
poscar_dict['fra2car_matrix_arr'] = basis_vector_dict['fra2car_matrix_arr']
elmt_species_info = False
# extract string from the 6th line
sixth_line_alpha_str_list = funcs.extract_alpha_str(lines[5])
sixth_line_num_list = funcs.extract_num(lines[5])
if len(sixth_line_alpha_str_list) == 0 and len(sixth_line_num_list) != 0:
elmt_species_info = False
temp_line_indx = 6
elif len(sixth_line_alpha_str_list) != 0 and len(sixth_line_num_list) == 0:
elmt_species_info = True
temp_line_indx = 7
##print(sixth_line_alpha_str_list)
##print(sixth_line_num_list)
first_char = lines[temp_line_indx][0:1]
if first_char == "S" or first_char == "s":
poscar_dict['slet_dyn_on'] = True
poscar_dict['num_header'] = temp_line_indx + 2
first_char = lines[poscar_dict['num_header'] -1][0:1]
if first_char == "D" or first_char == "d":
poscar_dict['coord_system'] = "Direct"
elif first_char == "C" or first_char == "c":
poscar_dict['coord_system'] = "Cartesian"
elif first_char == "D" or first_char == "d" or first_char == "C" or first_char == "c":
poscar_dict['slet_dyn_on'] = False
poscar_dict['num_header'] = temp_line_indx + 1
if first_char == "D" or first_char == "d":
poscar_dict['coord_system'] = "Direct"
elif first_char == "C" or first_char == "c":
poscar_dict['coord_system'] = "Cartesian"
#-save the header of the POSCAR
poscar_dict['header'] = lines[0:poscar_dict['num_header']]
#-Get number of element species
n_species = len(funcs.split_line(lines[5]))
#-Number of atoms in the system
poscar_dict['elmtindx_arr'] = np.array([0]*n_species,dtype = np.int)
poscar_dict['elmt_species_arr'] = np.array(['--']*n_species,dtype = np.str)
poscar_dict['elmt_num_arr'] = np.array([0]*n_species,dtype = np.int)
for i in range(0,n_species):
poscar_dict['elmtindx_arr'][i] = i
if elmt_species_info == True:
poscar_dict['elmt_species_arr'][i] = funcs.split_line(lines[5])[i]
poscar_dict['elmt_num_arr'][i] = funcs.split_line(lines[6])[i]
elif elmt_species_info == False:
#poscar_dict['elmt_species_arr'][i] = funcs.split_line(lines[5])[i]
poscar_dict['elmt_num_arr'][i] = funcs.split_line(lines[5])[i]
n_atoms = sum(poscar_dict['elmt_num_arr'][:])
# Chemical formula in the order of appearence of elements in the POSCAR file
poscar_dict['formula'] = ''.join([str(poscar_dict['elmt_species_arr'][x]) + str(poscar_dict['elmt_num_arr'][x]) for x in range(len(poscar_dict['elmt_species_arr']))])
# Chemical formula in alphabetical order
sorted_arg_arr = np.argsort(poscar_dict['elmt_species_arr'])
poscar_dict['alphabetical_formula'] = ''.join([str(poscar_dict['elmt_species_arr'][x]) + str(poscar_dict['elmt_num_arr'][x]) for x in sorted_arg_arr])
#Element start index
poscar_dict['elmt_start_indx_arr'] = np.array([0]*n_species,dtype=np.int)
for i in range(0,n_species):
if i == 0:
poscar_dict['elmt_start_indx_arr'][i] = 1
else:
poscar_dict['elmt_start_indx_arr'][i] = sum(poscar_dict['elmt_num_arr'][range(0,i)])+1
#-Array atom_species_arr and atom coordinates
atom_species_arr = np.array(['--']*n_atoms,dtype=np.str)
atom_elmtindx_arr = np.array([None]*n_atoms)
atom_subindx_arr = np.array([0]*n_atoms,dtype=np.int)
atomname_list = ['']*n_atoms
indx = 0;
for i in range(0,n_species):
atom_species_arr[range(indx,indx+poscar_dict['elmt_num_arr'][i])] = [poscar_dict['elmt_species_arr'][i]]*poscar_dict['elmt_num_arr'][i]
atom_elmtindx_arr[range(indx,indx+poscar_dict['elmt_num_arr'][i])] = [poscar_dict['elmtindx_arr'][i]]*poscar_dict['elmt_num_arr'][i]
for j in range(0,poscar_dict['elmt_num_arr'][i]):
i_atom = poscar_dict['elmt_start_indx_arr'][i] + j
atom_subindx_arr[i_atom-1] = j + 1
atomname_list[i_atom-1] = str(poscar_dict['elmt_species_arr'][i]) + str(atom_subindx_arr[i_atom-1])
indx += poscar_dict['elmt_num_arr'][i]
# user added atom data in the POSCAR file
num_atom_data_column = len(funcs.split_line(lines[poscar_dict['num_header']]))
if poscar_dict['slet_dyn_on'] == True:
num_added_atom_data_column = num_atom_data_column - 6
elif poscar_dict['slet_dyn_on'] == False:
num_added_atom_data_column = num_atom_data_column - 3
added_atom_data_arr = np.array([None] * n_atoms * num_added_atom_data_column)
added_atom_data_arr.shape = n_atoms, num_added_atom_data_column
#Atom coordinates
#pos_arr is the coordinates of all the atoms, first three columns are in Direct coordinate, last three columns are in Cartesian coordinate
#coord_arr is the x, y, z coordinate in POSCAR, without the influence of lattice vector or scale factor
coord_arr = np.array([0.0]*n_atoms*3,dtype = np.float)
coord_arr.shape = n_atoms,3
fix_arr = np.array(['T']*n_atoms*3,dtype = np.str)
fix_arr.shape = n_atoms,3
pos_arr = np.array([0.0]*n_atoms*6,dtype = np.float)
pos_arr.shape = n_atoms,6
l_inv_arr = np.linalg.inv(l_arr)
for i in range(0,n_atoms):
temp = funcs.split_line(lines[poscar_dict['num_header'] +i])
coord_arr[i,0] = float(temp[0])
coord_arr[i,1] = float(temp[1])
coord_arr[i,2] = float(temp[2])
if poscar_dict['slet_dyn_on'] == True:
fix_arr[i,0:3] = temp[3:6]
added_atom_data_arr[i,0:num_added_atom_data_column] = temp[6:(6+num_added_atom_data_column)]
elif poscar_dict['slet_dyn_on'] == False:
added_atom_data_arr[i,0:num_added_atom_data_column] = temp[3:(3+num_added_atom_data_column)]
if poscar_dict['coord_system'] == "Direct":
# fractional coordinate
pos_arr[i,0:3] = coord_arr[i,0:3]
# convert the coordinate to values between 0 and 1. Values close to 1 will be replaced by 0
pos_arr[i,0:3] = np.modf(np.modf(pos_arr[i,0:3])[0] + 1)[0]
pos_arr[i,0:3][np.isclose(pos_arr[i,0:3], 1, rtol = 1e-16)] = 0
# cartesian coordinate
#pos_arr[i,3:6] = np.dot(coord_arr[i,:], l_arr)
pos_arr[i,3:6] = np.dot(pos_arr[i,0:3], l_arr)
elif poscar_dict['coord_system'] == "Cartesian":
#cartesian coordinate
pos_arr[i,3:6] = coord_arr[i,0:3] * poscar_dict['uni_scale_fac']
# fractional coordinate
pos_arr[i,0:3] = basis_vector_dict['car2fra_matrix_arr'].dot(pos_arr[i,3:6])
pos_arr[i,0:3] = np.modf(np.modf(pos_arr[i,0:3])[0] + 1)[0]
pos_arr[i,0:3][np.isclose(pos_arr[i,0:3], 1, rtol = 1e-16)] = 0
poscar_dict['n_atoms'] = int(np.sum(poscar_dict['elmt_num_arr']))
poscar_dict['num_elmts'] = len(atom_species_arr)
poscar_dict['atom_species_arr'] = atom_species_arr
poscar_dict['atom_elmtindx_arr'] = atom_elmtindx_arr
poscar_dict['atom_subindx_arr'] = atom_subindx_arr
poscar_dict['atomname_list'] = atomname_list
poscar_dict['atom_indx_arr'] = np.array([ x + 1 for x in range(0, poscar_dict['n_atoms'])]) # atom index start from 1
poscar_dict['atom_key_arr'] = np.array([ x for x in range(0, poscar_dict['n_atoms'])]) # atom key start from 0
poscar_dict['pos_arr'] = pos_arr
poscar_dict['coord_arr'] = coord_arr
poscar_dict['fix_arr'] = fix_arr
poscar_dict['l_arr'] = l_arr
poscar_dict['l_inv_arr'] = l_inv_arr
poscar_dict['xlo'] = np.min([poscar_dict['l_arr'][0,0], poscar_dict['l_arr'][1,0], poscar_dict['l_arr'][2,0], 0])
poscar_dict['xhi'] = np.max([poscar_dict['l_arr'][0,0], poscar_dict['l_arr'][1,0], poscar_dict['l_arr'][2,0], 0])
poscar_dict['ylo'] = np.min([poscar_dict['l_arr'][0,1], poscar_dict['l_arr'][1,1], poscar_dict['l_arr'][2,1], 0])
poscar_dict['yhi'] = np.max([poscar_dict['l_arr'][0,1], poscar_dict['l_arr'][1,1], poscar_dict['l_arr'][2,1], 0])
poscar_dict['zlo'] = np.min([poscar_dict['l_arr'][0,2], poscar_dict['l_arr'][1,2], poscar_dict['l_arr'][2,2], 0])
poscar_dict['zhi'] = np.max([poscar_dict['l_arr'][0,2], poscar_dict['l_arr'][1,2], poscar_dict['l_arr'][2,2], 0])
poscar_dict['added_atom_data'] = added_atom_data_arr
poscar_dict['added_atom_property'] = None
poscar_dict['added_atom_property_columns'] = None
if suppress_atom_number_ortho == False:
# atom numbering according to the order of the three orthogonal directions. This may be time consuming for large number of ions.
for number_order_text in ['xyz','yzx','zxy','xzy','yxz','zyx']:
poscar_dict['atom_number_ortho_' + number_order_text] = funcs.atom_number_ortho(
atom_key_arr = poscar_dict['atom_key_arr'],
pos_arr_cartesian= poscar_dict['pos_arr'][:,3:6],
delta = 0.05,
number_order = number_order_text
)
if 'added_atom_property=' in poscar_dict['header'][0]:
poscar_dict['added_atom_property'] = funcs.split_line(line = (funcs.split_line(line = poscar_dict['header'][0], separator = '=')[-1]), separator = ':')[0]
poscar_dict['added_atom_property_columns'] = funcs.split_line(line = poscar_dict['header'][0], separator = ':')[-1]
#print(poscar_dict['atom_number_ortho_yxz'])
return poscar_dict
def read_outcar(outcar_file_path):
'''
Description:
Read information from OUTCAR file
Args:
outcar_file_path: String format. The directory of the OUTCAR file. It can either be full path or relative path
Return:
@.outcar_params_dict
'''
args_dict = locals()
import os
import numpy as np
from .. import funcs
from .. import convert
from .. import default_params
import copy
defaults_dict = default_params.default_params()
logfile = defaults_dict['logfile']
outcar_file_path = os.path.abspath(outcar_file_path)
work_dir, outcar_file = funcs.file_path_name(outcar_file_path)
# Initialize the outcar_params_dict
outcar_params_dict = {}
outcar_params_dict['file_path'] = None
outcar_params_dict['work_dir'] = None
outcar_params_dict['num_elmt_type'] = None
outcar_params_dict['num_elmt_type_list'] = None
outcar_params_dict['file_status'] = None
outcar_params_dict['read_status'] = None
outcar_params_dict['num_atoms'] = None
outcar_params_dict['num_elmt_type'] = None
outcar_params_dict['num_elmt_type_list'] = None
outcar_params_dict['num_ionic_step'] = None
outcar_params_dict['LORBIT'] = None
outcar_params_dict['ISPIN'] = None
outcar_params_dict['e_fermi'] = None
outcar_params_dict['e_fermi_mod'] = None
outcar_params_dict['XC(G=0)'] = None
outcar_params_dict['alpha+bet'] = None
outcar_params_dict['TOTEN'] = None
outcar_params_dict['energy_without_entropy'] = None
outcar_params_dict['energy(sigma->0)'] = None
outcar_params_dict['force'] = None
outcar_params_dict['NBANDS'] = None
outcar_params_dict['elapsed_time'] = None
outcar_params_dict['NELM'] = None
outcar_params_dict['NSW'] = None
outcar_params_dict['LMAXMIX'] = None
outcar_params_dict['initial_value_dict'] = {}
outcar_params_dict['initial_value_dict'] = copy.deepcopy(outcar_params_dict)
outcar_params_dict['file_path'] = outcar_file_path
outcar_params_dict['work_dir'] = work_dir
file_status = funcs.file_status(outcar_file_path)
outcar_params_dict['file_status'] = file_status
if file_status != 1:
print('WARNING #20120312 (from read_outcar): The file ' + outcar_file_path + ' does not exist or is empty, please check this file.')
outcar_params_dict['read_status'] = 0
else:
with open(outcar_file_path,'r') as f:
line = f.readlines()
# get the elapsed time
kwd = 'timing'
num_lines = len(line)
num_tail_lines = 300
num_tail_lines = min(num_lines, num_tail_lines)
outcar_params_dict['num_ionic_step'] = funcs.grep('TOTAL-FORCE',outcar_file_path).count('TOTAL-FORCE')
for indx in range(num_lines - 1, num_lines - num_tail_lines -1, -1):
i_line = line[indx]
if kwd in i_line:
temp_line_indx = indx + 6
outcar_params_dict['elapsed_time'] = float(funcs.split_line(line = line[temp_line_indx])[-1])
def outcar_extract_info(line, outcar_params_dict):
from .. import funcs
i_ionic_step = 0
for i in range(len(line)):
if 'ions per type' in line[i]:
try:
outcar_params_dict['num_elmt_type'] = len(funcs.split_line(line = line[i], separator='=')[-1].split())
except:
pass
try:
outcar_params_dict['num_elmt_type_list'] = funcs.split_line(line = funcs.split_line(line = line[i], separator='=')[-1], separator = ' ')[:]
except:
pass
try:
outcar_params_dict['num_atoms'] = np.sum([int(item) for item in outcar_params_dict['num_elmt_type_list']])
except:
pass
try:
outcar_params_dict['force'] = np.array([None] * outcar_params_dict['num_ionic_step'] * outcar_params_dict['num_atoms'] * 6)
except:
pass
try:
outcar_params_dict['force'].shape = outcar_params_dict['num_ionic_step'] , outcar_params_dict['num_atoms'] , 6
except:
pass
if 'LORBIT' in line[i]:
try:
outcar_params_dict['LORBIT'] = int(funcs.split_line(line = line[i],separator = '=')[-1].split()[0])
except:
pass
if 'NELM' in line[i] and 'NELMIN' in line[i]:
try:
outcar_params_dict['NELM'] = int(funcs.split_line(line = line[i],separator = ';')[0].split('=')[-1])
except:
pass
if 'LMAXMIX' in line[i] and 'LMAXMIX' in line[i]:
try:
outcar_params_dict['LMAXMIX'] = int(funcs.split_line(line = line[i],separator = '=')[1].split()[0])
except:
pass
if 'NSW' in line[i]:
try:
outcar_params_dict['NSW'] = int(funcs.split_line(line = line[i],separator = '=')[-1].split()[0])
except:
pass
if 'ISPIN' in line[i]:
try:
outcar_params_dict['ISPIN'] = int(funcs.split_line(line = line[i],separator = '=')[-1].split()[0])
except:
pass
if 'E-fermi' in line[i] and len(funcs.split_line(line = line[i],separator = ':')) > 1:
try:
outcar_params_dict['e_fermi'] = float(funcs.split_line(line = line[i],separator = ':')[1].split()[0])
except:
pass
try:
outcar_params_dict['XC(G=0)'] = float(funcs.split_line(line = line[i],separator = ':')[2].split()[0])
except:
pass
try:
outcar_params_dict['alpha+bet'] = float(funcs.split_line(line = line[i],separator = ':')[-1].strip())
except:
pass
try:
outcar_params_dict['e_fermi_mod'] = outcar_params_dict['e_fermi'] + outcar_params_dict['alpha+bet']
except:
pass
if 'TOTEN' in line[i] and 'time' not in line[i] and len(funcs.split_line(line[i], '=')) > 1:
try:
outcar_params_dict['TOTEN'] = float(funcs.split_line(line[i], '=')[1].split()[0])
except:
pass
if 'energy' in line[i] and 'without' in line[i] and 'entropy' in line[i] and 'time' not in line[i] and len(funcs.split_line(line[i], '=')) == 3 and 'energy(sigma->0)' in line[i]:
try:
outcar_params_dict['energy_without_entropy'] = float(funcs.split_line(line[i], '=')[1].split()[0])
except:
pass
if 'energy' in line[i] and 'sigma' in line[i] and 'entropy' in line[i] and 'time' not in line[i]:
try:
#print(outcar_file_path, line[i])
outcar_params_dict['energy(sigma->0)'] = float(funcs.split_line(line[i], '=')[-1].split()[0])
except:
pass
if 'NBANDS' in line[i] and 'NKPTS' in line[i] and 'NKDIM' in line[i]:
try:
outcar_params_dict['NBANDS'] = int(funcs.split_line(line = line[i],separator = '=')[-1].split()[0])
except:
pass
if 'TOTAL-FORCE' in line[i] and outcar_params_dict['num_elmt_type'] != None:
try:
for i_atom in range(0, outcar_params_dict['num_atoms']):
i_atom_line = i + i_atom + 2
if len(funcs.split_line(line[i_atom_line])) != 6:
# in case of the following situation, this problem still exists until vasp5.3:
#POSITION TOTAL-FORCE (eV/Angst)
#-----------------------------------------------------------------------------------
#0.02082 0.00016 -0.02030 473254.270891 -6163.613158-493186.317939
print('WARNING (from vasp_read): The OUTCAR file format is not correct for matsdp to read\n' + outcar_file_path + '\n' + 'line number: ' + str(i_atom_line + 1) + '\n' + line[i_atom_line] + '\n' + 'trying to solve this problem ...\n')
funcs.write_log(logfile, '# WARNING (from vasp_read): Please check the format of the file: ' + outcar_file_path + '\n' + '#line number: ' + str(i_atom_line + 1) + '\n' + '#' + line[i_atom_line] + '\n' + '#trying to solve this problem ...\n')
# this formatting problem is caused by too large force on an atom
line[i_atom_line] = ' '.join(funcs.split_line(line[i_atom_line])[0:3]) + ' ' + line[i_atom_line].strip('\n').strip()[-42:-28] + ' ' + line[i_atom_line].strip('\n').strip()[-28:-14] + ' ' + line[i_atom_line].strip('\n').strip()[-14:] + '\n'
all_are_digits = True
for item in funcs.split_line(line[i_atom_line]):
try:
float(item)
except ValueError:
# not a float
all_are_digits = False
if all_are_digits == True:
print('the line ' + str(i_atom_line + 1) + ' is converted to: \n' + line[i_atom_line])
funcs.write_log(logfile, '# the line ' + str(i_atom_line + 1) + ' is converted to: \n' + '#' + line[i_atom_line])
else:
print('WARNING #20120201 (from vasp_read). The problem has not been solved. Please check the OUTCAR file ' + outcar_file_path + '\n')
funcs.write_log(logfile, '# WARNING #20120201 (from vasp_read): The problem has not been solved. Please check the OUTCAR file ' + outcar_file_path + '\n')
else:
outcar_params_dict['force'][i_ionic_step,i_atom,:] = [float(item) for item in funcs.split_line(line[i_atom_line])]
except:
pass
i_ionic_step += 1
return outcar_params_dict
try:
outcar_params_dict = outcar_extract_info(line, outcar_params_dict)
outcar_params_dict['read_status'] = 1
except:
print('WARNING #2103301011 (from vasp_read.read_outcar). Error in reading OUTCAR file. Please check the OUTCAR file ' + outcar_file_path + '\n')
outcar_params_dict['read_status'] = 0
def check_outcar_params_dict(outcar_params_dict):
read_status = 1
for i_key in outcar_params_dict.keys():
i_value = outcar_params_dict[i_key]
j_value = outcar_params_dict['initial_value_dict'][i_key]
ij_equal = funcs.variables_equal(i_value, j_value)
if ij_equal == True:
print('WARNING #2103301030 (from vasp_read.read_outcar). Error in reading outcar_params_dict[\'' + str(i_key) + '\']. Please check the OUTCAR file ' + outcar_file_path + '\n')
read_status = 0
return read_status
outcar_params_dict['read_status'] = check_outcar_params_dict(outcar_params_dict)
return outcar_params_dict
def read_doscar(doscar_file_path, atom_indx, save_dos_arr = False, write_dos_header = True):
'''
Description:
Read information from DOSCAR file.
The energy is not shifed. i.e., the Fermi energy is not shifted.
spin down DOS is mutiplied by -1
atom_indx = 0 denotes extracting the total DOS
atom_indx > 0 denotes extracting the partial DOS of each atom
For The num_columnsol columns in DOSCAR, each column denotes:
num_col = 10. energy, s, py, pz, px, dxy, dyz, dz2, dxz, dx2
num_col = 19. energy, s(up), s(dn), py(up), py(dn), pz(up), pz(dn), px(up), px(dn), dxy(up), dxy(dn), dyz(up), dyz(dn), dz2(up), dz2(dn), dxz(up), dxz(dn), dx2(up), dx2(dn)
num_col = 17. energy, s, py, pz, px, dxy, dyz, dz2, dxz, dx2, f-3, f-2, f-1, f0, f1, f2, f3
num_col = 33. energy, s(up), s(dn), py(up), py(dn), pz(up), pz(dn), px(up), px(dn), dxy(up), dxy(dn), dyz(up), dyz(dn), dz2(up), dz2(dn), dxz(up), dxz(dn), dx2(up), dx2(dn) , f-3(up) , f-3(dn), f-2(up), f-2(dn), f-1(up), f-1(dn), f0(up), f0(dn), f1(up), f1(dn), f2(up), f2(dn), f3(up), f3(dn)
For the noncollinear case:
num_col = 37, energy, s, s(mx), s(my), s(mz),
py, py(mx), py(my), py(mz),
pz, pz(mx), pz(my), py(mz),
px, px(mx), px(my), px(mz),
dxy, dxy(mx), dxy(my), dxy(mz)
dyz, dyz(mx), dyz(my), dyz(mz)
dz2, dz2(mx), dz2(my), dz2(mz)
dxz, dxz(mx), dxz(my), dxz(mz)
dx2, dx2(mx), dx2(my), dx2(mz)
orbital designation:
YLM(:,1) -> s
YLM(:,2:4) -> p:= y, z, x
YLM(:,5:9) -> d:= xy, yz, z2, xz, x2
YLM(:,10:16) -> f:= y(3x2-y2), xyz, yz2, z3, xz2, z(x2-y2), x(x2-3y2)
Args:
@.doscar_file_path: String format. The directory of the DOSCAR file. It can either be full path or relative path
@.atom_indx: Integer format. The real atom index in the POSCAR. If there are N atoms then the atom indices are frim 1 to N. Note that atom_indx = 0 means to extract TDOS inoformation
@save_dos_arr: logical value. Determine whether to save the dos_arr to a file or not.
Return:
@.dos_arr: nedos * num_columnsol array type. It contains the density of states
'''
args_dict = locals()
import os
import numpy as np
from .. import funcs
from .. import default_params
defaults_dict = default_params.default_params()
logfile = defaults_dict['logfile']
doscar_file_path = os.path.abspath(doscar_file_path)
workdir, dos_file = funcs.file_path_name(doscar_file_path)
doscar_dict = {}
file_status = funcs.file_status(doscar_file_path)
doscar_dict['file_status'] = file_status
##doscar_dict['num_columns'] = None
nc3_list = ['energy', 'DOS', 'Int_DOS']
nc5_list = ['energy', 'DOS(up)', 'DOS(dn)', 'Int_DOS(up)', 'Int_DOS(dn)']
nc10_list = ['energy', 's', 'py', 'pz', 'px', 'dxy', 'dyz', 'dz2', 'dxz', 'dx2']
nc19_list = ['energy', 's(up)', 's(dn)', 'py(up)', 'py(dn)', 'pz(up)', 'pz(dn)', 'px(up)', 'px(dn)', 'dxy(up)', 'dxy(dn)', 'dyz(up)', 'dyz(dn)', 'dz2(up)', 'dz2(dn)', 'dxz(up)', 'dxz(dn)', 'dx2(up)', 'dx2(dn)']
nc17_list = ['energy', 's', 'py', 'pz', 'px', 'dxy', 'dyz', 'dz2', 'dxz', 'dx2', 'f-3', 'f-2', 'f-1', 'f0', 'f1', 'f2', 'f3']
nc33_list = ['energy', 's(up)', 's(dn)', 'py(up)', 'py(dn)', 'pz(up)', 'pz(dn)', 'px(up)', 'px(dn)', 'dxy(up)', 'dxy(dn)', 'dyz(up)', 'dyz(dn)', 'dz2(up)', 'dz2(dn)', 'dxz(up)', 'dxz(dn)', 'dx2(up)', 'dx2(dn)' , 'f-3(up)' , 'f-3(dn)', 'f-2(up)', 'f-2(dn)', 'f-1(up)', 'f-1(dn)', 'f0(up)', 'f0(dn)', 'f1(up)', 'f1(dn)', 'f2(up)', 'f2(dn)', 'f3(up)', 'f3(dn)']
nc37_list = ['energy', 's', 's(mx)', 's(my)', 's(mz)',
'py', 'py(mx)', 'py(my)', 'py(mz)',
'pz', 'pz(mx)', 'pz(my)', 'py(mz)',
'px', 'px(mx)', 'px(my)', 'px(mz)',
'dxy', 'dxy(mx)', 'dxy(my)', 'dxy(mz)',
'dyz', 'dyz(mx)', 'dyz(my)', 'dyz(mz)',
'dz2', 'dz2(mx)', 'dz2(my)', 'dz2(mz)',
'dxz', 'dxz(mx)', 'dxz(my)', 'dxz(mz)',
'dx2', 'dx2(mx)', 'dx2(my)', 'dx2(mz)'
]
nc65_list = ['energy', 's', 's(mx)', 's(my)', 's(mz)',
'py', 'py(mx)', 'py(my)', 'py(mz)',
'pz', 'pz(mx)', 'pz(my)', 'py(mz)',
'px', 'px(mx)', 'px(my)', 'px(mz)',
'dxy', 'dxy(mx)', 'dxy(my)', 'dxy(mz)',
'dyz', 'dyz(mx)', 'dyz(my)', 'dyz(mz)',
'dz2', 'dz2(mx)', 'dz2(my)', 'dz2(mz)',
'dxz', 'dxz(mx)', 'dxz(my)', 'dxz(mz)',
'dx2', 'dx2(mx)', 'dx2(my)', 'dx2(mz)'
'f-3', 'f-3(mx)', 'f-3(my)', 'f-3(mz)'
'f-2', 'f-2(mx)', 'f-2(my)', 'f-2(mz)'
'f-1', 'f-1(mx)', 'f-1(my)', 'f-1(mz)'
'f0', 'f0(mx)', 'f0(my)', 'f0(mz)'
'f1', 'f1(mx)', 'f1(my)', 'f1(mz)'
'f2', 'f2(mx)', 'f2(my)', 'f2(mz)'
'f3', 'f3(mx)', 'f3(my)', 'f3(mz)'
]
if file_status != 1:
print('WARNING #20120313 (from read_doscar): The file ' + doscar_file_path + ' does not exist or is empty, please check this file.')
else:
#Also Required files are OUTCAR and POSCAR
num_columns = None
with open(doscar_file_path,'r') as f:
lines = f.readlines()
n_atoms = int(funcs.split_line(lines[0])[0])
nedos = int(funcs.split_line(lines[5])[2])
e_fermi = float(funcs.split_line(lines[5])[3])
## funcs.write_log(logfile, 'n_atoms = ' + str(n_atoms) + ' nedos = ' + str(nedos) + ' e_fermi(Unmodified) = ' + str(e_fermi))
if isinstance(atom_indx, int) and atom_indx == 0:
#TDOS
start_line = 6
end_line = start_line + nedos - 1
num_columns = len(funcs.split_line(lines[start_line]))
dos_arr = np.array([0.000000]*nedos*num_columns,dtype = np.float)
dos_arr.shape = nedos,num_columns
for i in range(0,nedos):
for j in range(0,num_columns):
dos_arr[i][j] = float(funcs.split_line(lines[start_line + i])[j]) * funcs.logic_retn_val(j % 2 == 0 and j > 0, -1, 1)
dos_file = os.path.join(workdir, 'TDOS.dat')
elif isinstance(atom_indx, int) and atom_indx != 0:
#DOS
start_line = 6 + (nedos + 1) * atom_indx
end_line = start_line + nedos - 1
num_columns = len(funcs.split_line(lines[start_line]))
dos_arr = np.array([0.000000] * nedos * num_columns,dtype = np.float)
dos_arr.shape = nedos,num_columns
if num_columns == 10 or num_columns == 17 or num_columns == 37:
for i in range(0,nedos):
for j in range(0,num_columns):
dos_arr[i][j] = float(funcs.split_line(lines[start_line + i])[j])
elif num_columns == 19 or num_columns == 33:
for i in range(0,nedos):
for j in range(0,num_columns):
dos_arr[i][j] = float(funcs.split_line(lines[start_line + i])[j]) * funcs.logic_retn_val(j % 2 == 0 and j > 0, -1, 1)
dos_file = os.path.join(workdir, 'DOS' + str(atom_indx) + '.dat')
elif isinstance(atom_indx, list):
# This is for the case of LDOS of multiple atoms.
for i_atom_indx in atom_indx:
start_line = 6 + (nedos + 1) * i_atom_indx
end_line = start_line + nedos - 1
num_columns = len(funcs.split_line(lines[start_line]))
dos_arr = np.array([0.000000] * nedos * num_columns,dtype = np.float)
dos_arr.shape = nedos,num_columns
if num_columns == 10 or num_columns == 17 or num_columns == 37:
for i in range(0,nedos):
for j in range(0,num_columns):
dos_arr[i][j] = dos_arr[i][j] + float(funcs.split_line(lines[start_line + i])[j])
elif num_columns == 19 or num_columns == 33:
for i in range(0,nedos):
for j in range(0,num_columns):
dos_arr[i][j] = dos_arr[i][j] + float(funcs.split_line(lines[start_line + i])[j]) * funcs.logic_retn_val(j % 2 == 0 and j > 0, -1, 1)
dos_file = os.path.join(workdir, 'DOS_' + '+'.join([str(x) for x in atom_indx]) + '.dat')
temp_list = []
nc_list = [3, 5, 10, 19, 17, 33, 37, 65]
nc_tag_list = [nc3_list, nc5_list, nc10_list, nc19_list, nc17_list, nc33_list, nc37_list, nc65_list]
for i_indx in range(len(nc_list)):
if num_columns == nc_list[i_indx]:
temp_list = nc_tag_list[i_indx]
header_str = ''.join([funcs.str_format(x, max_len = 18, padding_str = ' ', padding_str_loc = 'l') for x in temp_list])
if save_dos_arr == True:
if write_dos_header == False or write_dos_header is None:
header_str = ''
np.savetxt(dos_file, dos_arr, fmt = '%17.4E', header = header_str)
else:
pass
doscar_dict['atom_indx'] = atom_indx
doscar_dict['num_col'] = num_columns
doscar_dict['dos_arr'] = dos_arr
doscar_dict['energy'] = dos_arr[:,[0]]
if doscar_dict['num_col'] == 3:
doscar_dict['TDOS'] = dos_arr[:,[1]]
doscar_dict['IntDOS'] = dos_arr[:,[2]]
elif doscar_dict['num_col'] == 5:
doscar_dict['TDOS_up'] = dos_arr[:,[1]]
doscar_dict['TDOS_dn'] = dos_arr[:,[2]]
doscar_dict['TDOS'] = doscar_dict['TDOS_up'] - doscar_dict['TDOS_dn']
doscar_dict['IntDOS_up'] = dos_arr[:,[3]]
doscar_dict['IntDOS_dn'] = dos_arr[:,[4]]
doscar_dict['IntDOS'] = doscar_dict['IntDOS_up'] - doscar_dict['IntDOS_dn']
elif doscar_dict['num_col'] == 37:
doscar_dict['s'] = dos_arr[:,[1]]
doscar_dict['s_mx'] = dos_arr[:,[2]]
doscar_dict['s_my'] = dos_arr[:,[3]]
doscar_dict['s_mz'] = dos_arr[:,[4]]
doscar_dict['py'] = dos_arr[:,[5]]
doscar_dict['py_mx'] = dos_arr[:,[6]]
doscar_dict['py_my'] = dos_arr[:,[7]]
doscar_dict['py_mz'] = dos_arr[:,[8]]
doscar_dict['pz'] = dos_arr[:,[9]]
doscar_dict['pz_mx'] = dos_arr[:,[10]]
doscar_dict['pz_my'] = dos_arr[:,[11]]
doscar_dict['pz_mz'] = dos_arr[:,[12]]
doscar_dict['px'] = dos_arr[:,[13]]
doscar_dict['px_mx'] = dos_arr[:,[14]]
doscar_dict['px_my'] = dos_arr[:,[15]]
doscar_dict['px_mz'] = dos_arr[:,[16]]
doscar_dict['dxy'] = dos_arr[:,[17]]
doscar_dict['dxy_mx'] = dos_arr[:,[18]]
doscar_dict['dxy_my'] = dos_arr[:,[19]]
doscar_dict['dxy_mz'] = dos_arr[:,[20]]
doscar_dict['dyz'] = dos_arr[:,[21]]
doscar_dict['dyz_mx'] = dos_arr[:,[22]]
doscar_dict['dyz_my'] = dos_arr[:,[23]]
doscar_dict['dyz_mz'] = dos_arr[:,[24]]
doscar_dict['dz2'] = dos_arr[:,[25]]
doscar_dict['dz2_mx'] = dos_arr[:,[26]]
doscar_dict['dz2_my'] = dos_arr[:,[27]]
doscar_dict['dz2_mz'] = dos_arr[:,[28]]
doscar_dict['dxz'] = dos_arr[:,[29]]
doscar_dict['dxz_mx'] = dos_arr[:,[30]]
doscar_dict['dxz_my'] = dos_arr[:,[31]]
doscar_dict['dxz_mz'] = dos_arr[:,[32]]
doscar_dict['dx2'] = dos_arr[:,[33]]
doscar_dict['dx2_mx'] = dos_arr[:,[34]]
doscar_dict['dx2_my'] = dos_arr[:,[35]]
doscar_dict['dx2_mz'] = dos_arr[:,[36]]
doscar_dict['p'] = doscar_dict['py'] + doscar_dict['pz'] + doscar_dict['px']
doscar_dict['d'] = doscar_dict['dxy'] + doscar_dict['dyz'] + doscar_dict['dz2'] + doscar_dict['dxz'] + doscar_dict['dx2']
doscar_dict['LDOS'] = doscar_dict['s'] + doscar_dict['p'] + doscar_dict['d']
elif doscar_dict['num_col'] == 10 or doscar_dict['num_col'] == 17:
doscar_dict['s'] = dos_arr[:,[1]]
doscar_dict['py'] = dos_arr[:,[2]]
doscar_dict['pz'] = dos_arr[:,[3]]
doscar_dict['px'] = dos_arr[:,[4]]
doscar_dict['dxy'] = dos_arr[:,[5]]
doscar_dict['dyz'] = dos_arr[:,[6]]
doscar_dict['dz2'] = dos_arr[:,[7]]
doscar_dict['dxz'] = dos_arr[:,[8]]
doscar_dict['dx2'] = dos_arr[:,[9]]
doscar_dict['p'] = doscar_dict['py'] + doscar_dict['pz'] + doscar_dict['px']
doscar_dict['d'] = doscar_dict['dxy'] + doscar_dict['dyz'] + doscar_dict['dz2'] + doscar_dict['dxz'] + doscar_dict['dx2']
doscar_dict['LDOS'] = doscar_dict['s'] + doscar_dict['p'] + doscar_dict['d']
if doscar_dict['num_col'] == 17:
doscar_dict['fm3'] = dos_arr[:,[10]]
doscar_dict['fm2'] = dos_arr[:,[11]]
doscar_dict['fm1'] = dos_arr[:,[12]]
doscar_dict['f0'] = dos_arr[:,[13]]
doscar_dict['f1'] = dos_arr[:,[14]]
doscar_dict['f2'] = dos_arr[:,[15]]
doscar_dict['f3'] = dos_arr[:,[16]]
doscar_dict['f'] = doscar_dict['fm3'] + doscar_dict['fm2'] + doscar_dict['fm1'] + doscar_dict['f0'] + doscar_dict['f1'] + doscar_dict['f2'] + doscar_dict['f3']
doscar_dict['LDOS'] = doscar_dict['s'] + doscar_dict['p'] + doscar_dict['d'] + doscar_dict['f']
elif doscar_dict['num_col'] == 19 or doscar_dict['num_col'] == 33:
doscar_dict['s_up'] = dos_arr[:,[1]]
doscar_dict['s_dn'] = dos_arr[:,[2]]
doscar_dict['py_up'] = dos_arr[:,[3]]
doscar_dict['py_dn'] = dos_arr[:,[4]]
doscar_dict['pz_up'] = dos_arr[:,[5]]
doscar_dict['pz_dn'] = dos_arr[:,[6]]
doscar_dict['px_up'] = dos_arr[:,[7]]
doscar_dict['px_dn'] = dos_arr[:,[8]]
doscar_dict['dxy_up'] = dos_arr[:,[9]]
doscar_dict['dxy_dn'] = dos_arr[:,[10]]
doscar_dict['dyz_up'] = dos_arr[:,[11]]
doscar_dict['dyz_dn'] = dos_arr[:,[12]]
doscar_dict['dz2_up'] = dos_arr[:,[13]]
doscar_dict['dz2_dn'] = dos_arr[:,[14]]
doscar_dict['dxz_up'] = dos_arr[:,[15]]
doscar_dict['dxz_dn'] = dos_arr[:,[16]]
doscar_dict['dx2_up'] = dos_arr[:,[17]]
doscar_dict['dx2_dn'] = dos_arr[:,[18]]
doscar_dict['s'] = doscar_dict['s_up'] - doscar_dict['s_dn']
doscar_dict['p_up'] = doscar_dict['py_up'] + doscar_dict['pz_up'] + doscar_dict['px_up']
doscar_dict['p_dn'] = doscar_dict['py_dn'] + doscar_dict['pz_dn'] + doscar_dict['px_dn']
doscar_dict['py'] = doscar_dict['py_up'] - doscar_dict['py_dn']
doscar_dict['pz'] = doscar_dict['pz_up'] - doscar_dict['pz_dn']
doscar_dict['px'] = doscar_dict['px_up'] - doscar_dict['px_dn']
doscar_dict['p'] = doscar_dict['p_up'] - doscar_dict['p_dn']
doscar_dict['d_up'] = doscar_dict['dxy_up'] + doscar_dict['dyz_up'] + doscar_dict['dz2_up'] + doscar_dict['dxz_up'] + doscar_dict['dx2_up']
doscar_dict['d_dn'] = doscar_dict['dxy_dn'] + doscar_dict['dyz_dn'] + doscar_dict['dz2_dn'] + doscar_dict['dxz_dn'] + doscar_dict['dx2_dn']
doscar_dict['dxy'] = doscar_dict['dxy_up'] - doscar_dict['dxy_dn']
doscar_dict['dyz'] = doscar_dict['dyz_up'] - doscar_dict['dyz_dn']
doscar_dict['dz2'] = doscar_dict['dz2_up'] - doscar_dict['dz2_dn']
doscar_dict['dxz'] = doscar_dict['dxz_up'] - doscar_dict['dx2_dn']
doscar_dict['dx2'] = doscar_dict['dx2_up'] - doscar_dict['dx2_dn']
doscar_dict['d'] = doscar_dict['d_up'] - doscar_dict['d_dn']
doscar_dict['LDOS'] = doscar_dict['s'] + doscar_dict['p'] + doscar_dict['d']
doscar_dict['LDOS_up'] = doscar_dict['s_up'] + doscar_dict['p_up'] + doscar_dict['d_up']
doscar_dict['LDOS_dn'] = doscar_dict['s_dn'] + doscar_dict['p_dn'] + doscar_dict['d_dn']
if doscar_dict['num_col'] == 33:
doscar_dict['fm3_up'] = dos_arr[:,[19]]
doscar_dict['fm3_dn'] = dos_arr[:,[20]]
doscar_dict['fm2_up'] = dos_arr[:,[21]]
doscar_dict['fm2_dn'] = dos_arr[:,[22]]
doscar_dict['fm1_up'] = dos_arr[:,[23]]
doscar_dict['fm1_dn'] = dos_arr[:,[24]]
doscar_dict['f0_up'] = dos_arr[:,[25]]
doscar_dict['f0_dn'] = dos_arr[:,[26]]
doscar_dict['f1_up'] = dos_arr[:,[27]]
doscar_dict['f1_dn'] = dos_arr[:,[28]]
doscar_dict['f2_up'] = dos_arr[:,[29]]
doscar_dict['f2_dn'] = dos_arr[:,[30]]
doscar_dict['f3_up'] = dos_arr[:,[31]]
doscar_dict['f3_dn'] = dos_arr[:,[32]]
doscar_dict['f_up'] = doscar_dict['fm3_up'] + doscar_dict['fm2_up'] + doscar_dict['fm1_up'] + doscar_dict['f0_up'] + doscar_dict['f1_up'] + doscar_dict['f2_up'] + doscar_dict['f3_up']
doscar_dict['f_dn'] = doscar_dict['fm3_dn'] + doscar_dict['fm2_dn'] + doscar_dict['fm1_dn'] + doscar_dict['f0_dn'] + doscar_dict['f1_dn'] + doscar_dict['f2_dn'] + doscar_dict['f3_dn']
doscar_dict['f'] = doscar_dict['f_up'] - doscar_dict['f_dn']
doscar_dict['LDOS'] = doscar_dict['s'] + doscar_dict['p'] + doscar_dict['d'] + doscar_dict['f']
doscar_dict['LDOS_up'] = doscar_dict['s_up'] + doscar_dict['p_up'] + doscar_dict['d_up'] + doscar_dict['f_up']
doscar_dict['LDOS_dn'] = doscar_dict['s_dn'] + doscar_dict['p_dn'] + doscar_dict['d_dn'] + doscar_dict['f_dn']
return doscar_dict
def read_oszicar(oszicar_file_path, save_fig = False, dpi = 100):
'''
Read OSZICAR
'''
args_dict = locals()
import os
import numpy as np
from .. import funcs
import copy
try:
import matplotlib.pyplot as plt
except:
pass
oszicar_file_path = os.path.abspath(oszicar_file_path)
work_dir, oszicar_file = funcs.file_path_name(oszicar_file_path)
#initializethe OSZICAR dictionary
oszicar_dict = {}
oszicar_dict['file_status'] = None
oszicar_dict['file_path'] = None
oszicar_dict['num_ionic_steps'] = None
oszicar_dict['ionic_step_line_indx_list'] = []
oszicar_dict['num_electronic_steps_list'] = []
oszicar_dict['mag_list'] = []
oszicar_dict['etot_arr'] = np.array([])
oszicar_dict['initial_value_dict'] = {}
oszicar_dict['initial_value_dict'] = copy.deepcopy(oszicar_dict)
oszicar_dict['file_status'] = funcs.file_status(oszicar_file_path)
oszicar_dict['file_path'] = oszicar_file_path
if oszicar_dict['file_status'] != 1:
print('WARNING #20120307 (from read_oszicar): File ' + oszicar_file_path + ' does not exist or is empty. Please check this file.')
else:
with open(oszicar_file_path,'r') as f:
line = f.readlines()
def oszicar_extract_info(line, oszicar_dict):
from .. import funcs
# get the number of ionic steps
num_ionic_steps = 0
for i_line in range(len(line)):
if len(funcs.split_line(line[i_line])) > 1:
if funcs.split_line(line[i_line])[1] == 'F=':
num_ionic_steps += 1
oszicar_dict['ionic_step_line_indx_list'].append(i_line)
mag_str = funcs.split_line(line = line[i_line], separator = '=')[-1]
mag_list = mag_str.replace('\t', ' ').strip('\n').strip().split(' ')
oszicar_dict['mag_list'].append(funcs.split_line(line = line[i_line], separator = '=')[-1])
oszicar_dict['num_ionic_steps'] = num_ionic_steps
# get num_electronic_steps_list
ionic_step = 0
for i_line in range(len(line)):
if len(funcs.split_line(line[i_line])) > 1:
if funcs.split_line(line[i_line])[1] == 'F=':
# get information about electronic steps
last_electronic_step_found = True
if ionic_step == 0:
temp_line = 0
else:
temp_line = oszicar_dict['ionic_step_line_indx_list'][ionic_step - 1]
#print('INI, FIN=', i_line, temp_line)
for j_line in range(i_line, temp_line, -1):
#print('ionic=', ionic_step, 'j_line=',j_line)
if line[j_line][0:5] in ['CG : ', 'DIA: ', 'NONE ', 'RMM: ', 'DAV: ']:
if last_electronic_step_found == True:
oszicar_dict['num_electronic_steps_list'].append(int(line[j_line][5:8]))
last_electronic_step_found = False
ionic_step = ionic_step + 1
#Get etot_arr
# solely read etot_arr will avoid interupting getting num_electronic)steps_list if etot_arr cannot be read.
oszicar_dict['etot_arr'] = np.array([None] * num_ionic_steps)
ionic_step = 0
for i_line in range(len(line)):
if len(funcs.split_line(line[i_line])) > 1:
if funcs.split_line(line[i_line])[1] == 'F=':
# get information about electronic steps
last_electronic_step_found = True
if ionic_step == 0:
temp_line = 0
else:
temp_line = oszicar_dict['ionic_step_line_indx_list'][ionic_step - 1]
for j_line in range(i_line, temp_line, -1):
if len(funcs.split_line(line[i_line])) > 2:
#print('------------ionic = ',ionic_step)
oszicar_dict['etot_arr'][ionic_step] = float(funcs.split_line(line[i_line])[2])
ionic_step = ionic_step + 1
return oszicar_dict
try:
oszicar_dict = oszicar_extract_info(line, oszicar_dict)
except:
print('WARNING #2103311236 (from vasp_read.read_oszicar). Error in reading OSZICAR file. Please check the OSZICAR file ' + oszicar_file_path + '\n')
if save_fig == True:
try:
fig, ax = plt.subplots()
plt.plot(range(len(etot_arr)), etot_arr, marker = '.')
ax.set(xlabel = 'Ionic steps')
ax.set(ylabel = '$E_{tot}(eV)$')
etot_oszicar_figfile = os.path.join(work_dir, 'etot_oszicar.pdf')
plt.savefig(etot_oszicar_figfile,dpi = dpi)
plt.close
except:
pass
def check_oszicar_dict(oszicar_dict):
for i_key in oszicar_dict.keys():
i_value = oszicar_dict[i_key]
j_value = oszicar_dict['initial_value_dict'][i_key]
#if isinstance(j_value,(list,pd.core.series.Series,np.ndarray)):
ij_equal = funcs.variables_equal(i_value, j_value)
if ij_equal == True:
print('WARNING #2103302253 (from vasp_read.read_oszicar). Error in reading oszicar_dict[\'' + str(i_key) + '\']. Please check the OSZICAR file ' + oszicar_file_path + '\n')
return 0
check_oszicar_dict(oszicar_dict)
return oszicar_dict
def read_kpoints(kpoints_file_path):
'''Read KPOINTS'''
args_dict = locals()
import os
import numpy as np
from .. import funcs
from .. import default_params
defaults_dict = default_params.default_params()
logfile = defaults_dict['logfile']
kpoints_file_path = os.path.abspath(kpoints_file_path)
work_dir, kpt_file_name = funcs.file_path_name(kpoints_file_path)
poscar_file_path = os.path.join(work_dir, 'POSCAR')
poscar_dict = read_poscar(poscar_file_path)
poscar_file_status = poscar_dict['file_status']
kpoints_dict = {}
kpoints_dict['file_path'] = None
kpoints_dict['file_status'] = None
kpoints_dict['comment'] = None
kpoints_dict['scheme'] = None
kpoints_dict['num_kpoints'] = None
kpoints_dict['length_param'] = None
kpoints_dict['subdivisions_arr'] = None
kpoints_dict['origin_shift_arr'] = None
kpoints_dict['coord_type'] = None
kpoints_dict['kpath'] = None
kpoints_dict['num_intersections'] = None
kpoints_dict['kpath_nodes_xaxis_tick_list'] = None
kpoints_dict['num_kpath_nodes'] = None
kpoints_dict['kpath_nodes_list'] = None
kpoints_dict['kpath_left_right_list'] = None
kpoints_dict['num_intersections_interval'] = None
kpoints_dict['num_kpoints_xaxis'] = None
kpoints_dict['intersections_end_kpt_list'] = None
kpoints_dict['kpoints_xaxis_arr'] = None
kpoints_dict['bs_xaxis_label_list'] = None
kpoints_dict['bs_xaxis_tick_list'] = None
kpoints_dict['file_path'] = kpoints_file_path
kpoints_file_status = funcs.file_status(kpoints_file_path)
kpoints_dict['file_status'] = kpoints_file_status
if kpoints_file_status != 1 or poscar_file_status != 1:
print('WARNING #20120308 (from read_kpoints): ' + kpoints_file_path + ' or ' + poscar_file_path + ' does not exist or is empty!')
else:
subdivisions_arr = np.array([None] * 3)
origin_shift_arr = np.array([None] * 3)
with open(kpoints_file_path,'r') as f:
line = f.readlines()
num_lines = len(line)
kpoints_dict['comment'] = line[0]
kpoints_dict['scheme'] = line[2][0]
if kpoints_dict['scheme'] in ['a', 'A']:
kpoints_dict['num_kpoints'] = int(funcs.split_line(line[1])[0])
kpoints_dict['length_param'] = float(funcs.split_line(line[3])[0])
elif kpoints_dict['scheme'] in ['g', 'G', 'm', 'M'] or kpoints_dict['scheme'] in ['c', 'C', 'k', 'K']:
try:
num_kpoints_temp = int(funcs.split_line(line[1])[0])
except:
num_kpoints_temp = funcs.split_line(line[1])[0]
if isinstance(num_kpoints_temp, str):
kpoints_dict['num_kpoints'] = 0
else:
kpoints_dict['num_kpoints'] = int(num_kpoints_temp)
if kpoints_dict['num_kpoints'] == 0:
subdivisions_arr_0 = funcs.split_line(line[3])[0]
subdivisions_arr_1 = funcs.split_line(line[3])[1]
subdivisions_arr_2 = funcs.split_line(line[3])[2]
try:
subdivisions_arr[0] = int(float(subdivisions_arr_0))
subdivisions_arr[1] = int(float(subdivisions_arr_1))
subdivisions_arr[2] = int(float(subdivisions_arr_2))
except:
#if the type of value is string, we denote it as a meaningless negative number
subdivisions_arr[0] = -999999
subdivisions_arr[1] = -999999
subdivisions_arr[2] = -999999
kpoints_dict['subdivisions_arr'] = subdivisions_arr
origin_shift_arr_0 = funcs.split_line(line[4])[0]
origin_shift_arr_1 = funcs.split_line(line[4])[1]
origin_shift_arr_2 = funcs.split_line(line[4])[2]
if isinstance(origin_shift_arr_0, str):
origin_shift_arr[0] = 0
else:
origin_shift_arr[0] = float(origin_shift_arr_0)
if isinstance(origin_shift_arr_1, str):
origin_shift_arr[1] = 0
else:
origin_shift_arr[1] = float(origin_shift_arr_1)
if isinstance(origin_shift_arr_2, str):
origin_shift_arr[2] = 0
else:
origin_shift_arr[2] = float(origin_shift_arr_2)
kpoints_dict['origin_shift_arr'] = origin_shift_arr
elif kpoints_dict['num_kpoints'] != 0:
kpoints_dict['num_intersections'] = int(funcs.split_line(line[1])[0])
kpoints_dict['coord_type'] = str(funcs.split_line(line[2])[0])[0]
kpath_nodes_coord_x_list = []
kpath_nodes_coord_y_list = []
kpath_nodes_coord_z_list = []
kpath_nodes_label_list = []
last_high_symm_kpt_label = None
kpt_label_list = []
#get high symmetry k points (units in cartesian coordinate)
kpoints_dict['bs_xaxis_label_list'] = []
for i_line in range(3, num_lines):
if len(funcs.split_line(line[i_line])) == 0:
continue
elif len(funcs.split_line(line[i_line])) != 0:
if funcs.split_line(line[i_line])[0][0] == '#':
continue
high_symm_kpt_x = float(funcs.split_line(line[i_line])[0])
high_symm_kpt_y = float(funcs.split_line(line[i_line])[1])
high_symm_kpt_z = float(funcs.split_line(line[i_line])[2])
temp_x = high_symm_kpt_x
temp_y = high_symm_kpt_y
temp_z = high_symm_kpt_z
high_symm_kpt_label = ''.join(funcs.split_line(line[i_line])[3:]).strip('!').strip('\\')
kpoints_dict['bs_xaxis_label_list'].append(high_symm_kpt_label)
###############################################################################################################
# if the coordinate is reciprocal, change it to Cartesian (See VASP manual: VASP the Guide)
# \vec{k}=x_{1}\vec{b}_{1}+x_{2}\vec{b}_{2}+x_{3}\vec{b}_{3}
# where {\vec b}}_{{1...3}} are the three reciprocal basis vectors, and x_{{1...3}} are the values you supply.
###############################################################################################################
if kpoints_dict['coord_type'] in ['R', 'r']:
high_symm_kpt_x = temp_x * poscar_dict['reciprocal_arr'][0,0] + temp_y * poscar_dict['reciprocal_arr'][1,0] + temp_z * poscar_dict['reciprocal_arr'][2,0]
high_symm_kpt_y = temp_x * poscar_dict['reciprocal_arr'][0,1] + temp_y * poscar_dict['reciprocal_arr'][1,1] + temp_z * poscar_dict['reciprocal_arr'][2,1]
high_symm_kpt_z = temp_x * poscar_dict['reciprocal_arr'][0,2] + temp_y * poscar_dict['reciprocal_arr'][1,2] + temp_z * poscar_dict['reciprocal_arr'][2,2]
############################################################################################
# if the coordinate is Cartesian, the kpoints are given by (See VASP manual: VASP the Guide)
# \vec{k}=2*\pi/a*(x_{1}, x_{2}, x_(3))
# where a is the scaling parameter you have specified on the second line of the POSCAR file.
############################################################################################
if kpoints_dict['coord_type'] in ['C', 'c']:
high_symm_kpt_x = 2 * np.pi / poscar_dict['uni_scale_fac'] * temp_x
high_symm_kpt_y = 2 * np.pi / poscar_dict['uni_scale_fac'] * temp_y
high_symm_kpt_z = 2 * np.pi / poscar_dict['uni_scale_fac'] * temp_z
# Change the labeling of the band to LaTeX format
kpt_label_list.append(high_symm_kpt_label)
kpath_nodes_coord_x_list.append(high_symm_kpt_x)
kpath_nodes_coord_y_list.append(high_symm_kpt_y)
kpath_nodes_coord_z_list.append(high_symm_kpt_z)
kpath_nodes_label_list.append(high_symm_kpt_label)
#build xaxis tick list for high symmetry k points
kpath_nodes_xaxis_tick_list = []
last_high_symm_kpt_x = kpath_nodes_coord_x_list[0]
last_high_symm_kpt_y = kpath_nodes_coord_x_list[0]
last_high_symm_kpt_z = kpath_nodes_coord_x_list[0]
last_xaxis_tick = 0
for i_kpt in range(0, len(kpath_nodes_label_list)):
kpts_dist = np.linalg.norm([kpath_nodes_coord_x_list[i_kpt] - last_high_symm_kpt_x,
kpath_nodes_coord_y_list[i_kpt] - last_high_symm_kpt_y,
kpath_nodes_coord_z_list[i_kpt] - last_high_symm_kpt_z])
new_xaxis_tick = last_xaxis_tick + kpts_dist
kpath_nodes_xaxis_tick_list.append(new_xaxis_tick)
last_high_symm_kpt_x = kpath_nodes_coord_x_list[i_kpt]
last_high_symm_kpt_y = kpath_nodes_coord_y_list[i_kpt]
last_high_symm_kpt_z = kpath_nodes_coord_z_list[i_kpt]
last_xaxis_tick = new_xaxis_tick
kpoints_dict['kpath_nodes_xaxis_tick_list'] = kpath_nodes_xaxis_tick_list
kpoints_dict['bs_xaxis_tick_list'] = kpath_nodes_xaxis_tick_list
#build kpoints_dict
num_kpath_nodes = len(kpath_nodes_label_list)
kpoints_dict['num_kpath_nodes'] = num_kpath_nodes
kpoints_dict['kpath_nodes_list'] = kpath_nodes_label_list
kpath_nodes_arr = np.array([None] * num_kpath_nodes * 8)
kpath_nodes_arr.shape = num_kpath_nodes, 8
bs_xaxis_label = None
bs_xaxis_label_arr = [None] * num_kpath_nodes
for i_kpt in range(0, num_kpath_nodes):
kpath_nodes_arr[i_kpt, 0] = i_kpt
kpath_nodes_arr[i_kpt, 1] = kpath_nodes_coord_x_list[i_kpt]
kpath_nodes_arr[i_kpt, 2] = kpath_nodes_coord_y_list[i_kpt]
kpath_nodes_arr[i_kpt, 3] = kpath_nodes_coord_z_list[i_kpt]
kpath_nodes_arr[i_kpt, 4] = kpath_nodes_label_list[i_kpt]
kpath_nodes_arr[i_kpt, 5] = format(kpath_nodes_xaxis_tick_list[i_kpt], '.9f')
kpath_nodes_arr[i_kpt, 6] = None #kpath_continuous_list[i_kpt]
kpath_nodes_arr[i_kpt, 7] = None #kpath_left_right_list[i_kpt]
kpoints_dict['kpath_nodes_arr'] = kpath_nodes_arr
# determine the k points in the xaxis for the band structure plot
kpoints_dict['num_kpoints_xaxis'] = kpoints_dict['num_intersections']
kpoints_dict['kpoints_xaxis_arr'] = kpoints_dict['kpath_nodes_xaxis_tick_list']
##elif kpoints_dict['scheme'] in ['c', 'C', 'k', 'K']:
## pass
elif kpoints_dict['scheme'] in ['l', 'L']:
'''
Build the kpath_left_right_list, this list reflects the continuity of the kpath. R means the left end of a section of kpath, L means the right end of a section of kpath, LR means a certain kpoint acts as left and right ends of a section of kpath at the same time.
Build the kpath_continuous_list, if two adjacent kpionts are the same, then it is denoted as continuous and the value of that point is set as True. Use the kpath_continuous_list, we can determin the 'LR' components in the kpath_left_right_list.
Build intersections_end_kpt_list, this list determines the whether the kpoint is an end of a kpath section. Use kpath_left_right_list to determine the intersections_end_kpt_list.
'''
# Line-mode
kpoints_dict['num_intersections'] = int(funcs.split_line(line[1])[0])
kpoints_dict['coord_type'] = str(funcs.split_line(line[3])[0])[0]
kpath_nodes_coord_x_list = []
kpath_nodes_coord_y_list = []
kpath_nodes_coord_z_list = []
kpath_nodes_label_list = []
last_high_symm_kpt_label = None
kpt_label_list = []
#get high symmetry k points (units in cartesian coordinate)
kpath_left_right_list = []
num_effective_kpt = 0
for i_line in range(4, num_lines):
if len(funcs.split_line(line[i_line])) == 0:
continue
elif len(funcs.split_line(line[i_line])) != 0:
if funcs.split_line(line[i_line])[0][0] == '#':
continue
high_symm_kpt_x = float(funcs.split_line(line[i_line])[0])
high_symm_kpt_y = float(funcs.split_line(line[i_line])[1])
high_symm_kpt_z = float(funcs.split_line(line[i_line])[2])
temp_x = high_symm_kpt_x
temp_y = high_symm_kpt_y
temp_z = high_symm_kpt_z
high_symm_kpt_label = ''.join(funcs.split_line(line[i_line])[3:]).strip('!').strip('\\')
num_effective_kpt += 1
##print('original',high_symm_kpt_x, high_symm_kpt_y, high_symm_kpt_z, high_symm_kpt_label)
###############################################################################################################
# if the coordinate is reciprocal, change it to Cartesian (See VASP manual: VASP the Guide)
# \vec{k}=x_{1}\vec{b}_{1}+x_{2}\vec{b}_{2}+x_{3}\vec{b}_{3}
# where {\vec b}}_{{1...3}} are the three reciprocal basis vectors, and x_{{1...3}} are the values you supply.
###############################################################################################################
if kpoints_dict['coord_type'] in ['R', 'r']:
high_symm_kpt_x = temp_x * poscar_dict['reciprocal_arr'][0,0] + temp_y * poscar_dict['reciprocal_arr'][1,0] + temp_z * poscar_dict['reciprocal_arr'][2,0]
high_symm_kpt_y = temp_x * poscar_dict['reciprocal_arr'][0,1] + temp_y * poscar_dict['reciprocal_arr'][1,1] + temp_z * poscar_dict['reciprocal_arr'][2,1]
high_symm_kpt_z = temp_x * poscar_dict['reciprocal_arr'][0,2] + temp_y * poscar_dict['reciprocal_arr'][1,2] + temp_z * poscar_dict['reciprocal_arr'][2,2]
############################################################################################
# if the coordinate is Cartesian, the kpoints are given by (See VASP manual: VASP the Guide)
# \vec{k}=2*\pi/a*(x_{1}, x_{2}, x_(3))
# where a is the scaling parameter you have specified on the second line of the POSCAR file.
############################################################################################
if kpoints_dict['coord_type'] in ['C', 'c']:
high_symm_kpt_x = 2 * np.pi / poscar_dict['uni_scale_fac'] * temp_x
high_symm_kpt_y = 2 * np.pi / poscar_dict['uni_scale_fac'] * temp_y
high_symm_kpt_z = 2 * np.pi / poscar_dict['uni_scale_fac'] * temp_z
##print('x,y,z',high_symm_kpt_x, high_symm_kpt_y, high_symm_kpt_z, high_symm_kpt_label)
# Change the labeling of the band to LaTeX format
##if high_symm_kpt_label.lower() in defaults_dict['greek_small_letter_list']:
## high_symm_kpt_label = '\\' + high_symm_kpt_label.title()
for i_greek_lower in defaults_dict['greek_small_letter_list']:
if i_greek_lower in high_symm_kpt_label.lower():
# also take the special case into account, e.g. $/Sigma_0$
high_symm_kpt_label = high_symm_kpt_label.lower().replace(i_greek_lower, '\\' + i_greek_lower.title())
high_symm_kpt_label = '$' + high_symm_kpt_label + '$'
kpt_label_list.append(high_symm_kpt_label)
if high_symm_kpt_label != last_high_symm_kpt_label:
kpath_nodes_coord_x_list.append(high_symm_kpt_x)
kpath_nodes_coord_y_list.append(high_symm_kpt_y)
kpath_nodes_coord_z_list.append(high_symm_kpt_z)
kpath_nodes_label_list.append(high_symm_kpt_label)
if num_effective_kpt %2 != 0:
kpath_left_right_list.append('R')
elif num_effective_kpt %2 == 0:
kpath_left_right_list.append('L')
last_high_symm_kpt_label = high_symm_kpt_label
kpath_left_right_list[0] = 'R'
kpath_left_right_list[-1] = 'L'
#print('kpath_nodes_label_list = ',kpath_nodes_label_list) #for debugging purpose
#check the continuity of the kpath
kpath_node_counter_list = [0] * len(kpath_nodes_label_list)
kpath_continuous_list = [False] * len(kpath_nodes_label_list)
last_kpt_label = None
start_indx = 0
for i_kpt in range(0, len(kpath_nodes_label_list)):
i_kpt_label = kpath_nodes_label_list[i_kpt]
for j_kpt in range(start_indx, len(kpt_label_list)):
j_kpt_label = kpt_label_list[j_kpt]
if i_kpt_label == j_kpt_label:
kpath_node_counter_list[i_kpt] += 1
elif i_kpt_label != j_kpt_label:
start_indx = j_kpt
break
for i_kpt in range(0, len(kpath_nodes_label_list)):
if kpath_node_counter_list[i_kpt] != 1:
kpath_continuous_list[i_kpt] = True
# based on the kpath_continuous_list, we determine the left_right_list
for i_kpt in range(0, len(kpath_nodes_label_list)):
if kpath_continuous_list[i_kpt] == True:
kpath_left_right_list[i_kpt] = 'LR'
##if kpath_continuous_list[i_kpt] == False and i_kpt != 0:
## #find the nearest point in the kpath_continuous_list which is True
## for temp_i_kpt in reversed(range(0,i_kpt)):
## if kpath_continuous_list[temp_i_kpt] == True and (i_kpt - temp_i_kpt) % 2 != 0:
## kpath_left_right_list[i_kpt] = 'R'
## continue
## elif kpath_continuous_list[temp_i_kpt] == True and (i_kpt - temp_i_kpt) % 2 == 0:
## kpath_left_right_list[i_kpt] = 'L'
## continue
#build xaxis tick list for high symmetry k points
kpath_nodes_xaxis_tick_list = []
last_high_symm_kpt_x = kpath_nodes_coord_x_list[0]
last_high_symm_kpt_y = kpath_nodes_coord_x_list[0]
last_high_symm_kpt_z = kpath_nodes_coord_x_list[0]
last_xaxis_tick = 0
for i_kpt in range(0, len(kpath_nodes_label_list)):
kpts_dist = np.linalg.norm([kpath_nodes_coord_x_list[i_kpt] - last_high_symm_kpt_x,
kpath_nodes_coord_y_list[i_kpt] - last_high_symm_kpt_y,
kpath_nodes_coord_z_list[i_kpt] - last_high_symm_kpt_z])
new_xaxis_tick = last_xaxis_tick + kpts_dist
##if (i_kpt % 2) == 0 and kpath_continuous_list[i_kpt] == False and kpath_continuous_list[i_kpt - 1] == False:
##if (i_kpt % 2) == 0 and kpath_continuous_list[i_kpt] == False and kpath_continuous_list[i_kpt - 1] == False and i_kpt != len(kpath_nodes_label_list) - 1:
##if kpath_continuous_list[i_kpt] == False and kpath_continuous_list[i_kpt - 1] == False and i_kpt != len(kpath_nodes_label_list) - 1:
if kpath_continuous_list[i_kpt] == False and kpath_left_right_list[i_kpt] == 'R':
#print('i_kpt=',i_kpt, 'last=', last_xaxis_tick, 'new=',new_xaxis_tick)
new_xaxis_tick = last_xaxis_tick
kpath_nodes_xaxis_tick_list.append(new_xaxis_tick)
last_high_symm_kpt_x = kpath_nodes_coord_x_list[i_kpt]
last_high_symm_kpt_y = kpath_nodes_coord_y_list[i_kpt]
last_high_symm_kpt_z = kpath_nodes_coord_z_list[i_kpt]
last_xaxis_tick = new_xaxis_tick
kpoints_dict['kpath_nodes_xaxis_tick_list'] = kpath_nodes_xaxis_tick_list
#build kpoints_dict
num_kpath_nodes = len(kpath_nodes_label_list)
kpoints_dict['num_kpath_nodes'] = num_kpath_nodes
kpoints_dict['kpath_nodes_list'] = kpath_nodes_label_list
kpoints_dict['kpath_left_right_list'] = kpath_left_right_list
kpath_nodes_arr = np.array([None] * num_kpath_nodes * 8)
kpath_nodes_arr.shape = num_kpath_nodes, 8
#bs_xaxis_indx = 0
bs_xaxis_label = None
bs_xaxis_label_arr = [None] * num_kpath_nodes
for i_kpt in range(0, num_kpath_nodes):
kpath_nodes_arr[i_kpt, 0] = i_kpt
kpath_nodes_arr[i_kpt, 1] = kpath_nodes_coord_x_list[i_kpt]
kpath_nodes_arr[i_kpt, 2] = kpath_nodes_coord_y_list[i_kpt]
kpath_nodes_arr[i_kpt, 3] = kpath_nodes_coord_z_list[i_kpt]
kpath_nodes_arr[i_kpt, 4] = kpath_nodes_label_list[i_kpt]
kpath_nodes_arr[i_kpt, 5] = format(kpath_nodes_xaxis_tick_list[i_kpt], '.9f')
kpath_nodes_arr[i_kpt, 6] = kpath_continuous_list[i_kpt]
kpath_nodes_arr[i_kpt, 7] = kpath_left_right_list[i_kpt]
kpoints_dict['kpath_nodes_arr'] = kpath_nodes_arr
# determine the k points in the xaxis for the band structure plot
intersections_end_kpt_list = [False] * len(kpath_continuous_list)
intersections_end_kpt_list[0] = False
num_intersections_interval = 0
for i_kpt in range(1, len(kpath_continuous_list)):
if i_kpt != len(kpath_continuous_list) - 1:
#if not (kpath_continuous_list[i_kpt - 1] == False and kpath_continuous_list[i_kpt] == False):
if kpath_left_right_list[i_kpt] == 'LR' or kpath_left_right_list[i_kpt] == 'L':
num_intersections_interval = num_intersections_interval + 1
intersections_end_kpt_list[i_kpt] = True
elif i_kpt == len(kpath_continuous_list) - 1:
num_intersections_interval = num_intersections_interval + 1
intersections_end_kpt_list[i_kpt] = True
kpoints_dict['num_intersections_interval'] = num_intersections_interval
num_kpoints_xaxis = num_intersections_interval * kpoints_dict['num_intersections']
kpoints_dict['num_kpoints_xaxis'] = num_kpoints_xaxis
kpoints_dict['intersections_end_kpt_list'] = intersections_end_kpt_list
#to avoid the following error: mask = np.isnan(self.x) TypeError: ufunc 'isnan' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''. Use dtype = np.float64 instead of dtype = object.
kpoints_xaxis_arr = np.array([None] * num_kpoints_xaxis, dtype=np.float64)
start_kpt = kpath_nodes_xaxis_tick_list[0]
i_intersection = 0
for i_kpt in range(1, len(intersections_end_kpt_list)):
if intersections_end_kpt_list[i_kpt] == True:
i_intersection = i_intersection + 1
start_indx = (i_intersection - 1) * kpoints_dict['num_intersections']
end_indx = start_indx + kpoints_dict['num_intersections']
end_kpt = kpath_nodes_xaxis_tick_list[i_kpt]
start_kpt = kpath_nodes_xaxis_tick_list[i_kpt - 1]
kpoints_xaxis_arr[start_indx:end_indx] = np.linspace(start_kpt, end_kpt, kpoints_dict['num_intersections'], True)
kpoints_dict['kpoints_xaxis_arr'] = kpoints_xaxis_arr
#get x axis tick for the band structure plot
bs_xaxis_label_list = []
bs_xaxis_tick_list = []
for i_kpt in range(1, len(intersections_end_kpt_list)):
if i_kpt != len(intersections_end_kpt_list) - 1:
if i_kpt == 1:
bs_xaxis_label_list.append(kpath_nodes_label_list[i_kpt - 1])
bs_xaxis_tick_list.append(kpath_nodes_xaxis_tick_list[i_kpt - 1])
if intersections_end_kpt_list[i_kpt] == True and intersections_end_kpt_list[i_kpt - 1] != False and i_kpt != 1:
bs_xaxis_label_list.append(kpath_nodes_label_list[i_kpt - 1])
bs_xaxis_tick_list.append(kpath_nodes_xaxis_tick_list[i_kpt - 1])
##elif intersections_end_kpt_list[i_kpt] == True and intersections_end_kpt_list[i_kpt - 1] == False and i_kpt != 1:
## bs_xaxis_label_list.append('')
## bs_xaxis_tick_list.append(kpath_nodes_xaxis_tick_list[i_kpt - 1])
elif intersections_end_kpt_list[i_kpt] == False and kpath_left_right_list[i_kpt] == 'R':
bs_xaxis_label_list.append(kpath_nodes_label_list[i_kpt - 1] + '|' + kpath_nodes_label_list[i_kpt])
bs_xaxis_tick_list.append(kpath_nodes_xaxis_tick_list[i_kpt - 1])
elif i_kpt == len(intersections_end_kpt_list) - 1:
if intersections_end_kpt_list[i_kpt - 1] == True:
bs_xaxis_label_list.append(kpath_nodes_label_list[i_kpt - 1])
bs_xaxis_label_list.append(kpath_nodes_label_list[i_kpt])
bs_xaxis_tick_list.append(kpath_nodes_xaxis_tick_list[i_kpt - 1])
bs_xaxis_tick_list.append(kpath_nodes_xaxis_tick_list[i_kpt])
elif intersections_end_kpt_list[i_kpt - 1] == False:
bs_xaxis_label_list.append(kpath_nodes_label_list[i_kpt])
bs_xaxis_tick_list.append(kpath_nodes_xaxis_tick_list[i_kpt])
kpoints_dict['bs_xaxis_label_list'] = bs_xaxis_label_list
kpoints_dict['bs_xaxis_tick_list'] = bs_xaxis_tick_list
return kpoints_dict
def read_eigenval(eigenval_file_path):
'''
Read EIGENVAL
'''
args_dict = locals()
import os
import numpy as np
from .. import funcs
from . import vasp_tools
from . import vasp_read
eigenval_file_path = os.path.abspath(eigenval_file_path)
file_path, filename = os.path.split(eigenval_file_path)
poscar_file_path = os.path.join(file_path, 'POSCAR')
poscar_dict = vasp_read.read_poscar(poscar_file_path)
eigenval_dict = {}
eigenval_dict['file_path'] = eigenval_file_path
eigenval_dict['dict_type'] = 'eigenval'
file_status = funcs.file_status(eigenval_file_path)
eigenval_dict['file_status'] = file_status
# read_status: 1: sucessfully read; 0: fail to read
eigenval_dict['read_status'] = None
eigenval_dict['num_lines'] = None
eigenval_dict['num_ions'] = None
eigenval_dict['loops_after_write_apcf_dos'] = None
eigenval_dict['ispin'] = None
eigenval_dict['cell_volume'] = None
eigenval_dict['box_size_list'] = None
eigenval_dict['num_valence_electrons'] = None
eigenval_dict['num_kpoints'] = None
eigenval_dict['num_bands'] = None
eigenval_dict['kpt_coord_arr'] = None
eigenval_dict['weights'] = None
eigenval_dict['eigs'] = None
eigenval_dict['eigs_up'] = None
eigenval_dict['eigs_dn'] = None
eigenval_dict['occupancy'] = None
eigenval_dict['occupancy_up'] = None
eigenval_dict['occupancy_dn'] = None
eigenval_dict['kpath_len_list'] = None
if file_status != 1:
print('WARNING #20120310 (from read_eigenval): The file ' + eigenval_dict['file_path'] + ' does not exist or is empty. Please check the EIGENVAL file.')
eigenval_dict['read_status'] = 0
else:
file_type = vasp_tools.check_file_type(eigenval_dict['file_path'])
if file_type != 'EIGENVAL':
print('WARNING #20120301 (from read_eigenval): Incorrect EIGENVAL format. Please check the file' + eigenval_dict['file_path'])
eigenval_dict['read_status'] = 0
elif file_type == 'EIGENVAL':
num_header = 7
with open(eigenval_file_path,'r') as f:
line = f.readlines()
eigenval_dict['num_lines'] = len(line)
eigenval_dict['num_ions'] = int(funcs.split_line(line[0])[0])
eigenval_dict['loops_after_write_apcf_dos'] = int(funcs.split_line(line[0])[2]) # number of loops after writing the averaged pair correlation functions and DOS.
#print(eigenval_file_path)
##print(line[0])
eigenval_dict['ispin'] = int(funcs.split_line(line[0])[3])
eigenval_dict['cell_volume'] = float(funcs.split_line(line[1])[0])
eigenval_dict['box_size_list'] = [float(funcs.split_line(line[1])[1]), float(funcs.split_line(line[1])[2]), float(funcs.split_line(line[1])[3])]
eigenval_dict['nnum_valence_electrons'] = int(funcs.split_line(line[5])[0])
eigenval_dict['num_kpoints'] = int(funcs.split_line(line[5])[1])
eigenval_dict['num_bands'] = int(funcs.split_line(line[5])[2])
#to avoid the following error: mask = np.isnan(self.x) TypeError: ufunc 'isnan' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''. Use dtype = np.float64 instead of dtype = object.
if eigenval_dict['ispin'] == 1:
eigenval_dict['eigs'] = np.array([None] * eigenval_dict['num_kpoints'] * eigenval_dict['num_bands'], dtype=np.float64)
eigenval_dict['eigs'].shape = eigenval_dict['num_kpoints'], eigenval_dict['num_bands']
eigenval_dict['occupancy'] = np.array([None] * eigenval_dict['num_kpoints'] * eigenval_dict['num_bands'], dtype=np.float64)
eigenval_dict['occupancy'].shape = eigenval_dict['num_kpoints'], eigenval_dict['num_bands']
elif eigenval_dict['ispin'] == 2:
eigenval_dict['eigs_up'] = np.array([None] * eigenval_dict['num_kpoints'] * eigenval_dict['num_bands'], dtype=np.float64)
eigenval_dict['eigs_up'].shape = eigenval_dict['num_kpoints'], eigenval_dict['num_bands']
eigenval_dict['eigs_dn'] = np.array([None] * eigenval_dict['num_kpoints'] * eigenval_dict['num_bands'], dtype=np.float64)
eigenval_dict['eigs_dn'].shape = eigenval_dict['num_kpoints'], eigenval_dict['num_bands']
eigenval_dict['occupancy_up'] = np.array([None] * eigenval_dict['num_kpoints'] * eigenval_dict['num_bands'], dtype=np.float64)
eigenval_dict['occupancy_up'].shape = eigenval_dict['num_kpoints'], eigenval_dict['num_bands']
eigenval_dict['occupancy_dn'] = np.array([None] * eigenval_dict['num_kpoints'] * eigenval_dict['num_bands'], dtype=np.float64)
eigenval_dict['occupancy_dn'].shape = eigenval_dict['num_kpoints'], eigenval_dict['num_bands']
eigenval_dict['kpt_coord_arr'] = np.array([None] * eigenval_dict['num_kpoints'] * 3)
eigenval_dict['kpt_coord_arr'].shape = eigenval_dict['num_kpoints'], 3
eigenval_dict['weights'] = np.array([None] * eigenval_dict['num_kpoints'])
i_line = num_header
if eigenval_dict['ispin'] == 1:
for i_kpoint in range(0, eigenval_dict['num_kpoints']):
eigenval_dict['kpt_coord_arr'][i_kpoint, 0] = float(funcs.split_line(line[i_line])[0])
eigenval_dict['kpt_coord_arr'][i_kpoint, 1] = float(funcs.split_line(line[i_line])[1])
eigenval_dict['kpt_coord_arr'][i_kpoint, 2] = float(funcs.split_line(line[i_line])[2])
eigenval_dict['weights'][i_kpoint] = float(funcs.split_line(line[i_line])[3])
for i_band in range(0, eigenval_dict['num_bands']):
i_line = i_line + 1
try:
eigenval_dict['eigs'][i_kpoint,i_band] = float(funcs.split_line(line[i_line])[1])
except:
# This happens when the parameter cannot be converted to string, for example: sting: '***************'
eigenval_dict['eigs'][i_kpoint,i_band] = 999999
# Currently, the occupancy will not be read, because the format is unclear for now
##occupancy[i_kpoint, i_band] = float(funcs.split_line(line[i_line])[2])
if i_band == (eigenval_dict['num_bands'] - 1):
i_line = i_line + 2
elif eigenval_dict['ispin'] == 2:
for i_kpoint in range(0, eigenval_dict['num_kpoints']):
eigenval_dict['kpt_coord_arr'][i_kpoint, 0] = float(funcs.split_line(line[i_line])[0])
eigenval_dict['kpt_coord_arr'][i_kpoint, 1] = float(funcs.split_line(line[i_line])[1])
eigenval_dict['kpt_coord_arr'][i_kpoint, 2] = float(funcs.split_line(line[i_line])[2])
eigenval_dict['weights'][i_kpoint] = float(funcs.split_line(line[i_line])[3])
for i_band in range(0, eigenval_dict['num_bands']):
i_line = i_line + 1
try:
eigenval_dict['eigs_up'][i_kpoint,i_band] = float(funcs.split_line(line[i_line])[1])
eigenval_dict['eigs_dn'][i_kpoint,i_band] = float(funcs.split_line(line[i_line])[2])
except:
# This happens when the parameter cannot be converted to string, for example: sting: '***************'
eigenval_dict['eigs_up'][i_kpoint,i_band] = 999999
eigenval_dict['eigs_dn'][i_kpoint,i_band] = 999999
# Currently, the occupancy will not be read, because the format is unclear for now
#occupancy_up[i_kpoint, i_band] = float(funcs.split_line(line[i_line])[3])
#occupancy_dn[i_kpoint, i_band] = float(funcs.split_line(line[i_line])[4])
if i_band == (eigenval_dict['num_bands'] - 1):
i_line = i_line + 2
eigenval_dict['read_status'] = 1
###################################
# Determine the k=path length list
###################################
kpath_len_car = 0
characteristic_len = np.linalg.norm(vasp_tools.kpoint_rec2car(eigenval_dict['kpt_coord_arr'][1,:] - eigenval_dict['kpt_coord_arr'][0,:], poscar_dict['reciprocal_arr']))
eigenval_dict['kpath_len_list'] = [None] * eigenval_dict['num_kpoints']
eigenval_dict['kpath_len_list'][0] = 0
for i_kpt in range(1, eigenval_dict['num_kpoints']):
kpt_dist_car = np.linalg.norm(vasp_tools.kpoint_rec2car(eigenval_dict['kpt_coord_arr'][i_kpt,:] - eigenval_dict['kpt_coord_arr'][i_kpt - 1,:], poscar_dict['reciprocal_arr']))
if kpt_dist_car < characteristic_len * 3:
kpath_len_car += kpt_dist_car
eigenval_dict['kpath_len_list'][i_kpt] = kpath_len_car
return eigenval_dict
def read_procar(procar_file_path):
'''Read PROCAR'''
args_dict = locals()
import os
import numpy as np
from . import vasp_read
from . import vasp_tools
from .. import funcs
procar_file_path = os.path.abspath(procar_file_path)
file_path, filename = os.path.split(procar_file_path)
poscar_file_path = os.path.join(file_path, 'POSCAR')
poscar_dict = vasp_read.read_poscar(poscar_file_path)
procar_dict = {}
procar_dict['file_path'] = None
procar_dict['num_lines'] = None
procar_dict['num_kpoints'] = None
procar_dict['num_bands'] = None
procar_dict['num_ions'] = None
procar_dict['num_cols'] = None
procar_dict['num_orbits'] = None
procar_dict['ispin'] = None
procar_dict['kpt_coord_arr'] = None
procar_dict['weights'] = None
procar_dict['eigs'] = None
procar_dict['occupancy'] = None
procar_dict['projections'] = None
procar_dict['projections_noncollinear'] = None
procar_dict['eigs_up'] = None
procar_dict['eigs_dn'] = None
procar_dict['occupancy_up'] = None
procar_dict['occupancy_dn'] = None
procar_dict['projections_up'] = None
procar_dict['projections_dn'] = None
procar_dict['projections_up_noncollinear'] = None
procar_dict['projections_dn_noncollinear'] = None
procar_dict['kpath_len_list'] = 0
procar_dict['file_path'] = procar_file_path
procar_dict['dict_type'] = 'procar'
file_status = funcs.file_status(procar_file_path)
procar_dict['file_status'] = file_status
if file_status != 1:
print('WARNING #20120311 (from read_procar): The file ' + procar_file_path + ' does not exist or is empty. PLease check the PROCAR file.')
else:
#num_header = 3
num_header = 1
#two kinds of PROCAR files: 'PROCAR_collinear' or 'PROCAR_noncollinear'
file_type = vasp_tools.check_file_type(procar_file_path)
with open(procar_file_path,'r') as f:
line = f.readlines()
#num_lines = len(line)
num_lines = funcs.line_num(procar_file_path)
num_kpoints = int(funcs.split_line(line = line[1], separator = ':')[1].split('#')[0])
num_bands = int(funcs.split_line(line = line[1], separator = ':')[2].split('#')[0])
num_ions = int(funcs.split_line(line = line[1], separator = ':')[3].split('#')[0])
# the PROCAR file has different file format for the collilnear and noncollinear calculations. Care must be taken when dealing with the PROCAR file.
if file_type == 'PROCAR_collinear':
#estimated number of lines for PROCAR file in collinear calculations
estimated_num_lines_ispin1 = num_header + 1 * ((num_kpoints * ((num_bands * (num_ions + 1 + 4)) + 3)) + 1)
estimated_num_lines_ispin2 = num_header + 2 * ((num_kpoints * ((num_bands * (num_ions + 1 + 4)) + 3)) + 1)
estimated_num_lines_ispin2_variant = num_header + 2 * ((num_kpoints * ((num_bands * (num_ions + 1 + 5)) + 3)) + 1)
elif file_type == 'PROCAR_noncollinear':
#estimated number of lines for PROCAR file in noncollinear calculations
estimated_num_lines_ispin1 = num_header + 1 * ((num_kpoints * ((num_bands * ((num_ions + 1) * 4 + 4)) + 3)) + 1)
estimated_num_lines_ispin2 = num_header + 2 * ((num_kpoints * ((num_bands * ((num_ions + 1) * 4 + 4)) + 3)) + 1)
estimated_num_lines_ispin2_variant = num_header + 2 * ((num_kpoints * ((num_bands * ((num_ions + 1) * 4 + 5)) + 3)) + 1)
if num_lines == estimated_num_lines_ispin1:
ispin = 1
elif num_lines == estimated_num_lines_ispin2:
ispin = 2
empty_lines_before_band_i = 1
elif num_lines == estimated_num_lines_ispin2_variant:
# this corresponds to the PROCAR with two empty lines before the line:
# band 2 # energy -35.39571890 # occ. 1.00000000
ispin = 2
empty_lines_before_band_i = 2
else:
print('ERROR (#2106281158) from vasp_read: The format of PROCAR file cannot be recognized. Please check your PROCAR file: ' + procar_file_path)
exit()
num_m = 4 #total partial charge, mx, my and mz (m = magnetization) contributions to that state
# orbitals 0 1 2 3 4 5 6 7 8 9
# orbitals s py pz px dxy dyz dz2 dxz dx2 tot
procar_dict['num_cols'] = len(funcs.split_line(line = line[7], separator = ' '))
if procar_dict['num_cols'] == 11:
num_orbits = 9
elif procar_dict['num_cols'] == 18:
num_orbits = 16
procar_dict['num_orbits'] = num_orbits
#to avoid the following error: mask = np.isnan(self.x) TypeError: ufunc 'isnan' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''. Use dtype = np.float64 instead of dtype = object.
if ispin == 1:
eigs = np.array([None] * num_kpoints * num_bands, dtype=np.float64)
eigs.shape = num_kpoints, num_bands
occupancy = np.array([None] * num_kpoints * num_bands, dtype=np.float64)
occupancy.shape = num_kpoints, num_bands
if file_type == 'PROCAR_collinear':
projections = np.array([None] * num_kpoints * num_bands * (num_ions + 1) * (num_orbits + 1), dtype=np.float64)
projections.shape = num_kpoints, num_bands, (num_ions + 1), (num_orbits + 1)
if file_type == 'PROCAR_noncollinear':
projections_noncollinear = | np.array([None] * num_kpoints * num_bands * (num_ions + 1) * num_m * (num_orbits + 1), dtype=np.float64) | numpy.array |
import numpy as np
import cv2
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import pickle
from threshold import binarize_with_threshold
from perspective_transform import perspective_transform
def viz1(binary_warped, ret, save_file=None):
"""
Visualize each sliding window location and predicted lane lines, on binary warped image
save_file is a string representing where to save the image (if None, then just display)
binary_warped: input warped image
ret: returns from fit_line
"""
# Grab variables from ret dictionary
left_fit = ret['left_fit']
right_fit = ret['right_fit']
nonzerox = ret['nonzerox']
nonzeroy = ret['nonzeroy']
out_img = ret['out_img']
left_lane_inds = ret['left_lane_inds']
right_lane_inds = ret['right_lane_inds']
# Generate x and y values for plotting
ploty = np.linspace(0, binary_warped.shape[0] - 1, binary_warped.shape[0])
left_fitx = left_fit[0] * ploty ** 2 + left_fit[1] * ploty + left_fit[2]
right_fitx = right_fit[0] * ploty ** 2 + right_fit[1] * ploty + right_fit[2]
out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]
plt.imshow(out_img)
plt.plot(left_fitx, ploty, color='yellow')
plt.plot(right_fitx, ploty, color='yellow')
plt.xlim(0, 1280)
plt.ylim(720, 0)
if save_file is None:
plt.show()
else:
plt.savefig(save_file)
plt.gcf().clear()
def viz2(binary_warped, ret, margin=100, save_file=None):
"""
Visualize the predicted lane lines with margin, on binary warped image
save_file is a string representing where to save the image (if None, then just display)
"""
# Grab variables from ret dictionary
left_fit = ret['left_fit']
right_fit = ret['right_fit']
nonzerox = ret['nonzerox']
nonzeroy = ret['nonzeroy']
left_lane_inds = ret['left_lane_inds']
right_lane_inds = ret['right_lane_inds']
# Create an image to draw on and an image to show the selection window
out_img = (np.dstack((binary_warped, binary_warped, binary_warped)) * 255).astype('uint8')
window_img = np.zeros_like(out_img)
# Color in left and right line pixels
out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]
# Generate x and y values for plotting
ploty = np.linspace(0, binary_warped.shape[0] - 1, binary_warped.shape[0])
left_fitx = left_fit[0] * ploty ** 2 + left_fit[1] * ploty + left_fit[2]
right_fitx = right_fit[0] * ploty ** 2 + right_fit[1] * ploty + right_fit[2]
# Generate a polygon to illustrate the search window area
# And recast the x and y points into usable format for cv2.fillPoly()
left_line_window1 = np.array([np.transpose(np.vstack([left_fitx - margin, ploty]))])
left_line_window2 = np.array([np.flipud(np.transpose(np.vstack([left_fitx + margin, ploty])))])
left_line_pts = np.hstack((left_line_window1, left_line_window2))
right_line_window1 = np.array([np.transpose(np.vstack([right_fitx - margin, ploty]))])
right_line_window2 = np.array([np.flipud(np.transpose( | np.vstack([right_fitx + margin, ploty]) | numpy.vstack |
import itertools
import numpy as np
from . import common
class Interpolator:
def __init__(self, resolution=1024, width=128):
self.width = width
self.resolution = resolution
N = resolution * width
u = np.arange(-N, N, dtype=float)
window = | np.cos(0.5 * np.pi * u / N) | numpy.cos |
import numpy as np
import tensorflow.keras as KK
from src.ffnn.data_load import load_MNIST, create_not_mnist_doubleset
from numpy.core._multiarray_umath import ndarray
from scipy.stats import entropy
def model_predictor(model_repo_path: str, x_test_values: ndarray, y_test_values: ndarray) -> (ndarray, ndarray):
"""
The function for predicting the given images using the given model.
:param model_repo_path: relative path to the model used
:param x_test_values: array of images to be predicted
:param y_test_values: array of labels corresponding to the x_test_values.
:return: a set of predictions and a set of labels
"""
model = KK.models.load_model(model_repo_path)
dropout_runs = 100
if model_repo_path.split("/")[0] == "dropout_models":
pred = np.zeros((len(x_test_values), 10))
for i in range(dropout_runs):
temp_predict = model.predict(x_test_values)
# Quicker version -- avoids loop over all elements in the test-set
pred[np.arange(pred.shape[0]), np.argmax(temp_predict, axis=1)] += 1
predictions = pred / dropout_runs
else:
predictions = model.predict(x_test_values)
return predictions, y_test_values
def get_int_predictions(model_repo_path: str, data_load_function=load_MNIST) -> (ndarray, ndarray):
_, _, x_test, y_test = data_load_function()
predicted, correct = model_predictor(model_repo_path, x_test, y_test)
return np.argmax(predicted, axis=1), correct
def test_nMNIST_prediction(model_repo_path: str, data: ndarray):
model = KK.models.load_model(model_repo_path)
return model.predict(data)
def train_MNIST_entropy():
x_train, _, _, _ = load_MNIST()
x_train = x_train[:10000]
return do_MNIST_entropy(input_data=x_train)
def do_MNIST_entropy(input_data):
model_paths = ["ffnn_models", "dropout_models"]
dropout_runs = 100
d = {}
sizes = [1000, 2500, 7000, 19000, 50000]
for folder in model_paths:
for size in sizes:
path = folder + "/model_" + str(size)
model = KK.models.load_model(path)
if folder == "dropout_models":
pred = np.zeros((len(input_data), 10))
for i in range(dropout_runs):
temp_predict = model.predict(input_data)
# Should average out predictions at "output level" -- prior to argmax.
# Doing it *after* argmax suppresses a situation where, e.g., the model
# has a 60% chance of class0 and 40% for class1 in all realizations of the dropouts.
pred += temp_predict
"""
for idx, n in enumerate(np.argmax(temp_predict, axis=1)):
pred[idx][n] += 1
"""
pred = pred / dropout_runs
else:
pred = model.predict(input_data)
model_entropy = entropy(pred, axis=1)
d[folder[0] + str(size)] = model_entropy
return d
def not_MNIST_entropy(no_random_images=10000):
x, _ = create_not_mnist_doubleset()
chooser = np.random.permutation(x.shape[0])[:no_random_images]
x = x[chooser, :]
return do_MNIST_entropy(input_data=x)
def test_MNIST_entropy():
_, _, x_test, _ = load_MNIST()
return do_MNIST_entropy(input_data=x_test)
def get_all_predictions():
"""
Function for getting the predictions of models on the mnist test dataset.
:return: a dictionary with predictions of all models.
"""
all_results = {}
model_paths = ["ffnn_models", "dropout_models"]
sizes = [1000, 2500, 7000, 19000, 50000]
pred, correct = None, None
for folder in model_paths:
for size in sizes:
path = folder + "/model_" + str(size)
if len(all_results) == 0:
pred, correct = get_int_predictions(folder + "/model_" + str(size), load_MNIST)
all_results["y"] = correct
all_results[path] = pred
else:
all_results[path] = get_int_predictions(folder + "/model_" + str(size), load_MNIST)[0]
print(f"Test-set accuracy = {np.mean( | np.equal(all_results[path], correct) | numpy.equal |
#!/usr/bin/python3
# -*- coding: utf-8 -*-
##===-----------------------------------------------------------------------------*- Python -*-===##
##
## S E R I A L B O X
##
## This file is distributed under terms of BSD license.
## See LICENSE.txt for more information.
##
##===------------------------------------------------------------------------------------------===##
##
## This example demonstrates the asynchronous API of Serialbox which can improve the throughput of
## read operations.
##
##===------------------------------------------------------------------------------------------===##
#
# First, we have to make sure Python finds the Serialbox module. Alternatively, you can also set the
# environment variable PYTHONPATH.
#
import os
import sys
import time
sys.path.append(os.path.dirname(os.path.realpath(__file__)) + '/../python')
sys.path.append(os.path.dirname(os.path.realpath(__file__)) + '/../../src/serialbox-python')
#
# Import Serialbox
#
import serialbox as ser
import numpy as np
def main():
N = 512; M = 512; K = 80
savepoint = ser.Savepoint('sp')
#
# First, we write some data to disk ...
#
serializer_write = ser.Serializer(ser.OpenModeKind.Write, "./async", "Field", "Binary")
field_1 = np.random.rand(N, M, K)
field_2 = np.random.rand(N, M, K)
field_3 = np.random.rand(N, M, K)
field_4 = np.random.rand(N, M, K)
field_5 = np.random.rand(N, M, K)
field_6 = np.random.rand(N, M, K)
serializer_write.write('field_1', savepoint, field_1)
serializer_write.write('field_2', savepoint, field_2)
serializer_write.write('field_3', savepoint, field_3)
serializer_write.write('field_4', savepoint, field_4)
serializer_write.write('field_5', savepoint, field_5)
serializer_write.write('field_6', savepoint, field_6)
#
# ... and read it again.
#
serializer_read = ser.Serializer(ser.OpenModeKind.Read, "./async", "Field", "Binary")
start = time.time()
field_1_rd = serializer_read.read('field_1', savepoint)
field_2_rd = serializer_read.read('field_2', savepoint)
field_3_rd = serializer_read.read('field_3', savepoint)
field_4_rd = serializer_read.read('field_4', savepoint)
field_5_rd = serializer_read.read('field_5', savepoint)
field_6_rd = serializer_read.read('field_6', savepoint)
print("Serializer.read : %8.2f s" % (time.time() - start))
#
# Read operations are usually embarrassingly parallel and we can leverage this parallelism by
# launching the operations asynchronously. If the archive is not thread-safe or if the library
# was not configured with `SERIALBOX_ASYNC_API` the method falls back to synchronous execution.
# To synchronize the tasks in the end, we can add a blocking Serializer.wait_for_all().
#
start = time.time()
field_1_rd_async = serializer_read.read_async('field_1', savepoint)
field_2_rd_async = serializer_read.read_async('field_2', savepoint)
field_3_rd_async = serializer_read.read_async('field_3', savepoint)
field_4_rd_async = serializer_read.read_async('field_4', savepoint)
field_5_rd_async = serializer_read.read_async('field_5', savepoint)
field_6_rd_async = serializer_read.read_async('field_6', savepoint)
serializer_read.wait_for_all()
print("Serializer.read_async : %8.2f s" % (time.time() - start))
#
# Finally, we verify the read operations actually do the same.
#
assert(np.allclose(field_1_rd, field_1_rd_async))
assert(np.allclose(field_2_rd, field_2_rd_async))
assert( | np.allclose(field_3_rd, field_3_rd_async) | numpy.allclose |
# Copyright 2022 Xanadu Quantum Technologies Inc.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Functions for reducing a macronode lattice to a canonical lattice."""
# pylint: disable=protected-access,too-many-statements,too-many-locals,too-many-arguments
import numpy as np
from numpy.random import default_rng
from scipy.linalg import block_diag
from flamingpy.cv.ops import CVLayer, SCZ_apply
from flamingpy.cv.gkp import GKP_binner, Z_err_cond
from thewalrus.symplectic import expand, beam_splitter
def invert_permutation(p):
"""Invert the permutation associated with p."""
p_inverted = | np.empty(p.size, p.dtype) | numpy.empty |
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import pandas as pd
# Part 1 - Methods for visualization for basic usage of PyREPO library
# bar chart for basic version
def plot_barplot(df_plot):
"""Visualization method to display column chart of alternatives rankings obtained with
different methods.
Parameters
----------
df_plot : DataFrame
DataFrame containing rankings of alternatives obtained with different methods.
The particular rankings are contained in subsequent columns of DataFrame.
"""
step = 1
list_rank = np.arange(1, len(df_plot) + 1, step)
ax = df_plot.plot(kind='bar', width = 0.8, stacked=False, edgecolor = 'black', figsize = (9,4))
ax.set_xlabel('Alternatives', fontsize = 12)
ax.set_ylabel('Rank', fontsize = 12)
ax.set_yticks(list_rank)
ax.set_xticklabels(df_plot.index, rotation = 'horizontal')
ax.tick_params(axis = 'both', labelsize = 12)
y_ticks = ax.yaxis.get_major_ticks()
ax.set_ylim(0, len(df_plot) + 1)
plt.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc='lower left',
ncol=4, mode="expand", borderaxespad=0., edgecolor = 'black', title = 'Methods', fontsize = 12)
ax.grid(True, linestyle = ':')
ax.set_axisbelow(True)
plt.tight_layout()
plt.savefig('./output/' + 'bar_chart' + '.png')
plt.show()
# bar chart for sensitivity analysis in basic version
def plot_barplot_sensitivity(df_plot, method_name, criterion_name):
"""Visualization method to display column chart of alternatives rankings obtained with
modification of weight of given criterion.
Parameters
----------
df_plot : DataFrame
DataFrame containing rankings of alternatives obtained with different weight of
selected criterion. The particular rankings are contained in subsequent columns of
DataFrame.
"""
step = 1
list_rank = np.arange(1, len(df_plot) + 1, step)
ax = df_plot.plot(kind='bar', width = 0.8, stacked=False, edgecolor = 'black', figsize = (9,4))
ax.set_xlabel('Alternatives', fontsize = 12)
ax.set_ylabel('Rank', fontsize = 12)
ax.set_yticks(list_rank)
ax.set_xticklabels(df_plot.index, rotation = 'horizontal')
ax.tick_params(axis='both', labelsize=12)
y_ticks = ax.yaxis.get_major_ticks()
ax.set_ylim(0, len(df_plot) + 1)
ax.set_title(method_name + ', modification of ' + criterion_name + ' weights')
plt.legend(bbox_to_anchor=(1.0, 0.82, 0.3, 0.2), loc='upper left', title = 'Weights change', edgecolor = 'black', fontsize = 12)
ax.grid(True, linestyle = ':')
ax.set_axisbelow(True)
plt.tight_layout()
plt.savefig('./output/sensitivity_analysis_results/' + 'sens_' + 'hist_' + method_name + '_' + criterion_name + '.png')
plt.show()
# plot line chart for sensitivity analysis in basic version
def plot_lineplot_sensitivity(data_sens, method_name, criterion_name):
"""Visualization method to display line chart of alternatives rankings obtained with
modification of weight of given criterion.
Parameters
----------
df_plot : DataFrame
DataFrame containing rankings of alternatives obtained with different weight of
selected criterion. The particular rankings are contained in subsequent columns of
DataFrame.
"""
plt.figure(figsize = (6, 3))
for j in range(data_sens.shape[0]):
plt.plot(data_sens.iloc[j, :], linewidth = 2)
ax = plt.gca()
y_min, y_max = ax.get_ylim()
x_min, x_max = ax.get_xlim()
plt.annotate(data_sens.index[j], (x_max, data_sens.iloc[j, -1]),
fontsize = 12, style='italic',
horizontalalignment='left')
plt.xlabel("Weight modification", fontsize = 12)
plt.ylabel("Rank", fontsize = 12)
plt.yticks(fontsize = 12)
plt.xticks(fontsize = 12)
plt.title(method_name + ', modification of ' + criterion_name + ' weights')
plt.grid(True, linestyle = ':')
plt.tight_layout()
plt.savefig('./output/sensitivity_analysis_results/' + 'sens_' + 'lineplot_' + method_name + '_' + criterion_name + '.png')
plt.show()
# heat maps with correlations for basic version
def draw_heatmap(df_new_heatmap, title):
"""
Visualization method to display heatmap with correlations of compared rankings generated using different methods
Parameters
----------
data : DataFrame
DataFrame with correlation values between compared rankings
title : str
title of chart containing name of used correlation coefficient
"""
plt.figure(figsize = (8,5))
sns.set(font_scale=1.4)
heatmap = sns.heatmap(df_new_heatmap, annot=True, fmt=".2f", cmap="PuBu",
linewidth=0.5, linecolor='w')
plt.yticks(va="center")
plt.xlabel('Methods')
plt.title('Correlation: ' + title)
plt.tight_layout()
plt.savefig('./output/' + 'correlations_' + title + '.png')
plt.show()
# radar plot for basic version
def plot_radar(data):
"""
Visualization method to display rankings of alternatives obtained with different methods
on the radar chart.
Parameters
-----------
data : DataFrame
DataFrame containing containing rankings of alternatives obtained with different
methods. The particular rankings are contained in subsequent columns of DataFrame.
"""
fig=plt.figure()
ax = fig.add_subplot(111, polar = True)
for col in list(data.columns):
labels=np.array(list(data.index))
stats = data.loc[labels, col].values
angles=np.linspace(0, 2*np.pi, len(labels), endpoint=False)
# close the plot
stats=np.concatenate((stats,[stats[0]]))
angles= | np.concatenate((angles,[angles[0]])) | numpy.concatenate |
import os
import cv2
import numpy as np
import matplotlib.pyplot as plt
from utils import utils_sr
import torch
from argparse import ArgumentParser
from utils.utils_restoration import rgb2y, psnr, array2tensor, tensor2array
import sys
from matplotlib.ticker import MaxNLocator
class PnP_restoration():
def __init__(self, hparams):
self.hparams = hparams
self.device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
self.initialize_cuda_denoiser()
def initialize_cuda_denoiser(self):
'''
Initialize the denoiser model with the given pretrained ckpt
'''
sys.path.append('../GS_denoising/')
from lightning_denoiser import GradMatch
parser2 = ArgumentParser(prog='utils_restoration.py')
parser2 = GradMatch.add_model_specific_args(parser2)
parser2 = GradMatch.add_optim_specific_args(parser2)
hparams = parser2.parse_known_args()[0]
if 'nb_4' in self.hparams.pretrained_checkpoint :
hparams.DRUNET_nb = 4
hparams.grad_matching = self.hparams.grad_matching
hparams.act_mode = 's'
self.denoiser_model = GradMatch(hparams)
checkpoint = torch.load(self.hparams.pretrained_checkpoint, map_location=self.device)
self.denoiser_model.load_state_dict(checkpoint['state_dict'])
self.denoiser_model.eval()
for i, v in self.denoiser_model.named_parameters():
v.requires_grad = False
self.denoiser_model = self.denoiser_model.to(self.device)
if self.hparams.precision == 'double' :
if self.denoiser_model is not None:
self.denoiser_model.double()
def initialize_prox(self, img, degradation):
'''
calculus for future prox computatations
:param img: degraded image
:param degradation: 2D blur kernel for deblurring and SR, mask for inpainting
'''
if self.hparams.degradation_mode == 'deblurring' :
self.k = degradation
self.k_tensor = array2tensor(np.expand_dims(self.k, 2)).double().to(self.device)
self.FB, self.FBC, self.F2B, self.FBFy = utils_sr.pre_calculate_prox(img, self.k_tensor, 1)
elif self.hparams.degradation_mode == 'SR':
self.k = degradation
self.k_tensor = array2tensor(np.expand_dims(self.k, 2)).double().to(self.device)
self.FB, self.FBC, self.F2B, self.FBFy = utils_sr.pre_calculate_prox(img, self.k_tensor, 2)
elif self.hparams.degradation_mode == 'inpainting':
self.M = array2tensor(degradation).double().to(self.device)
self.My = self.M*img
else:
print('degradation mode not treated')
def calculate_prox(self, img):
'''
Calculation of the proximal mapping of the data term f
:param img: input for the prox
:return: prox_f(img)
'''
if self.hparams.degradation_mode == 'deblurring':
rho = torch.tensor([1/self.hparams.lamb]).double().repeat(1, 1, 1, 1).to(self.device)
px = utils_sr.prox_solution(img.double(), self.FB, self.FBC, self.F2B, self.FBFy, rho, 1)
elif self.hparams.degradation_mode == 'SR':
rho = torch.tensor([1 /self.hparams.lamb]).double().repeat(1, 1, 1, 1).to(self.device)
px = utils_sr.prox_solution(img.double(), self.FB, self.FBC, self.F2B, self.FBFy, rho, self.hparams.sf)
elif self.hparams.degradation_mode == 'inpainting':
if self.hparams.noise_level_img > 1e-2:
px = (self.hparams.lamb*self.My + img)/(self.hparams.lamb*self.M+1)
else :
px = self.My + (1-self.M)*img
else:
print('degradation mode not treated')
return px
def calculate_grad(self, img):
'''
Calculation of the gradient of the data term f
:param img: input for the prox
:return: \nabla_f(img)
'''
if self.hparams.degradation_mode == 'deblurring' :
grad = utils_sr.grad_solution(img.double(), self.FB, self.FBC, self.FBFy, 1)
if self.hparams.degradation_mode == 'SR' :
grad = utils_sr.grad_solution(img.double(), self.FB, self.FBC, self.FBFy, self.hparams.sf)
return grad
def calculate_regul(self,y,x,g):
'''
Calculation of the regularization (1/tau)*phi_sigma(y)
:param y: Point where to evaluate
:param x: D^{-1}(y)
:param g: Precomputed regularization function value at x
:return: regul(y)
'''
regul = (1 / self.hparams.lamb) * (g - (1 / 2) * torch.norm(x - y, p=2) ** 2)
return regul
def calulate_data_term(self,y,img):
'''
Calculation of the data term value f(y)
:param y: Point where to evaluate F
:param img: Degraded image
:return: f(y)
'''
if self.hparams.degradation_mode == 'deblurring':
deg_y = utils_sr.imfilter(y.double(), self.k_tensor[0].double().flip(1).flip(2).expand(3, -1, -1, -1))
f = 0.5 * torch.norm(img - deg_y, p=2) ** 2
elif self.hparams.degradation_mode == 'SR':
deg_y = utils_sr.imfilter(y.double(), self.k_tensor[0].double().flip(1).flip(2).expand(3, -1, -1, -1))
deg_y = deg_y[..., 0::self.hparams.sf, 0::self.hparams.sf]
f = 0.5 * torch.norm(img - deg_y, p=2) ** 2
elif self.hparams.degradation_mode == 'inpainting':
deg_y = self.M * y.double()
f = 0.5 * torch.norm(img - deg_y, p=2) ** 2
else:
print('degradation not implemented')
return f
def calculate_F(self, y, x, g, img):
'''
Calculation of the objective function value f(y) + (1/tau)*phi_sigma(y)
:param y: Point where to evaluate F
:param x: D^{-1}(y)
:param g: Precomputed regularization function value at x
:param img: Degraded image
:return: F(y)
'''
regul = self.calculate_regul(y,x,g)
if self.hparams.no_data_term:
F = regul
else:
f = self.calulate_data_term(y,img)
F = f + regul
return F.item()
def calculate_lyapunov_DRS(self,y,z,x,g,img):
'''
Calculation of the Lyapunov function value Psi(x)
:param x: Point where to evaluate F
:param y,z: DRS iterations initialized at x
:param g: Precomputed regularization function value at x
:param img: Degraded image
:return: Psi(x)
'''
regul = self.calculate_regul(y,x,g)
f = self.calulate_data_term(z, img)
Psi = regul + f + (1 / self.hparams.lamb) * (torch.sum(torch.mul(y-x,y-z)) + (1/2) * torch.norm(y - z, p=2) ** 2)
return Psi
def restore(self, img, init_im, clean_img, degradation,extract_results=False):
'''
Compute GS-PnP restoration algorithm
:param img: Degraded image
:param clean_img: ground-truth clean image
:param degradation: 2D blur kernel for deblurring and SR, mask for inpainting
:param extract_results: Extract information for subsequent image or curve saving
'''
if extract_results:
y_list, z_list, x_list, Dg_list, psnr_tab, g_list, Dx_list, F_list, Psi_list = [], [], [], [], [], [], [], [], []
i = 0 # iteration counter
img_tensor = array2tensor(init_im).to(self.device) # for GPU computations (if GPU available)
self.initialize_prox(img_tensor, degradation) # prox calculus that can be done outside of the loop
# Initialization of the algorithm
if self.hparams.degradation_mode == 'SR':
x0 = cv2.resize(init_im, (img.shape[1] * self.hparams.sf, img.shape[0] * self.hparams.sf),interpolation=cv2.INTER_CUBIC)
x0 = utils_sr.shift_pixel(x0, self.hparams.sf)
x0 = array2tensor(x0).to(self.device)
else:
x0 = array2tensor(init_im).to(self.device)
if extract_results: # extract np images and PSNR values
out_x = tensor2array(x0.cpu())
current_x_psnr = psnr(clean_img, out_x)
if self.hparams.print_each_step:
print('current x PSNR : ', current_x_psnr)
psnr_tab.append(current_x_psnr)
x_list.append(out_x)
x = x0
if self.hparams.use_hard_constraint:
x = torch.clamp(x, 0, 1)
# Initialize Lyapunov
diff_Psi = 1
Psi_old = 1
Psi = Psi_old
while i < self.hparams.maxitr and abs(diff_Psi)/Psi_old > self.hparams.relative_diff_Psi_min:
if self.hparams.inpainting_init :
if i < self.hparams.n_init:
self.sigma_denoiser = 50
else :
self.sigma_denoiser = self.hparams.sigma_denoiser
else :
self.sigma_denoiser = self.hparams.sigma_denoiser
x_old = x
Psi_old = Psi
if self.hparams.PnP_algo == 'PGD':
# Gradient step
gradx = self.calculate_grad(x_old)
z = x_old - self.hparams.lamb*gradx
# Denoising step
torch.set_grad_enabled(True)
Dg, N = self.denoiser_model.calculate_grad(z, self.hparams.sigma_denoiser / 255.)
torch.set_grad_enabled(False)
Dg = Dg.detach()
N = N.detach()
g = 0.5 * (torch.norm(z.double() - N.double(), p=2) ** 2)
Dz = z - Dg
Dx = Dz
x = (1 - self.hparams.alpha) * z + self.hparams.alpha*Dz
y = x
# Hard constraint
if self.hparams.use_hard_constraint:
x = torch.clamp(x,0,1)
# Calculate Objective
F = self.calculate_F(x, z, g, img_tensor)
elif self.hparams.PnP_algo == 'DRS':
# Denoising step
torch.set_grad_enabled(True)
Dg, N = self.denoiser_model.calculate_grad(x_old, self.hparams.sigma_denoiser / 255.)
torch.set_grad_enabled(False)
Dg = Dg.detach()
N = N.detach()
g = 0.5 * (torch.norm(x_old.double() - N.double(), p=2) ** 2)
Dx = x_old - Dg
y = (1 - self.hparams.alpha)*x_old + self.hparams.alpha*Dx
# Hard constraint
if self.hparams.use_hard_constraint:
y = torch.clamp(y,0,1)
# Proximal step
z = self.calculate_prox(2*y-x_old)
# Calculate Lyapunov
Psi = self.calculate_lyapunov_DRS(y,z,x,g,img_tensor)
diff_Psi = Psi-Psi_old
# Calculate Objective
F = self.calculate_F(y, x, g, img_tensor)
# Final step
x = x_old + (z-y)
elif self.hparams.PnP_algo == 'DRSdiff':
# Proximal step
y = self.calculate_prox(x_old)
y2 = 2*y-x_old
# Denoising step
torch.set_grad_enabled(True)
Dg, N = self.denoiser_model.calculate_grad(y2, self.hparams.sigma_denoiser / 255.)
torch.set_grad_enabled(False)
Dg = Dg.detach()
N = N.detach()
g = 0.5 * (torch.norm(y2.double() - N.double(), p=2) ** 2)
Dx = y2 - Dg
z = (1 - self.hparams.alpha) * y2 + self.hparams.alpha * Dx
# Hard constraint
if self.hparams.use_hard_constraint:
z = torch.clamp(z, 0, 1)
# Calculate Lyapunov
Psi = self.calculate_lyapunov_DRS(y,z,x,g,img_tensor)
diff_Psi = Psi-Psi_old
# Calculate Objective
F = self.calculate_F(y, x, g, img_tensor)
# Final step
x = x_old + (z-y)
else :
print('algo not implemented')
# Logging
if extract_results:
out_y = tensor2array(y.cpu())
out_z = tensor2array(z.cpu())
out_x = tensor2array(x.cpu())
current_y_psnr = psnr(clean_img, out_y)
current_z_psnr = psnr(clean_img, out_z)
current_x_psnr = psnr(clean_img, out_x)
if self.hparams.print_each_step:
print('iteration : ', i)
print('current y PSNR : ', current_y_psnr)
print('current z PSNR : ', current_z_psnr)
print('current x PSNR : ', current_x_psnr)
y_list.append(out_y)
x_list.append(out_x)
z_list.append(out_z)
Dx_list.append(tensor2array(Dx.cpu()))
Dg_list.append(torch.norm(Dg).cpu().item())
g_list.append(g.cpu().item())
psnr_tab.append(current_x_psnr)
F_list.append(F)
Psi_list.append(Psi)
# next iteration
i += 1
output_img = tensor2array(y.cpu())
output_psnr = psnr(clean_img, output_img)
output_psnrY = psnr(rgb2y(clean_img), rgb2y(output_img))
if extract_results:
return output_img, output_psnr, output_psnrY, x_list, np.array(z_list), np.array(y_list), np.array(Dg_list), np.array(psnr_tab), np.array(Dx_list), np.array(g_list), np.array(F_list), np.array(Psi_list)
else:
return output_img, output_psnr, output_psnrY
def initialize_curves(self):
self.conv = []
self.PSNR = []
self.g = []
self.Dg = []
self.F = []
self.Psi = []
self.lip_algo = []
self.lip_D = []
self.lip_Dg = []
def update_curves(self, x_list, Dx_list, psnr_tab, Dg_list, g_list, F_list, Psi_list):
self.F.append(F_list)
self.Psi.append(Psi_list)
self.g.append(g_list)
self.Dg.append(Dg_list)
self.PSNR.append(psnr_tab)
self.conv.append(np.array([(np.linalg.norm(x_list[k + 1] - x_list[k]) ** 2) for k in range(len(x_list) - 1)]) / np.sum(np.abs(x_list[0]) ** 2))
self.lip_algo.append(np.sqrt(np.array([np.sum(np.abs(x_list[k + 1] - x_list[k]) ** 2) for k in range(1, len(x_list) - 1)]) / np.array([np.sum(np.abs(x_list[k] - x_list[k - 1]) ** 2) for k in range(1, len(x_list[:-1]))])))
self.lip_D.append(np.sqrt(np.array([np.sum(np.abs(Dx_list[i + 2] - Dx_list[i+1]) ** 2) for i in range(len(Dx_list) - 2)]) / np.array([np.sum(np.abs(x_list[i+1] - x_list[i]) ** 2) for i in range(len(Dx_list) - 2)])))
self.lip_Dg.append(np.sqrt(np.array([np.sum(np.abs(Dg_list[i + 2] - Dg_list[i+1]) ** 2) for i in range(len(Dx_list) - 2)]) / np.array([np.sum(np.abs(x_list[i+1] - x_list[i]) ** 2) for i in range(len(Dg_list) - 2)])))
def save_curves(self, save_path):
import matplotlib
matplotlib.rcParams.update({'font.size': 10})
matplotlib.rcParams['lines.linewidth'] = 2
matplotlib.style.use('seaborn-darkgrid')
plt.figure(0)
fig, ax = plt.subplots()
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
for i in range(len(self.g)):
plt.plot(self.g[i], markevery=10)
ax.xaxis.set_major_locator(MaxNLocator(integer=True))
plt.legend()
plt.savefig(os.path.join(save_path, 'g.png'),bbox_inches="tight")
plt.figure(1)
fig, ax = plt.subplots()
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
for i in range(len(self.PSNR)):
plt.plot(self.PSNR[i], markevery=10)
ax.xaxis.set_major_locator(MaxNLocator(integer=True))
plt.legend()
plt.savefig(os.path.join(save_path, 'PSNR.png'),bbox_inches="tight")
plt.figure(2)
fig, ax = plt.subplots()
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
for i in range(len(self.F)):
plt.plot(self.Psi[i], markevery=10)
ax.xaxis.set_major_locator(MaxNLocator(integer=True))
plt.legend()
plt.savefig(os.path.join(save_path, 'Liapunov.png'), bbox_inches="tight")
plt.figure(22)
fig, ax = plt.subplots()
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
for i in range(len(self.F)):
plt.plot(self.F[i], markevery=10)
ax.xaxis.set_major_locator(MaxNLocator(integer=True))
plt.legend()
plt.savefig(os.path.join(save_path, 'F.png'), bbox_inches="tight")
plt.figure(4)
fig, ax = plt.subplots()
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
for i in range(len(self.Dg)):
Ds_norm = [np.linalg.norm(np.array(self.Dg[i][j])) for j in range(len(self.Dg[i]))]
plt.plot(Ds_norm, linewidth=1.5, markevery=10)
ax.xaxis.set_major_locator(MaxNLocator(integer=True))
plt.legend()
plt.savefig(os.path.join(save_path, 'Dg.png'), bbox_inches="tight")
plt.figure(5)
fig, ax = plt.subplots()
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
for i in range(len(self.conv)):
plt.plot(self.conv[i], '-o', markevery=10)
ax.xaxis.set_major_locator(MaxNLocator(integer=True))
plt.legend()
plt.savefig(os.path.join(save_path, 'conv_log.png'), bbox_inches="tight")
self.conv2 = [[np.min(self.conv[i][:k]) for k in range(1, len(self.conv[i]))] for i in range(len(self.conv))]
conv_rate = [self.conv2[i][0]*np.array([(1/k) for k in range(1,len(self.conv2[i]))]) for i in range(len(self.conv2))]
plt.figure(6)
fig, ax = plt.subplots()
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
for i in range(len(self.conv)):
plt.plot(self.conv2[i], '-', markevery=10)
plt.plot(conv_rate[i], '--', color='red', label=r'$\mathcal{O}(\frac{1}{K})$')
plt.semilogy()
plt.legend()
ax.xaxis.set_major_locator(MaxNLocator(integer=True))
plt.savefig(os.path.join(save_path, 'conv_log2.png'), bbox_inches="tight")
self.conv_sum = [[ | np.sum(self.conv[i][:k]) | numpy.sum |
# -*- coding: utf-8 -*-
"""
Created on Fri Jan 8 12:35:52 2021
@author: harik
"""
import os
import numpy as np
import pandas as pd
import scipy
from scipy.io import wavfile
from numpy.fft import fft
from sklearn.model_selection import train_test_split
import logging
def get_data(DATA_NAME):
if DATA_NAME == "Jackson-speech":
source = 'free-spoken-digit-dataset/free-spoken-digit-dataset-master/FSDD/'+DATA_NAME+'/'
data_instances = len(os.listdir(source))
labels = np.zeros((data_instances, 1), dtype='int')
data_length = []
for fileno, filename in enumerate(os.listdir(source)):
sampling_frequency, data = wavfile.read(os.path.join(source,filename))
data_length.append(len(data))
input_features = np.min(data_length)
fourier_data = np.zeros((data_instances, input_features))
normal_data = np.zeros((data_instances, input_features))
# Applying FFT
for fileno, filename in enumerate(os.listdir(source)):
sampling_frequency, data = wavfile.read(os.path.join(source,filename))
data_length.append(len(data))
normal_data[fileno, :] = data[0:input_features]
fourier_data[fileno, :] = np.abs(fft(data[0:input_features]))
labels[fileno, 0] = filename[0]
'''
if preprocessing == "fourier":
DATA = fourier_data
elif preprocessing == "no-preprocessing":
DATA = normal_data
'''
DATA = fourier_data
X_TRAIN, X_TEST, Y_TRAIN, Y_TEST = train_test_split(DATA, labels, test_size=0.2, random_state=21)
X_TRAIN_NORM = ((X_TRAIN.T - np.min(X_TRAIN, axis = 1))/(np.max(X_TRAIN, axis= 1) - np.min(X_TRAIN, axis = 1))).T
X_TEST_NORM = ((X_TEST.T - np.min(X_TEST, axis = 1))/(np.max(X_TEST, axis= 1) - np.min(X_TEST, axis = 1))).T
print("Shape of Train data: ", X_TRAIN_NORM.shape)
print("Shape of Test data: ", X_TEST_NORM.shape)
return X_TRAIN_NORM, Y_TRAIN, X_TEST_NORM, Y_TEST
elif DATA_NAME == "concentric_circle":
folder_path = "Data/" + DATA_NAME + "/"
# Load Train data
X_train = np.array( pd.read_csv(folder_path+"X_train.csv", header = None) )
# Load Train label
trainlabel = np.array( pd.read_csv(folder_path+"y_train.csv", header = None) )
# Load Test data
X_test = np.array( pd.read_csv(folder_path+"X_test.csv", header = None) )
# Load Test label
testlabel = np.array( pd.read_csv(folder_path+"y_test.csv", header = None) )
## Data_normalization - A Compulsory step
# Normalization is done along each column
X_train_norm = (X_train - np.min(X_train, 0))/(np.max(X_train, 0) - np.min(X_train, 0))
X_test_norm = (X_test - np.min(X_test, 0))/(np.max(X_test, 0) - np.min(X_test, 0))
try:
assert np.min(X_train_norm) >= 0.0 and np.max(X_train_norm <= 1.0)
except AssertionError:
logging.error("Train Data is NOT normalized. Hint: Go to get_data() function and normalize the data to lie in the range [0, 1]", exc_info=True)
try:
assert np.min(X_test_norm) >= 0.0 and np.max(X_test_norm <= 1.0)
except AssertionError:
logging.error("Test Data is NOT normalized. Hint: Go to get_data() function and normalize the data to lie in the range [0, 1]", exc_info=True)
return X_train_norm, trainlabel, X_test_norm, testlabel
elif DATA_NAME == "concentric_circle_noise":
folder_path = "Data/" + DATA_NAME + "/"
# Load Train data
X_train = np.array( pd.read_csv(folder_path+"X_train.csv", header = None) )
# Load Train label
trainlabel = np.array( pd.read_csv(folder_path+"y_train.csv", header = None) )
# Load Test data
X_test = np.array( pd.read_csv(folder_path+"X_test.csv", header = None) )
# Load Test label
testlabel = np.array( pd.read_csv(folder_path+"y_test.csv", header = None) )
## Data_normalization - A Compulsory step
# Normalization is done along each column
X_train_norm = (X_train - np.min(X_train, 0))/(np.max(X_train, 0) - | np.min(X_train, 0) | numpy.min |
import unittest
import numpy as np
from scikit_roughsets.roughsets import RoughSetsReducer
class TestRoughsets(unittest.TestCase):
red = RoughSetsReducer()
S = | np.array([[0, 0], [0, 0], [0, 0], [0, 1], [1, 1], [1, 1], [1, 1], [1, 2], [2, 2], [2, 2]]) | numpy.array |
##Syntax: run dssp_output_analysis.py length_of_protein dssp_output*.txt
import sys
from numpy import genfromtxt
import numpy as np
import os
from shutil import copy
phi_psi_outfile = 'output_phi_phi.txt'
tco_outfile = 'output_tco.txt'
racc_outfile = 'output_racc.txt'
hbond_outfile = 'output_hbond.txt'
hbond_total_outfile = 'output_hbondtotal.txt'
acc_total_outfile = 'output_acc_total.txt'
phi_psi_2his_outfile = 'output_phi_psi_2his.txt'
phi_psi_2his_no_GLY_outfile = 'output_phi_psi_no_GLY_2his.txt'
import_for_length = genfromtxt(sys.argv[1], delimiter='\t', dtype=float)
length = len(import_for_length)
#Creating Keys for computing relative solvent accessible surface area
#Values obtained from Wilke: Tien et al. 2013 http://dx.doi.org/10.1371/journal.pone.0080635
aa_acc_max = { \
'A': 129.0, 'R': 274.0, 'N': 195.0, 'D': 193.0,\
'C': 167.0, 'Q': 225.0, 'E': 223.0, 'G': 104.0,\
'H': 224.0, 'I': 197.0, 'L': 201.0, 'K': 236.0,\
'M': 224.0, 'F': 240.0, 'P': 159.0, 'S': 155.0,\
'T': 172.0, 'W': 285.0, 'Y': 263.0, 'V': 174.0}
#Creating Key for linking each amino acid to a Phi-Psi matrix
ALA = []
ARG = []
ASN = []
ASP = []
CYS = []
GLN = []
GLU = []
GLY = []
HIS = []
ILE = []
LEU = []
LYS = []
MET = []
PHE = []
PRO = []
SER = []
THR = []
TRP = []
TYR = []
VAL = []
aa_phi_mat = { \
'A': ALA, 'R': ARG, 'N': ASN, 'D': ASP,\
'C': CYS, 'Q': GLN, 'E': GLU, 'G': GLY,\
'H': HIS, 'I': ILE, 'L': LEU, 'K': LYS,\
'M': MET, 'F': PHE, 'P': PRO, 'S': SER,\
'T': THR, 'W': TRP, 'Y': TYR, 'V': VAL}
ALA_2 = []
ARG_2 = []
ASN_2 = []
ASP_2 = []
CYS_2 = []
GLN_2 = []
GLU_2 = []
GLY_2 = []
HIS_2 = []
ILE_2 = []
LEU_2 = []
LYS_2 = []
MET_2 = []
PHE_2 = []
PRO_2 = []
SER_2 = []
THR_2 = []
TRP_2 = []
TYR_2 = []
VAL_2 = []
Full_phi_psi_matrix = [ALA, ALA_2, ARG, ARG_2, ASN, ASN_2, ASP, ASP_2, CYS, CYS_2, GLN, GLN_2, GLU, GLU_2, GLY, GLY_2, HIS, HIS_2, ILE, ILE_2, LEU, LEU_2, LYS, LYS_2, MET, MET_2, PHE, PHE_2, PRO, PRO_2, SER, SER_2, THR, THR_2, TRP, TRP_2, TYR, TYR_2, VAL, VAL_2]
aa_psi_mat = { \
'A': ALA_2, 'R': ARG_2, 'N': ASN_2, 'D': ASP_2,\
'C': CYS_2, 'Q': GLN_2, 'E': GLU_2, 'G': GLY_2,\
'H': HIS_2, 'I': ILE_2, 'L': LEU_2, 'K': LYS_2,\
'M': MET_2, 'F': PHE_2, 'P': PRO_2, 'S': SER_2,\
'T': THR_2, 'W': TRP_2, 'Y': TYR_2, 'V': VAL_2}
#Building Matricies for Holding/Analyzing Data
racc_matrix = np.empty([len(sys.argv), int(length)])
tco_matrix = np.empty([len(sys.argv), int(length)])
full_hbonding_matrix = np.empty([len(sys.argv), 14])
total_acc_matrix = []
total_hbond_matrix = []
percent_data_array = np.zeros([length, 3]) # Helix, Sheet, Loop
for fnu,fna in enumerate(sys.argv[2:]):
lines = open(fna).readlines()
total_acc_matrix.append(float(lines[7][1:8]))
total_hbond_matrix.append(float(lines[8][2:6]))
for idx,item in enumerate(lines[8:22]):
full_hbonding_matrix[fnu][idx] = int(item[2:6])
for idx,item in enumerate(lines[28:]):
res_num = int(item[6:10])
res_aa = item[13]
if res_aa == 'X':
res_aa = 'Y'
max_for_rel = aa_acc_max[res_aa]
res_ss = item[16]
res_acc = float(int(item[35:38]))
res_rel_acc = res_acc/max_for_rel
racc_matrix[fnu][idx] = res_rel_acc
res_tco = float(item[85:92])
#if res_tco > 0.75:
# res_ss = 'H'
#if res_tco < -0.75:
# res_ss = 'E'
if res_ss == 'E' or res_ss == 'B':
percent_data_array[idx][1] += 1
elif res_ss == 'H' or res_ss == 'G' or res_ss == 'I':
percent_data_array[idx][0] += 1
else:
percent_data_array[idx][2] += 1
tco_matrix[fnu][idx] = res_tco
res_phi = float(item[103:109])
aa_phi_mat[res_aa].append(res_phi)
res_psi = float(item[109:115])
aa_psi_mat[res_aa].append(res_psi)
#Full_phi_psi_matrix_map = map(None, *Full_phi_psi_matrix)
#pp_out = open(phi_psi_outfile, 'w')
#for i in range(len(Full_phi_psi_matrix_map)):
# for j in range(len(Full_phi_psi_matrix_map[0])):
# pp_out.write("%s\t" % Full_phi_psi_matrix_map[i][j])
# pp_out.write("\n")
#pp_out.close()
full_phi_list = np.empty((0,0))
full_phi_list = np.append(full_phi_list, ALA)
full_phi_list = np.append(full_phi_list, ARG)
full_phi_list = np.append(full_phi_list, ASN)
full_phi_list = np.append(full_phi_list, ASP)
full_phi_list = np.append(full_phi_list, CYS)
full_phi_list = np.append(full_phi_list, GLN)
full_phi_list = np.append(full_phi_list, GLU)
full_phi_list = np.append(full_phi_list, GLY)
full_phi_list = np.append(full_phi_list, HIS)
full_phi_list = np.append(full_phi_list, ILE)
full_phi_list = np.append(full_phi_list, LEU)
full_phi_list = np.append(full_phi_list, LYS)
full_phi_list = np.append(full_phi_list, MET)
full_phi_list = np.append(full_phi_list, PHE)
full_phi_list = np.append(full_phi_list, PRO)
full_phi_list = np.append(full_phi_list, SER)
full_phi_list = np.append(full_phi_list, THR)
full_phi_list = np.append(full_phi_list, TRP)
full_phi_list = np.append(full_phi_list, TYR)
full_phi_list = np.append(full_phi_list, VAL)
full_phi_list_no_GLY = []
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, ALA)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, ARG)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, ASN)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, ASP)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, CYS)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, GLN)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, GLU)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, HIS)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, ILE)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, LEU)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, LYS)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, MET)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, PHE)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, PRO)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, SER)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, THR)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, TRP)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, TYR)
full_phi_list_no_GLY = np.append(full_phi_list_no_GLY, VAL)
full_psi_list = []
full_psi_list = np.append(full_psi_list, ALA_2)
full_psi_list = | np.append(full_psi_list, ARG_2) | numpy.append |
from os.path import dirname, exists, join, relpath
from unittest.mock import Mock
import pytest
import torch
from rflib.runner import build_optimizer
from rfvision.core import BitmapMasks, PolygonMasks
from rfvision.datasets.builder import DATASETS
from rfvision.datasets.utils import NumClassCheckHook
def _get_config_directory():
"""Find the predefined detector config directory."""
try:
# Assume we are running in the source rfvisionection repo
repo_dpath = dirname(dirname(__file__))
repo_dpath = join(repo_dpath, '..')
except NameError:
# For IPython development when this __file__ is not defined
import rfvision
repo_dpath = dirname(dirname(rfvision.__file__))
config_dpath = join(repo_dpath, 'configs')
if not exists(config_dpath):
raise Exception('Cannot find config path')
return config_dpath
def _check_numclasscheckhook(detector, config_mod):
dummy_runner = Mock()
dummy_runner.model = detector
def get_dataset_name_classes(dataset):
# deal with `RepeatDataset`,`ConcatDataset`,`ClassBalancedDataset`..
if isinstance(dataset, (list, tuple)):
dataset = dataset[0]
while ('dataset' in dataset):
dataset = dataset['dataset']
# ConcatDataset
if isinstance(dataset, (list, tuple)):
dataset = dataset[0]
return dataset['type'], dataset.get('classes', None)
compatible_check = NumClassCheckHook()
dataset_name, CLASSES = get_dataset_name_classes(
config_mod['data']['train'])
if CLASSES is None:
CLASSES = DATASETS.get(dataset_name).CLASSES
dummy_runner.data_loader.dataset.CLASSES = CLASSES
compatible_check.before_train_epoch(dummy_runner)
dummy_runner.data_loader.dataset.CLASSES = None
compatible_check.before_train_epoch(dummy_runner)
dataset_name, CLASSES = get_dataset_name_classes(config_mod['data']['val'])
if CLASSES is None:
CLASSES = DATASETS.get(dataset_name).CLASSES
dummy_runner.data_loader.dataset.CLASSES = CLASSES
compatible_check.before_val_epoch(dummy_runner)
dummy_runner.data_loader.dataset.CLASSES = None
compatible_check.before_val_epoch(dummy_runner)
def test_config_build_detector():
"""Test that all detection models defined in the configs can be
initialized."""
from rflib import Config
from rfvision.models import build_detector
config_dpath = _get_config_directory()
print(f'Found config_dpath = {config_dpath}')
import glob
config_fpaths = list(glob.glob(join(config_dpath, '**', '*.py')))
config_fpaths = [
p for p in config_fpaths
if p.find('_base_') == -1 and p.find('common') == -1
]
config_names = [relpath(p, config_dpath) for p in config_fpaths]
print(f'Using {len(config_names)} config files')
for config_fname in config_names:
config_fpath = join(config_dpath, config_fname)
config_mod = Config.fromfile(config_fpath)
config_mod.model
print(f'Building detector, config_fpath = {config_fpath}')
# Remove pretrained/init_cfg keys to allow for testing in an offline environment
if 'init_cfg' in config_mod.model:
config_mod.model['init_cfg'] = None
detector = build_detector(config_mod.model)
assert detector is not None
_check_numclasscheckhook(detector, config_mod)
optimizer = build_optimizer(detector, config_mod.optimizer)
assert isinstance(optimizer, torch.optim.Optimizer)
if 'roi_head' in config_mod.model.keys():
# for two stage detector
# detectors must have bbox head
assert detector.roi_head.with_bbox and detector.with_bbox
assert detector.roi_head.with_mask == detector.with_mask
head_config = config_mod.model['roi_head']
_check_roi_head(head_config, detector.roi_head)
# else:
# # for single stage detector
# # detectors must have bbox head
# # assert detector.with_bbox
# head_config = config_mod.model['bbox_head']
# _check_bbox_head(head_config, detector.bbox_head)
def _check_roi_head(config, head):
# check consistency between head_config and roi_head
assert config['type'] == head.__class__.__name__
# check roi_align
bbox_roi_cfg = config.bbox_roi_extractor
bbox_roi_extractor = head.bbox_roi_extractor
_check_roi_extractor(bbox_roi_cfg, bbox_roi_extractor)
# check bbox head infos
bbox_cfg = config.bbox_head
bbox_head = head.bbox_head
_check_bbox_head(bbox_cfg, bbox_head)
if head.with_mask:
# check roi_align
if config.mask_roi_extractor:
mask_roi_cfg = config.mask_roi_extractor
mask_roi_extractor = head.mask_roi_extractor
_check_roi_extractor(mask_roi_cfg, mask_roi_extractor,
bbox_roi_extractor)
# check mask head infos
mask_head = head.mask_head
mask_cfg = config.mask_head
_check_mask_head(mask_cfg, mask_head)
# check arch specific settings, e.g., cascade/htc
if config['type'] in ['CascadeRoIHead', 'HybridTaskCascadeRoIHead']:
assert config.num_stages == len(head.bbox_head)
assert config.num_stages == len(head.bbox_roi_extractor)
if head.with_mask:
assert config.num_stages == len(head.mask_head)
assert config.num_stages == len(head.mask_roi_extractor)
elif config['type'] in ['MaskScoringRoIHead']:
assert (hasattr(head, 'mask_iou_head')
and head.mask_iou_head is not None)
mask_iou_cfg = config.mask_iou_head
mask_iou_head = head.mask_iou_head
assert (mask_iou_cfg.fc_out_channels ==
mask_iou_head.fc_mask_iou.in_features)
elif config['type'] in ['GridRoIHead']:
grid_roi_cfg = config.grid_roi_extractor
grid_roi_extractor = head.grid_roi_extractor
_check_roi_extractor(grid_roi_cfg, grid_roi_extractor,
bbox_roi_extractor)
config.grid_head.grid_points = head.grid_head.grid_points
def _check_roi_extractor(config, roi_extractor, prev_roi_extractor=None):
import torch.nn as nn
# Separate roi_extractor and prev_roi_extractor checks for flexibility
if isinstance(roi_extractor, nn.ModuleList):
roi_extractor = roi_extractor[0]
if prev_roi_extractor and isinstance(prev_roi_extractor, nn.ModuleList):
prev_roi_extractor = prev_roi_extractor[0]
assert (len(config.featmap_strides) == len(roi_extractor.roi_layers))
assert (config.out_channels == roi_extractor.out_channels)
from torch.nn.modules.utils import _pair
assert (_pair(config.roi_layer.output_size) ==
roi_extractor.roi_layers[0].output_size)
if 'use_torchvision' in config.roi_layer:
assert (config.roi_layer.use_torchvision ==
roi_extractor.roi_layers[0].use_torchvision)
elif 'aligned' in config.roi_layer:
assert (
config.roi_layer.aligned == roi_extractor.roi_layers[0].aligned)
if prev_roi_extractor:
assert (roi_extractor.roi_layers[0].aligned ==
prev_roi_extractor.roi_layers[0].aligned)
assert (roi_extractor.roi_layers[0].use_torchvision ==
prev_roi_extractor.roi_layers[0].use_torchvision)
def _check_mask_head(mask_cfg, mask_head):
import torch.nn as nn
if isinstance(mask_cfg, list):
for single_mask_cfg, single_mask_head in zip(mask_cfg, mask_head):
_check_mask_head(single_mask_cfg, single_mask_head)
elif isinstance(mask_head, nn.ModuleList):
for single_mask_head in mask_head:
_check_mask_head(mask_cfg, single_mask_head)
else:
assert mask_cfg['type'] == mask_head.__class__.__name__
assert mask_cfg.in_channels == mask_head.in_channels
class_agnostic = mask_cfg.get('class_agnostic', False)
out_dim = (1 if class_agnostic else mask_cfg.num_classes)
if hasattr(mask_head, 'conv_logits'):
assert (mask_cfg.conv_out_channels ==
mask_head.conv_logits.in_channels)
assert mask_head.conv_logits.out_channels == out_dim
else:
assert mask_cfg.fc_out_channels == mask_head.fc_logits.in_features
assert (mask_head.fc_logits.out_features == out_dim *
mask_head.output_area)
def _check_bbox_head(bbox_cfg, bbox_head):
import torch.nn as nn
if isinstance(bbox_cfg, list):
for single_bbox_cfg, single_bbox_head in zip(bbox_cfg, bbox_head):
_check_bbox_head(single_bbox_cfg, single_bbox_head)
elif isinstance(bbox_head, nn.ModuleList):
for single_bbox_head in bbox_head:
_check_bbox_head(bbox_cfg, single_bbox_head)
else:
assert bbox_cfg['type'] == bbox_head.__class__.__name__
if bbox_cfg['type'] == 'SABLHead':
assert bbox_cfg.cls_in_channels == bbox_head.cls_in_channels
assert bbox_cfg.reg_in_channels == bbox_head.reg_in_channels
cls_out_channels = bbox_cfg.get('cls_out_channels', 1024)
assert (cls_out_channels == bbox_head.fc_cls.in_features)
assert (bbox_cfg.num_classes + 1 == bbox_head.fc_cls.out_features)
elif bbox_cfg['type'] == 'DIIHead':
assert bbox_cfg['num_ffn_fcs'] == bbox_head.ffn.num_fcs
# 3 means FC and LN and Relu
assert bbox_cfg['num_cls_fcs'] == len(bbox_head.cls_fcs) // 3
assert bbox_cfg['num_reg_fcs'] == len(bbox_head.reg_fcs) // 3
assert bbox_cfg['in_channels'] == bbox_head.in_channels
assert bbox_cfg['in_channels'] == bbox_head.fc_cls.in_features
assert bbox_cfg['in_channels'] == bbox_head.fc_reg.in_features
assert bbox_cfg['in_channels'] == bbox_head.attention.embed_dims
assert bbox_cfg[
'feedforward_channels'] == bbox_head.ffn.feedforward_channels
else:
assert bbox_cfg.in_channels == bbox_head.in_channels
with_cls = bbox_cfg.get('with_cls', True)
if with_cls:
fc_out_channels = bbox_cfg.get('fc_out_channels', 2048)
assert (fc_out_channels == bbox_head.fc_cls.in_features)
if bbox_head.custom_cls_channels:
assert (bbox_head.loss_cls.get_cls_channels(
bbox_head.num_classes) == bbox_head.fc_cls.out_features
)
else:
assert (bbox_cfg.num_classes +
1 == bbox_head.fc_cls.out_features)
with_reg = bbox_cfg.get('with_reg', True)
if with_reg:
out_dim = (4 if bbox_cfg.reg_class_agnostic else 4 *
bbox_cfg.num_classes)
assert bbox_head.fc_reg.out_features == out_dim
def _check_anchorhead(config, head):
# check consistency between head_config and roi_head
assert config['type'] == head.__class__.__name__
assert config.in_channels == head.in_channels
num_classes = (
config.num_classes -
1 if config.loss_cls.get('use_sigmoid', False) else config.num_classes)
if config['type'] == 'ATSSHead':
assert (config.feat_channels == head.atss_cls.in_channels)
assert (config.feat_channels == head.atss_reg.in_channels)
assert (config.feat_channels == head.atss_centerness.in_channels)
elif config['type'] == 'SABLRetinaHead':
assert (config.feat_channels == head.retina_cls.in_channels)
assert (config.feat_channels == head.retina_bbox_reg.in_channels)
assert (config.feat_channels == head.retina_bbox_cls.in_channels)
else:
assert (config.in_channels == head.conv_cls.in_channels)
assert (config.in_channels == head.conv_reg.in_channels)
assert (head.conv_cls.out_channels == num_classes * head.num_anchors)
assert head.fc_reg.out_channels == 4 * head.num_anchors
# Only tests a representative subset of configurations
# TODO: test pipelines using Albu, current Albu throw None given empty GT
@pytest.mark.parametrize(
'config_rpath',
[
'wider_face/ssd300_wider_face.py',
'pascal_voc/ssd300_voc0712.py',
'pascal_voc/ssd512_voc0712.py',
# 'albu_example/mask_rcnn_r50_fpn_1x.py',
'foveabox/fovea_align_r50_fpn_gn-head_mstrain_640-800_4x4_2x_coco.py',
'mask_rcnn/mask_rcnn_r50_caffe_fpn_mstrain-poly_1x_coco.py',
'mask_rcnn/mask_rcnn_r50_caffe_fpn_mstrain_1x_coco.py',
'fp16/mask_rcnn_r50_fpn_fp16_1x_coco.py'
])
def test_config_data_pipeline(config_rpath):
"""Test whether the data pipeline is valid and can process corner cases.
CommandLine:
xdoctest -m tests/test_runtime/
test_config.py test_config_build_data_pipeline
"""
from rflib import Config
from rfvision.datasets.pipelines import Compose
import numpy as np
config_dpath = _get_config_directory()
print(f'Found config_dpath = {config_dpath}')
def dummy_masks(h, w, num_obj=3, mode='bitmap'):
assert mode in ('polygon', 'bitmap')
if mode == 'bitmap':
masks = np.random.randint(0, 2, (num_obj, h, w), dtype=np.uint8)
masks = BitmapMasks(masks, h, w)
else:
masks = []
for i in range(num_obj):
masks.append([])
masks[-1].append(
np.random.uniform(0, min(h - 1, w - 1), (8 + 4 * i, )))
masks[-1].append(
np.random.uniform(0, min(h - 1, w - 1), (10 + 4 * i, )))
masks = PolygonMasks(masks, h, w)
return masks
config_fpath = join(config_dpath, config_rpath)
cfg = Config.fromfile(config_fpath)
# remove loading pipeline
loading_pipeline = cfg.train_pipeline.pop(0)
loading_ann_pipeline = cfg.train_pipeline.pop(0)
cfg.test_pipeline.pop(0)
train_pipeline = Compose(cfg.train_pipeline)
test_pipeline = Compose(cfg.test_pipeline)
print(f'Building data pipeline, config_fpath = {config_fpath}')
print(f'Test training data pipeline: \n{train_pipeline!r}')
img = np.random.randint(0, 255, size=(888, 666, 3), dtype=np.uint8)
if loading_pipeline.get('to_float32', False):
img = img.astype(np.float32)
mode = 'bitmap' if loading_ann_pipeline.get('poly2mask',
True) else 'polygon'
results = dict(
filename='test_img.png',
ori_filename='test_img.png',
img=img,
img_shape=img.shape,
ori_shape=img.shape,
gt_bboxes=np.array([[35.2, 11.7, 39.7, 15.7]], dtype=np.float32),
gt_labels= | np.array([1], dtype=np.int64) | numpy.array |
# 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]) | numpy.array |
# Copyright 2021 The FastEstimator Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
from typing import Any, Dict, Iterable, Optional, TypeVar, Union
import cv2
import numpy as np
import tensorflow as tf
import torch
from fastestimator.backend.argmax import argmax
from fastestimator.backend.concat import concat
from fastestimator.backend.get_image_dims import get_image_dims
from fastestimator.backend.reduce_max import reduce_max
from fastestimator.backend.squeeze import squeeze
from fastestimator.trace.trace import Trace
from fastestimator.util.data import Data
from fastestimator.util.img_data import ImgData
from fastestimator.util.traceability_util import traceable
from fastestimator.util.util import to_number
Tensor = TypeVar('Tensor', tf.Tensor, torch.Tensor, np.ndarray)
@traceable()
class GradCAM(Trace):
"""A trace which draws GradCAM heatmaps on top of images.
These are useful for visualizing supports for a model's classification. See https://arxiv.org/pdf/1610.02391.pdf
for more details.
Args:
images: The key corresponding to images onto which to draw the CAM outputs.
grads: The key corresponding to gradients of the model output with respect to a convolution layer of the model.
You can easily extract these from any model by using the 'intermediate_layers' variable in a ModelOp, along
with the GradientOp. Make sure to select a particular component of y_pred when computing gradients rather
than using the entire vector. See our GradCAM XAI tutorial for an example.
n_components: How many principal components to visualize.
n_samples: How many images in total to display every epoch (or None to display all available images).
labels: The key corresponding to the true labels of the images to be visualized.
preds: The key corresponding to the model prediction for each image.
label_mapping: {class_string: model_output_value}.
outputs: The key into which to write the eigencam images.
mode: What mode(s) to execute this Op in. For example, "train", "eval", "test", or "infer". To execute
regardless of mode, pass None. To execute in all modes except for a particular one, you can pass an argument
like "!infer" or "!train".
"""
def __init__(self, images: str, grads: str, n_components: int = 3, n_samples: Optional[int] = 5,
labels: Optional[str] = None, preds: Optional[str] = None,
label_mapping: Optional[Dict[str, Any]] = None, outputs: str = "gradcam",
mode: Union[None, str, Iterable[str]] = "!train"):
self.image_key = images
self.grad_key = grads
self.true_label_key = labels
self.pred_label_key = preds
inputs = [x for x in (images, grads, labels, preds) if x is not None]
self.n_components = n_components
self.n_samples = n_samples
# TODO - handle non-hashable labels
self.label_mapping = {val: key for key, val in label_mapping.items()} if label_mapping else None
super().__init__(inputs=inputs, outputs=outputs, mode=mode)
self.images = []
self.grads = []
self.labels = []
self.preds = []
self.n_found = 0
def _reset(self) -> None:
"""Clear memory for next epoch.
"""
self.images = []
self.grads = []
self.labels = []
self.preds = []
self.n_found = 0
def on_batch_end(self, data: Data) -> None:
if self.n_samples is None or self.n_found < self.n_samples:
self.images.append(data[self.image_key])
self.grads.append(data[self.grad_key])
if self.true_label_key:
self.labels.append(data[self.true_label_key])
if self.pred_label_key:
self.preds.append(data[self.pred_label_key])
self.n_found += len(data[self.image_key])
def on_epoch_end(self, data: Data) -> None:
# Keep only the user-specified number of samples
images = concat(self.images)[:self.n_samples or self.n_found]
_, height, width = get_image_dims(images)
grads = to_number(concat(self.grads)[:self.n_samples or self.n_found])
if tf.is_tensor(images):
grads = np.moveaxis(grads, source=-1, destination=1) # grads should be channel first
args = {}
labels = None if not self.labels else concat(self.labels)[:self.n_samples or self.n_found]
if labels is not None:
if len(labels.shape) > 1:
labels = argmax(labels, axis=-1)
if self.label_mapping:
labels = np.array([self.label_mapping[clazz] for clazz in to_number(squeeze(labels))])
args[self.true_label_key] = labels
preds = None if not self.preds else concat(self.preds)[:self.n_samples or self.n_found]
if preds is not None:
if len(preds.shape) > 1:
preds = argmax(preds, axis=-1)
if self.label_mapping:
preds = np.array([self.label_mapping[clazz] for clazz in to_number(squeeze(preds))])
args[self.pred_label_key] = preds
args[self.image_key] = images
# Clear memory
self._reset()
# Make the image
# TODO: In future maybe allow multiple different grads to have side-by-side comparisons of classes
components = [np.mean(grads, axis=1)]
components = [ | np.maximum(component, 0) | numpy.maximum |
# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0
import functools
import math
from collections import OrderedDict
from importlib import import_module
import numpy as np
import pytest
import funsor
import funsor.ops as ops
from funsor.cnf import Contraction, GaussianMixture
from funsor.delta import Delta
from funsor.distribution import BACKEND_TO_DISTRIBUTIONS_BACKEND
from funsor.domains import bint, reals
from funsor.interpreter import interpretation, reinterpret
from funsor.integrate import Integrate
from funsor.tensor import Einsum, Tensor, align_tensors, numeric_array
from funsor.terms import Independent, Variable, eager, lazy
from funsor.testing import assert_close, check_funsor, rand, randint, randn, random_mvn, random_tensor, xfail_param
from funsor.util import get_backend
pytestmark = pytest.mark.skipif(get_backend() == "numpy",
reason="numpy does not have distributions backend")
if get_backend() != "numpy":
dist = import_module(BACKEND_TO_DISTRIBUTIONS_BACKEND[get_backend()])
backend_dist = dist.dist
if get_backend() == "torch":
from funsor.pyro.convert import dist_to_funsor
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
@pytest.mark.parametrize('eager', [False, True])
def test_beta_density(batch_shape, eager):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
@funsor.function(reals(), reals(), reals(), reals())
def beta(concentration1, concentration0, value):
return backend_dist.Beta(concentration1, concentration0).log_prob(value)
check_funsor(beta, {'concentration1': reals(), 'concentration0': reals(), 'value': reals()}, reals())
concentration1 = Tensor(ops.exp(randn(batch_shape)), inputs)
concentration0 = Tensor(ops.exp(randn(batch_shape)), inputs)
value = Tensor(rand(batch_shape), inputs)
expected = beta(concentration1, concentration0, value)
check_funsor(expected, inputs, reals())
d = Variable('value', reals())
actual = dist.Beta(concentration1, concentration0, value) if eager else \
dist.Beta(concentration1, concentration0, d)(value=value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
@pytest.mark.parametrize('syntax', ['eager', 'lazy', 'generic'])
def test_bernoulli_probs_density(batch_shape, syntax):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
@funsor.function(reals(), reals(), reals())
def bernoulli(probs, value):
return backend_dist.Bernoulli(probs).log_prob(value)
check_funsor(bernoulli, {'probs': reals(), 'value': reals()}, reals())
probs = Tensor(rand(batch_shape), inputs)
value = Tensor(rand(batch_shape).round(), inputs)
expected = bernoulli(probs, value)
check_funsor(expected, inputs, reals())
d = Variable('value', reals())
if syntax == 'eager':
actual = dist.BernoulliProbs(probs, value)
elif syntax == 'lazy':
actual = dist.BernoulliProbs(probs, d)(value=value)
elif syntax == 'generic':
actual = dist.Bernoulli(probs=probs)(value=value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
@pytest.mark.parametrize('syntax', ['eager', 'lazy', 'generic'])
def test_bernoulli_logits_density(batch_shape, syntax):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
@funsor.function(reals(), reals(), reals())
def bernoulli(logits, value):
return backend_dist.Bernoulli(logits=logits).log_prob(value)
check_funsor(bernoulli, {'logits': reals(), 'value': reals()}, reals())
logits = Tensor(rand(batch_shape), inputs)
value = Tensor(ops.astype(rand(batch_shape) >= 0.5, 'float'), inputs)
expected = bernoulli(logits, value)
check_funsor(expected, inputs, reals())
d = Variable('value', reals())
if syntax == 'eager':
actual = dist.BernoulliLogits(logits, value)
elif syntax == 'lazy':
actual = dist.BernoulliLogits(logits, d)(value=value)
elif syntax == 'generic':
actual = dist.Bernoulli(logits=logits)(value=value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
@pytest.mark.parametrize('eager', [False, True])
def test_binomial_density(batch_shape, eager):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
max_count = 10
@funsor.function(reals(), reals(), reals(), reals())
def binomial(total_count, probs, value):
return backend_dist.Binomial(total_count, probs).log_prob(value)
check_funsor(binomial, {'total_count': reals(), 'probs': reals(), 'value': reals()}, reals())
value_data = ops.astype(random_tensor(inputs, bint(max_count)).data, 'float')
total_count_data = value_data + ops.astype(random_tensor(inputs, bint(max_count)).data, 'float')
value = Tensor(value_data, inputs)
total_count = Tensor(total_count_data, inputs)
probs = Tensor(rand(batch_shape), inputs)
expected = binomial(total_count, probs, value)
check_funsor(expected, inputs, reals())
m = Variable('value', reals())
actual = dist.Binomial(total_count, probs, value) if eager else \
dist.Binomial(total_count, probs, m)(value=value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected, rtol=1e-5)
def test_categorical_defaults():
probs = Variable('probs', reals(3))
value = Variable('value', bint(3))
assert dist.Categorical(probs) is dist.Categorical(probs, value)
@pytest.mark.parametrize('size', [4])
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
def test_categorical_density(size, batch_shape):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
@funsor.of_shape(reals(size), bint(size))
def categorical(probs, value):
return probs[value].log()
check_funsor(categorical, {'probs': reals(size), 'value': bint(size)}, reals())
probs_data = ops.exp(randn(batch_shape + (size,)))
probs_data /= probs_data.sum(-1)[..., None]
probs = Tensor(probs_data, inputs)
value = random_tensor(inputs, bint(size))
expected = categorical(probs, value)
check_funsor(expected, inputs, reals())
actual = dist.Categorical(probs, value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected)
def test_delta_defaults():
v = Variable('v', reals())
log_density = Variable('log_density', reals())
backend_dist_module = BACKEND_TO_DISTRIBUTIONS_BACKEND[get_backend()]
assert isinstance(dist.Delta(v, log_density), import_module(backend_dist_module).Delta)
value = Variable('value', reals())
assert dist.Delta(v, log_density, 'value') is dist.Delta(v, log_density, value)
@pytest.mark.parametrize('event_shape', [(), (4,), (3, 2)], ids=str)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
def test_delta_density(batch_shape, event_shape):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
@funsor.function(reals(*event_shape), reals(), reals(*event_shape), reals())
def delta(v, log_density, value):
eq = (v == value)
for _ in range(len(event_shape)):
eq = ops.all(eq, -1)
return ops.log(ops.astype(eq, 'float32')) + log_density
check_funsor(delta, {'v': reals(*event_shape),
'log_density': reals(),
'value': reals(*event_shape)}, reals())
v = Tensor(randn(batch_shape + event_shape), inputs)
log_density = Tensor(ops.exp(randn(batch_shape)), inputs)
for value in [v, Tensor(randn(batch_shape + event_shape), inputs)]:
expected = delta(v, log_density, value)
check_funsor(expected, inputs, reals())
actual = dist.Delta(v, log_density, value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected)
def test_delta_delta():
v = Variable('v', reals(2))
point = Tensor(randn(2))
log_density = Tensor(numeric_array(0.5))
d = dist.Delta(point, log_density, v)
assert d is Delta('v', point, log_density)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
@pytest.mark.parametrize('event_shape', [(1,), (4,), (5,)], ids=str)
def test_dirichlet_density(batch_shape, event_shape):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
@funsor.function(reals(*event_shape), reals(*event_shape), reals())
def dirichlet(concentration, value):
return backend_dist.Dirichlet(concentration).log_prob(value)
check_funsor(dirichlet, {'concentration': reals(*event_shape), 'value': reals(*event_shape)}, reals())
concentration = Tensor(ops.exp(randn(batch_shape + event_shape)), inputs)
value_data = rand(batch_shape + event_shape)
value_data = value_data / value_data.sum(-1)[..., None]
value = Tensor(value_data, inputs)
expected = dirichlet(concentration, value)
check_funsor(expected, inputs, reals())
actual = dist.Dirichlet(concentration, value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
@pytest.mark.parametrize('event_shape', [(1,), (4,), (5,)], ids=str)
@pytest.mark.xfail(get_backend() != 'torch', reason="DirichletMultinomial is not implemented yet in NumPyro")
def test_dirichlet_multinomial_density(batch_shape, event_shape):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
max_count = 10
@funsor.function(reals(*event_shape), reals(), reals(*event_shape), reals())
def dirichlet_multinomial(concentration, total_count, value):
return backend_dist.DirichletMultinomial(concentration, total_count).log_prob(value)
check_funsor(dirichlet_multinomial, {'concentration': reals(*event_shape),
'total_count': reals(),
'value': reals(*event_shape)},
reals())
concentration = Tensor(ops.exp(randn(batch_shape + event_shape)), inputs)
value_data = ops.astype(randint(0, max_count, size=batch_shape + event_shape), 'float32')
total_count_data = value_data.sum(-1) + ops.astype(randint(0, max_count, size=batch_shape), 'float32')
value = Tensor(value_data, inputs)
total_count = Tensor(total_count_data, inputs)
expected = dirichlet_multinomial(concentration, total_count, value)
check_funsor(expected, inputs, reals())
actual = dist.DirichletMultinomial(concentration, total_count, value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
def test_lognormal_density(batch_shape):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
@funsor.function(reals(), reals(), reals(), reals())
def log_normal(loc, scale, value):
return backend_dist.LogNormal(loc, scale).log_prob(value)
check_funsor(log_normal, {'loc': reals(), 'scale': reals(), 'value': reals()}, reals())
loc = Tensor(randn(batch_shape), inputs)
scale = Tensor(ops.exp(randn(batch_shape)), inputs)
value = Tensor(ops.exp(randn(batch_shape)), inputs)
expected = log_normal(loc, scale, value)
check_funsor(expected, inputs, reals())
actual = dist.LogNormal(loc, scale, value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
@pytest.mark.parametrize('event_shape', [(1,), (4,), (5,)], ids=str)
def test_multinomial_density(batch_shape, event_shape):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
max_count = 10
@funsor.function(reals(), reals(*event_shape), reals(*event_shape), reals())
def multinomial(total_count, probs, value):
if get_backend() == "torch":
total_count = total_count.max().item()
return backend_dist.Multinomial(total_count, probs).log_prob(value)
check_funsor(multinomial, {'total_count': reals(), 'probs': reals(*event_shape), 'value': reals(*event_shape)},
reals())
probs_data = rand(batch_shape + event_shape)
probs_data = probs_data / probs_data.sum(-1)[..., None]
probs = Tensor(probs_data, inputs)
value_data = ops.astype(randint(0, max_count, size=batch_shape + event_shape), 'float')
total_count_data = value_data.sum(-1)
value = Tensor(value_data, inputs)
total_count = Tensor(total_count_data, inputs)
expected = multinomial(total_count, probs, value)
check_funsor(expected, inputs, reals())
actual = dist.Multinomial(total_count, probs, value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected)
def test_normal_defaults():
loc = Variable('loc', reals())
scale = Variable('scale', reals())
value = Variable('value', reals())
assert dist.Normal(loc, scale) is dist.Normal(loc, scale, value)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
def test_normal_density(batch_shape):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
@funsor.of_shape(reals(), reals(), reals())
def normal(loc, scale, value):
return -((value - loc) ** 2) / (2 * scale ** 2) - scale.log() - math.log(math.sqrt(2 * math.pi))
check_funsor(normal, {'loc': reals(), 'scale': reals(), 'value': reals()}, reals())
loc = Tensor(randn(batch_shape), inputs)
scale = Tensor(ops.exp(randn(batch_shape)), inputs)
value = Tensor(randn(batch_shape), inputs)
expected = normal(loc, scale, value)
check_funsor(expected, inputs, reals())
actual = dist.Normal(loc, scale, value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
def test_normal_gaussian_1(batch_shape):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
loc = Tensor(randn(batch_shape), inputs)
scale = Tensor(ops.exp(randn(batch_shape)), inputs)
value = Tensor(randn(batch_shape), inputs)
expected = dist.Normal(loc, scale, value)
assert isinstance(expected, Tensor)
check_funsor(expected, inputs, reals())
g = dist.Normal(loc, scale, 'value')
assert isinstance(g, Contraction)
actual = g(value=value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected, atol=1e-4)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
def test_normal_gaussian_2(batch_shape):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
loc = Tensor(randn(batch_shape), inputs)
scale = Tensor(ops.exp(randn(batch_shape)), inputs)
value = Tensor(randn(batch_shape), inputs)
expected = dist.Normal(loc, scale, value)
assert isinstance(expected, Tensor)
check_funsor(expected, inputs, reals())
g = dist.Normal(Variable('value', reals()), scale, loc)
assert isinstance(g, Contraction)
actual = g(value=value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected, atol=1e-4)
@pytest.mark.parametrize('batch_shape', [(), (5,), (2, 3)], ids=str)
def test_normal_gaussian_3(batch_shape):
batch_dims = ('i', 'j', 'k')[:len(batch_shape)]
inputs = OrderedDict((k, bint(v)) for k, v in zip(batch_dims, batch_shape))
loc = Tensor(randn(batch_shape), inputs)
scale = Tensor(ops.exp(randn(batch_shape)), inputs)
value = Tensor(randn(batch_shape), inputs)
expected = dist.Normal(loc, scale, value)
assert isinstance(expected, Tensor)
check_funsor(expected, inputs, reals())
g = dist.Normal(Variable('loc', reals()), scale, 'value')
assert isinstance(g, Contraction)
actual = g(loc=loc, value=value)
check_funsor(actual, inputs, reals())
assert_close(actual, expected, atol=1e-4)
NORMAL_AFFINE_TESTS = [
'dist.Normal(x+2, scale, y+2)',
'dist.Normal(y, scale, x)',
'dist.Normal(x - y, scale, 0)',
'dist.Normal(0, scale, y - x)',
'dist.Normal(2 * x - y, scale, x)',
'dist.Normal(0, 1, (x - y) / scale) - scale.log()',
'dist.Normal(2 * y, 2 * scale, 2 * x) + math.log(2)',
]
@pytest.mark.parametrize('expr', NORMAL_AFFINE_TESTS)
def test_normal_affine(expr):
scale = Tensor(numeric_array(0.3), OrderedDict())
x = Variable('x', reals())
y = Variable('y', reals())
expected = dist.Normal(x, scale, y)
actual = eval(expr)
assert isinstance(actual, Contraction)
assert dict(actual.inputs) == dict(expected.inputs), (actual.inputs, expected.inputs)
for ta, te in zip(actual.terms, expected.terms):
assert_close(ta.align(tuple(te.inputs)), te)
def test_normal_independent():
loc = random_tensor(OrderedDict(), reals(2))
scale = ops.exp(random_tensor(OrderedDict(), reals(2)))
fn = dist.Normal(loc['i'], scale['i'], value='z_i')
assert fn.inputs['z_i'] == reals()
d = Independent(fn, 'z', 'i', 'z_i')
assert d.inputs['z'] == reals(2)
rng_key = None if get_backend() == "torch" else | np.array([0, 0], dtype=np.uint32) | numpy.array |
import numpy as np
def first_node_process(data):
selected_nodes = []
distances = []
selected_nodes.append(1)
selected_nodes.append((data[0].index(min(data[0])) + 1))
distances.append(min(data[0]))
return selected_nodes, distances
def print_values(selected_nodes, distances, distances_sum):
print("------------------------------------------")
# print("Aktualny stan wartości")
print("Wybrane węzły: ", selected_nodes)
print("Kolejne długości krawędzi: ", distances)
print("Suma: ", distances_sum)
print("------------------------------------------")
def find_min_and_first_index(array):
current_min = np.amin(array)
current_indexes = np.where(array == current_min)
row_index = current_indexes[0][0]
col_index = current_indexes[1][0]
return row_index, col_index
def find_tree(data):
selected_nodes = []
distances = []
distances_sum = 0
temp_matrix = np.empty((0, len(data)))
selected_nodes, distances = first_node_process(data)
distances_sum = distances[0]
# print_values(selected_nodes, distances, distances_sum)
for i in range(len(selected_nodes)):
temp_matrix = np.vstack([temp_matrix, data[selected_nodes[i] - 1]])
while len(selected_nodes) != len(data):
# print("aktualna tabela do poszukiwania wartości")
# print(temp_matrix)
curr_min = | np.amin(temp_matrix) | numpy.amin |
#!/usr/bin/python
from __future__ import division
from __future__ import print_function
import sys
import os
import re
import datetime
import zipfile
import tempfile
import argparse
import math
import warnings
import json
import csv
import numpy as np
import scipy.stats as scp
from lxml import etree as et
def get_rdml_lib_version():
"""Return the version string of the RDML library.
Returns:
The version string of the RDML library.
"""
return "1.0.0"
class NpEncoder(json.JSONEncoder):
def default(self, obj):
if isinstance(obj, np.integer):
return int(obj)
elif isinstance(obj, np.floating):
return float(obj)
elif isinstance(obj, np.bool_):
return bool(obj)
elif isinstance(obj, np.ndarray):
return obj.tolist()
else:
return super(NpEncoder, self).default(obj)
class RdmlError(Exception):
"""Basic exception for errors raised by the RDML-Python library"""
def __init__(self, message):
Exception.__init__(self, message)
pass
class secondError(RdmlError):
"""Just to have, not used yet"""
def __init__(self, message):
RdmlError.__init__(self, message)
pass
def _get_first_child(base, tag):
"""Get a child element of the base node with a given tag.
Args:
base: The base node element. (lxml node)
tag: Child elements group tag used to select the elements. (string)
Returns:
The first child lxml node element found or None.
"""
for node in base:
if node.tag.replace("{http://www.rdml.org}", "") == tag:
return node
return None
def _get_first_child_text(base, tag):
"""Get a child element of the base node with a given tag.
Args:
base: The base node element. (lxml node)
tag: Child elements group tag used to select the elements. (string)
Returns:
The text of first child node element found or an empty string.
"""
for node in base:
if node.tag.replace("{http://www.rdml.org}", "") == tag:
return node.text
return ""
def _get_first_child_bool(base, tag, triple=True):
"""Get a child element of the base node with a given tag.
Args:
base: The base node element. (lxml node)
tag: Child elements group tag used to select the elements. (string)
triple: If True, None is returned if not found, if False, False
Returns:
The a bool value of tag or if triple is True None.
"""
for node in base:
if node.tag.replace("{http://www.rdml.org}", "") == tag:
return _string_to_bool(node.text, triple)
if triple is False:
return False
else:
return None
def _get_step_sort_nr(elem):
"""Get the number of the step eg. for sorting.
Args:
elem: The node element. (lxml node)
Returns:
The a int value of the step node nr.
"""
if elem is None:
raise RdmlError('A step element must be provided for sorting.')
ret = _get_first_child_text(elem, "nr")
if ret == "":
raise RdmlError('A step element must have a \"nr\" element for sorting.')
return int(ret)
def _sort_list_int(elem):
"""Get the first element of the array as int. for sorting.
Args:
elem: The 2d list
Returns:
The a int value of the first list element.
"""
return int(elem[0])
def _sort_list_float(elem):
"""Get the first element of the array as float. for sorting.
Args:
elem: The 2d list
Returns:
The a float value of the first list element.
"""
return float(elem[0])
def _sort_list_digital_PCR(elem):
"""Get the first column of the list as int. for sorting.
Args:
elem: The list
Returns:
The a int value of the first list element.
"""
arr = elem.split("\t")
return int(arr[0]), arr[4]
def _string_to_bool(value, triple=True):
"""Translates a string into bool value or None.
Args:
value: The string value to evaluate. (string)
triple: If True, None is returned if not found, if False, False
Returns:
The a bool value of tag or if triple is True None.
"""
if value is None or value == "":
if triple is True:
return None
else:
return False
if type(value) is bool:
return value
if type(value) is int:
if value != 0:
return True
else:
return False
if type(value) is str:
if value.lower() in ['false', '0', 'f', '-', 'n', 'no']:
return False
else:
return True
return
def _value_to_booldic(value):
"""Translates a string, list or dic to a dictionary with true/false.
Args:
value: The string value to evaluate. (string)
Returns:
The a bool value of tag or if triple is True None.
"""
ret = {}
if type(value) is str:
ret[value] = True
if type(value) is list:
for ele in value:
ret[ele] = True
if type(value) is dict:
for key, val in value.items():
ret[key] = _string_to_bool(val, triple=False)
return ret
def _get_first_child_by_pos_or_id(base, tag, by_id, by_pos):
"""Get a child element of the base node with a given tag and position or id.
Args:
base: The base node element. (lxml node)
tag: Child elements group tag used to select the elements. (string)
by_id: The unique id to search for. (string)
by_pos: The position of the element in the list (int)
Returns:
The child node element found or raise error.
"""
if by_id is None and by_pos is None:
raise RdmlError('Either an ' + tag + ' id or a position must be provided.')
if by_id is not None and by_pos is not None:
raise RdmlError('Only an ' + tag + ' id or a position can be provided.')
allChildren = _get_all_children(base, tag)
if by_id is not None:
for node in allChildren:
if node.get('id') == by_id:
return node
raise RdmlError('The ' + tag + ' id: ' + by_id + ' was not found in RDML file.')
if by_pos is not None:
if by_pos < 0 or by_pos > len(allChildren) - 1:
raise RdmlError('The ' + tag + ' position ' + by_pos + ' is out of range.')
return allChildren[by_pos]
def _add_first_child_to_dic(base, dic, opt, tag):
"""Adds the first child element with a given tag to a dictionary.
Args:
base: The base node element. (lxml node)
dic: The dictionary to add the element to (dictionary)
opt: If false and id is not found in base, the element is added with an empty string (Bool)
tag: Child elements group tag used to select the elements. (string)
Returns:
The dictionary with the added element.
"""
for node in base:
if node.tag.replace("{http://www.rdml.org}", "") == tag:
dic[tag] = node.text
return dic
if not opt:
dic[tag] = ""
return dic
def _get_all_children(base, tag):
"""Get a list of all child elements with a given tag.
Args:
base: The base node element. (lxml node)
tag: Child elements group tag used to select the elements. (string)
Returns:
A list with all child node elements found or an empty list.
"""
ret = []
for node in base:
if node.tag.replace("{http://www.rdml.org}", "") == tag:
ret.append(node)
return ret
def _get_all_children_id(base, tag):
"""Get a list of ids of all child elements with a given tag.
Args:
base: The base node element. (lxml node)
tag: Child elements group tag used to select the elements. (string)
Returns:
A list with all child id strings found or an empty list.
"""
ret = []
for node in base:
if node.tag.replace("{http://www.rdml.org}", "") == tag:
ret.append(node.get('id'))
return ret
def _get_number_of_children(base, tag):
"""Count all child elements with a given tag.
Args:
base: The base node element. (lxml node)
tag: Child elements group tag used to select the elements. (string)
Returns:
A int number of the found child elements with the id.
"""
counter = 0
for node in base:
if node.tag.replace("{http://www.rdml.org}", "") == tag:
counter += 1
return counter
def _check_unique_id(base, tag, id):
"""Find all child elements with a given group and check if the id is already used.
Args:
base: The base node element. (lxml node)
tag: Child elements group tag used to select the elements. (string)
id: The unique id to search for. (string)
Returns:
False if the id is already used, True if not.
"""
for node in base:
if node.tag.replace("{http://www.rdml.org}", "") == tag:
if node.get('id') == id:
return False
return True
def _create_new_element(base, tag, id):
"""Create a new element with a given tag and id.
Args:
base: The base node element. (lxml node)
tag: Child elements group tag. (string)
id: The unique id of the new element. (string)
Returns:
False if the id is already used, True if not.
"""
if id is None or id == "":
raise RdmlError('An ' + tag + ' id must be provided.')
if not _check_unique_id(base, tag, id):
raise RdmlError('The ' + tag + ' id "' + id + '" must be unique.')
return et.Element(tag, id=id)
def _add_new_subelement(base, basetag, tag, text, opt):
"""Create a new element with a given tag and id.
Args:
base: The base node element. (lxml node)
basetag: Child elements group tag. (string)
tag: Child elements own tag, to be created. (string)
text: The text content of the new element. (string)
opt: If true, the element is optional (Bool)
Returns:
Nothing, the base lxml element is modified.
"""
if opt is False:
if text is None or text == "":
raise RdmlError('An ' + basetag + ' ' + tag + ' must be provided.')
et.SubElement(base, tag).text = text
else:
if text is not None and text != "":
et.SubElement(base, tag).text = text
def _change_subelement(base, tag, xmlkeys, value, opt, vtype, id_as_element=False):
"""Change the value of the element with a given tag.
Args:
base: The base node element. (lxml node)
tag: Child elements own tag, to be created. (string)
xmlkeys: The list of possible keys in the right order for xml (list strings)
value: The text content of the new element.
opt: If true, the element is optional (Bool)
vtype: If true, the element is optional ("string", "int", "float")
id_as_element: If true, handle tag "id" as element, else as attribute
Returns:
Nothing, the base lxml element is modified.
"""
# Todo validate values with vtype
goodVal = value
if vtype == "bool":
ev = _string_to_bool(value, triple=True)
if ev is None or ev == "":
goodVal = ""
else:
if ev:
goodVal = "true"
else:
goodVal = "false"
if opt is False:
if goodVal is None or goodVal == "":
raise RdmlError('A value for ' + tag + ' must be provided.')
if tag == "id" and id_as_element is False:
if base.get('id') != goodVal:
par = base.getparent()
groupTag = base.tag.replace("{http://www.rdml.org}", "")
if not _check_unique_id(par, groupTag, goodVal):
raise RdmlError('The ' + groupTag + ' id "' + goodVal + '" is not unique.')
base.attrib['id'] = goodVal
return
# Check if the tag already excists
elem = _get_first_child(base, tag)
if elem is not None:
if goodVal is None or goodVal == "":
base.remove(elem)
else:
elem.text = goodVal
else:
if goodVal is not None and goodVal != "":
new_node = et.Element(tag)
new_node.text = goodVal
place = _get_tag_pos(base, tag, xmlkeys, 0)
base.insert(place, new_node)
def _get_or_create_subelement(base, tag, xmlkeys):
"""Get element with a given tag, if not present, create it.
Args:
base: The base node element. (lxml node)
tag: Child elements own tag, to be created. (string)
xmlkeys: The list of possible keys in the right order for xml (list strings)
Returns:
The node element with the tag.
"""
# Check if the tag already excists
if _get_first_child(base, tag) is None:
new_node = et.Element(tag)
place = _get_tag_pos(base, tag, xmlkeys, 0)
base.insert(place, new_node)
return _get_first_child(base, tag)
def _remove_irrelevant_subelement(base, tag):
"""If element with a given tag has no children, remove it.
Args:
base: The base node element. (lxml node)
tag: Child elements own tag, to be created. (string)
Returns:
The node element with the tag.
"""
# Check if the tag already excists
elem = _get_first_child(base, tag)
if elem is None:
return
if len(elem) == 0:
base.remove(elem)
def _move_subelement(base, tag, id, xmlkeys, position):
"""Change the value of the element with a given tag.
Args:
base: The base node element. (lxml node)
tag: The id to search for. (string)
id: The unique id of the new element. (string)
xmlkeys: The list of possible keys in the right order for xml (list strings)
position: the new position of the element (int)
Returns:
Nothing, the base lxml element is modified.
"""
pos = _get_tag_pos(base, tag, xmlkeys, position)
ele = _get_first_child_by_pos_or_id(base, tag, id, None)
base.insert(pos, ele)
def _move_subelement_pos(base, tag, oldpos, xmlkeys, position):
"""Change the value of the element with a given tag.
Args:
base: The base node element. (lxml node)
tag: The id to search for. (string)
oldpos: The unique id of the new element. (string)
xmlkeys: The list of possible keys in the right order for xml (list strings)
position: the new position of the element (int)
Returns:
Nothing, the base lxml element is modified.
"""
pos = _get_tag_pos(base, tag, xmlkeys, position)
ele = _get_first_child_by_pos_or_id(base, tag, None, oldpos)
base.insert(pos, ele)
def _get_tag_pos(base, tag, xmlkeys, pos):
"""Returns a position were to add a subelement with the given tag inc. pos offset.
Args:
base: The base node element. (lxml node)
tag: The id to search for. (string)
xmlkeys: The list of possible keys in the right order for xml (list strings)
pos: The position relative to the tag elements (int)
Returns:
The int number of were to add the element with the tag.
"""
count = _get_number_of_children(base, tag)
offset = pos
if pos is None or pos < 0:
offset = 0
pos = 0
if pos > count:
offset = count
return _get_first_tag_pos(base, tag, xmlkeys) + offset
def _get_first_tag_pos(base, tag, xmlkeys):
"""Returns a position were to add a subelement with the given tag.
Args:
base: The base node element. (lxml node)
tag: The id to search for. (string)
xmlkeys: The list of possible keys in the right order for xml (list strings)
Returns:
The int number of were to add the element with the tag.
"""
listrest = xmlkeys[xmlkeys.index(tag):]
counter = 0
for node in base:
if node.tag.replace("{http://www.rdml.org}", "") in listrest:
return counter
counter += 1
return counter
def _writeFileInRDML(rdmlName, fileName, data):
"""Writes a file in the RDML zip, even if it existed before.
Args:
rdmlName: The name of the RDML zip file
fileName: The name of the file to write into the zip
data: The data string of the file
Returns:
Nothing, modifies the RDML file.
"""
needRewrite = False
if os.path.isfile(rdmlName):
with zipfile.ZipFile(rdmlName, 'r') as RDMLin:
for item in RDMLin.infolist():
if item.filename == fileName:
needRewrite = True
if needRewrite:
tempFolder, tempName = tempfile.mkstemp(dir=os.path.dirname(rdmlName))
os.close(tempFolder)
# copy everything except the filename
with zipfile.ZipFile(rdmlName, 'r') as RDMLin:
with zipfile.ZipFile(tempName, mode='w', compression=zipfile.ZIP_DEFLATED) as RDMLout:
RDMLout.comment = RDMLin.comment
for item in RDMLin.infolist():
if item.filename != fileName:
RDMLout.writestr(item, RDMLin.read(item.filename))
if data != "":
RDMLout.writestr(fileName, data)
os.remove(rdmlName)
os.rename(tempName, rdmlName)
else:
with zipfile.ZipFile(rdmlName, mode='a', compression=zipfile.ZIP_DEFLATED) as RDMLout:
RDMLout.writestr(fileName, data)
def _lrp_linReg(xIn, yUse):
"""A function which calculates the slope or the intercept by linear regression.
Args:
xIn: The numpy array of the cycles
yUse: The numpy array that contains the fluorescence
Returns:
An array with the slope and intercept.
"""
counts = np.ones(yUse.shape)
xUse = xIn.copy()
xUse[np.isnan(yUse)] = 0
counts[np.isnan(yUse)] = 0
cycSqared = xUse * xUse
cycFluor = xUse * yUse
sumCyc = np.nansum(xUse, axis=1)
sumFluor = np.nansum(yUse, axis=1)
sumCycSquared = np.nansum(cycSqared, axis=1)
sumCycFluor = np.nansum(cycFluor, axis=1)
n = np.nansum(counts, axis=1)
ssx = sumCycSquared - (sumCyc * sumCyc) / n
sxy = sumCycFluor - (sumCyc * sumFluor) / n
slope = sxy / ssx
intercept = (sumFluor / n) - slope * (sumCyc / n)
return [slope, intercept]
def _lrp_findStopCyc(fluor, aRow):
"""Find the stop cycle of the log lin phase in fluor.
Args:
fluor: The array with the fluorescence values
aRow: The row to work on
Returns:
An int with the stop cycle.
"""
# Take care of nan values
validTwoLessCyc = 3 # Cycles so +1 to array
while (validTwoLessCyc <= fluor.shape[1] and
(np.isnan(fluor[aRow, validTwoLessCyc - 1]) or
np.isnan(fluor[aRow, validTwoLessCyc - 2]) or
np.isnan(fluor[aRow, validTwoLessCyc - 3]))):
validTwoLessCyc += 1
# First and Second Derivative values calculation
fluorShift = np.roll(fluor[aRow], 1, axis=0) # Shift to right - real position is -0.5
fluorShift[0] = np.nan
firstDerivative = fluor[aRow] - fluorShift
if np.isfinite(firstDerivative).any():
FDMaxCyc = np.nanargmax(firstDerivative, axis=0) + 1 # Cycles so +1 to array
else:
return fluor.shape[1]
firstDerivativeShift = np.roll(firstDerivative, -1, axis=0) # Shift to left
firstDerivativeShift[-1] = np.nan
secondDerivative = firstDerivativeShift - firstDerivative
if FDMaxCyc + 2 <= fluor.shape[1]:
# Only add two cycles if there is an increase without nan
if (not np.isnan(fluor[aRow, FDMaxCyc - 1]) and
not np.isnan(fluor[aRow, FDMaxCyc]) and
not np.isnan(fluor[aRow, FDMaxCyc + 1]) and
fluor[aRow, FDMaxCyc + 1] > fluor[aRow, FDMaxCyc] > fluor[aRow, FDMaxCyc - 1]):
FDMaxCyc += 2
else:
FDMaxCyc = fluor.shape[1]
maxMeanSD = 0.0
stopCyc = fluor.shape[1]
for cycInRange in range(validTwoLessCyc, FDMaxCyc):
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
tempMeanSD = np.mean(secondDerivative[cycInRange - 2: cycInRange + 1], axis=0)
# The > 0.000000000001 is to avoid float differences to the pascal version
if not np.isnan(tempMeanSD) and (tempMeanSD - maxMeanSD) > 0.000000000001:
maxMeanSD = tempMeanSD
stopCyc = cycInRange
if stopCyc + 2 >= fluor.shape[1]:
stopCyc = fluor.shape[1]
return stopCyc
def _lrp_findStartCyc(fluor, aRow, stopCyc):
"""A function which finds the start cycle of the log lin phase in fluor.
Args:
fluor: The array with the fluorescence values
aRow: The row to work on
stopCyc: The stop cycle
Returns:
An array [int, int] with the start cycle and the fixed start cycle.
"""
startCyc = stopCyc - 1
# startCyc might be NaN, so shift it to the first value
firstNotNaN = 1 # Cycles so +1 to array
while np.isnan(fluor[aRow, firstNotNaN - 1]) and firstNotNaN < startCyc:
firstNotNaN += 1
while startCyc > firstNotNaN and np.isnan(fluor[aRow, startCyc - 1]):
startCyc -= 1
# As long as there are no NaN and new values are increasing
while (startCyc > firstNotNaN and
not np.isnan(fluor[aRow, startCyc - 2]) and
fluor[aRow, startCyc - 2] <= fluor[aRow, startCyc - 1]):
startCyc -= 1
startCycFix = startCyc
if (not np.isnan(fluor[aRow, startCyc]) and
not np.isnan(fluor[aRow, startCyc - 1]) and
not np.isnan(fluor[aRow, stopCyc - 1]) and
not np.isnan(fluor[aRow, stopCyc - 2])):
startStep = np.log10(fluor[aRow, startCyc]) - np.log10(fluor[aRow, startCyc - 1])
stopStep = np.log10(fluor[aRow, stopCyc - 1]) - np.log10(fluor[aRow, stopCyc - 2])
if startStep > 1.1 * stopStep:
startCycFix += 1
return [startCyc, startCycFix]
def _lrp_testSlopes(fluor, aRow, stopCyc, startCycFix):
"""Splits the values and calculates a slope for the upper and the lower half.
Args:
fluor: The array with the fluorescence values
aRow: The row to work on
stopCyc: The stop cycle
startCycFix: The start cycle
Returns:
An array with [slopelow, slopehigh].
"""
# Both start with full range
loopStart = [startCycFix[aRow], stopCyc[aRow]]
loopStop = [startCycFix[aRow], stopCyc[aRow]]
# Now find the center ignoring nan
while True:
loopStart[1] -= 1
loopStop[0] += 1
while (loopStart[1] - loopStop[0]) > 1 and np.isnan(fluor[aRow, loopStart[1] - 1]):
loopStart[1] -= 1
while (loopStart[1] - loopStop[0]) > 1 and np.isnan(fluor[aRow, loopStop[1] - 1]):
loopStop[0] += 1
if (loopStart[1] - loopStop[0]) <= 1:
break
# basic regression per group
ssx = [0, 0]
sxy = [0, 0]
slope = [0, 0]
for j in range(0, 2):
sumx = 0.0
sumy = 0.0
sumx2 = 0.0
sumxy = 0.0
nincl = 0.0
for i in range(loopStart[j], loopStop[j] + 1):
if not np.isnan(fluor[aRow, i - 1]):
sumx += i
sumy += np.log10(fluor[aRow, i - 1])
sumx2 += i * i
sumxy += i * np.log10(fluor[aRow, i - 1])
nincl += 1
ssx[j] = sumx2 - sumx * sumx / nincl
sxy[j] = sumxy - sumx * sumy / nincl
slope[j] = sxy[j] / ssx[j]
return [slope[0], slope[1]]
def _lrp_lastCycMeanMax(fluor, vecSkipSample, vecNoPlateau):
"""A function which calculates the mean of the max fluor in the last ten cycles.
Args:
fluor: The array with the fluorescence values
vecSkipSample: Skip the sample
vecNoPlateau: Sample has no plateau
Returns:
An float with the max mean.
"""
maxFlour = np.nanmax(fluor[:, -11:], axis=1)
maxFlour[vecSkipSample] = np.nan
maxFlour[vecNoPlateau] = np.nan
# Ignore all nan slices, to fix them below
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
maxMean = np.nanmean(maxFlour)
if np.isnan(maxMean):
maxMean = np.nanmax(maxFlour)
return maxMean
def _lrp_meanPcrEff(tarGroup, vecTarget, pcrEff, vecSkipSample, vecNoPlateau, vecShortLogLin):
"""A function which calculates the mean efficiency of the selected target group excluding bad ones.
Args:
tarGroup: The target number
vecTarget: The vector with the targets numbers
pcrEff: The array with the PCR efficiencies
vecSkipSample: Skip the sample
vecNoPlateau: True if there is no plateau
vecShortLogLin: True indicates a short log lin phase
Returns:
An array with [meanPcrEff, pcrEffVar].
"""
cnt = 0
sumEff = 0.0
sumEff2 = 0.0
for j in range(0, len(pcrEff)):
if tarGroup is None or tarGroup == vecTarget[j]:
if (not (vecSkipSample[j] or vecNoPlateau[j] or vecShortLogLin[j])) and pcrEff[j] > 1.0:
cnt += 1
sumEff += pcrEff[j]
sumEff2 += pcrEff[j] * pcrEff[j]
if cnt > 1:
meanPcrEff = sumEff / cnt
pcrEffVar = (sumEff2 - (sumEff * sumEff) / cnt) / (cnt - 1)
else:
meanPcrEff = 1.0
pcrEffVar = 100
return [meanPcrEff, pcrEffVar]
def _lrp_startStopInWindow(fluor, aRow, upWin, lowWin):
"""Find the start and the stop of the part of the curve which is inside the window.
Args:
fluor: The array with the fluorescence values
aRow: The row to work on
upWin: The upper limit of the window
lowWin: The lower limit of the window
Returns:
The int startWinCyc, stopWinCyc and the bool notInWindow.
"""
startWinCyc = 0
stopWinCyc = 0
# Find the stopCyc and the startCyc cycle of the log lin phase
stopCyc = _lrp_findStopCyc(fluor, aRow)
[startCyc, startCycFix] = _lrp_findStartCyc(fluor, aRow, stopCyc)
if np.isfinite(fluor[aRow, startCycFix - 1:]).any():
stopMaxCyc = np.nanargmax(fluor[aRow, startCycFix - 1:]) + startCycFix
else:
return startCyc, startCyc, True
# If is true if outside the window
if fluor[aRow, startCyc - 1] > upWin or fluor[aRow, stopMaxCyc - 1] < lowWin:
notInWindow = True
if fluor[aRow, startCyc - 1] > upWin:
startWinCyc = startCyc
stopWinCyc = startCyc
if fluor[aRow, stopMaxCyc - 1] < lowWin:
startWinCyc = stopMaxCyc
stopWinCyc = stopMaxCyc
else:
notInWindow = False
# look for stopWinCyc
if fluor[aRow, stopMaxCyc - 1] < upWin:
stopWinCyc = stopMaxCyc
else:
for i in range(stopMaxCyc, startCyc, -1):
if fluor[aRow, i - 1] > upWin > fluor[aRow, i - 2]:
stopWinCyc = i - 1
# look for startWinCyc
if fluor[aRow, startCycFix - 1] > lowWin:
startWinCyc = startCycFix
else:
for i in range(stopMaxCyc, startCyc, -1):
if fluor[aRow, i - 1] > lowWin > fluor[aRow, i - 2]:
startWinCyc = i
return startWinCyc, stopWinCyc, notInWindow
def _lrp_paramInWindow(fluor, aRow, upWin, lowWin):
"""Calculates slope, nNull, PCR efficiency and mean x/y for the curve part in the window.
Args:
fluor: The array with the fluorescence values
aRow: The row to work on
upWin: The upper limit of the window
lowWin: The lower limit of the window
Returns:
The calculated values: indMeanX, indMeanY, pcrEff, nnulls, ninclu, correl.
"""
startWinCyc, stopWinCyc, notInWindow = _lrp_startStopInWindow(fluor, aRow, upWin, lowWin)
sumx = 0.0
sumy = 0.0
sumx2 = 0.0
sumy2 = 0.0
sumxy = 0.0
nincl = 0.0
ssx = 0.0
ssy = 0.0
sxy = 0.0
for i in range(startWinCyc, stopWinCyc + 1):
fluorSamp = fluor[aRow, i - 1]
if not np.isnan(fluorSamp):
logFluorSamp = np.log10(fluorSamp)
sumx += i
sumy += logFluorSamp
sumx2 += i * i
sumy2 += logFluorSamp * logFluorSamp
sumxy += i * logFluorSamp
nincl += 1
if nincl > 1:
ssx = sumx2 - sumx * sumx / nincl
ssy = sumy2 - sumy * sumy / nincl
sxy = sumxy - sumx * sumy / nincl
if ssx > 0.0 and ssy > 0.0 and nincl > 0.0:
cslope = sxy / ssx
cinterc = sumy / nincl - cslope * sumx / nincl
correl = sxy / np.sqrt(ssx * ssy)
indMeanX = sumx / nincl
indMeanY = sumy / nincl
pcrEff = np.power(10, cslope)
nnulls = np.power(10, cinterc)
else:
correl = np.nan
indMeanX = np.nan
indMeanY = np.nan
pcrEff = np.nan
nnulls = np.nan
if notInWindow:
ninclu = 0
else:
ninclu = stopWinCyc - startWinCyc + 1
return indMeanX, indMeanY, pcrEff, nnulls, ninclu, correl
def _lrp_allParamInWindow(fluor, tarGroup, vecTarget, indMeanX, indMeanY, pcrEff, nnulls, ninclu, correl, upWin, lowWin, vecNoAmplification, vecBaselineError):
"""A function which calculates the mean of the max fluor in the last ten cycles.
Args:
fluor: The array with the fluorescence values
tarGroup: The target number
vecTarget: The vector with the targets numbers
indMeanX: The vector with the x mean position
indMeanY: The vector with the y mean position
pcrEff: The array with the PCR efficiencies
nnulls: The array with the calculated nnulls
ninclu: The array with the calculated ninclu
correl: The array with the calculated correl
upWin: The upper limit of the window
lowWin: The lower limit of the window
vecNoAmplification: True if there is a amplification error
vecBaselineError: True if there is a baseline error
Returns:
An array with [indMeanX, indMeanY, pcrEff, nnulls, ninclu, correl].
"""
for row in range(0, fluor.shape[0]):
if tarGroup is None or tarGroup == vecTarget[row]:
if not (vecNoAmplification[row] or vecBaselineError[row]):
if tarGroup is None:
indMeanX[row], indMeanY[row], pcrEff[row], nnulls[row], ninclu[row], correl[row] = _lrp_paramInWindow(fluor, row, upWin[0], lowWin[0])
else:
indMeanX[row], indMeanY[row], pcrEff[row], nnulls[row], ninclu[row], correl[row] = _lrp_paramInWindow(fluor, row, upWin[tarGroup], lowWin[tarGroup])
else:
correl[row] = np.nan
indMeanX[row] = np.nan
indMeanY[row] = np.nan
pcrEff[row] = np.nan
nnulls[row] = np.nan
ninclu[row] = 0
return indMeanX, indMeanY, pcrEff, nnulls, ninclu, correl
def _lrp_meanStopFluor(fluor, tarGroup, vecTarget, stopCyc, vecSkipSample, vecNoPlateau):
"""Return the mean of the stop fluor or the max fluor if all rows have no plateau.
Args:
fluor: The array with the fluorescence values
tarGroup: The target number
vecTarget: The vector with the targets numbers
stopCyc: The vector with the stop cycle of the log lin phase
vecSkipSample: Skip the sample
vecNoPlateau: True if there is no plateau
Returns:
The meanMax fluorescence.
"""
meanMax = 0.0
maxFluor = 0.0000001
cnt = 0
if tarGroup is None:
for aRow in range(0, fluor.shape[0]):
if not vecSkipSample[aRow]:
if not vecNoPlateau[aRow]:
cnt += 1
meanMax += fluor[aRow, stopCyc[aRow] - 1]
else:
for i in range(0, fluor.shape[1]):
if fluor[aRow, i] > maxFluor:
maxFluor = fluor[aRow, i]
else:
for aRow in range(0, fluor.shape[0]):
if tarGroup == vecTarget[aRow] and not vecSkipSample[aRow]:
if not vecNoPlateau[aRow]:
cnt += 1
meanMax += fluor[aRow, stopCyc[aRow] - 1]
else:
for i in range(0, fluor.shape[1]):
if fluor[aRow, i] > maxFluor:
maxFluor = fluor[aRow, i]
if cnt > 0:
meanMax = meanMax / cnt
else:
meanMax = maxFluor
return meanMax
def _lrp_maxStartFluor(fluor, tarGroup, vecTarget, startCyc, vecSkipSample):
"""Return the maximum of the start fluorescence
Args:
fluor: The array with the fluorescence values
tarGroup: The target number
vecTarget: The vector with the targets numbers
startCyc: The vector with the start cycle of the log lin phase
vecSkipSample: Skip the sample
Returns:
The maxStart fluorescence.
"""
maxStart = -10.0
if tarGroup is None:
for aRow in range(0, fluor.shape[0]):
if not vecSkipSample[aRow]:
if fluor[aRow, startCyc[aRow] - 1] > maxStart:
maxStart = fluor[aRow, startCyc[aRow] - 1]
else:
for aRow in range(0, fluor.shape[0]):
if tarGroup == vecTarget[aRow] and not vecSkipSample[aRow]:
if fluor[aRow, startCyc[aRow] - 1] > maxStart:
maxStart = fluor[aRow, startCyc[aRow] - 1]
return 0.999 * maxStart
def _lrp_setLogWin(tarGroup, newUpWin, foldWidth, upWin, lowWin, maxFluorTotal, minFluorTotal):
"""Sets a new window and ensures its within the total fluorescence values.
Args:
tarGroup: The target number
newUpWin: The new upper window
foldWidth: The foldWith to the lower window
upWin: The upper window fluorescence
lowWin: The lower window fluorescence
maxFluorTotal: The maximum fluorescence over all rows
minFluorTotal: The minimum fluorescence over all rows
Returns:
An array with [indMeanX, indMeanY, pcrEff, nnulls, ninclu, correl].
"""
# No rounding needed, only present for exact identical output with Pascal version
tempUpWin = np.power(10, np.round(1000 * newUpWin) / 1000)
tempLowWin = np.power(10, np.round(1000 * (newUpWin - foldWidth)) / 1000)
tempUpWin = np.minimum(tempUpWin, maxFluorTotal)
tempUpWin = np.maximum(tempUpWin, minFluorTotal)
tempLowWin = np.minimum(tempLowWin, maxFluorTotal)
tempLowWin = np.maximum(tempLowWin, minFluorTotal)
if tarGroup is None:
upWin[0] = tempUpWin
lowWin[0] = tempLowWin
else:
upWin[tarGroup] = tempUpWin
lowWin[tarGroup] = tempLowWin
return upWin, lowWin
def _lrp_logStepStop(fluor, tarGroup, vecTarget, stopCyc, vecSkipSample, vecNoPlateau):
"""Calculates the log of the fluorescence increase at the stop cycle.
Args:
fluor: The array with the fluorescence values
tarGroup: The target number
vecTarget: The vector with the targets numbers
stopCyc: The vector with the stop cycle of the log lin phase
vecSkipSample: True if row should be skipped
vecNoPlateau: True if there is no plateau
Returns:
An array with [indMeanX, indMeanY, pcrEff, nnulls, ninclu, correl].
"""
cnt = 0
step = 0.0
for aRow in range(0, fluor.shape[0]):
if (tarGroup is None or tarGroup == vecTarget[aRow]) and not (vecSkipSample[aRow] or vecNoPlateau[aRow]):
cnt += 1
step += np.log10(fluor[aRow, stopCyc[aRow] - 1]) - np.log10(fluor[aRow, stopCyc[aRow] - 2])
if cnt > 0:
step = step / cnt
else:
step = np.log10(1.8)
return step
def _lrp_setWoL(fluor, tarGroup, vecTarget, pointsInWoL, indMeanX, indMeanY, pcrEff, nNulls, nInclu, correl,
upWin, lowWin, maxFluorTotal, minFluorTotal, stopCyc, startCyc, threshold,
vecNoAmplification, vecBaselineError, vecSkipSample, vecNoPlateau, vecShortLogLin, vecIsUsedInWoL):
"""Find the window with the lowest variation in PCR efficiency and calculate its values.
Args:
fluor: The array with the fluorescence values
tarGroup: The target number
vecTarget: The vector with the targets numbers
pointsInWoL: The number of points in the window
indMeanX: The vector with the x mean position
indMeanY: The vector with the y mean position
pcrEff: The array with the PCR efficiencies
nNulls: The array with the calculated nNulls
nInclu: The array with the calculated nInclu
correl: The array with the calculated correl
upWin: The upper limit of the window
lowWin: The lower limit of the window
maxFluorTotal: The maximum fluorescence over all rows
minFluorTotal: The minimum fluorescence over all rows
stopCyc: The vector with the stop cycle of the log lin phase
startCyc: The vector with the start cycle of the log lin phase
threshold: The threshold fluorescence
vecNoAmplification: True if there is a amplification error
vecBaselineError: True if there is a baseline error
vecSkipSample: Skip the sample
vecNoPlateau: True if there is no plateau
vecShortLogLin: True indicates a short log lin phase
vecIsUsedInWoL: True if used in the WoL
Returns:
The values indMeanX, indMeanY, pcrEff, nNulls, nInclu, correl, upWin, lowWin, threshold, vecIsUsedInWoL.
"""
skipGroup = False
stepSize = 0.2 # was 0.5, smaller steps help in finding WoL
# Keep 60 calculated results
memVarEff = np.zeros(60, dtype=np.float64)
memUpWin = np.zeros(60, dtype=np.float64)
memFoldWidth = np.zeros(60, dtype=np.float64)
maxFluorWin = _lrp_meanStopFluor(fluor, tarGroup, vecTarget, stopCyc, vecSkipSample, vecNoPlateau)
if maxFluorWin > 0.0:
maxFluorWin = np.log10(maxFluorWin)
else:
skipGroup = True
minFluorLim = _lrp_maxStartFluor(fluor, tarGroup, vecTarget, startCyc, vecSkipSample)
if minFluorLim > 0.0:
minFluorLim = np.log10(minFluorLim)
else:
skipGroup = True
checkMeanEff = 1.0
if not skipGroup:
foldWidth = pointsInWoL * _lrp_logStepStop(fluor, tarGroup, vecTarget, stopCyc, vecSkipSample, vecNoPlateau)
upWin, lowWin = _lrp_setLogWin(tarGroup, maxFluorWin, foldWidth, upWin, lowWin, maxFluorTotal, minFluorTotal)
_unused, _unused2, checkPcrEff, _unused3, _unused4, _unused5 = _lrp_allParamInWindow(fluor, tarGroup, vecTarget,
indMeanX, indMeanY, pcrEff,
nNulls, nInclu, correl,
upWin, lowWin,
vecNoAmplification,
vecBaselineError)
[checkMeanEff, _unused] = _lrp_meanPcrEff(tarGroup, vecTarget, checkPcrEff,
vecSkipSample, vecNoPlateau, vecShortLogLin)
if checkMeanEff < 1.001:
skipGroup = True
if skipGroup:
if tarGroup is None:
threshold[0] = (0.5 * np.round(1000 * upWin[0]) / 1000)
else:
threshold[tarGroup] = (0.5 * np.round(1000 * upWin[tarGroup]) / 1000)
if not skipGroup:
foldWidth = np.log10(np.power(checkMeanEff, pointsInWoL))
counter = -1
maxVarEff = 0.0
maxVarEffStep = -1
lastUpWin = 2 + maxFluorWin
while True:
counter += 1
step = np.log10(checkMeanEff)
newUpWin = maxFluorWin - counter * stepSize * step
if newUpWin < lastUpWin:
upWin, lowWin = _lrp_setLogWin(tarGroup, newUpWin, foldWidth, upWin, lowWin, maxFluorTotal, minFluorTotal)
_unused, _unused2, checkPcrEff, _unused3, _unused4, _unused5 = _lrp_allParamInWindow(fluor, tarGroup,
vecTarget, indMeanX,
indMeanY, pcrEff,
nNulls, nInclu,
correl,
upWin, lowWin,
vecNoAmplification,
vecBaselineError)
[checkMeanEff, _unused] = _lrp_meanPcrEff(tarGroup, vecTarget, checkPcrEff,
vecSkipSample, vecNoPlateau, vecShortLogLin)
foldWidth = np.log10(np.power(checkMeanEff, pointsInWoL))
if foldWidth < 0.5:
foldWidth = 0.5 # to avoid width = 0 above stopCyc
upWin, lowWin = _lrp_setLogWin(tarGroup, newUpWin, foldWidth, upWin, lowWin, maxFluorTotal, minFluorTotal)
_unused, _unused2, checkPcrEff, _unused3, _unused4, _unused5 = _lrp_allParamInWindow(fluor, tarGroup,
vecTarget, indMeanX,
indMeanY, pcrEff,
nNulls, nInclu,
correl,
upWin, lowWin,
vecNoAmplification,
vecBaselineError)
[checkMeanEff, checkVarEff] = _lrp_meanPcrEff(tarGroup, vecTarget, checkPcrEff,
vecSkipSample, vecNoPlateau, vecShortLogLin)
if checkVarEff > 0.0:
memVarEff[counter] = np.sqrt(checkVarEff) / checkMeanEff
else:
memVarEff[counter] = 0.0
if checkVarEff > maxVarEff:
maxVarEff = checkVarEff
maxVarEffStep = counter
memUpWin[counter] = newUpWin
memFoldWidth[counter] = foldWidth
lastUpWin = newUpWin
else:
checkVarEff = 0.0
if counter >= 60 or newUpWin - foldWidth / (pointsInWoL / 2.0) < minFluorLim or checkVarEff < 0.00000000001:
break
# corrections: start
if checkVarEff < 0.00000000001:
counter -= 1 # remove window with vareff was 0.0
validSteps = -1
while True:
validSteps += 1
if memVarEff[validSteps] < 0.000001:
break
validSteps -= 1 # i = number of valid steps
minSmooth = memVarEff[0]
minStep = 0 # default top window
# next 3 if conditions on i: added to correct smoothing
if validSteps == 0:
minStep = 0
if 0 < validSteps < 4:
n = -1
while True:
n += 1
if memVarEff[n] < minSmooth:
minSmooth = memVarEff[n]
minStep = n
if n == validSteps:
break
if validSteps >= 4:
n = 0
while True:
n += 1
smoothVar = 0.0
for m in range(n - 1, n + 2):
smoothVar = smoothVar + memVarEff[m]
smoothVar = smoothVar / 3.0
if smoothVar < minSmooth:
minSmooth = smoothVar
minStep = n
if n >= validSteps - 1 or n > maxVarEffStep:
break
# corrections: stop
# Calculate the final values again
upWin, lowWin = _lrp_setLogWin(tarGroup, memUpWin[minStep], memFoldWidth[minStep],
upWin, lowWin, maxFluorTotal, minFluorTotal)
if tarGroup is None:
threshold[0] = (0.5 * np.round(1000 * upWin[0]) / 1000)
else:
threshold[tarGroup] = (0.5 * np.round(1000 * upWin[tarGroup]) / 1000)
indMeanX, indMeanY, pcrEff, nNulls, nInclu, correl = _lrp_allParamInWindow(fluor, tarGroup, vecTarget,
indMeanX, indMeanY, pcrEff, nNulls,
nInclu, correl, upWin, lowWin,
vecNoAmplification, vecBaselineError)
for aRow in range(0, len(pcrEff)):
if tarGroup is None or tarGroup == vecTarget[aRow]:
if (not (vecSkipSample[aRow] or vecNoPlateau[aRow] or vecShortLogLin[aRow])) and pcrEff[aRow] > 1.0:
vecIsUsedInWoL[aRow] = True
else:
vecIsUsedInWoL[aRow] = False
return indMeanX, indMeanY, pcrEff, nNulls, nInclu, correl, upWin, lowWin, threshold, vecIsUsedInWoL
def _lrp_assignNoPlateau(fluor, tarGroup, vecTarget, pointsInWoL, indMeanX, indMeanY, pcrEff, nNulls, nInclu, correl,
upWin, lowWin, maxFluorTotal, minFluorTotal, stopCyc, startCyc, threshold,
vecNoAmplification, vecBaselineError, vecSkipSample, vecNoPlateau, vecShortLogLin, vecIsUsedInWoL):
"""Assign no plateau again and possibly recalculate WoL if new no plateau was found.
Args:
fluor: The array with the fluorescence values
tarGroup: The target number
vecTarget: The vector with the targets numbers
pointsInWoL: The number of points in the window
indMeanX: The vector with the x mean position
indMeanY: The vector with the y mean position
pcrEff: The array with the PCR efficiencies
nNulls: The array with the calculated nNulls
nInclu: The array with the calculated nInclu
correl: The array with the calculated correl
upWin: The upper limit of the window
lowWin: The lower limit of the window
maxFluorTotal: The maximum fluorescence over all rows
minFluorTotal: The minimum fluorescence over all rows
stopCyc: The vector with the stop cycle of the log lin phase
startCyc: The vector with the start cycle of the log lin phase
threshold: The threshold fluorescence
vecNoAmplification: True if there is a amplification error
vecBaselineError: True if there is a baseline error
vecSkipSample: Skip the sample
vecNoPlateau: True if there is no plateau
vecShortLogLin: True indicates a short log lin phase
vecIsUsedInWoL: True if used in the WoL
Returns:
The values indMeanX, indMeanY, pcrEff, nNulls, nInclu, correl, upWin, lowWin, threshold, vecIsUsedInWoL, vecNoPlateau.
"""
newNoPlateau = False
for aRow in range(0, fluor.shape[0]):
if (tarGroup is None or tarGroup == vecTarget[aRow]) and not (vecNoAmplification[aRow] or
vecBaselineError[aRow] or
vecNoPlateau[aRow]):
expectedFluor = nNulls[aRow] * np.power(pcrEff[aRow], fluor.shape[1])
if expectedFluor / fluor[aRow, fluor.shape[1] - 1] < 5:
newNoPlateau = True
vecNoPlateau[aRow] = True
if newNoPlateau:
indMeanX, indMeanY, pcrEff, nNulls, nInclu, correl, upWin, lowWin, threshold, vecIsUsedInWoL = _lrp_setWoL(fluor, tarGroup, vecTarget,
pointsInWoL, indMeanX, indMeanY, pcrEff,
nNulls, nInclu, correl, upWin,
lowWin, maxFluorTotal, minFluorTotal,
stopCyc, startCyc, threshold,
vecNoAmplification,
vecBaselineError,
vecSkipSample, vecNoPlateau,
vecShortLogLin, vecIsUsedInWoL)
return indMeanX, indMeanY, pcrEff, nNulls, nInclu, correl, upWin, lowWin, threshold, vecIsUsedInWoL, vecNoPlateau
def _lrp_removeOutlier(data, vecNoPlateau, alpha=0.05):
"""A function which calculates the skewness and Grubbs test to identify outliers ignoring nan.
Args:
data: The numpy array with the data
vecNoPlateau: The vector of samples without plateau.
alpha: The the significance level (default 0.05)
Returns:
The a bool array with the removed outliers set true.
"""
oData = np.copy(data)
oLogic = np.zeros(data.shape, dtype=np.bool_)
loopOn = True
while loopOn:
count = np.count_nonzero(~np.isnan(oData))
if count < 3:
loopOn = False
else:
mean = np.nanmean(oData)
std = np.nanstd(oData, ddof=1)
skewness = scp.skew(oData, bias=False, nan_policy='omit')
skewness_SE = np.sqrt((6 * count * (count - 1)) / ((count - 2) * (count + 1) * (count + 3)))
skewness_t = np.abs(skewness) / skewness_SE
skewness_P = scp.t.sf(skewness_t, df=np.power(10, 10)) * 2
if skewness_P < alpha / 2.0:
# It's skewed!
grubbs_t = scp.t.ppf(1 - (alpha / count) / 2, (count - 2))
grubbs_Gcrit = ((count - 1) / np.sqrt(count)) * np.sqrt(np.power(grubbs_t, 2) /
((count - 2) + np.power(grubbs_t, 2)))
if skewness > 0.0:
data_max = np.nanmax(oData)
grubbs_res = (data_max - mean) / std
max_pos = np.nanargmax(oData)
if grubbs_res > grubbs_Gcrit:
# It's a true outlier
oData[max_pos] = np.nan
oLogic[max_pos] = True
else:
if vecNoPlateau[max_pos]:
# It has no plateau
oData[max_pos] = np.nan
oLogic[max_pos] = True
else:
loopOn = False
else:
data_min = np.nanmin(oData)
grubbs_res = (mean - data_min) / std
min_pos = np.nanargmin(oData)
if grubbs_res > grubbs_Gcrit:
# It's a true outlier
oData[min_pos] = np.nan
oLogic[min_pos] = True
else:
if vecNoPlateau[min_pos]:
# It has no plateau
oData[min_pos] = np.nan
oLogic[min_pos] = True
else:
loopOn = False
else:
loopOn = False
return oLogic
def _mca_smooth(tempList, rawFluor):
"""A function to smooth the melt curve date based on Friedmans supersmoother.
# https://www.slac.stanford.edu/pubs/slacpubs/3250/slac-pub-3477.pdf
Args:
tempList:
rawFluor: The numpy array with the raw data
Returns:
The numpy array with the smoothed data.
"""
span_s = 0.05
span_m = 0.2
span_l = 0.5
smoothFluor = np.zeros(rawFluor.shape, dtype=np.float64)
padTemp = np.append(0.0, tempList)
zeroPad = np.zeros((rawFluor.shape[0], 1), dtype=np.float64)
padFluor = np.append(zeroPad, rawFluor, axis=1)
n = len(padTemp) - 1
# Find the increase in x from 0.25 to 0.75 over the total range
firstQuarter = int(0.5 + n / 4)
thirdQuarter = 3 * firstQuarter
scale = -1.0
while scale <= 0.0:
if thirdQuarter < n:
thirdQuarter += 1
if firstQuarter > 1:
firstQuarter -= 1
scale = padTemp[thirdQuarter] - padTemp[firstQuarter]
vsmlsq = 0.0001 * scale * 0.0001 * scale
countUp = 0
for fluor in padFluor:
[res_s_a, res_s_t] = _mca_sub_smooth(padTemp, fluor, span_s, vsmlsq, True)
[res_s_b, _unused] = _mca_sub_smooth(padTemp, res_s_t, span_m, vsmlsq, False)
[res_s_c, res_s_t] = _mca_sub_smooth(padTemp, fluor, span_m, vsmlsq, True)
[res_s_d, _unused] = _mca_sub_smooth(padTemp, res_s_t, span_m, vsmlsq, False)
[res_s_e, res_s_t] = _mca_sub_smooth(padTemp, fluor, span_l, vsmlsq, True)
[res_s_f, _unused] = _mca_sub_smooth(padTemp, res_s_t, span_m, vsmlsq, False)
res_s_fin = np.zeros(res_s_a.shape, dtype=np.float64)
for thirdQuarter in range(1, n + 1):
resmin = 1.0e20
if res_s_b[thirdQuarter] < resmin:
resmin = res_s_b[thirdQuarter]
res_s_fin[thirdQuarter] = span_s
if res_s_d[thirdQuarter] < resmin:
resmin = res_s_d[thirdQuarter]
res_s_fin[thirdQuarter] = span_m
if res_s_f[thirdQuarter] < resmin:
res_s_fin[thirdQuarter] = span_l
[res_s_bb, _unused] = _mca_sub_smooth(padTemp, res_s_fin, span_m, vsmlsq, False)
res_s_cc = np.zeros(res_s_a.shape, dtype=np.float64)
for thirdQuarter in range(1, n + 1):
# compare res_s_bb with spans[] and make sure the no res_s_bb[] is below span_s or above span_l
if res_s_bb[thirdQuarter] <= span_s:
res_s_bb[thirdQuarter] = span_s
if res_s_bb[thirdQuarter] >= span_l:
res_s_bb[thirdQuarter] = span_l
f = res_s_bb[thirdQuarter] - span_m
if f >= 0.0:
# in case res_s_bb[] is higher than span_m: calculate res_s_cc[] from res_s_c and res_s_e
# using linear interpolation between span_l and span_m
f = f / (span_l - span_m)
res_s_cc[thirdQuarter] = (1.0 - f) * res_s_c[thirdQuarter] + f * res_s_e[thirdQuarter]
else:
# in case res_s_bb[] is less than span_m: calculate res_s_cc[] from res_s_c and res_s_a
# using linear interpolation between span_s and span_m
f = -f / (span_m - span_s)
res_s_cc[thirdQuarter] = (1.0 - f) * res_s_c[thirdQuarter] + f * res_s_a[thirdQuarter]
# final smoothing of combined optimally smoothed values in res_s_cc[] into smo[]
[res_s_t, _unused] = _mca_sub_smooth(padTemp, res_s_cc, span_s, vsmlsq, False)
smoothFluor[countUp] = res_s_t[1:]
countUp += 1
return smoothFluor
def _mca_sub_smooth(temperature, fluor, span, vsmlsq, saveVarianceData):
"""A function to smooth the melt curve date based on Friedmans supersmoother.
# https://www.slac.stanford.edu/pubs/slacpubs/3250/slac-pub-3477.pdf
Args:
temperature:
fluor: The numpy array with the raw data
span: The selected span
vsmlsq: The width
saveVarianceData: Sava variance data
Returns:
[smoothData[], varianceData[]] where smoothData[] contains smoothed data,
varianceData[] contains residuals scaled to variance.
"""
n = len(temperature) - 1
smoothData = np.zeros(len(temperature), dtype=np.float64)
varianceData = np.zeros(len(temperature), dtype=np.float64)
windowSize = int(0.5 * span * n + 0.6)
if windowSize < 2:
windowSize = 2
windowStop = 2 * windowSize + 1 # range of smoothing window
xm = temperature[1]
ym = fluor[1]
tempVar = 0.0
fluorVar = 0.0
for i in range(2, windowStop + 1):
xm = ((i - 1) * xm + temperature[i]) / i
ym = ((i - 1) * ym + fluor[i]) / i
tmp = i * (temperature[i] - xm) / (i - 1)
tempVar += tmp * (temperature[i] - xm)
fluorVar += tmp * (fluor[i] - ym)
fbw = windowStop
for j in range(1, n + 1): # Loop through all
windowStart = j - windowSize - 1
windowEnd = j + windowSize
if not (windowStart < 1 or windowEnd > n):
tempStart = temperature[windowStart]
tempEnd = temperature[windowEnd]
fbo = fbw
fbw = fbw - 1.0
tmp = 0.0
if fbw > 0.0:
xm = (fbo * xm - tempStart) / fbw
if fbw > 0.0:
ym = (fbo * ym - fluor[windowStart]) / fbw
if fbw > 0.0:
tmp = fbo * (tempStart - xm) / fbw
tempVar = tempVar - tmp * (tempStart - xm)
fluorVar = fluorVar - tmp * (fluor[windowStart] - ym)
fbo = fbw
fbw = fbw + 1.0
tmp = 0.0
if fbw > 0.0:
xm = (fbo * xm + tempEnd) / fbw
if fbw > 0.0:
ym = (fbo * ym + fluor[windowEnd]) / fbw
if fbo > 0.0:
tmp = fbw * (tempEnd - xm) / fbo
tempVar = tempVar + tmp * (tempEnd - xm)
fluorVar = fluorVar + tmp * (fluor[windowEnd] - ym)
if tempVar > vsmlsq:
smoothData[j] = (temperature[j] - xm) * fluorVar / tempVar + ym # contains smoothed data
else:
smoothData[j] = ym # contains smoothed data
if saveVarianceData:
h = 0.0
if fbw > 0.0:
h = 1.0 / fbw
if tempVar > vsmlsq:
h = h + (temperature[j] - xm) * (temperature[j] - xm) / tempVar
if 1.0 - h > 0.0:
varianceData[j] = abs(fluor[j] - smoothData[j]) / (1.0 - h) # contains residuals scaled to variance
else:
if j > 1:
varianceData[j] = varianceData[j - 1] # contains residuals scaled to variance
else:
varianceData[j] = 0.0
return [smoothData, varianceData]
def _mca_linReg(xIn, yUse, start, stop):
"""A function which calculates the slope or the intercept by linear regression.
Args:
xIn: The numpy array of the temperatures
yUse: The numpy array that contains the fluorescence
Returns:
An array with the slope and intercept.
"""
counts = np.ones(yUse.shape)
xUse = xIn.copy()
xUse[np.isnan(yUse)] = 0
counts[np.isnan(yUse)] = 0
myStop = stop + 1
tempSqared = xUse * xUse
tempFluor = xUse * yUse
sumCyc = np.nansum(xUse[:, start:myStop], axis=1)
sumFluor = np.nansum(yUse[:, start:myStop], axis=1)
sumCycSquared = np.nansum(tempSqared[:, start:myStop], axis=1)
sumCycFluor = np.nansum(tempFluor[:, start:myStop], axis=1)
n = np.nansum(counts[:, start:myStop], axis=1)
ssx = sumCycSquared - (sumCyc * sumCyc) / n
sxy = sumCycFluor - (sumCyc * sumFluor) / n
slope = sxy / ssx
intercept = (sumFluor / n) - slope * (sumCyc / n)
return [slope, intercept]
def _cleanErrorString(inStr, cleanStyle):
outStr = ";"
inStr += ";"
if cleanStyle == "melt":
outStr = inStr.replace('several products with different melting temperatures detected', '')
outStr = outStr.replace('product with different melting temperatures detected', '')
outStr = outStr.replace('no product with expected melting temperature', '')
else:
strList = inStr.split(";")
knownWarn = ["amplification in negative control", "plateau in negative control",
"no amplification in positive control", "baseline error in positive control",
"no plateau in positive control", "noisy sample in positive control",
"Cq < 10, N0 unreliable", "Cq > 34", "no indiv PCR eff can be calculated",
"PCR efficiency outlier", "no amplification", "baseline error", "no plateau",
"noisy sample", "Cq too high"]
for ele in strList:
if ele in knownWarn:
continue
if re.search(r"^only \d+ values in log phase", ele):
continue
if re.search(r"^indiv PCR eff is .+", ele):
continue
outStr += ele + ";"
# if inStr.find('several products with different melting temperatures detected') >= 0:
# outStr += ';several products with different melting temperatures detected;'
# if inStr.find('product with different melting temperatures detected') >= 0:
# outStr += ';product with different melting temperatures detected;'
# if inStr.find('no product with expected melting temperature') >= 0:
# outStr += ';no product with expected melting temperature;'
outStr = re.sub(r';+', ';', outStr)
return outStr
def _numpyTwoAxisSave(var, fileName):
with np.printoptions(precision=3, suppress=True):
np.savetxt(fileName, var, fmt='%.6f', delimiter='\t', newline='\n')
def _getXMLDataType():
return ["tar", "cq", "N0", "ampEffMet", "ampEff", "ampEffSE", "corrF", "meltTemp",
"excl", "note", "adp", "mdp", "endPt", "bgFluor", "quantFluor"]
class Rdml:
"""RDML-Python library
The root element used to open, write, read and edit RDML files.
Attributes:
_rdmlData: The RDML XML object from lxml.
_node: The root node of the RDML XML object.
"""
def __init__(self, filename=None):
"""Inits an empty RDML instance with new() or load RDML file with load().
Args:
self: The class self parameter.
filename: The name of the RDML file to load.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._rdmlData = None
self._rdmlFilename = None
self._node = None
if filename:
self.load(filename)
else:
self.new()
def __getitem__(self, key):
"""Returns data of the key.
Args:
self: The class self parameter.
key: The key of the experimenter subelement
Returns:
A string of the data or None.
"""
if key == "version":
return self.version()
if key in ["dateMade", "dateUpdated"]:
return _get_first_child_text(self._node, key)
raise KeyError
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["version", "dateMade", "dateUpdated"]
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["dateMade", "dateUpdated", "id", "experimenter", "documentation", "dye",
"sample", "target", "thermalCyclingConditions", "experiment"]
def new(self):
"""Creates an new empty RDML object with the current date.
Args:
self: The class self parameter.
Returns:
No return value. Function may raise RdmlError if required.
"""
data = "<rdml version='1.2' xmlns:rdml='http://www.rdml.org' xmlns='http://www.rdml.org'>\n<dateMade>"
data += datetime.datetime.utcnow().strftime("%Y-%m-%dT%H:%M:%S")
data += "</dateMade>\n<dateUpdated>"
data += datetime.datetime.utcnow().strftime("%Y-%m-%dT%H:%M:%S")
data += "</dateUpdated>\n</rdml>"
self.loadXMLString(data)
return
def load(self, filename):
"""Load an RDML file with decompression of rdml_data.xml or an XML file. Uses loadXMLString().
Args:
self: The class self parameter.
filename: The name of the RDML file to load.
Returns:
No return value. Function may raise RdmlError if required.
"""
if zipfile.is_zipfile(filename):
self._rdmlFilename = filename
zf = zipfile.ZipFile(filename, 'r')
try:
data = zf.read('rdml_data.xml').decode('utf-8')
except KeyError:
raise RdmlError('No rdml_data.xml in compressed RDML file found.')
else:
self.loadXMLString(data)
finally:
zf.close()
else:
with open(filename, 'r') as txtfile:
data = txtfile.read()
if data:
self.loadXMLString(data)
else:
raise RdmlError('File format error, not a valid RDML or XML file.')
def save(self, filename):
"""Save an RDML file with compression of rdml_data.xml.
Args:
self: The class self parameter.
filename: The name of the RDML file to save to.
Returns:
No return value. Function may raise RdmlError if required.
"""
elem = _get_or_create_subelement(self._node, "dateUpdated", self.xmlkeys())
elem.text = datetime.datetime.utcnow().strftime("%Y-%m-%dT%H:%M:%S")
data = et.tostring(self._rdmlData, pretty_print=True)
_writeFileInRDML(filename, 'rdml_data.xml', data)
def loadXMLString(self, data):
"""Create RDML object from xml string. !ENTITY and DOCSTRINGS will be removed.
Args:
self: The class self parameter.
data: The xml string of the RDML file to load.
Returns:
No return value. Function may raise RdmlError if required.
"""
# To avoid some xml attacs based on
# <!ENTITY entityname "replacement text">
data = re.sub(r"<\W*!ENTITY[^>]+>", "", data)
data = re.sub(r"!ENTITY", "", data)
try:
self._rdmlData = et.ElementTree(et.fromstring(data.encode('utf-8')))
# Change to bytecode and defused?
except et.XMLSyntaxError:
raise RdmlError('XML load error, not a valid RDML or XML file.')
self._node = self._rdmlData.getroot()
if self._node.tag.replace("{http://www.rdml.org}", "") != 'rdml':
raise RdmlError('Root element is not \'rdml\', not a valid RDML or XML file.')
rdml_version = self._node.get('version')
# Remainder: Update version in new() and validate()
if rdml_version not in ['1.0', '1.1', '1.2', '1.3']:
raise RdmlError('Unknown or unsupported RDML file version.')
def validate(self, filename=None):
"""Validate the RDML object against its schema or load file and validate it.
Args:
self: The class self parameter.
filename: The name of the RDML file to load.
Returns:
A string with the validation result as a two column table.
"""
notes = ""
if filename:
try:
vd = Rdml(filename)
except RdmlError as err:
notes += 'RDML file structure:\tFalse\t' + str(err) + '\n'
return notes
notes += "RDML file structure:\tTrue\tValid file structure.\n"
else:
vd = self
version = vd.version()
rdmlws = os.path.dirname(os.path.abspath(__file__))
if version == '1.0':
xmlschema_doc = et.parse(os.path.join(rdmlws, 'schema', 'RDML_v1_0_REC.xsd'))
elif version == '1.1':
xmlschema_doc = et.parse(os.path.join(rdmlws, 'schema', 'RDML_v1_1_REC.xsd'))
elif version == '1.2':
xmlschema_doc = et.parse(os.path.join(rdmlws, 'schema', 'RDML_v1_2_REC.xsd'))
elif version == '1.3':
xmlschema_doc = et.parse(os.path.join(rdmlws, 'schema', 'RDML_v1_3_CR.xsd'))
else:
notes += 'RDML version:\tFalse\tUnknown schema version' + version + '\n'
return notes
notes += "RDML version:\tTrue\t" + version + "\n"
xmlschema = et.XMLSchema(xmlschema_doc)
result = xmlschema.validate(vd._rdmlData)
if result:
notes += 'Schema validation result:\tTrue\tRDML file is valid.\n'
else:
notes += 'Schema validation result:\tFalse\tRDML file is not valid.\n'
log = xmlschema.error_log
for err in log:
notes += 'Schema validation error:\tFalse\t'
notes += "Line %s, Column %s: %s \n" % (err.line, err.column, err.message)
return notes
def isvalid(self, filename=None):
"""Validate the RDML object against its schema or load file and validate it.
Args:
self: The class self parameter.
filename: The name of the RDML file to load.
Returns:
True or false as the validation result.
"""
if filename:
try:
vd = Rdml(filename)
except RdmlError:
return False
else:
vd = self
version = vd.version()
rdmlws = os.path.dirname(os.path.abspath(__file__))
if version == '1.0':
xmlschema_doc = et.parse(os.path.join(rdmlws, 'schema', 'RDML_v1_0_REC.xsd'))
elif version == '1.1':
xmlschema_doc = et.parse(os.path.join(rdmlws, 'schema', 'RDML_v1_1_REC.xsd'))
elif version == '1.2':
xmlschema_doc = et.parse(os.path.join(rdmlws, 'schema', 'RDML_v1_2_REC.xsd'))
elif version == '1.3':
xmlschema_doc = et.parse(os.path.join(rdmlws, 'schema', 'RDML_v1_3_CR.xsd'))
else:
return False
xmlschema = et.XMLSchema(xmlschema_doc)
result = xmlschema.validate(vd._rdmlData)
if result:
return True
else:
return False
def version(self):
"""Returns the version string of the RDML object.
Args:
self: The class self parameter.
Returns:
A string of the version like '1.1'.
"""
return self._node.get('version')
def migrate_version_1_0_to_1_1(self):
"""Migrates the rdml version from v1.0 to v1.1.
Args:
self: The class self parameter.
Returns:
A list of strings with the modifications made.
"""
ret = []
rdml_version = self._node.get('version')
if rdml_version != '1.0':
raise RdmlError('RDML version for migration has to be v1.0.')
exp = _get_all_children(self._node, "thirdPartyExtensions")
if len(exp) > 0:
ret.append("Migration to v1.1 deleted \"thirdPartyExtensions\" elements.")
for node in exp:
self._node.remove(node)
hint = ""
exp1 = _get_all_children(self._node, "experiment")
for node1 in exp1:
exp2 = _get_all_children(node1, "run")
for node2 in exp2:
exp3 = _get_all_children(node2, "react")
for node3 in exp3:
exp4 = _get_all_children(node3, "data")
for node4 in exp4:
exp5 = _get_all_children(node4, "quantity")
for node5 in exp5:
hint = "Migration to v1.1 deleted react data \"quantity\" elements."
node4.remove(node5)
if hint != "":
ret.append(hint)
xml_keys = ["description", "documentation", "xRef", "type", "interRunCalibrator",
"quantity", "calibratorSample", "cdnaSynthesisMethod",
"templateRNAQuantity", "templateRNAQuality", "templateDNAQuantity", "templateDNAQuality"]
exp1 = _get_all_children(self._node, "sample")
for node1 in exp1:
hint = ""
exp2 = _get_all_children(node1, "templateRNAQuantity")
if len(exp2) > 0:
templateRNAQuantity = _get_first_child_text(node1, "templateRNAQuantity")
node1.remove(exp2[0])
if templateRNAQuantity != "":
hint = "Migration to v1.1 modified sample \"templateRNAQuantity\" element without loss."
ele = _get_or_create_subelement(node1, "templateRNAQuantity", xml_keys)
_change_subelement(ele, "value", ["value", "unit"], templateRNAQuantity, True, "float")
_change_subelement(ele, "unit", ["value", "unit"], "ng", True, "float")
if hint != "":
ret.append(hint)
hint = ""
exp2 = _get_all_children(node1, "templateRNAQuantity")
if len(exp2) > 0:
templateDNAQuantity = _get_first_child_text(node1, "templateDNAQuantity")
node1.remove(exp2[0])
if templateDNAQuantity != "":
hint = "Migration to v1.1 modified sample \"templateDNAQuantity\" element without loss."
ele = _get_or_create_subelement(node1, "templateDNAQuantity", xml_keys)
_change_subelement(ele, "value", ["value", "unit"], templateDNAQuantity, True, "float")
_change_subelement(ele, "unit", ["value", "unit"], "ng", True, "float")
if hint != "":
ret.append(hint)
xml_keys = ["description", "documentation", "xRef", "type", "amplificationEfficiencyMethod",
"amplificationEfficiency", "detectionLimit", "dyeId", "sequences", "commercialAssay"]
exp1 = _get_all_children(self._node, "target")
all_dyes = {}
hint = ""
for node1 in exp1:
hint = ""
dye_ele = _get_first_child_text(node1, "dyeId")
node1.remove(_get_first_child(node1, "dyeId"))
if dye_ele == "":
dye_ele = "conversion_dye_missing"
hint = "Migration to v1.1 created target nonsense \"dyeId\"."
forId = _get_or_create_subelement(node1, "dyeId", xml_keys)
forId.attrib['id'] = dye_ele
all_dyes[dye_ele] = True
if hint != "":
ret.append(hint)
for dkey in all_dyes.keys():
if _check_unique_id(self._node, "dye", dkey):
new_node = et.Element("dye", id=dkey)
place = _get_tag_pos(self._node, "dye", self.xmlkeys(), 999999)
self._node.insert(place, new_node)
xml_keys = ["description", "documentation", "experimenter", "instrument", "dataCollectionSoftware",
"backgroundDeterminationMethod", "cqDetectionMethod", "thermalCyclingConditions", "pcrFormat",
"runDate", "react"]
exp1 = _get_all_children(self._node, "experiment")
for node1 in exp1:
exp2 = _get_all_children(node1, "run")
for node2 in exp2:
old_format = _get_first_child_text(node2, "pcrFormat")
exp3 = _get_all_children(node2, "pcrFormat")
for node3 in exp3:
node2.remove(node3)
rows = "1"
columns = "1"
rowLabel = "ABC"
columnLabel = "123"
if old_format == "single-well":
rowLabel = "123"
if old_format == "48-well plate; A1-F8":
rows = "6"
columns = "8"
if old_format == "96-well plate; A1-H12":
rows = "8"
columns = "12"
if old_format == "384-well plate; A1-P24":
rows = "16"
columns = "24"
if old_format == "3072-well plate; A1a1-D12h8":
rows = "32"
columns = "96"
rowLabel = "A1a1"
columnLabel = "A1a1"
if old_format == "32-well rotor; 1-32":
rows = "32"
rowLabel = "123"
if old_format == "72-well rotor; 1-72":
rows = "72"
rowLabel = "123"
if old_format == "100-well rotor; 1-100":
rows = "100"
rowLabel = "123"
if old_format == "free format":
rows = "-1"
columns = "1"
rowLabel = "123"
ele3 = _get_or_create_subelement(node2, "pcrFormat", xml_keys)
_change_subelement(ele3, "rows", ["rows", "columns", "rowLabel", "columnLabel"], rows, True, "string")
_change_subelement(ele3, "columns", ["rows", "columns", "rowLabel", "columnLabel"], columns, True, "string")
_change_subelement(ele3, "rowLabel", ["rows", "columns", "rowLabel", "columnLabel"], rowLabel, True, "string")
_change_subelement(ele3, "columnLabel", ["rows", "columns", "rowLabel", "columnLabel"], columnLabel, True, "string")
if old_format == "48-well plate A1-F8" or \
old_format == "96-well plate; A1-H12" or \
old_format == "384-well plate; A1-P24":
exp3 = _get_all_children(node2, "react")
for node3 in exp3:
old_id = node3.get('id')
old_letter = ord(re.sub(r"\d", "", old_id).upper()) - ord("A")
old_nr = int(re.sub(r"\D", "", old_id))
newId = old_nr + old_letter * int(columns)
node3.attrib['id'] = str(newId)
if old_format == "3072-well plate; A1a1-D12h8":
exp3 = _get_all_children(node2, "react")
for node3 in exp3:
old_id = node3.get('id')
old_left = re.sub(r"\D\d+$", "", old_id)
old_left_letter = ord(re.sub(r"\d", "", old_left).upper()) - ord("A")
old_left_nr = int(re.sub(r"\D", "", old_left)) - 1
old_right = re.sub(r"^\D\d+", "", old_id)
old_right_letter = ord(re.sub(r"\d", "", old_right).upper()) - ord("A")
old_right_nr = int(re.sub(r"\D", "", old_right))
newId = old_left_nr * 8 + old_right_nr + old_left_letter * 768 + old_right_letter * 96
node3.attrib['id'] = str(newId)
self._node.attrib['version'] = "1.1"
return ret
def migrate_version_1_1_to_1_2(self):
"""Migrates the rdml version from v1.1 to v1.2.
Args:
self: The class self parameter.
Returns:
A list of strings with the modifications made.
"""
ret = []
rdml_version = self._node.get('version')
if rdml_version != '1.1':
raise RdmlError('RDML version for migration has to be v1.1.')
exp1 = _get_all_children(self._node, "sample")
for node1 in exp1:
hint = ""
exp2 = _get_all_children(node1, "templateRNAQuality")
for node2 in exp2:
node1.remove(node2)
hint = "Migration to v1.2 deleted sample \"templateRNAQuality\" element."
if hint != "":
ret.append(hint)
hint = ""
exp2 = _get_all_children(node1, "templateRNAQuantity")
for node2 in exp2:
node1.remove(node2)
hint = "Migration to v1.2 deleted sample \"templateRNAQuantity\" element."
if hint != "":
ret.append(hint)
hint = ""
exp2 = _get_all_children(node1, "templateDNAQuality")
for node2 in exp2:
node1.remove(node2)
hint = "Migration to v1.2 deleted sample \"templateDNAQuality\" element."
if hint != "":
ret.append(hint)
hint = ""
exp2 = _get_all_children(node1, "templateDNAQuantity")
for node2 in exp2:
node1.remove(node2)
hint = "Migration to v1.2 deleted sample \"templateDNAQuantity\" element."
if hint != "":
ret.append(hint)
self._node.attrib['version'] = "1.2"
return ret
def migrate_version_1_2_to_1_1(self):
"""Migrates the rdml version from v1.2 to v1.1.
Args:
self: The class self parameter.
Returns:
A list of strings with the modifications made.
"""
ret = []
rdml_version = self._node.get('version')
if rdml_version != '1.2':
raise RdmlError('RDML version for migration has to be v1.2.')
exp1 = _get_all_children(self._node, "sample")
for node1 in exp1:
hint = ""
exp2 = _get_all_children(node1, "annotation")
for node2 in exp2:
node1.remove(node2)
hint = "Migration to v1.1 deleted sample \"annotation\" element."
if hint != "":
ret.append(hint)
hint = ""
exp2 = _get_all_children(node1, "templateQuantity")
for node2 in exp2:
node1.remove(node2)
hint = "Migration to v1.1 deleted sample \"templateQuantity\" element."
if hint != "":
ret.append(hint)
exp1 = _get_all_children(self._node, "target")
for node1 in exp1:
hint = ""
exp2 = _get_all_children(node1, "amplificationEfficiencySE")
for node2 in exp2:
node1.remove(node2)
hint = "Migration to v1.1 deleted target \"amplificationEfficiencySE\" element."
if hint != "":
ret.append(hint)
hint = ""
exp1 = _get_all_children(self._node, "experiment")
for node1 in exp1:
exp2 = _get_all_children(node1, "run")
for node2 in exp2:
exp3 = _get_all_children(node2, "react")
for node3 in exp3:
exp4 = _get_all_children(node3, "data")
for node4 in exp4:
exp5 = _get_all_children(node4, "bgFluorSlp")
for node5 in exp5:
hint = "Migration to v1.1 deleted react data \"bgFluorSlp\" elements."
node4.remove(node5)
if hint != "":
ret.append(hint)
self._node.attrib['version'] = "1.1"
return ret
def migrate_version_1_2_to_1_3(self):
"""Migrates the rdml version from v1.2 to v1.3.
Args:
self: The class self parameter.
Returns:
A list of strings with the modifications made.
"""
ret = []
rdml_version = self._node.get('version')
if rdml_version != '1.2':
raise RdmlError('RDML version for migration has to be v1.2.')
self._node.attrib['version'] = "1.3"
return ret
def migrate_version_1_3_to_1_2(self):
"""Migrates the rdml version from v1.3 to v1.2.
Args:
self: The class self parameter.
Returns:
A list of strings with the modifications made.
"""
ret = []
rdml_version = self._node.get('version')
if rdml_version != '1.3':
raise RdmlError('RDML version for migration has to be v1.3.')
hint = ""
hint2 = ""
hint3 = ""
hint4 = ""
hint5 = ""
hint6 = ""
hint7 = ""
hint8 = ""
exp1 = _get_all_children(self._node, "experiment")
for node1 in exp1:
exp2 = _get_all_children(node1, "run")
for node2 in exp2:
exp3 = _get_all_children(node2, "react")
for node3 in exp3:
exp4 = _get_all_children(node3, "partitions")
for node4 in exp4:
hint = "Migration to v1.2 deleted react \"partitions\" elements."
node3.remove(node4)
# No data element, no react element in v 1.2
exp5 = _get_all_children(node3, "data")
if len(exp5) == 0:
hint = "Migration to v1.2 deleted run \"react\" elements."
node2.remove(node3)
exp4b = _get_all_children(node3, "data")
for node4 in exp4b:
exp5 = _get_all_children(node4, "ampEffMet")
for node5 in exp5:
hint2 = "Migration to v1.2 deleted react data \"ampEffMet\" elements."
node4.remove(node5)
exp5 = _get_all_children(node4, "N0")
for node5 in exp5:
hint3 = "Migration to v1.2 deleted react data \"N0\" elements."
node4.remove(node5)
exp5 = _get_all_children(node4, "ampEff")
for node5 in exp5:
hint4 = "Migration to v1.2 deleted react data \"ampEff\" elements."
node4.remove(node5)
exp5 = _get_all_children(node4, "ampEffSE")
for node5 in exp5:
hint5 = "Migration to v1.2 deleted react data \"ampEffSE\" elements."
node4.remove(node5)
exp5 = _get_all_children(node4, "corrF")
for node5 in exp5:
hint6 = "Migration to v1.2 deleted react data \"corrF\" elements."
node4.remove(node5)
exp5 = _get_all_children(node4, "meltTemp")
for node5 in exp5:
hint7 = "Migration to v1.2 deleted react data \"meltTemp\" elements."
node4.remove(node5)
exp5 = _get_all_children(node4, "note")
for node5 in exp5:
hint8 = "Migration to v1.2 deleted react data \"note\" elements."
node4.remove(node5)
if hint != "":
ret.append(hint)
if hint2 != "":
ret.append(hint2)
if hint3 != "":
ret.append(hint3)
if hint4 != "":
ret.append(hint4)
if hint5 != "":
ret.append(hint5)
if hint6 != "":
ret.append(hint6)
if hint7 != "":
ret.append(hint7)
if hint8 != "":
ret.append(hint8)
exp1 = _get_all_children(self._node, "sample")
hint = ""
hint2 = ""
for node1 in exp1:
exp2 = _get_all_children(node1, "type")
if "targetId" in exp2[0].attrib:
del exp2[0].attrib["targetId"]
hint = "Migration to v1.2 deleted sample type \"targetId\" attribute."
for elCount in range(1, len(exp2)):
node1.remove(exp2[elCount])
hint2 = "Migration to v1.2 deleted sample \"type\" elements."
if hint != "":
ret.append(hint)
if hint2 != "":
ret.append(hint2)
exp1 = _get_all_children(self._node, "target")
hint = ""
for node1 in exp1:
exp2 = _get_all_children(node1, "meltingTemperature")
for node2 in exp2:
node1.remove(node2)
hint = "Migration to v1.2 deleted target \"meltingTemperature\" elements."
if hint != "":
ret.append(hint)
exp1 = _get_all_children(self._node, "dye")
hint = ""
for node1 in exp1:
exp2 = _get_all_children(node1, "dyeChemistry")
for node2 in exp2:
node1.remove(node2)
hint = "Migration to v1.2 deleted dye \"dyeChemistry\" elements."
if hint != "":
ret.append(hint)
self._node.attrib['version'] = "1.2"
return ret
def recreate_lost_ids(self):
"""Searches for lost ids and repairs them.
Args:
self: The class self parameter.
Returns:
A string with the modifications.
"""
mess = ""
# Find lost dyes
foundIds = {}
allTar = _get_all_children(self._node, "target")
for node in allTar:
forId = _get_first_child(node, "dyeId")
if forId is not None:
foundIds[forId.attrib['id']] = 0
presentIds = []
exp = _get_all_children(self._node, "dye")
for node in exp:
presentIds.append(node.attrib['id'])
for used_id in foundIds:
if used_id not in presentIds:
self.new_dye(id=used_id, newposition=0)
mess += "Recreated new dye: " + used_id + "\n"
# Find lost thermalCycCon
foundIds = {}
allSam = _get_all_children(self._node, "sample")
for node in allSam:
subNode = _get_first_child(node, "cdnaSynthesisMethod")
if subNode is not None:
forId = _get_first_child(node, "thermalCyclingConditions")
if forId is not None:
foundIds[forId.attrib['id']] = 0
allExp = _get_all_children(self._node, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
forId = _get_first_child(subNode, "thermalCyclingConditions")
if forId is not None:
foundIds[forId.attrib['id']] = 0
presentIds = []
exp = _get_all_children(self._node, "thermalCyclingConditions")
for node in exp:
presentIds.append(node.attrib['id'])
for used_id in foundIds:
if used_id not in presentIds:
self.new_therm_cyc_cons(id=used_id, newposition=0)
mess += "Recreated thermal cycling conditions: " + used_id + "\n"
# Find lost experimenter
foundIds = {}
allTh = _get_all_children(self._node, "thermalCyclingConditions")
for node in allTh:
subNodes = _get_all_children(node, "experimenter")
for subNode in subNodes:
foundIds[subNode.attrib['id']] = 0
allExp = _get_all_children(self._node, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
lastNodes = _get_all_children(subNode, "experimenter")
for lastNode in lastNodes:
foundIds[lastNode.attrib['id']] = 0
presentIds = []
exp = _get_all_children(self._node, "experimenter")
for node in exp:
presentIds.append(node.attrib['id'])
for used_id in foundIds:
if used_id not in presentIds:
self.new_experimenter(id=used_id, firstName="unknown first name", lastName="unknown last name", newposition=0)
mess += "Recreated experimenter: " + used_id + "\n"
# Find lost documentation
foundIds = {}
allSam = _get_all_children(self._node, "sample")
for node in allSam:
subNodes = _get_all_children(node, "documentation")
for subNode in subNodes:
foundIds[subNode.attrib['id']] = 0
allTh = _get_all_children(self._node, "target")
for node in allTh:
subNodes = _get_all_children(node, "documentation")
for subNode in subNodes:
foundIds[subNode.attrib['id']] = 0
allTh = _get_all_children(self._node, "thermalCyclingConditions")
for node in allTh:
subNodes = _get_all_children(node, "documentation")
for subNode in subNodes:
foundIds[subNode.attrib['id']] = 0
allExp = _get_all_children(self._node, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "documentation")
for subNode in subNodes:
foundIds[subNode.attrib['id']] = 0
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
lastNodes = _get_all_children(subNode, "documentation")
for lastNode in lastNodes:
foundIds[lastNode.attrib['id']] = 0
presentIds = []
exp = _get_all_children(self._node, "documentation")
for node in exp:
presentIds.append(node.attrib['id'])
for used_id in foundIds:
if used_id not in presentIds:
self.new_documentation(id=used_id, newposition=0)
mess += "Recreated documentation: " + used_id + "\n"
# Find lost sample
foundIds = {}
allExp = _get_all_children(self._node, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
reactNodes = _get_all_children(subNode, "react")
for reactNode in reactNodes:
lastNodes = _get_all_children(reactNode, "sample")
for lastNode in lastNodes:
foundIds[lastNode.attrib['id']] = 0
presentIds = []
exp = _get_all_children(self._node, "sample")
for node in exp:
presentIds.append(node.attrib['id'])
for used_id in foundIds:
if used_id not in presentIds:
self.new_sample(id=used_id, type="unkn", newposition=0)
mess += "Recreated sample: " + used_id + "\n"
# Find lost target
foundIds = {}
allExp = _get_all_children(self._node, "sample")
for node in allExp:
subNodes = _get_all_children(node, "type")
for subNode in subNodes:
if "targetId" in subNode.attrib:
foundIds[subNode.attrib['targetId']] = 0
allExp = _get_all_children(self._node, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
reactNodes = _get_all_children(subNode, "react")
for reactNode in reactNodes:
dataNodes = _get_all_children(reactNode, "data")
for dataNode in dataNodes:
lastNodes = _get_all_children(dataNode, "tar")
for lastNode in lastNodes:
foundIds[lastNode.attrib['id']] = 0
partNodes = _get_all_children(reactNode, "partitions")
for partNode in partNodes:
dataNodes = _get_all_children(partNode, "data")
for dataNode in dataNodes:
lastNodes = _get_all_children(dataNode, "tar")
for lastNode in lastNodes:
foundIds[lastNode.attrib['id']] = 0
# Search in Table files
if self._rdmlFilename is not None and self._rdmlFilename != "":
if zipfile.is_zipfile(self._rdmlFilename):
zf = zipfile.ZipFile(self._rdmlFilename, 'r')
for item in zf.infolist():
if re.search("^partitions/", item.filename):
fileContent = zf.read(item.filename).decode('utf-8')
newlineFix = fileContent.replace("\r\n", "\n")
tabLines = newlineFix.split("\n")
header = tabLines[0].split("\t")
for cell in header:
if cell != "":
foundIds[cell] = 0
zf.close()
presentIds = []
exp = _get_all_children(self._node, "target")
for node in exp:
presentIds.append(node.attrib['id'])
for used_id in foundIds:
if used_id not in presentIds:
self.new_target(id=used_id, type="toi", newposition=0)
mess += "Recreated target: " + used_id + "\n"
return mess
def repair_rdml_file(self):
"""Searches for known errors and repairs them.
Args:
self: The class self parameter.
Returns:
A string with the modifications.
"""
mess = ""
mess += self.fixExclFalse()
mess += self.fixDuplicateReact()
return mess
def fixExclFalse(self):
"""Searches in experiment-run-react-data for excl=false and deletes the elements.
Args:
self: The class self parameter.
Returns:
A string with the modifications.
"""
mess = ""
count = 0
allExp = _get_all_children(self._node, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
reactNodes = _get_all_children(subNode, "react")
for reactNode in reactNodes:
dataNodes = _get_all_children(reactNode, "data")
for dataNode in dataNodes:
lastNodes = _get_all_children(dataNode, "excl")
for lastNode in lastNodes:
if lastNode.text.lower() == "false":
count += 1
dataNode.remove(lastNode)
if count > 0:
mess = "The element excl=false was removed " + str(count) + " times!\n"
return mess
def fixDuplicateReact(self):
"""Searches in experiment-run-react for duplicates and keeps only the first.
Args:
self: The class self parameter.
Returns:
A string with the modifications.
"""
mess = ""
foundIds = {}
count = 0
allExp = _get_all_children(self._node, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
reactNodes = _get_all_children(subNode, "react")
for reactNode in reactNodes:
tId = reactNode.attrib['id']
if tId not in foundIds:
foundIds[tId] = 0
else:
count += 1
subNode.remove(reactNode)
if count > 0:
mess = str(count) + " duplicate react elements were removed!\n"
return mess
def rdmlids(self):
"""Returns a list of all rdml id elements.
Args:
self: The class self parameter.
Returns:
A list of all rdml id elements.
"""
exp = _get_all_children(self._node, "id")
ret = []
for node in exp:
ret.append(Rdmlid(node))
return ret
def new_rdmlid(self, publisher, serialNumber, MD5Hash=None, newposition=None):
"""Creates a new rdml id element.
Args:
self: The class self parameter.
publisher: Publisher who created the serialNumber (required)
serialNumber: Serial Number for this file provided by publisher (required)
MD5Hash: A MD5 hash for this file (optional)
newposition: The new position of the element in the list (optional)
Returns:
Nothing, changes self.
"""
new_node = et.Element("id")
_add_new_subelement(new_node, "id", "publisher", publisher, False)
_add_new_subelement(new_node, "id", "serialNumber", serialNumber, False)
_add_new_subelement(new_node, "id", "MD5Hash", MD5Hash, True)
place = _get_tag_pos(self._node, "id", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def move_rdmlid(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "id", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "id", None, oldposition)
self._node.insert(pos, ele)
def get_rdmlid(self, byposition=None):
"""Returns an experimenter element by position or id.
Args:
self: The class self parameter.
byposition: Select the element by position in the list.
Returns:
The found element or None.
"""
return Rdmlid(_get_first_child_by_pos_or_id(self._node, "id", None, byposition))
def delete_rdmlid(self, byposition=None):
"""Deletes an experimenter element.
Args:
self: The class self parameter.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "id", None, byposition)
self._node.remove(elem)
def experimenters(self):
"""Returns a list of all experimenter elements.
Args:
self: The class self parameter.
Returns:
A list of all experimenter elements.
"""
exp = _get_all_children(self._node, "experimenter")
ret = []
for node in exp:
ret.append(Experimenter(node))
return ret
def new_experimenter(self, id, firstName, lastName, email=None, labName=None, labAddress=None, newposition=None):
"""Creates a new experimenter element.
Args:
self: The class self parameter.
id: Experimenter unique id
firstName: Experimenters first name (required)
lastName: Experimenters last name (required)
email: Experimenters email (optional)
labName: Experimenters lab name (optional)
labAddress: Experimenters lab address (optional)
newposition: Experimenters position in the list of experimenters (optional)
Returns:
Nothing, changes self.
"""
new_node = _create_new_element(self._node, "experimenter", id)
_add_new_subelement(new_node, "experimenter", "firstName", firstName, False)
_add_new_subelement(new_node, "experimenter", "lastName", lastName, False)
_add_new_subelement(new_node, "experimenter", "email", email, True)
_add_new_subelement(new_node, "experimenter", "labName", labName, True)
_add_new_subelement(new_node, "experimenter", "labAddress", labAddress, True)
place = _get_tag_pos(self._node, "experimenter", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def move_experimenter(self, id, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
id: Experimenter unique id
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
_move_subelement(self._node, "experimenter", id, self.xmlkeys(), newposition)
def get_experimenter(self, byid=None, byposition=None):
"""Returns an experimenter element by position or id.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
The found element or None.
"""
return Experimenter(_get_first_child_by_pos_or_id(self._node, "experimenter", byid, byposition))
def delete_experimenter(self, byid=None, byposition=None):
"""Deletes an experimenter element.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "experimenter", byid, byposition)
self._node.remove(elem)
def documentations(self):
"""Returns a list of all documentation elements.
Args:
self: The class self parameter.
Returns:
A list of all documentation elements.
"""
exp = _get_all_children(self._node, "documentation")
ret = []
for node in exp:
ret.append(Documentation(node))
return ret
def new_documentation(self, id, text=None, newposition=None):
"""Creates a new documentation element.
Args:
self: The class self parameter.
id: Documentation unique id
text: Documentation descriptive test (optional)
newposition: Experimenters position in the list of experimenters (optional)
Returns:
Nothing, changes self.
"""
new_node = _create_new_element(self._node, "documentation", id)
_add_new_subelement(new_node, "documentation", "text", text, True)
place = _get_tag_pos(self._node, "documentation", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def move_documentation(self, id, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
id: Documentation unique id
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
_move_subelement(self._node, "documentation", id, self.xmlkeys(), newposition)
def get_documentation(self, byid=None, byposition=None):
"""Returns an documentation element by position or id.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
The found element or None.
"""
return Documentation(_get_first_child_by_pos_or_id(self._node, "documentation", byid, byposition))
def delete_documentation(self, byid=None, byposition=None):
"""Deletes an documentation element.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "documentation", byid, byposition)
self._node.remove(elem)
def dyes(self):
"""Returns a list of all dye elements.
Args:
self: The class self parameter.
Returns:
A list of all dye elements.
"""
exp = _get_all_children(self._node, "dye")
ret = []
for node in exp:
ret.append(Dye(node))
return ret
def new_dye(self, id, description=None, newposition=None):
"""Creates a new dye element.
Args:
self: The class self parameter.
id: Dye unique id
description: Dye descriptive test (optional)
newposition: Dye position in the list of dyes (optional)
Returns:
Nothing, changes self.
"""
new_node = _create_new_element(self._node, "dye", id)
_add_new_subelement(new_node, "dye", "description", description, True)
place = _get_tag_pos(self._node, "dye", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def move_dye(self, id, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
id: Dye unique id
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
_move_subelement(self._node, "dye", id, self.xmlkeys(), newposition)
def get_dye(self, byid=None, byposition=None):
"""Returns an dye element by position or id.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
The found element or None.
"""
return Dye(_get_first_child_by_pos_or_id(self._node, "dye", byid, byposition))
def delete_dye(self, byid=None, byposition=None):
"""Deletes an dye element.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "dye", byid, byposition)
self._node.remove(elem)
def samples(self):
"""Returns a list of all sample elements.
Args:
self: The class self parameter.
Returns:
A list of all sample elements.
"""
exp = _get_all_children(self._node, "sample")
ret = []
for node in exp:
ret.append(Sample(node))
return ret
def new_sample(self, id, type, targetId=None, newposition=None):
"""Creates a new sample element.
Args:
self: The class self parameter.
id: Sample unique id (required)
type: Sample type (required)
targetId: The target linked to the type (makes sense in "pos" or "ntp" context) (optional)
newposition: Experimenters position in the list of experimenters (optional)
Returns:
Nothing, changes self.
"""
if type not in ["unkn", "ntc", "nac", "std", "ntp", "nrt", "pos", "opt"]:
raise RdmlError('Unknown or unsupported sample type value "' + type + '".')
new_node = _create_new_element(self._node, "sample", id)
typeEL = et.SubElement(new_node, "type")
typeEL.text = type
ver = self._node.get('version')
if ver == "1.3":
if targetId is not None:
if not targetId == "":
typeEL.attrib["targetId"] = targetId
place = _get_tag_pos(self._node, "sample", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def move_sample(self, id, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
id: Sample unique id
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
_move_subelement(self._node, "sample", id, self.xmlkeys(), newposition)
def get_sample(self, byid=None, byposition=None):
"""Returns an sample element by position or id.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
The found element or None.
"""
return Sample(_get_first_child_by_pos_or_id(self._node, "sample", byid, byposition))
def delete_sample(self, byid=None, byposition=None):
"""Deletes an sample element.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "sample", byid, byposition)
self._node.remove(elem)
def targets(self):
"""Returns a list of all target elements.
Args:
self: The class self parameter.
Returns:
A list of all target elements.
"""
exp = _get_all_children(self._node, "target")
ret = []
for node in exp:
ret.append(Target(node, self._rdmlFilename))
return ret
def new_target(self, id, type, newposition=None):
"""Creates a new target element.
Args:
self: The class self parameter.
id: Target unique id (required)
type: Target type (required)
newposition: Targets position in the list of targets (optional)
Returns:
Nothing, changes self.
"""
if type not in ["ref", "toi"]:
raise RdmlError('Unknown or unsupported target type value "' + type + '".')
new_node = _create_new_element(self._node, "target", id)
_add_new_subelement(new_node, "target", "type", type, False)
place = _get_tag_pos(self._node, "target", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def move_target(self, id, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
id: Target unique id
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
_move_subelement(self._node, "target", id, self.xmlkeys(), newposition)
def get_target(self, byid=None, byposition=None):
"""Returns an target element by position or id.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
The found element or None.
"""
return Target(_get_first_child_by_pos_or_id(self._node, "target", byid, byposition), self._rdmlFilename)
def delete_target(self, byid=None, byposition=None):
"""Deletes an target element.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "target", byid, byposition)
self._node.remove(elem)
def therm_cyc_cons(self):
"""Returns a list of all thermalCyclingConditions elements.
Args:
self: The class self parameter.
Returns:
A list of all target elements.
"""
exp = _get_all_children(self._node, "thermalCyclingConditions")
ret = []
for node in exp:
ret.append(Therm_cyc_cons(node))
return ret
def new_therm_cyc_cons(self, id, newposition=None):
"""Creates a new thermalCyclingConditions element.
Args:
self: The class self parameter.
id: ThermalCyclingConditions unique id (required)
newposition: ThermalCyclingConditions position in the list of ThermalCyclingConditions (optional)
Returns:
Nothing, changes self.
"""
new_node = _create_new_element(self._node, "thermalCyclingConditions", id)
step = et.SubElement(new_node, "step")
et.SubElement(step, "nr").text = "1"
et.SubElement(step, "lidOpen")
place = _get_tag_pos(self._node, "thermalCyclingConditions", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def move_therm_cyc_cons(self, id, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
id: ThermalCyclingConditions unique id
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
_move_subelement(self._node, "thermalCyclingConditions", id, self.xmlkeys(), newposition)
def get_therm_cyc_cons(self, byid=None, byposition=None):
"""Returns an thermalCyclingConditions element by position or id.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
The found element or None.
"""
return Therm_cyc_cons(_get_first_child_by_pos_or_id(self._node, "thermalCyclingConditions", byid, byposition))
def delete_therm_cyc_cons(self, byid=None, byposition=None):
"""Deletes an thermalCyclingConditions element.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "thermalCyclingConditions", byid, byposition)
self._node.remove(elem)
def experiments(self):
"""Returns a list of all experiment elements.
Args:
self: The class self parameter.
Returns:
A list of all experiment elements.
"""
exp = _get_all_children(self._node, "experiment")
ret = []
for node in exp:
ret.append(Experiment(node, self._rdmlFilename))
return ret
def new_experiment(self, id, newposition=None):
"""Creates a new experiment element.
Args:
self: The class self parameter.
id: Experiment unique id (required)
newposition: Experiment position in the list of experiments (optional)
Returns:
Nothing, changes self.
"""
new_node = _create_new_element(self._node, "experiment", id)
place = _get_tag_pos(self._node, "experiment", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def move_experiment(self, id, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
id: Experiments unique id
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
_move_subelement(self._node, "experiment", id, self.xmlkeys(), newposition)
def get_experiment(self, byid=None, byposition=None):
"""Returns an experiment element by position or id.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
The found element or None.
"""
return Experiment(_get_first_child_by_pos_or_id(self._node, "experiment", byid, byposition), self._rdmlFilename)
def delete_experiment(self, byid=None, byposition=None):
"""Deletes an experiment element.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "experiment", byid, byposition)
experiment = Experiment(elem, self._rdmlFilename)
# Required to delete digital files
runs = _get_all_children(elem, "run")
for node in runs:
run = Run(node, self._rdmlFilename)
experiment.delete_run(byid=run["id"])
# Now delete the experiment element
self._node.remove(elem)
def tojson(self):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
allRdmlids = self.rdmlids()
rdmlids = []
for elem in allRdmlids:
rdmlids.append(elem.tojson())
allExperimenters = self.experimenters()
experimenters = []
for exp in allExperimenters:
experimenters.append(exp.tojson())
allDocumentations = self.documentations()
documentations = []
for exp in allDocumentations:
documentations.append(exp.tojson())
allDyes = self.dyes()
dyes = []
for exp in allDyes:
dyes.append(exp.tojson())
allSamples = self.samples()
samples = []
for exp in allSamples:
samples.append(exp.tojson())
allTargets = self.targets()
targets = []
for exp in allTargets:
targets.append(exp.tojson())
allTherm_cyc_cons = self.therm_cyc_cons()
therm_cyc_cons = []
for exp in allTherm_cyc_cons:
therm_cyc_cons.append(exp.tojson())
allExperiments = self.experiments()
experiments = []
for exp in allExperiments:
experiments.append(exp.tojson())
data = {
"rdml": {
"version": self["version"],
"dateMade": self["dateMade"],
"dateUpdated": self["dateUpdated"],
"ids": rdmlids,
"experimenters": experimenters,
"documentations": documentations,
"dyes": dyes,
"samples": samples,
"targets": targets,
"therm_cyc_cons": therm_cyc_cons,
"experiments": experiments
}
}
return data
class Rdmlid:
"""RDML-Python library
The rdml id element used to read and edit one experimenter.
Attributes:
_node: The rdml id node of the RDML XML object.
"""
def __init__(self, node):
"""Inits an rdml id instance.
Args:
self: The class self parameter.
node: The experimenter node.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._node = node
def __getitem__(self, key):
"""Returns the value for the key.
Args:
self: The class self parameter.
key: The key of the experimenter subelement
Returns:
A string of the data or None.
"""
if key in ["publisher", "serialNumber"]:
return _get_first_child_text(self._node, key)
if key in ["MD5Hash"]:
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
raise KeyError
def __setitem__(self, key, value):
"""Changes the value for the key.
Args:
self: The class self parameter.
key: The key of the experimenter subelement
value: The new value for the key
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
if key in ["publisher", "serialNumber"]:
return _change_subelement(self._node, key, self.xmlkeys(), value, False, "string")
if key in ["MD5Hash"]:
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
raise KeyError
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["publisher", "serialNumber", "MD5Hash"]
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return self.keys()
def tojson(self):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
data = {
"publisher": _get_first_child_text(self._node, "publisher"),
"serialNumber": _get_first_child_text(self._node, "serialNumber")
}
_add_first_child_to_dic(self._node, data, True, "MD5Hash")
return data
class Experimenter:
"""RDML-Python library
The experimenter element used to read and edit one experimenter.
Attributes:
_node: The experimenter node of the RDML XML object.
"""
def __init__(self, node):
"""Inits an experimenter instance.
Args:
self: The class self parameter.
node: The experimenter node.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._node = node
def __getitem__(self, key):
"""Returns the value for the key.
Args:
self: The class self parameter.
key: The key of the experimenter subelement
Returns:
A string of the data or None.
"""
if key == "id":
return self._node.get('id')
if key in ["firstName", "lastName"]:
return _get_first_child_text(self._node, key)
if key in ["email", "labName", "labAddress"]:
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
raise KeyError
def __setitem__(self, key, value):
"""Changes the value for the key.
Args:
self: The class self parameter.
key: The key of the experimenter subelement
value: The new value for the key
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
if key == "id":
self.change_id(value, merge_with_id=False)
return
if key in ["firstName", "lastName"]:
return _change_subelement(self._node, key, self.xmlkeys(), value, False, "string")
if key in ["email", "labName", "labAddress"]:
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
raise KeyError
def change_id(self, value, merge_with_id=False):
"""Changes the value for the id.
Args:
self: The class self parameter.
value: The new value for the id.
merge_with_id: If True only allow a unique id, if False only rename its uses with existing id.
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
oldValue = self._node.get('id')
if oldValue != value:
par = self._node.getparent()
if not _string_to_bool(merge_with_id, triple=False):
_change_subelement(self._node, "id", self.xmlkeys(), value, False, "string")
else:
groupTag = self._node.tag.replace("{http://www.rdml.org}", "")
if _check_unique_id(par, groupTag, value):
raise RdmlError('The ' + groupTag + ' id "' + value + '" does not exist.')
allTh = _get_all_children(par, "thermalCyclingConditions")
for node in allTh:
subNodes = _get_all_children(node, "experimenter")
for subNode in subNodes:
if subNode.attrib['id'] == oldValue:
subNode.attrib['id'] = value
allExp = _get_all_children(par, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
lastNodes = _get_all_children(subNode, "experimenter")
for lastNode in lastNodes:
if lastNode.attrib['id'] == oldValue:
lastNode.attrib['id'] = value
return
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["id", "firstName", "lastName", "email", "labName", "labAddress"]
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return self.keys()
def tojson(self):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
data = {
"id": self._node.get('id'),
"firstName": _get_first_child_text(self._node, "firstName"),
"lastName": _get_first_child_text(self._node, "lastName")
}
_add_first_child_to_dic(self._node, data, True, "email")
_add_first_child_to_dic(self._node, data, True, "labName")
_add_first_child_to_dic(self._node, data, True, "labAddress")
return data
class Documentation:
"""RDML-Python library
The documentation element used to read and edit one documentation tag.
Attributes:
_node: The documentation node of the RDML XML object.
"""
def __init__(self, node):
"""Inits an documentation instance.
Args:
self: The class self parameter.
node: The documentation node.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._node = node
def __getitem__(self, key):
"""Returns the value for the key.
Args:
self: The class self parameter.
key: The key of the documentation subelement
Returns:
A string of the data or None.
"""
if key == "id":
return self._node.get('id')
if key == "text":
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
raise KeyError
def __setitem__(self, key, value):
"""Changes the value for the key.
Args:
self: The class self parameter.
key: The key of the documentation subelement
value: The new value for the key
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
if key == "id":
self.change_id(value, merge_with_id=False)
return
if key == "text":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
raise KeyError
def change_id(self, value, merge_with_id=False):
"""Changes the value for the id.
Args:
self: The class self parameter.
value: The new value for the id.
merge_with_id: If True only allow a unique id, if False only rename its uses with existing id.
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
oldValue = self._node.get('id')
if oldValue != value:
par = self._node.getparent()
if not _string_to_bool(merge_with_id, triple=False):
_change_subelement(self._node, "id", self.xmlkeys(), value, False, "string")
else:
groupTag = self._node.tag.replace("{http://www.rdml.org}", "")
if _check_unique_id(par, groupTag, value):
raise RdmlError('The ' + groupTag + ' id "' + value + '" does not exist.')
allSam = _get_all_children(par, "sample")
for node in allSam:
subNodes = _get_all_children(node, "documentation")
for subNode in subNodes:
if subNode.attrib['id'] == oldValue:
subNode.attrib['id'] = value
allTh = _get_all_children(par, "target")
for node in allTh:
subNodes = _get_all_children(node, "documentation")
for subNode in subNodes:
if subNode.attrib['id'] == oldValue:
subNode.attrib['id'] = value
allTh = _get_all_children(par, "thermalCyclingConditions")
for node in allTh:
subNodes = _get_all_children(node, "documentation")
for subNode in subNodes:
if subNode.attrib['id'] == oldValue:
subNode.attrib['id'] = value
allExp = _get_all_children(par, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "documentation")
for subNode in subNodes:
if subNode.attrib['id'] == oldValue:
subNode.attrib['id'] = value
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
lastNodes = _get_all_children(subNode, "documentation")
for lastNode in lastNodes:
if lastNode.attrib['id'] == oldValue:
lastNode.attrib['id'] = value
return
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["id", "text"]
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return self.keys()
def tojson(self):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
data = {
"id": self._node.get('id'),
}
_add_first_child_to_dic(self._node, data, True, "text")
return data
class Dye:
"""RDML-Python library
The dye element used to read and edit one dye.
Attributes:
_node: The dye node of the RDML XML object.
"""
def __init__(self, node):
"""Inits an dye instance.
Args:
self: The class self parameter.
node: The dye node.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._node = node
def __getitem__(self, key):
"""Returns the value for the key.
Args:
self: The class self parameter.
key: The key of the dye subelement
Returns:
A string of the data or None.
"""
if key == "id":
return self._node.get('id')
if key in ["description", "dyeChemistry"]:
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
raise KeyError
def __setitem__(self, key, value):
"""Changes the value for the key.
Args:
self: The class self parameter.
key: The key of the dye subelement
value: The new value for the key
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
if key == "dyeChemistry":
if value not in ["non-saturating DNA binding dye", "saturating DNA binding dye", "hybridization probe",
"hydrolysis probe", "labelled forward primer", "labelled reverse primer",
"DNA-zyme probe"]:
raise RdmlError('Unknown or unsupported sample type value "' + value + '".')
if key == "id":
self.change_id(value, merge_with_id=False)
return
if key == "description":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
par = self._node.getparent()
ver = par.get('version')
if ver == "1.3":
if key == "dyeChemistry":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
raise KeyError
def change_id(self, value, merge_with_id=False):
"""Changes the value for the id.
Args:
self: The class self parameter.
value: The new value for the id.
merge_with_id: If True only allow a unique id, if False only rename its uses with existing id.
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
oldValue = self._node.get('id')
if oldValue != value:
par = self._node.getparent()
if not _string_to_bool(merge_with_id, triple=False):
_change_subelement(self._node, "id", self.xmlkeys(), value, False, "string")
else:
groupTag = self._node.tag.replace("{http://www.rdml.org}", "")
if _check_unique_id(par, groupTag, value):
raise RdmlError('The ' + groupTag + ' id "' + value + '" does not exist.')
allTar = _get_all_children(par, "target")
for node in allTar:
forId = _get_first_child(node, "dyeId")
if forId is not None:
if forId.attrib['id'] == oldValue:
forId.attrib['id'] = value
return
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["id", "description", "dyeChemistry"]
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return self.keys()
def tojson(self):
"""Returns a json of the RDML object.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
data = {
"id": self._node.get('id'),
}
_add_first_child_to_dic(self._node, data, True, "description")
_add_first_child_to_dic(self._node, data, True, "dyeChemistry")
return data
class Sample:
"""RDML-Python library
The samples element used to read and edit one sample.
Attributes:
_node: The sample node of the RDML XML object.
"""
def __init__(self, node):
"""Inits an sample instance.
Args:
self: The class self parameter.
node: The sample node.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._node = node
def __getitem__(self, key):
"""Returns the value for the key.
Args:
self: The class self parameter.
key: The key of the sample subelement
Returns:
A string of the data or None.
"""
if key == "id":
return self._node.get('id')
if key == "description":
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
if key in ["interRunCalibrator", "calibratorSample"]:
return _get_first_child_bool(self._node, key, triple=True)
if key in ["cdnaSynthesisMethod_enzyme", "cdnaSynthesisMethod_primingMethod",
"cdnaSynthesisMethod_dnaseTreatment", "cdnaSynthesisMethod_thermalCyclingConditions"]:
ele = _get_first_child(self._node, "cdnaSynthesisMethod")
if ele is None:
return None
if key == "cdnaSynthesisMethod_enzyme":
return _get_first_child_text(ele, "enzyme")
if key == "cdnaSynthesisMethod_primingMethod":
return _get_first_child_text(ele, "primingMethod")
if key == "cdnaSynthesisMethod_dnaseTreatment":
return _get_first_child_text(ele, "dnaseTreatment")
if key == "cdnaSynthesisMethod_thermalCyclingConditions":
forId = _get_first_child(ele, "thermalCyclingConditions")
if forId is not None:
return forId.attrib['id']
else:
return None
raise RdmlError('Sample cdnaSynthesisMethod programming read error.')
if key == "quantity":
ele = _get_first_child(self._node, key)
vdic = {}
vdic["value"] = _get_first_child_text(ele, "value")
vdic["unit"] = _get_first_child_text(ele, "unit")
if len(vdic.keys()) != 0:
return vdic
else:
return None
par = self._node.getparent()
ver = par.get('version')
if ver == "1.1":
if key in ["templateRNAQuality", "templateDNAQuality"]:
ele = _get_first_child(self._node, key)
vdic = {}
vdic["method"] = _get_first_child_text(ele, "method")
vdic["result"] = _get_first_child_text(ele, "result")
if len(vdic.keys()) != 0:
return vdic
else:
return None
if key in ["templateRNAQuantity", "templateDNAQuantity"]:
ele = _get_first_child(self._node, key)
vdic = {}
vdic["value"] = _get_first_child_text(ele, "value")
vdic["unit"] = _get_first_child_text(ele, "unit")
if len(vdic.keys()) != 0:
return vdic
else:
return None
if ver == "1.2" or ver == "1.3":
if key == "templateQuantity":
ele = _get_first_child(self._node, key)
vdic = {}
vdic["nucleotide"] = _get_first_child_text(ele, "nucleotide")
vdic["conc"] = _get_first_child_text(ele, "conc")
if len(vdic.keys()) != 0:
return vdic
else:
return None
raise KeyError
def __setitem__(self, key, value):
"""Changes the value for the key.
Args:
self: The class self parameter.
key: The key of the sample subelement
value: The new value for the key
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
if key == "id":
self.change_id(value, merge_with_id=False)
return
if key == "description":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
if key in ["interRunCalibrator", "calibratorSample"]:
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "bool")
if key in ["cdnaSynthesisMethod_enzyme", "cdnaSynthesisMethod_primingMethod",
"cdnaSynthesisMethod_dnaseTreatment", "cdnaSynthesisMethod_thermalCyclingConditions"]:
ele = _get_or_create_subelement(self._node, "cdnaSynthesisMethod", self.xmlkeys())
if key == "cdnaSynthesisMethod_enzyme":
_change_subelement(ele, "enzyme",
["enzyme", "primingMethod", "dnaseTreatment", "thermalCyclingConditions"],
value, True, "string")
if key == "cdnaSynthesisMethod_primingMethod":
if value not in ["", "oligo-dt", "random", "target-specific", "oligo-dt and random", "other"]:
raise RdmlError('Unknown or unsupported sample ' + key + ' value "' + value + '".')
_change_subelement(ele, "primingMethod",
["enzyme", "primingMethod", "dnaseTreatment", "thermalCyclingConditions"],
value, True, "string")
if key == "cdnaSynthesisMethod_dnaseTreatment":
_change_subelement(ele, "dnaseTreatment",
["enzyme", "primingMethod", "dnaseTreatment", "thermalCyclingConditions"],
value, True, "bool")
if key == "cdnaSynthesisMethod_thermalCyclingConditions":
forId = _get_or_create_subelement(ele, "thermalCyclingConditions",
["enzyme", "primingMethod", "dnaseTreatment",
"thermalCyclingConditions"])
if value is not None and value != "":
# We do not check that ID is valid to allow recreate_lost_ids()
forId.attrib['id'] = value
else:
ele.remove(forId)
_remove_irrelevant_subelement(self._node, "cdnaSynthesisMethod")
return
if key == "quantity":
if value is None:
return
if "value" not in value or "unit" not in value:
raise RdmlError('Sample ' + key + ' must have a dictionary with "value" and "unit" as value.')
if value["unit"] not in ["", "cop", "fold", "dil", "ng", "nMol", "other"]:
raise RdmlError('Unknown or unsupported sample ' + key + ' value "' + value + '".')
ele = _get_or_create_subelement(self._node, key, self.xmlkeys())
_change_subelement(ele, "value", ["value", "unit"], value["value"], True, "float")
if value["value"] != "":
_change_subelement(ele, "unit", ["value", "unit"], value["unit"], True, "string")
else:
_change_subelement(ele, "unit", ["value", "unit"], "", True, "string")
_remove_irrelevant_subelement(self._node, key)
return
par = self._node.getparent()
ver = par.get('version')
if ver == "1.1":
if key in ["templateRNAQuality", "templateDNAQuality"]:
if value is None:
return
if "method" not in value or "result" not in value:
raise RdmlError('"' + key + '" must have a dictionary with "method" and "result" as value.')
ele = _get_or_create_subelement(self._node, key, self.xmlkeys())
_change_subelement(ele, "method", ["method", "result"], value["method"], True, "string")
_change_subelement(ele, "result", ["method", "result"], value["result"], True, "float")
_remove_irrelevant_subelement(self._node, key)
return
if key in ["templateRNAQuantity", "templateDNAQuantity"]:
if value is None:
return
if "value" not in value or "unit" not in value:
raise RdmlError('Sample ' + key + ' must have a dictionary with "value" and "unit" as value.')
if value["unit"] not in ["", "cop", "fold", "dil", "ng", "nMol", "other"]:
raise RdmlError('Unknown or unsupported sample ' + key + ' value "' + value + '".')
ele = _get_or_create_subelement(self._node, key, self.xmlkeys())
_change_subelement(ele, "value", ["value", "unit"], value["value"], True, "float")
if value["value"] != "":
_change_subelement(ele, "unit", ["value", "unit"], value["unit"], True, "string")
else:
_change_subelement(ele, "unit", ["value", "unit"], "", True, "string")
_remove_irrelevant_subelement(self._node, key)
return
if ver == "1.2" or ver == "1.3":
if key == "templateQuantity":
if value is None:
return
if "nucleotide" not in value or "conc" not in value:
raise RdmlError('Sample ' + key + ' must have a dictionary with "nucleotide" and "conc" as value.')
if value["nucleotide"] not in ["", "DNA", "genomic DNA", "cDNA", "RNA"]:
raise RdmlError('Unknown or unsupported sample ' + key + ' value "' + value + '".')
ele = _get_or_create_subelement(self._node, key, self.xmlkeys())
_change_subelement(ele, "conc", ["conc", "nucleotide"], value["conc"], True, "float")
if value["conc"] != "":
_change_subelement(ele, "nucleotide", ["conc", "nucleotide"], value["nucleotide"], True, "string")
else:
_change_subelement(ele, "nucleotide", ["conc", "nucleotide"], "", True, "string")
_remove_irrelevant_subelement(self._node, key)
return
raise KeyError
def change_id(self, value, merge_with_id=False):
"""Changes the value for the id.
Args:
self: The class self parameter.
value: The new value for the id.
merge_with_id: If True only allow a unique id, if False only rename its uses with existing id.
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
oldValue = self._node.get('id')
if oldValue != value:
par = self._node.getparent()
if not _string_to_bool(merge_with_id, triple=False):
_change_subelement(self._node, "id", self.xmlkeys(), value, False, "string")
else:
groupTag = self._node.tag.replace("{http://www.rdml.org}", "")
if _check_unique_id(par, groupTag, value):
raise RdmlError('The ' + groupTag + ' id "' + value + '" does not exist.')
allExp = _get_all_children(par, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
reactNodes = _get_all_children(subNode, "react")
for reactNode in reactNodes:
lastNodes = _get_all_children(reactNode, "sample")
for lastNode in lastNodes:
if lastNode.attrib['id'] == oldValue:
lastNode.attrib['id'] = value
return
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
par = self._node.getparent()
ver = par.get('version')
if ver == "1.1":
return ["id", "description", "interRunCalibrator", "quantity", "calibratorSample",
"cdnaSynthesisMethod_enzyme", "cdnaSynthesisMethod_primingMethod",
"cdnaSynthesisMethod_dnaseTreatment", "cdnaSynthesisMethod_thermalCyclingConditions",
"templateRNAQuantity", "templateRNAQuality", "templateDNAQuantity", "templateDNAQuality"]
return ["id", "description", "annotation", "interRunCalibrator", "quantity", "calibratorSample",
"cdnaSynthesisMethod_enzyme", "cdnaSynthesisMethod_primingMethod",
"cdnaSynthesisMethod_dnaseTreatment", "cdnaSynthesisMethod_thermalCyclingConditions",
"templateQuantity"]
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
par = self._node.getparent()
ver = par.get('version')
if ver == "1.1":
return ["description", "documentation", "xRef", "type", "interRunCalibrator",
"quantity", "calibratorSample", "cdnaSynthesisMethod",
"templateRNAQuantity", "templateRNAQuality", "templateDNAQuantity", "templateDNAQuality"]
return ["description", "documentation", "xRef", "annotation", "type", "interRunCalibrator",
"quantity", "calibratorSample", "cdnaSynthesisMethod", "templateQuantity"]
def types(self):
"""Returns a list of the types in the xml file.
Args:
self: The class self parameter.
Returns:
A list of dics with type and id strings.
"""
typesList = _get_all_children(self._node, "type")
ret = []
for node in typesList:
data = {}
data["type"] = node.text
if "targetId" in node.attrib:
data["targetId"] = node.attrib["targetId"]
else:
data["targetId"] = ""
ret.append(data)
return ret
def new_type(self, type, targetId=None, newposition=None):
"""Creates a new type element.
Args:
self: The class self parameter.
type: The "unkn", "ntc", "nac", "std", "ntp", "nrt", "pos" or "opt" type of sample
targetId: The target linked to the type (makes sense in "pos" or "ntp" context)
newposition: The new position of the element
Returns:
Nothing, changes self.
"""
if type not in ["unkn", "ntc", "nac", "std", "ntp", "nrt", "pos", "opt"]:
raise RdmlError('Unknown or unsupported sample type value "' + type + '".')
new_node = et.Element("type")
new_node.text = type
par = self._node.getparent()
ver = par.get('version')
if ver == "1.3":
if targetId is not None:
if not targetId == "":
new_node.attrib["targetId"] = targetId
place = _get_tag_pos(self._node, "type", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def edit_type(self, type, oldposition, newposition=None, targetId=None):
"""Edits a type element.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
type: The "unkn", "ntc", "nac", "std", "ntp", "nrt", "pos" or "opt" type of sample
targetId: The target linked to the type (makes sense in "pos" or "ntp" context)
Returns:
Nothing, changes self.
"""
if type not in ["unkn", "ntc", "nac", "std", "ntp", "nrt", "pos", "opt"]:
raise RdmlError('Unknown or unsupported sample type value "' + type + '".')
if oldposition is None:
raise RdmlError('A oldposition is required to edit a type.')
pos = _get_tag_pos(self._node, "type", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "type", None, oldposition)
ele.text = type
par = self._node.getparent()
ver = par.get('version')
if "targetId" in ele.attrib:
del ele.attrib["targetId"]
if ver == "1.3":
if targetId is not None:
if not targetId == "":
ele.attrib["targetId"] = targetId
self._node.insert(pos, ele)
def move_type(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "type", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "type", None, oldposition)
self._node.insert(pos, ele)
def delete_type(self, byposition):
"""Deletes an type element.
Args:
self: The class self parameter.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
ls = self.types()
if len(ls) < 2:
return
elem = _get_first_child_by_pos_or_id(self._node, "type", None, byposition)
self._node.remove(elem)
def xrefs(self):
"""Returns a list of the xrefs in the xml file.
Args:
self: The class self parameter.
Returns:
A list of dics with name and id strings.
"""
xref = _get_all_children(self._node, "xRef")
ret = []
for node in xref:
data = {}
_add_first_child_to_dic(node, data, True, "name")
_add_first_child_to_dic(node, data, True, "id")
ret.append(data)
return ret
def new_xref(self, name=None, id=None, newposition=None):
"""Creates a new xrefs element.
Args:
self: The class self parameter.
name: Publisher who created the xRef
id: Serial Number for this sample provided by publisher
newposition: The new position of the element
Returns:
Nothing, changes self.
"""
if name is None and id is None:
raise RdmlError('Either name or id is required to create a xRef.')
new_node = et.Element("xRef")
_add_new_subelement(new_node, "xRef", "name", name, True)
_add_new_subelement(new_node, "xRef", "id", id, True)
place = _get_tag_pos(self._node, "xRef", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def edit_xref(self, oldposition, newposition=None, name=None, id=None):
"""Creates a new xrefs element.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
name: Publisher who created the xRef
id: Serial Number for this sample provided by publisher
Returns:
Nothing, changes self.
"""
if oldposition is None:
raise RdmlError('A oldposition is required to edit a xRef.')
if (name is None or name == "") and (id is None or id == ""):
self.delete_xref(oldposition)
return
pos = _get_tag_pos(self._node, "xRef", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "xRef", None, oldposition)
_change_subelement(ele, "name", ["name", "id"], name, True, "string")
_change_subelement(ele, "id", ["name", "id"], id, True, "string", id_as_element=True)
self._node.insert(pos, ele)
def move_xref(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "xRef", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "xRef", None, oldposition)
self._node.insert(pos, ele)
def delete_xref(self, byposition):
"""Deletes an experimenter element.
Args:
self: The class self parameter.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "xRef", None, byposition)
self._node.remove(elem)
def annotations(self):
"""Returns a list of the annotations in the xml file.
Args:
self: The class self parameter.
Returns:
A list of dics with property and value strings.
"""
par = self._node.getparent()
ver = par.get('version')
if ver == "1.1":
return []
xref = _get_all_children(self._node, "annotation")
ret = []
for node in xref:
data = {}
_add_first_child_to_dic(node, data, True, "property")
_add_first_child_to_dic(node, data, True, "value")
ret.append(data)
return ret
def new_annotation(self, property=None, value=None, newposition=None):
"""Creates a new annotation element.
Args:
self: The class self parameter.
property: The property
value: Its value
newposition: The new position of the element
Returns:
Nothing, changes self.
"""
par = self._node.getparent()
ver = par.get('version')
if ver == "1.1":
return
if property is None or value is None:
raise RdmlError('Property and value are required to create a annotation.')
new_node = et.Element("annotation")
_add_new_subelement(new_node, "annotation", "property", property, True)
_add_new_subelement(new_node, "annotation", "value", value, True)
place = _get_tag_pos(self._node, "annotation", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def edit_annotation(self, oldposition, newposition=None, property=None, value=None):
"""Edits an annotation element.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
property: The property
value: Its value
Returns:
Nothing, changes self.
"""
par = self._node.getparent()
ver = par.get('version')
if ver == "1.1":
return
if oldposition is None:
raise RdmlError('A oldposition is required to edit a annotation.')
if (property is None or property == "") or (value is None or value == ""):
self.delete_annotation(oldposition)
return
pos = _get_tag_pos(self._node, "annotation", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "annotation", None, oldposition)
_change_subelement(ele, "property", ["property", "value"], property, True, "string")
_change_subelement(ele, "value", ["property", "value"], value, True, "string")
self._node.insert(pos, ele)
def move_annotation(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
par = self._node.getparent()
ver = par.get('version')
if ver == "1.1":
return
pos = _get_tag_pos(self._node, "annotation", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "annotation", None, oldposition)
self._node.insert(pos, ele)
def delete_annotation(self, byposition):
"""Deletes an annotation element.
Args:
self: The class self parameter.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
par = self._node.getparent()
ver = par.get('version')
if ver == "1.1":
return
elem = _get_first_child_by_pos_or_id(self._node, "annotation", None, byposition)
self._node.remove(elem)
def documentation_ids(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return _get_all_children_id(self._node, "documentation")
def update_documentation_ids(self, ids):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
ids: A dictionary with id and true/false pairs
Returns:
True if a change was made, else false. Function may raise RdmlError if required.
"""
old = self.documentation_ids()
good_ids = _value_to_booldic(ids)
mod = False
for id, inc in good_ids.items():
if inc is True:
if id not in old:
new_node = _create_new_element(self._node, "documentation", id)
place = _get_tag_pos(self._node, "documentation", self.xmlkeys(), 999999999)
self._node.insert(place, new_node)
mod = True
else:
if id in old:
elem = _get_first_child_by_pos_or_id(self._node, "documentation", id, None)
self._node.remove(elem)
mod = True
return mod
def move_documentation(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "documentation", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "documentation", None, oldposition)
self._node.insert(pos, ele)
def tojson(self):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
par = self._node.getparent()
ver = par.get('version')
data = {
"id": self._node.get('id'),
}
_add_first_child_to_dic(self._node, data, True, "description")
data["documentations"] = self.documentation_ids()
data["xRefs"] = self.xrefs()
if ver == "1.2" or ver == "1.3":
data["annotations"] = self.annotations()
data["types"] = self.types()
_add_first_child_to_dic(self._node, data, True, "interRunCalibrator")
elem = _get_first_child(self._node, "quantity")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "value")
_add_first_child_to_dic(elem, qdic, False, "unit")
data["quantity"] = qdic
_add_first_child_to_dic(self._node, data, True, "calibratorSample")
elem = _get_first_child(self._node, "cdnaSynthesisMethod")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, True, "enzyme")
_add_first_child_to_dic(elem, qdic, True, "primingMethod")
_add_first_child_to_dic(elem, qdic, True, "dnaseTreatment")
forId = _get_first_child(elem, "thermalCyclingConditions")
if forId is not None:
if forId.attrib['id'] != "":
qdic["thermalCyclingConditions"] = forId.attrib['id']
if len(qdic.keys()) != 0:
data["cdnaSynthesisMethod"] = qdic
if ver == "1.1":
elem = _get_first_child(self._node, "templateRNAQuantity")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "value")
_add_first_child_to_dic(elem, qdic, False, "unit")
data["templateRNAQuantity"] = qdic
elem = _get_first_child(self._node, "templateRNAQuality")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "method")
_add_first_child_to_dic(elem, qdic, False, "result")
data["templateRNAQuality"] = qdic
elem = _get_first_child(self._node, "templateDNAQuantity")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "value")
_add_first_child_to_dic(elem, qdic, False, "unit")
data["templateDNAQuantity"] = qdic
elem = _get_first_child(self._node, "templateDNAQuality")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "method")
_add_first_child_to_dic(elem, qdic, False, "result")
data["templateDNAQuality"] = qdic
if ver == "1.2" or ver == "1.3":
elem = _get_first_child(self._node, "templateQuantity")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "nucleotide")
_add_first_child_to_dic(elem, qdic, False, "conc")
data["templateQuantity"] = qdic
return data
class Target:
"""RDML-Python library
The target element used to read and edit one target.
Attributes:
_node: The target node of the RDML XML object.
_rdmlFilename: The RDML filename
"""
def __init__(self, node, rdmlFilename):
"""Inits an target instance.
Args:
self: The class self parameter.
node: The target node.
rdmlFilename: The RDML filename.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._node = node
self._rdmlFilename = rdmlFilename
def __getitem__(self, key):
"""Returns the value for the key.
Args:
self: The class self parameter.
key: The key of the target subelement
Returns:
A string of the data or None.
"""
if key == "id":
return self._node.get('id')
if key == "type":
return _get_first_child_text(self._node, key)
if key in ["description", "amplificationEfficiencyMethod", "amplificationEfficiency",
"amplificationEfficiencySE", "meltingTemperature", "detectionLimit"]:
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
if key == "dyeId":
forId = _get_first_child(self._node, key)
if forId is not None:
return forId.attrib['id']
else:
return None
if key in ["sequences_forwardPrimer_threePrimeTag", "sequences_forwardPrimer_fivePrimeTag",
"sequences_forwardPrimer_sequence", "sequences_reversePrimer_threePrimeTag",
"sequences_reversePrimer_fivePrimeTag", "sequences_reversePrimer_sequence",
"sequences_probe1_threePrimeTag", "sequences_probe1_fivePrimeTag",
"sequences_probe1_sequence", "sequences_probe2_threePrimeTag",
"sequences_probe2_fivePrimeTag", "sequences_probe2_sequence",
"sequences_amplicon_threePrimeTag", "sequences_amplicon_fivePrimeTag",
"sequences_amplicon_sequence"]:
prim = _get_first_child(self._node, "sequences")
if prim is None:
return None
sec = None
if key in ["sequences_forwardPrimer_threePrimeTag", "sequences_forwardPrimer_fivePrimeTag",
"sequences_forwardPrimer_sequence"]:
sec = _get_first_child(prim, "forwardPrimer")
if key in ["sequences_reversePrimer_threePrimeTag", "sequences_reversePrimer_fivePrimeTag",
"sequences_reversePrimer_sequence"]:
sec = _get_first_child(prim, "reversePrimer")
if key in ["sequences_probe1_threePrimeTag", "sequences_probe1_fivePrimeTag", "sequences_probe1_sequence"]:
sec = _get_first_child(prim, "probe1")
if key in ["sequences_probe2_threePrimeTag", "sequences_probe2_fivePrimeTag", "sequences_probe2_sequence"]:
sec = _get_first_child(prim, "probe2")
if key in ["sequences_amplicon_threePrimeTag", "sequences_amplicon_fivePrimeTag",
"sequences_amplicon_sequence"]:
sec = _get_first_child(prim, "amplicon")
if sec is None:
return None
if key in ["sequences_forwardPrimer_threePrimeTag", "sequences_reversePrimer_threePrimeTag",
"sequences_probe1_threePrimeTag", "sequences_probe2_threePrimeTag",
"sequences_amplicon_threePrimeTag"]:
return _get_first_child_text(sec, "threePrimeTag")
if key in ["sequences_forwardPrimer_fivePrimeTag", "sequences_reversePrimer_fivePrimeTag",
"sequences_probe1_fivePrimeTag", "sequences_probe2_fivePrimeTag",
"sequences_amplicon_fivePrimeTag"]:
return _get_first_child_text(sec, "fivePrimeTag")
if key in ["sequences_forwardPrimer_sequence", "sequences_reversePrimer_sequence",
"sequences_probe1_sequence", "sequences_probe2_sequence",
"sequences_amplicon_sequence"]:
return _get_first_child_text(sec, "sequence")
raise RdmlError('Target sequences programming read error.')
if key in ["commercialAssay_company", "commercialAssay_orderNumber"]:
prim = _get_first_child(self._node, "commercialAssay")
if prim is None:
return None
if key == "commercialAssay_company":
return _get_first_child_text(prim, "company")
if key == "commercialAssay_orderNumber":
return _get_first_child_text(prim, "orderNumber")
par = self._node.getparent()
ver = par.get('version')
if ver == "1.2" or ver == "1.3":
if key == "amplificationEfficiencySE":
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
raise KeyError
def __setitem__(self, key, value):
"""Changes the value for the key.
Args:
self: The class self parameter.
key: The key of the target subelement
value: The new value for the key
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
par = self._node.getparent()
ver = par.get('version')
if key == "type":
if value not in ["ref", "toi"]:
raise RdmlError('Unknown or unsupported target type value "' + value + '".')
if key == "id":
self.change_id(value, merge_with_id=False)
return
if key == "type":
return _change_subelement(self._node, key, self.xmlkeys(), value, False, "string")
if key in ["description", "amplificationEfficiencyMethod"]:
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
if key in ["amplificationEfficiency", "detectionLimit"]:
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "float")
if ver == "1.2" or ver == "1.3":
if key == "amplificationEfficiencySE":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "float")
if ver == "1.3":
if key == "meltingTemperature":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "float")
if key == "dyeId":
forId = _get_or_create_subelement(self._node, "dyeId", self.xmlkeys())
if value is not None and value != "":
# We do not check that ID is valid to allow recreate_lost_ids()
forId.attrib['id'] = value
else:
self._node.remove(forId)
return
if key in ["sequences_forwardPrimer_threePrimeTag", "sequences_forwardPrimer_fivePrimeTag",
"sequences_forwardPrimer_sequence", "sequences_reversePrimer_threePrimeTag",
"sequences_reversePrimer_fivePrimeTag", "sequences_reversePrimer_sequence",
"sequences_probe1_threePrimeTag", "sequences_probe1_fivePrimeTag",
"sequences_probe1_sequence", "sequences_probe2_threePrimeTag",
"sequences_probe2_fivePrimeTag", "sequences_probe2_sequence",
"sequences_amplicon_threePrimeTag", "sequences_amplicon_fivePrimeTag",
"sequences_amplicon_sequence"]:
prim = _get_or_create_subelement(self._node, "sequences", self.xmlkeys())
sec = None
if key in ["sequences_forwardPrimer_threePrimeTag", "sequences_forwardPrimer_fivePrimeTag",
"sequences_forwardPrimer_sequence"]:
sec = _get_or_create_subelement(prim, "forwardPrimer",
["forwardPrimer", "reversePrimer", "probe1", "probe2", "amplicon"])
if key in ["sequences_reversePrimer_threePrimeTag", "sequences_reversePrimer_fivePrimeTag",
"sequences_reversePrimer_sequence"]:
sec = _get_or_create_subelement(prim, "reversePrimer",
["forwardPrimer", "reversePrimer", "probe1", "probe2", "amplicon"])
if key in ["sequences_probe1_threePrimeTag", "sequences_probe1_fivePrimeTag", "sequences_probe1_sequence"]:
sec = _get_or_create_subelement(prim, "probe1",
["forwardPrimer", "reversePrimer", "probe1", "probe2", "amplicon"])
if key in ["sequences_probe2_threePrimeTag", "sequences_probe2_fivePrimeTag", "sequences_probe2_sequence"]:
sec = _get_or_create_subelement(prim, "probe2",
["forwardPrimer", "reversePrimer", "probe1", "probe2", "amplicon"])
if key in ["sequences_amplicon_threePrimeTag", "sequences_amplicon_fivePrimeTag",
"sequences_amplicon_sequence"]:
sec = _get_or_create_subelement(prim, "amplicon",
["forwardPrimer", "reversePrimer", "probe1", "probe2", "amplicon"])
if sec is None:
return None
if key in ["sequences_forwardPrimer_threePrimeTag", "sequences_reversePrimer_threePrimeTag",
"sequences_probe1_threePrimeTag", "sequences_probe2_threePrimeTag",
"sequences_amplicon_threePrimeTag"]:
_change_subelement(sec, "threePrimeTag",
["threePrimeTag", "fivePrimeTag", "sequence"], value, True, "string")
if key in ["sequences_forwardPrimer_fivePrimeTag", "sequences_reversePrimer_fivePrimeTag",
"sequences_probe1_fivePrimeTag", "sequences_probe2_fivePrimeTag",
"sequences_amplicon_fivePrimeTag"]:
_change_subelement(sec, "fivePrimeTag",
["threePrimeTag", "fivePrimeTag", "sequence"], value, True, "string")
if key in ["sequences_forwardPrimer_sequence", "sequences_reversePrimer_sequence",
"sequences_probe1_sequence", "sequences_probe2_sequence",
"sequences_amplicon_sequence"]:
_change_subelement(sec, "sequence",
["threePrimeTag", "fivePrimeTag", "sequence"], value, True, "string")
if key in ["sequences_forwardPrimer_threePrimeTag", "sequences_forwardPrimer_fivePrimeTag",
"sequences_forwardPrimer_sequence"]:
_remove_irrelevant_subelement(prim, "forwardPrimer")
if key in ["sequences_reversePrimer_threePrimeTag", "sequences_reversePrimer_fivePrimeTag",
"sequences_reversePrimer_sequence"]:
_remove_irrelevant_subelement(prim, "reversePrimer")
if key in ["sequences_probe1_threePrimeTag", "sequences_probe1_fivePrimeTag", "sequences_probe1_sequence"]:
_remove_irrelevant_subelement(prim, "probe1")
if key in ["sequences_probe2_threePrimeTag", "sequences_probe2_fivePrimeTag", "sequences_probe2_sequence"]:
_remove_irrelevant_subelement(prim, "probe2")
if key in ["sequences_amplicon_threePrimeTag", "sequences_amplicon_fivePrimeTag",
"sequences_amplicon_sequence"]:
_remove_irrelevant_subelement(prim, "amplicon")
_remove_irrelevant_subelement(self._node, "sequences")
return
if key in ["commercialAssay_company", "commercialAssay_orderNumber"]:
ele = _get_or_create_subelement(self._node, "commercialAssay", self.xmlkeys())
if key == "commercialAssay_company":
_change_subelement(ele, "company", ["company", "orderNumber"], value, True, "string")
if key == "commercialAssay_orderNumber":
_change_subelement(ele, "orderNumber", ["company", "orderNumber"], value, True, "string")
_remove_irrelevant_subelement(self._node, "commercialAssay")
return
par = self._node.getparent()
ver = par.get('version')
if ver == "1.2" or ver == "1.3":
if key == "amplificationEfficiencySE":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "float")
raise KeyError
def change_id(self, value, merge_with_id=False):
"""Changes the value for the id.
Args:
self: The class self parameter.
value: The new value for the id.
merge_with_id: If True only allow a unique id, if False only rename its uses with existing id.
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
oldValue = self._node.get('id')
if oldValue != value:
par = self._node.getparent()
if not _string_to_bool(merge_with_id, triple=False):
_change_subelement(self._node, "id", self.xmlkeys(), value, False, "string")
else:
groupTag = self._node.tag.replace("{http://www.rdml.org}", "")
if _check_unique_id(par, groupTag, value):
raise RdmlError('The ' + groupTag + ' id "' + value + '" does not exist.')
allExp = _get_all_children(par, "sample")
for node in allExp:
subNodes = _get_all_children(node, "type")
for subNode in subNodes:
if "targetId" in subNode.attrib:
if subNode.attrib['targetId'] == oldValue:
subNode.attrib['targetId'] = value
allExp = _get_all_children(par, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
reactNodes = _get_all_children(subNode, "react")
for reactNode in reactNodes:
dataNodes = _get_all_children(reactNode, "data")
for dataNode in dataNodes:
lastNodes = _get_all_children(dataNode, "tar")
for lastNode in lastNodes:
if lastNode.attrib['id'] == oldValue:
lastNode.attrib['id'] = value
partit = _get_first_child(reactNode, "partitions")
if partit is not None:
digDataNodes = _get_all_children(partit, "data")
for digDataNode in digDataNodes:
lastNodes = _get_all_children(digDataNode, "tar")
for lastNode in lastNodes:
if lastNode.attrib['id'] == oldValue:
lastNode.attrib['id'] = value
# Search in Table files
if self._rdmlFilename is not None and self._rdmlFilename != "":
if zipfile.is_zipfile(self._rdmlFilename):
fileList = []
tempName = ""
flipFiles = False
with zipfile.ZipFile(self._rdmlFilename, 'r') as RDMLin:
for item in RDMLin.infolist():
if re.search("^partitions/", item.filename):
fileContent = RDMLin.read(item.filename).decode('utf-8')
newlineFix = fileContent.replace("\r\n", "\n")
tabLines = newlineFix.split("\n")
header = tabLines[0].split("\t")
needRewrite = False
for cell in header:
if cell == oldValue:
needRewrite = True
if needRewrite:
fileList.append(item.filename)
if len(fileList) > 0:
tempFolder, tempName = tempfile.mkstemp(dir=os.path.dirname(self._rdmlFilename))
os.close(tempFolder)
flipFiles = True
with zipfile.ZipFile(tempName, mode='w', compression=zipfile.ZIP_DEFLATED) as RDMLout:
RDMLout.comment = RDMLin.comment
for item in RDMLin.infolist():
if item.filename not in fileList:
RDMLout.writestr(item, RDMLin.read(item.filename))
else:
fileContent = RDMLin.read(item.filename).decode('utf-8')
newlineFix = fileContent.replace("\r\n", "\n")
tabLines = newlineFix.split("\n")
header = tabLines[0].split("\t")
headerText = ""
for cell in header:
if cell == oldValue:
headerText += value + "\t"
else:
headerText += cell + "\t"
outFileStr = re.sub(r'\t$', '\n', headerText)
for tabLine in tabLines[1:]:
if tabLine != "":
outFileStr += tabLine + "\n"
RDMLout.writestr(item.filename, outFileStr)
if flipFiles:
os.remove(self._rdmlFilename)
os.rename(tempName, self._rdmlFilename)
return
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["id", "description", "type", "amplificationEfficiencyMethod", "amplificationEfficiency",
"amplificationEfficiencySE", "meltingTemperature", "detectionLimit", "dyeId",
"sequences_forwardPrimer_threePrimeTag",
"sequences_forwardPrimer_fivePrimeTag", "sequences_forwardPrimer_sequence",
"sequences_reversePrimer_threePrimeTag", "sequences_reversePrimer_fivePrimeTag",
"sequences_reversePrimer_sequence", "sequences_probe1_threePrimeTag",
"sequences_probe1_fivePrimeTag", "sequences_probe1_sequence", "sequences_probe2_threePrimeTag",
"sequences_probe2_fivePrimeTag", "sequences_probe2_sequence", "sequences_amplicon_threePrimeTag",
"sequences_amplicon_fivePrimeTag", "sequences_amplicon_sequence", "commercialAssay_company",
"commercialAssay_orderNumber"] # Also change in LinRegPCR save RDML
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["description", "documentation", "xRef", "type", "amplificationEfficiencyMethod",
"amplificationEfficiency", "amplificationEfficiencySE", "meltingTemperature",
"detectionLimit", "dyeId", "sequences", "commercialAssay"]
def xrefs(self):
"""Returns a list of the xrefs in the xml file.
Args:
self: The class self parameter.
Returns:
A list of dics with name and id strings.
"""
xref = _get_all_children(self._node, "xRef")
ret = []
for node in xref:
data = {}
_add_first_child_to_dic(node, data, True, "name")
_add_first_child_to_dic(node, data, True, "id")
ret.append(data)
return ret
def new_xref(self, name=None, id=None, newposition=None):
"""Creates a new xrefs element.
Args:
self: The class self parameter.
name: Publisher who created the xRef
id: Serial Number for this target provided by publisher
newposition: The new position of the element
Returns:
Nothing, changes self.
"""
if name is None and id is None:
raise RdmlError('Either name or id is required to create a xRef.')
new_node = et.Element("xRef")
_add_new_subelement(new_node, "xRef", "name", name, True)
_add_new_subelement(new_node, "xRef", "id", id, True)
place = _get_tag_pos(self._node, "xRef", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def edit_xref(self, oldposition, newposition=None, name=None, id=None):
"""Creates a new xrefs element.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
name: Publisher who created the xRef
id: Serial Number for this target provided by publisher
Returns:
Nothing, changes self.
"""
if oldposition is None:
raise RdmlError('A oldposition is required to edit a xRef.')
if (name is None or name == "") and (id is None or id == ""):
self.delete_xref(oldposition)
return
pos = _get_tag_pos(self._node, "xRef", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "xRef", None, oldposition)
_change_subelement(ele, "name", ["name", "id"], name, True, "string")
_change_subelement(ele, "id", ["name", "id"], id, True, "string", id_as_element=True)
self._node.insert(pos, ele)
def move_xref(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "xRef", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "xRef", None, oldposition)
self._node.insert(pos, ele)
def delete_xref(self, byposition):
"""Deletes an experimenter element.
Args:
self: The class self parameter.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "xRef", None, byposition)
self._node.remove(elem)
def documentation_ids(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return _get_all_children_id(self._node, "documentation")
def update_documentation_ids(self, ids):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
ids: A dictionary with id and true/false pairs
Returns:
True if a change was made, else false. Function may raise RdmlError if required.
"""
old = self.documentation_ids()
good_ids = _value_to_booldic(ids)
mod = False
for id, inc in good_ids.items():
if inc is True:
if id not in old:
new_node = _create_new_element(self._node, "documentation", id)
place = _get_tag_pos(self._node, "documentation", self.xmlkeys(), 999999999)
self._node.insert(place, new_node)
mod = True
else:
if id in old:
elem = _get_first_child_by_pos_or_id(self._node, "documentation", id, None)
self._node.remove(elem)
mod = True
return mod
def move_documentation(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "documentation", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "documentation", None, oldposition)
self._node.insert(pos, ele)
def tojson(self):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
data = {
"id": self._node.get('id'),
}
_add_first_child_to_dic(self._node, data, True, "description")
data["documentations"] = self.documentation_ids()
data["xRefs"] = self.xrefs()
_add_first_child_to_dic(self._node, data, False, "type")
_add_first_child_to_dic(self._node, data, True, "amplificationEfficiencyMethod")
_add_first_child_to_dic(self._node, data, True, "amplificationEfficiency")
_add_first_child_to_dic(self._node, data, True, "amplificationEfficiencySE")
_add_first_child_to_dic(self._node, data, True, "meltingTemperature")
_add_first_child_to_dic(self._node, data, True, "detectionLimit")
forId = _get_first_child(self._node, "dyeId")
if forId is not None:
if forId.attrib['id'] != "":
data["dyeId"] = forId.attrib['id']
elem = _get_first_child(self._node, "sequences")
if elem is not None:
qdic = {}
sec = _get_first_child(elem, "forwardPrimer")
if sec is not None:
sdic = {}
_add_first_child_to_dic(sec, sdic, True, "threePrimeTag")
_add_first_child_to_dic(sec, sdic, True, "fivePrimeTag")
_add_first_child_to_dic(sec, sdic, True, "sequence")
if len(sdic.keys()) != 0:
qdic["forwardPrimer"] = sdic
sec = _get_first_child(elem, "reversePrimer")
if sec is not None:
sdic = {}
_add_first_child_to_dic(sec, sdic, True, "threePrimeTag")
_add_first_child_to_dic(sec, sdic, True, "fivePrimeTag")
_add_first_child_to_dic(sec, sdic, True, "sequence")
if len(sdic.keys()) != 0:
qdic["reversePrimer"] = sdic
sec = _get_first_child(elem, "probe1")
if sec is not None:
sdic = {}
_add_first_child_to_dic(sec, sdic, True, "threePrimeTag")
_add_first_child_to_dic(sec, sdic, True, "fivePrimeTag")
_add_first_child_to_dic(sec, sdic, True, "sequence")
if len(sdic.keys()) != 0:
qdic["probe1"] = sdic
sec = _get_first_child(elem, "probe2")
if sec is not None:
sdic = {}
_add_first_child_to_dic(sec, sdic, True, "threePrimeTag")
_add_first_child_to_dic(sec, sdic, True, "fivePrimeTag")
_add_first_child_to_dic(sec, sdic, True, "sequence")
if len(sdic.keys()) != 0:
qdic["probe2"] = sdic
sec = _get_first_child(elem, "amplicon")
if sec is not None:
sdic = {}
_add_first_child_to_dic(sec, sdic, True, "threePrimeTag")
_add_first_child_to_dic(sec, sdic, True, "fivePrimeTag")
_add_first_child_to_dic(sec, sdic, True, "sequence")
if len(sdic.keys()) != 0:
qdic["amplicon"] = sdic
if len(qdic.keys()) != 0:
data["sequences"] = qdic
elem = _get_first_child(self._node, "commercialAssay")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, True, "company")
_add_first_child_to_dic(elem, qdic, True, "orderNumber")
if len(qdic.keys()) != 0:
data["commercialAssay"] = qdic
return data
class Therm_cyc_cons:
"""RDML-Python library
The thermalCyclingConditions element used to read and edit one thermal Cycling Conditions.
Attributes:
_node: The thermalCyclingConditions node of the RDML XML object.
"""
def __init__(self, node):
"""Inits an thermalCyclingConditions instance.
Args:
self: The class self parameter.
node: The thermalCyclingConditions node.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._node = node
def __getitem__(self, key):
"""Returns the value for the key.
Args:
self: The class self parameter.
key: The key of the thermalCyclingConditions subelement
Returns:
A string of the data or None.
"""
if key == "id":
return self._node.get('id')
if key in ["description", "lidTemperature"]:
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
raise KeyError
def __setitem__(self, key, value):
"""Changes the value for the key.
Args:
self: The class self parameter.
key: The key of the thermalCyclingConditions subelement
value: The new value for the key
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
if key == "id":
self.change_id(value, merge_with_id=False)
return
if key == "description":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
if key == "lidTemperature":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "float")
raise KeyError
def change_id(self, value, merge_with_id=False):
"""Changes the value for the id.
Args:
self: The class self parameter.
value: The new value for the id.
merge_with_id: If True only allow a unique id, if False only rename its uses with existing id.
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
oldValue = self._node.get('id')
if oldValue != value:
par = self._node.getparent()
if not _string_to_bool(merge_with_id, triple=False):
_change_subelement(self._node, "id", self.xmlkeys(), value, False, "string")
else:
groupTag = self._node.tag.replace("{http://www.rdml.org}", "")
if _check_unique_id(par, groupTag, value):
raise RdmlError('The ' + groupTag + ' id "' + value + '" does not exist.')
allSam = _get_all_children(par, "sample")
for node in allSam:
subNode = _get_first_child(node, "cdnaSynthesisMethod")
if subNode is not None:
forId = _get_first_child(subNode, "thermalCyclingConditions")
if forId is not None:
if forId.attrib['id'] == oldValue:
forId.attrib['id'] = value
allExp = _get_all_children(par, "experiment")
for node in allExp:
subNodes = _get_all_children(node, "run")
for subNode in subNodes:
forId = _get_first_child(subNode, "thermalCyclingConditions")
if forId is not None:
if forId.attrib['id'] == oldValue:
forId.attrib['id'] = value
return
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["id", "description", "lidTemperature"]
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["description", "documentation", "lidTemperature", "experimenter", "step"]
def documentation_ids(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return _get_all_children_id(self._node, "documentation")
def update_documentation_ids(self, ids):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
ids: A dictionary with id and true/false pairs
Returns:
True if a change was made, else false. Function may raise RdmlError if required.
"""
old = self.documentation_ids()
good_ids = _value_to_booldic(ids)
mod = False
for id, inc in good_ids.items():
if inc is True:
if id not in old:
new_node = _create_new_element(self._node, "documentation", id)
place = _get_tag_pos(self._node, "documentation", self.xmlkeys(), 999999999)
self._node.insert(place, new_node)
mod = True
else:
if id in old:
elem = _get_first_child_by_pos_or_id(self._node, "documentation", id, None)
self._node.remove(elem)
mod = True
return mod
def move_documentation(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "documentation", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "documentation", None, oldposition)
self._node.insert(pos, ele)
def experimenter_ids(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return _get_all_children_id(self._node, "experimenter")
def update_experimenter_ids(self, ids):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
ids: A dictionary with id and true/false pairs
Returns:
True if a change was made, else false. Function may raise RdmlError if required.
"""
old = self.experimenter_ids()
good_ids = _value_to_booldic(ids)
mod = False
for id, inc in good_ids.items():
if inc is True:
if id not in old:
new_node = _create_new_element(self._node, "experimenter", id)
place = _get_tag_pos(self._node, "experimenter", self.xmlkeys(), 999999999)
self._node.insert(place, new_node)
mod = True
else:
if id in old:
elem = _get_first_child_by_pos_or_id(self._node, "experimenter", id, None)
self._node.remove(elem)
mod = True
return mod
def move_experimenter(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "experimenter", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "experimenter", None, oldposition)
self._node.insert(pos, ele)
def steps(self):
"""Returns a list of all step elements.
Args:
self: The class self parameter.
Returns:
A list of all step elements.
"""
# The steps are sorted transiently to not modify the file in a read situation
exp = _get_all_children(self._node, "step")
srt_exp = sorted(exp, key=_get_step_sort_nr)
ret = []
for node in srt_exp:
ret.append(Step(node))
return ret
def new_step_temperature(self, temperature, duration,
temperatureChange=None, durationChange=None,
measure=None, ramp=None, nr=None):
"""Creates a new step element.
Args:
self: The class self parameter.
temperature: The temperature of the step in degrees Celsius (required)
duration: The duration of this step in seconds (required)
temperatureChange: The change of the temperature from one cycle to the next (optional)
durationChange: The change of the duration from one cycle to the next (optional)
measure: Indicates to make a measurement and store it as meltcurve or real-time data (optional)
ramp: Limit temperature change from one step to the next in degrees Celsius per second (optional)
nr: Step unique nr (optional)
Returns:
Nothing, changes self.
"""
if measure is not None and measure not in ["", "real time", "meltcurve"]:
raise RdmlError('Unknown or unsupported step measure value: "' + measure + '".')
nr = int(nr)
count = _get_number_of_children(self._node, "step")
new_node = et.Element("step")
xml_temp_step = ["temperature", "duration", "temperatureChange", "durationChange", "measure", "ramp"]
_add_new_subelement(new_node, "step", "nr", str(count + 1), False)
subel = et.SubElement(new_node, "temperature")
_change_subelement(subel, "temperature", xml_temp_step, temperature, False, "float")
_change_subelement(subel, "duration", xml_temp_step, duration, False, "posint")
_change_subelement(subel, "temperatureChange", xml_temp_step, temperatureChange, True, "float")
_change_subelement(subel, "durationChange", xml_temp_step, durationChange, True, "int")
_change_subelement(subel, "measure", xml_temp_step, measure, True, "string")
_change_subelement(subel, "ramp", xml_temp_step, ramp, True, "float")
place = _get_first_tag_pos(self._node, "step", self.xmlkeys()) + count
self._node.insert(place, new_node)
# Now move step at final position
self.move_step(count + 1, nr)
def new_step_gradient(self, highTemperature, lowTemperature, duration,
temperatureChange=None, durationChange=None,
measure=None, ramp=None, nr=None):
"""Creates a new step element.
Args:
self: The class self parameter.
highTemperature: The high gradient temperature of the step in degrees Celsius (required)
lowTemperature: The low gradient temperature of the step in degrees Celsius (required)
duration: The duration of this step in seconds (required)
temperatureChange: The change of the temperature from one cycle to the next (optional)
durationChange: The change of the duration from one cycle to the next (optional)
measure: Indicates to make a measurement and store it as meltcurve or real-time data (optional)
ramp: Limit temperature change from one step to the next in degrees Celsius per second (optional)
nr: Step unique nr (optional)
Returns:
Nothing, changes self.
"""
if measure is not None and measure not in ["", "real time", "meltcurve"]:
raise RdmlError('Unknown or unsupported step measure value: "' + measure + '".')
nr = int(nr)
count = _get_number_of_children(self._node, "step")
new_node = et.Element("step")
xml_temp_step = ["highTemperature", "lowTemperature", "duration", "temperatureChange",
"durationChange", "measure", "ramp"]
_add_new_subelement(new_node, "step", "nr", str(count + 1), False)
subel = et.SubElement(new_node, "gradient")
_change_subelement(subel, "highTemperature", xml_temp_step, highTemperature, False, "float")
_change_subelement(subel, "lowTemperature", xml_temp_step, lowTemperature, False, "float")
_change_subelement(subel, "duration", xml_temp_step, duration, False, "posint")
_change_subelement(subel, "temperatureChange", xml_temp_step, temperatureChange, True, "float")
_change_subelement(subel, "durationChange", xml_temp_step, durationChange, True, "int")
_change_subelement(subel, "measure", xml_temp_step, measure, True, "string")
_change_subelement(subel, "ramp", xml_temp_step, ramp, True, "float")
place = _get_first_tag_pos(self._node, "step", self.xmlkeys()) + count
self._node.insert(place, new_node)
# Now move step at final position
self.move_step(count + 1, nr)
def new_step_loop(self, goto, repeat, nr=None):
"""Creates a new step element.
Args:
self: The class self parameter.
goto: The step nr to go back to (required)
repeat: The number of times to go back to goto step, one less than cycles (optional)
nr: Step unique nr (optional)
Returns:
Nothing, changes self.
"""
nr = int(nr)
count = _get_number_of_children(self._node, "step")
new_node = et.Element("step")
xml_temp_step = ["goto", "repeat"]
_add_new_subelement(new_node, "step", "nr", str(count + 1), False)
subel = et.SubElement(new_node, "loop")
_change_subelement(subel, "goto", xml_temp_step, goto, False, "posint")
_change_subelement(subel, "repeat", xml_temp_step, repeat, False, "posint")
place = _get_first_tag_pos(self._node, "step", self.xmlkeys()) + count
self._node.insert(place, new_node)
# Now move step at final position
self.move_step(count + 1, nr)
def new_step_pause(self, temperature, nr=None):
"""Creates a new step element.
Args:
self: The class self parameter.
temperature: The temperature of the step in degrees Celsius (required)
nr: Step unique nr (optional)
Returns:
Nothing, changes self.
"""
nr = int(nr)
count = _get_number_of_children(self._node, "step")
new_node = et.Element("step")
xml_temp_step = ["temperature"]
_add_new_subelement(new_node, "step", "nr", str(count + 1), False)
subel = et.SubElement(new_node, "pause")
_change_subelement(subel, "temperature", xml_temp_step, temperature, False, "float")
place = _get_first_tag_pos(self._node, "step", self.xmlkeys()) + count
self._node.insert(place, new_node)
# Now move step at final position
self.move_step(count + 1, nr)
def new_step_lidOpen(self, nr=None):
"""Creates a new step element.
Args:
self: The class self parameter.
nr: Step unique nr (optional)
Returns:
Nothing, changes self.
"""
nr = int(nr)
count = _get_number_of_children(self._node, "step")
new_node = et.Element("step")
_add_new_subelement(new_node, "step", "nr", str(count + 1), False)
et.SubElement(new_node, "lidOpen")
place = _get_first_tag_pos(self._node, "step", self.xmlkeys()) + count
self._node.insert(place, new_node)
# Now move step at final position
self.move_step(count + 1, nr)
def cleanup_steps(self):
"""The steps may not be in a order that makes sense. This function fixes it.
Args:
self: The class self parameter.
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
# The steps in the xml may be not sorted by "nr", so sort first
exp = _get_all_children(self._node, "step")
srt_exp = sorted(exp, key=_get_step_sort_nr)
i = 0
for node in srt_exp:
if _get_step_sort_nr(node) != _get_step_sort_nr(exp[i]):
pos = _get_first_tag_pos(self._node, "step", self.xmlkeys()) + i
self._node.insert(pos, node)
i += 1
# The steps in the xml may not have the correct numbering, so fix it
exp = _get_all_children(self._node, "step")
i = 1
for node in exp:
if _get_step_sort_nr(node) != i:
elem = _get_first_child(node, "nr")
elem.text = str(i)
i += 1
def move_step(self, oldnr, newnr):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldnr: The old position of the element
newnr: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
# The steps in the xml may be not sorted well, so fix it
self.cleanup_steps()
# Change the nr
_move_subelement_pos(self._node, "step", oldnr - 1, self.xmlkeys(), newnr - 1)
# Fix the nr
exp = _get_all_children(self._node, "step")
i = 1
goto_mod = 0
goto_start = newnr
goto_end = oldnr
if oldnr > newnr:
goto_mod = 1
if oldnr < newnr:
goto_mod = -1
goto_start = oldnr
goto_end = newnr
for node in exp:
if _get_step_sort_nr(node) != i:
elem = _get_first_child(node, "nr")
elem.text = str(i)
# Fix the goto steps
ele_type = _get_first_child(node, "loop")
if ele_type is not None:
ele_goto = _get_first_child(ele_type, "goto")
if ele_goto is not None:
jump_to = int(ele_goto.text)
if goto_start <= jump_to < goto_end:
ele_goto.text = str(jump_to + goto_mod)
i += 1
def get_step(self, bystep):
"""Returns an sample element by position or id.
Args:
self: The class self parameter.
bystep: Select the element by step nr in the list.
Returns:
The found element or None.
"""
return Step(_get_first_child_by_pos_or_id(self._node, "step", None, bystep - 1))
def delete_step(self, bystep=None):
"""Deletes an step element.
Args:
self: The class self parameter.
bystep: Select the element by step nr in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "step", None, bystep - 1)
self._node.remove(elem)
self.cleanup_steps()
# Fix the goto steps
exp = _get_all_children(self._node, "step")
for node in exp:
ele_type = _get_first_child(node, "loop")
if ele_type is not None:
ele_goto = _get_first_child(ele_type, "goto")
if ele_goto is not None:
jump_to = int(ele_goto.text)
if bystep < jump_to:
ele_goto.text = str(jump_to - 1)
def tojson(self):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
allSteps = self.steps()
steps = []
for exp in allSteps:
steps.append(exp.tojson())
data = {
"id": self._node.get('id'),
}
_add_first_child_to_dic(self._node, data, True, "description")
data["documentations"] = self.documentation_ids()
_add_first_child_to_dic(self._node, data, True, "lidTemperature")
data["experimenters"] = self.experimenter_ids()
data["steps"] = steps
return data
class Step:
"""RDML-Python library
The samples element used to read and edit one sample.
Attributes:
_node: The sample node of the RDML XML object.
"""
def __init__(self, node):
"""Inits an sample instance.
Args:
self: The class self parameter.
node: The sample node.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._node = node
def __getitem__(self, key):
"""Returns the value for the key.
Args:
self: The class self parameter.
key: The key of the sample subelement. Be aware that change of type deletes all entries
except nr and description
Returns:
A string of the data or None.
"""
if key == "nr":
return _get_first_child_text(self._node, key)
if key == "description":
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
ele_type = _get_first_child(self._node, "temperature")
if ele_type is not None:
if key == "type":
return "temperature"
if key in ["temperature", "duration"]:
return _get_first_child_text(ele_type, key)
if key in ["temperatureChange", "durationChange", "measure", "ramp"]:
var = _get_first_child_text(ele_type, key)
if var == "":
return None
else:
return var
ele_type = _get_first_child(self._node, "gradient")
if ele_type is not None:
if key == "type":
return "gradient"
if key in ["highTemperature", "lowTemperature", "duration"]:
return _get_first_child_text(ele_type, key)
if key in ["temperatureChange", "durationChange", "measure", "ramp"]:
var = _get_first_child_text(ele_type, key)
if var == "":
return None
else:
return var
ele_type = _get_first_child(self._node, "loop")
if ele_type is not None:
if key == "type":
return "loop"
if key in ["goto", "repeat"]:
return _get_first_child_text(ele_type, key)
ele_type = _get_first_child(self._node, "pause")
if ele_type is not None:
if key == "type":
return "pause"
if key == "temperature":
return _get_first_child_text(ele_type, key)
ele_type = _get_first_child(self._node, "lidOpen")
if ele_type is not None:
if key == "type":
return "lidOpen"
raise KeyError
def __setitem__(self, key, value):
"""Changes the value for the key.
Args:
self: The class self parameter.
key: The key of the sample subelement
value: The new value for the key
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
if key in ["nr", "type"]:
raise RdmlError('"' + key + '" can not be set. Use thermal cycling conditions methods instead')
if key == "description":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
ele_type = _get_first_child(self._node, "temperature")
if ele_type is not None:
xml_temp_step = ["temperature", "duration", "temperatureChange", "durationChange", "measure", "ramp"]
if key == "temperature":
return _change_subelement(ele_type, key, xml_temp_step, value, False, "float")
if key == "duration":
return _change_subelement(ele_type, key, xml_temp_step, value, False, "posint")
if key in ["temperatureChange", "ramp"]:
return _change_subelement(ele_type, key, xml_temp_step, value, True, "float")
if key == "durationChange":
return _change_subelement(ele_type, key, xml_temp_step, value, True, "int")
if key == "measure":
if value not in ["", "real time", "meltcurve"]:
raise RdmlError('Unknown or unsupported step measure value: "' + value + '".')
return _change_subelement(ele_type, key, xml_temp_step, value, True, "string")
ele_type = _get_first_child(self._node, "gradient")
if ele_type is not None:
xml_temp_step = ["highTemperature", "lowTemperature", "duration", "temperatureChange",
"durationChange", "measure", "ramp"]
if key in ["highTemperature", "lowTemperature"]:
return _change_subelement(ele_type, key, xml_temp_step, value, False, "float")
if key == "duration":
return _change_subelement(ele_type, key, xml_temp_step, value, False, "posint")
if key in ["temperatureChange", "ramp"]:
return _change_subelement(ele_type, key, xml_temp_step, value, True, "float")
if key == "durationChange":
return _change_subelement(ele_type, key, xml_temp_step, value, True, "int")
if key == "measure":
if value not in ["", "real time", "meltcurve"]:
raise RdmlError('Unknown or unsupported step measure value: "' + value + '".')
return _change_subelement(ele_type, key, xml_temp_step, value, True, "string")
ele_type = _get_first_child(self._node, "loop")
if ele_type is not None:
xml_temp_step = ["goto", "repeat"]
if key in xml_temp_step:
return _change_subelement(ele_type, key, xml_temp_step, value, False, "posint")
ele_type = _get_first_child(self._node, "pause")
if ele_type is not None:
xml_temp_step = ["temperature"]
if key == "temperature":
return _change_subelement(ele_type, key, xml_temp_step, value, False, "float")
raise KeyError
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
ele_type = _get_first_child(self._node, "temperature")
if ele_type is not None:
return ["nr", "type", "description", "temperature", "duration", "temperatureChange",
"durationChange", "measure", "ramp"]
ele_type = _get_first_child(self._node, "gradient")
if ele_type is not None:
return ["nr", "type", "description", "highTemperature", "lowTemperature", "duration",
"temperatureChange", "durationChange", "measure", "ramp"]
ele_type = _get_first_child(self._node, "loop")
if ele_type is not None:
return ["nr", "type", "description", "goto", "repeat"]
ele_type = _get_first_child(self._node, "pause")
if ele_type is not None:
return ["nr", "type", "description", "temperature"]
ele_type = _get_first_child(self._node, "lidOpen")
if ele_type is not None:
return ["nr", "type", "description"]
return []
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
ele_type = _get_first_child(self._node, "temperature")
if ele_type is not None:
return ["temperature", "duration", "temperatureChange", "durationChange", "measure", "ramp"]
ele_type = _get_first_child(self._node, "gradient")
if ele_type is not None:
return ["highTemperature", "lowTemperature", "duration", "temperatureChange",
"durationChange", "measure", "ramp"]
ele_type = _get_first_child(self._node, "loop")
if ele_type is not None:
return ["goto", "repeat"]
ele_type = _get_first_child(self._node, "pause")
if ele_type is not None:
return ["temperature"]
ele_type = _get_first_child(self._node, "lidOpen")
if ele_type is not None:
return []
return []
def tojson(self):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
data = {}
_add_first_child_to_dic(self._node, data, False, "nr")
_add_first_child_to_dic(self._node, data, True, "description")
elem = _get_first_child(self._node, "temperature")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "temperature")
_add_first_child_to_dic(elem, qdic, False, "duration")
_add_first_child_to_dic(elem, qdic, True, "temperatureChange")
_add_first_child_to_dic(elem, qdic, True, "durationChange")
_add_first_child_to_dic(elem, qdic, True, "measure")
_add_first_child_to_dic(elem, qdic, True, "ramp")
data["temperature"] = qdic
elem = _get_first_child(self._node, "gradient")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "highTemperature")
_add_first_child_to_dic(elem, qdic, False, "lowTemperature")
_add_first_child_to_dic(elem, qdic, False, "duration")
_add_first_child_to_dic(elem, qdic, True, "temperatureChange")
_add_first_child_to_dic(elem, qdic, True, "durationChange")
_add_first_child_to_dic(elem, qdic, True, "measure")
_add_first_child_to_dic(elem, qdic, True, "ramp")
data["gradient"] = qdic
elem = _get_first_child(self._node, "loop")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "goto")
_add_first_child_to_dic(elem, qdic, False, "repeat")
data["loop"] = qdic
elem = _get_first_child(self._node, "pause")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "temperature")
data["pause"] = qdic
elem = _get_first_child(self._node, "lidOpen")
if elem is not None:
data["lidOpen"] = "lidOpen"
return data
class Experiment:
"""RDML-Python library
The target element used to read and edit one experiment.
Attributes:
_node: The target node of the RDML XML object.
_rdmlFilename: The RDML filename
"""
def __init__(self, node, rdmlFilename):
"""Inits an experiment instance.
Args:
self: The class self parameter.
node: The experiment node.
rdmlFilename: The RDML filename.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._node = node
self._rdmlFilename = rdmlFilename
def __getitem__(self, key):
"""Returns the value for the key.
Args:
self: The class self parameter.
key: The key of the experiment subelement
Returns:
A string of the data or None.
"""
if key == "id":
return self._node.get('id')
if key == "description":
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
raise KeyError
def __setitem__(self, key, value):
"""Changes the value for the key.
Args:
self: The class self parameter.
key: The key of the target subelement
value: The new value for the key
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
if key == "id":
return _change_subelement(self._node, key, self.xmlkeys(), value, False, "string")
if key == "description":
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
raise KeyError
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["id", "description"]
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["description", "documentation", "run"]
def documentation_ids(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return _get_all_children_id(self._node, "documentation")
def update_documentation_ids(self, ids):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
ids: A dictionary with id and true/false pairs
Returns:
True if a change was made, else false. Function may raise RdmlError if required.
"""
old = self.documentation_ids()
good_ids = _value_to_booldic(ids)
mod = False
for id, inc in good_ids.items():
if inc is True:
if id not in old:
new_node = _create_new_element(self._node, "documentation", id)
place = _get_tag_pos(self._node, "documentation", self.xmlkeys(), 999999999)
self._node.insert(place, new_node)
mod = True
else:
if id in old:
elem = _get_first_child_by_pos_or_id(self._node, "documentation", id, None)
self._node.remove(elem)
mod = True
return mod
def move_documentation(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "documentation", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "documentation", None, oldposition)
self._node.insert(pos, ele)
def runs(self):
"""Returns a list of all run elements.
Args:
self: The class self parameter.
Returns:
A list of all run elements.
"""
exp = _get_all_children(self._node, "run")
ret = []
for node in exp:
ret.append(Run(node, self._rdmlFilename))
return ret
def new_run(self, id, newposition=None):
"""Creates a new run element.
Args:
self: The class self parameter.
id: Run unique id (required)
newposition: Run position in the list of experiments (optional)
Returns:
Nothing, changes self.
"""
new_node = _create_new_element(self._node, "run", id)
place = _get_tag_pos(self._node, "run", self.xmlkeys(), newposition)
self._node.insert(place, new_node)
def move_run(self, id, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
id: Run unique id
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
_move_subelement(self._node, "run", id, self.xmlkeys(), newposition)
def get_run(self, byid=None, byposition=None):
"""Returns an run element by position or id.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
The found element or None.
"""
return Run(_get_first_child_by_pos_or_id(self._node, "run", byid, byposition), self._rdmlFilename)
def delete_run(self, byid=None, byposition=None):
"""Deletes an run element.
Args:
self: The class self parameter.
byid: Select the element by the element id.
byposition: Select the element by position in the list.
Returns:
Nothing, changes self.
"""
elem = _get_first_child_by_pos_or_id(self._node, "run", byid, byposition)
# Delete in Table files
fileList = []
exp = _get_all_children(elem, "react")
for node in exp:
partit = _get_first_child(node, "partitions")
if partit is not None:
finalFileName = "partitions/" + _get_first_child_text(partit, "endPtTable")
if finalFileName != "partitions/":
fileList.append(finalFileName)
if len(fileList) > 0:
if self._rdmlFilename is not None and self._rdmlFilename != "":
if zipfile.is_zipfile(self._rdmlFilename):
with zipfile.ZipFile(self._rdmlFilename, 'r') as RDMLin:
tempFolder, tempName = tempfile.mkstemp(dir=os.path.dirname(self._rdmlFilename))
os.close(tempFolder)
with zipfile.ZipFile(tempName, mode='w', compression=zipfile.ZIP_DEFLATED) as RDMLout:
RDMLout.comment = RDMLin.comment
for item in RDMLin.infolist():
if item.filename not in fileList:
RDMLout.writestr(item, RDMLin.read(item.filename))
os.remove(self._rdmlFilename)
os.rename(tempName, self._rdmlFilename)
# Delete the node
self._node.remove(elem)
def tojson(self):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
allRuns = self.runs()
runs = []
for exp in allRuns:
runs.append(exp.tojson())
data = {
"id": self._node.get('id'),
}
_add_first_child_to_dic(self._node, data, True, "description")
data["documentations"] = self.documentation_ids()
data["runs"] = runs
return data
class Run:
"""RDML-Python library
The run element used to read and edit one run.
Attributes:
_node: The run node of the RDML XML object.
_rdmlFilename: The RDML filename.
"""
def __init__(self, node, rdmlFilename):
"""Inits an run instance.
Args:
self: The class self parameter.
node: The sample node.
rdmlFilename: The RDML filename.
Returns:
No return value. Function may raise RdmlError if required.
"""
self._node = node
self._rdmlFilename = rdmlFilename
def __getitem__(self, key):
"""Returns the value for the key.
Args:
self: The class self parameter.
key: The key of the run subelement
Returns:
A string of the data or None.
"""
if key == "id":
return self._node.get('id')
if key in ["description", "instrument", "backgroundDeterminationMethod", "cqDetectionMethod", "runDate"]:
var = _get_first_child_text(self._node, key)
if var == "":
return None
else:
return var
if key == "thermalCyclingConditions":
forId = _get_first_child(self._node, "thermalCyclingConditions")
if forId is not None:
return forId.attrib['id']
else:
return None
if key in ["dataCollectionSoftware_name", "dataCollectionSoftware_version"]:
ele = _get_first_child(self._node, "dataCollectionSoftware")
if ele is None:
return None
if key == "dataCollectionSoftware_name":
return _get_first_child_text(ele, "name")
if key == "dataCollectionSoftware_version":
return _get_first_child_text(ele, "version")
raise RdmlError('Run dataCollectionSoftware programming read error.')
if key in ["pcrFormat_rows", "pcrFormat_columns", "pcrFormat_rowLabel", "pcrFormat_columnLabel"]:
ele = _get_first_child(self._node, "pcrFormat")
if ele is None:
return None
if key == "pcrFormat_rows":
return _get_first_child_text(ele, "rows")
if key == "pcrFormat_columns":
return _get_first_child_text(ele, "columns")
if key == "pcrFormat_rowLabel":
return _get_first_child_text(ele, "rowLabel")
if key == "pcrFormat_columnLabel":
return _get_first_child_text(ele, "columnLabel")
raise RdmlError('Run pcrFormat programming read error.')
raise KeyError
def __setitem__(self, key, value):
"""Changes the value for the key.
Args:
self: The class self parameter.
key: The key of the run subelement
value: The new value for the key
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
if key == "cqDetectionMethod":
if value not in ["", "automated threshold and baseline settings", "manual threshold and baseline settings",
"second derivative maximum", "other"]:
raise RdmlError('Unknown or unsupported run cqDetectionMethod value "' + value + '".')
if key in ["pcrFormat_rowLabel", "pcrFormat_columnLabel"]:
if value not in ["ABC", "123", "A1a1"]:
raise RdmlError('Unknown or unsupported run ' + key + ' value "' + value + '".')
if key == "id":
return _change_subelement(self._node, key, self.xmlkeys(), value, False, "string")
if key in ["description", "instrument", "backgroundDeterminationMethod", "cqDetectionMethod", "runDate"]:
return _change_subelement(self._node, key, self.xmlkeys(), value, True, "string")
if key == "thermalCyclingConditions":
forId = _get_or_create_subelement(self._node, "thermalCyclingConditions", self.xmlkeys())
if value is not None and value != "":
# We do not check that ID is valid to allow recreate_lost_ids()
forId.attrib['id'] = value
else:
self._node.remove(forId)
return
if key in ["dataCollectionSoftware_name", "dataCollectionSoftware_version"]:
ele = _get_or_create_subelement(self._node, "dataCollectionSoftware", self.xmlkeys())
if key == "dataCollectionSoftware_name":
_change_subelement(ele, "name", ["name", "version"], value, True, "string")
if key == "dataCollectionSoftware_version":
_change_subelement(ele, "version", ["name", "version"], value, True, "string")
_remove_irrelevant_subelement(self._node, "dataCollectionSoftware")
return
if key in ["pcrFormat_rows", "pcrFormat_columns", "pcrFormat_rowLabel", "pcrFormat_columnLabel"]:
ele = _get_or_create_subelement(self._node, "pcrFormat", self.xmlkeys())
if key == "pcrFormat_rows":
_change_subelement(ele, "rows", ["rows", "columns", "rowLabel", "columnLabel"], value, True, "string")
if key == "pcrFormat_columns":
_change_subelement(ele, "columns", ["rows", "columns", "rowLabel", "columnLabel"], value, True, "string")
if key == "pcrFormat_rowLabel":
_change_subelement(ele, "rowLabel", ["rows", "columns", "rowLabel", "columnLabel"], value, True, "string")
if key == "pcrFormat_columnLabel":
_change_subelement(ele, "columnLabel", ["rows", "columns", "rowLabel", "columnLabel"], value, True, "string")
_remove_irrelevant_subelement(self._node, "pcrFormat")
return
raise KeyError
def keys(self):
"""Returns a list of the keys.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["id", "description", "instrument", "dataCollectionSoftware_name", "dataCollectionSoftware_version",
"backgroundDeterminationMethod", "cqDetectionMethod", "thermalCyclingConditions", "pcrFormat_rows",
"pcrFormat_columns", "pcrFormat_rowLabel", "pcrFormat_columnLabel", "runDate", "react"]
def xmlkeys(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return ["description", "documentation", "experimenter", "instrument", "dataCollectionSoftware",
"backgroundDeterminationMethod", "cqDetectionMethod", "thermalCyclingConditions", "pcrFormat",
"runDate", "react"]
def documentation_ids(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return _get_all_children_id(self._node, "documentation")
def update_documentation_ids(self, ids):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
ids: A dictionary with id and true/false pairs
Returns:
True if a change was made, else false. Function may raise RdmlError if required.
"""
old = self.documentation_ids()
good_ids = _value_to_booldic(ids)
mod = False
for id, inc in good_ids.items():
if inc is True:
if id not in old:
new_node = _create_new_element(self._node, "documentation", id)
place = _get_tag_pos(self._node, "documentation", self.xmlkeys(), 999999999)
self._node.insert(place, new_node)
mod = True
else:
if id in old:
elem = _get_first_child_by_pos_or_id(self._node, "documentation", id, None)
self._node.remove(elem)
mod = True
return mod
def move_documentation(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "documentation", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "documentation", None, oldposition)
self._node.insert(pos, ele)
def experimenter_ids(self):
"""Returns a list of the keys in the xml file.
Args:
self: The class self parameter.
Returns:
A list of the key strings.
"""
return _get_all_children_id(self._node, "experimenter")
def update_experimenter_ids(self, ids):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
ids: A dictionary with id and true/false pairs
Returns:
True if a change was made, else false. Function may raise RdmlError if required.
"""
old = self.experimenter_ids()
good_ids = _value_to_booldic(ids)
mod = False
for id, inc in good_ids.items():
if inc is True:
if id not in old:
new_node = _create_new_element(self._node, "experimenter", id)
place = _get_tag_pos(self._node, "experimenter", self.xmlkeys(), 999999999)
self._node.insert(place, new_node)
mod = True
else:
if id in old:
elem = _get_first_child_by_pos_or_id(self._node, "experimenter", id, None)
self._node.remove(elem)
mod = True
return mod
def move_experimenter(self, oldposition, newposition):
"""Moves the element to the new position in the list.
Args:
self: The class self parameter.
oldposition: The old position of the element
newposition: The new position of the element
Returns:
No return value, changes self. Function may raise RdmlError if required.
"""
pos = _get_tag_pos(self._node, "experimenter", self.xmlkeys(), newposition)
ele = _get_first_child_by_pos_or_id(self._node, "experimenter", None, oldposition)
self._node.insert(pos, ele)
def tojson(self):
"""Returns a json of the RDML object without fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
data = {
"id": self._node.get('id'),
}
_add_first_child_to_dic(self._node, data, True, "description")
data["documentations"] = self.documentation_ids()
data["experimenters"] = self.experimenter_ids()
_add_first_child_to_dic(self._node, data, True, "instrument")
elem = _get_first_child(self._node, "dataCollectionSoftware")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, True, "name")
_add_first_child_to_dic(elem, qdic, True, "version")
if len(qdic.keys()) != 0:
data["dataCollectionSoftware"] = qdic
_add_first_child_to_dic(self._node, data, True, "backgroundDeterminationMethod")
_add_first_child_to_dic(self._node, data, True, "cqDetectionMethod")
forId = _get_first_child(self._node, "thermalCyclingConditions")
if forId is not None:
if forId.attrib['id'] != "":
data["thermalCyclingConditions"] = forId.attrib['id']
elem = _get_first_child(self._node, "pcrFormat")
if elem is not None:
qdic = {}
_add_first_child_to_dic(elem, qdic, False, "rows")
_add_first_child_to_dic(elem, qdic, False, "columns")
_add_first_child_to_dic(elem, qdic, False, "rowLabel")
_add_first_child_to_dic(elem, qdic, False, "columnLabel")
data["pcrFormat"] = qdic
_add_first_child_to_dic(self._node, data, True, "runDate")
data["react"] = _get_number_of_children(self._node, "react")
return data
def export_table(self, dMode):
"""Returns a tab seperated table file with the react fluorescence data.
Args:
self: The class self parameter.
dMode: amp for amplification data, melt for meltcurve data
Returns:
A string with the data.
"""
samTypeLookup = {}
tarTypeLookup = {}
tarDyeLookup = {}
data = ""
# Get the information for the lookup dictionaries
pExp = self._node.getparent()
pRoot = pExp.getparent()
samples = _get_all_children(pRoot, "sample")
for sample in samples:
if sample.attrib['id'] != "":
samId = sample.attrib['id']
forType = _get_first_child_text(sample, "type")
if forType != "":
samTypeLookup[samId] = forType
targets = _get_all_children(pRoot, "target")
for target in targets:
if target.attrib['id'] != "":
tarId = target.attrib['id']
forType = _get_first_child_text(target, "type")
if forType != "":
tarTypeLookup[tarId] = forType
forId = _get_first_child(target, "dyeId")
if forId is not None:
if forId.attrib['id'] != "":
tarDyeLookup[tarId] = forId.attrib['id']
# Now create the header line
data += "Well\tSample\tSample Type\tTarget\tTarget Type\tDye\t"
reacts = _get_all_children(self._node, "react")
if len(reacts) < 1:
return ""
react_datas = _get_all_children(reacts[0], "data")
if len(react_datas) < 1:
return ""
headArr = []
if dMode == "amp":
adps = _get_all_children(react_datas[0], "adp")
for adp in adps:
headArr.append(_get_first_child_text(adp, "cyc"))
headArr = sorted(headArr, key=int)
else:
mdps = _get_all_children(react_datas[0], "mdp")
for mdp in mdps:
headArr.append(_get_first_child_text(mdp, "tmp"))
headArr = sorted(headArr, key=float, reverse=True)
for hElem in headArr:
data += hElem + "\t"
data += '\n'
# Now create the data lines
reacts = _get_all_children(self._node, "react")
wellData = []
for react in reacts:
reactId = react.get('id')
dataSample = reactId + '\t'
react_sample = "No Sample"
react_sample_type = "No Sample Type"
forId = _get_first_child(react, "sample")
if forId is not None:
if forId.attrib['id'] != "":
react_sample = forId.attrib['id']
react_sample_type = samTypeLookup[react_sample]
dataSample += react_sample + '\t' + react_sample_type
react_datas = _get_all_children(react, "data")
for react_data in react_datas:
dataLine = dataSample
react_target = "No Target"
react_target_type = "No Target Type"
react_target_dye = "No Dye"
forId = _get_first_child(react_data, "tar")
if forId is not None:
if forId.attrib['id'] != "":
react_target = forId.attrib['id']
react_target_type = tarTypeLookup[react_target]
react_target_dye = tarDyeLookup[react_target]
dataLine += "\t" + react_target + '\t' + react_target_type + '\t' + react_target_dye
fluorList = []
if dMode == "amp":
adps = _get_all_children(react_data, "adp")
for adp in adps:
cyc = _get_first_child_text(adp, "cyc")
fluor = _get_first_child_text(adp, "fluor")
fluorList.append([cyc, fluor])
fluorList = sorted(fluorList, key=_sort_list_int)
else:
mdps = _get_all_children(react_data, "mdp")
for mdp in mdps:
tmp = _get_first_child_text(mdp, "tmp")
fluor = _get_first_child_text(mdp, "fluor")
fluorList.append([tmp, fluor])
fluorList = sorted(fluorList, key=_sort_list_float)
for hElem in fluorList:
dataLine += "\t" + hElem[1]
dataLine += '\n'
wellData.append([reactId, dataLine])
wellData = sorted(wellData, key=_sort_list_int)
for hElem in wellData:
data += hElem[1]
return data
def import_table(self, rootEl, filename, dMode):
"""Imports data from a tab seperated table file with react fluorescence data.
Args:
self: The class self parameter.
rootEl: The rdml root element.
filename: The tab file to open.
dMode: amp for amplification data, melt for meltcurve data.
Returns:
A string with the modifications made.
"""
ret = ""
with open(filename, "r") as tfile:
fileContent = tfile.read()
newlineFix = fileContent.replace("\r\n", "\n")
tabLines = newlineFix.split("\n")
head = tabLines[0].split("\t")
if (head[0] != "Well" or head[1] != "Sample" or head[2] != "Sample Type" or
head[3] != "Target" or head[4] != "Target Type" or head[5] != "Dye"):
raise RdmlError('The tab-format is not valid, essential columns are missing.')
# Get the information for the lookup dictionaries
samTypeLookup = {}
tarTypeLookup = {}
dyeLookup = {}
samples = _get_all_children(rootEl._node, "sample")
for sample in samples:
if sample.attrib['id'] != "":
samId = sample.attrib['id']
forType = _get_first_child_text(sample, "type")
if forType != "":
samTypeLookup[samId] = forType
targets = _get_all_children(rootEl._node, "target")
for target in targets:
if target.attrib['id'] != "":
tarId = target.attrib['id']
forType = _get_first_child_text(target, "type")
if forType != "":
tarTypeLookup[tarId] = forType
forId = _get_first_child(target, "dyeId")
if forId is not None and forId.attrib['id'] != "":
dyeLookup[forId.attrib['id']] = 1
# Process the lines
for tabLine in tabLines[1:]:
sLin = tabLine.split("\t")
if len(sLin) < 7 or sLin[1] == "" or sLin[2] == "" or sLin[3] == "" or sLin[4] == "" or sLin[5] == "":
continue
if sLin[1] not in samTypeLookup:
rootEl.new_sample(sLin[1], sLin[2])
samTypeLookup[sLin[1]] = sLin[2]
ret += "Created sample \"" + sLin[1] + "\" with type \"" + sLin[2] + "\"\n"
if sLin[3] not in tarTypeLookup:
if sLin[5] not in dyeLookup:
rootEl.new_dye(sLin[5])
dyeLookup[sLin[5]] = 1
ret += "Created dye \"" + sLin[5] + "\"\n"
rootEl.new_target(sLin[3], sLin[4])
elem = rootEl.get_target(byid=sLin[3])
elem["dyeId"] = sLin[5]
tarTypeLookup[sLin[3]] = sLin[4]
ret += "Created " + sLin[3] + " with type \"" + sLin[4] + "\" and dye \"" + sLin[5] + "\"\n"
react = None
data = None
# Get the position number if required
wellPos = sLin[0]
if re.search(r"\D\d+", sLin[0]):
old_letter = ord(re.sub(r"\d", "", sLin[0]).upper()) - ord("A")
old_nr = int(re.sub(r"\D", "", sLin[0]))
newId = old_nr + old_letter * int(self["pcrFormat_columns"])
wellPos = str(newId)
if re.search(r"\D\d+\D\d+", sLin[0]):
old_left = re.sub(r"\D\d+$", "", sLin[0])
old_left_letter = ord(re.sub(r"\d", "", old_left).upper()) - ord("A")
old_left_nr = int(re.sub(r"\D", "", old_left)) - 1
old_right = re.sub(r"^\D\d+", "", sLin[0])
old_right_letter = ord(re.sub(r"\d", "", old_right).upper()) - ord("A")
old_right_nr = int(re.sub(r"\D", "", old_right))
newId = old_left_nr * 8 + old_right_nr + old_left_letter * 768 + old_right_letter * 96
wellPos = str(newId)
exp = _get_all_children(self._node, "react")
for node in exp:
if wellPos == node.attrib['id']:
react = node
forId = _get_first_child_text(react, "sample")
if forId and forId != "" and forId.attrib['id'] != sLin[1]:
ret += "Missmatch: Well " + wellPos + " (" + sLin[0] + ") has sample \"" + forId.attrib['id'] + \
"\" in RDML file and sample \"" + sLin[1] + "\" in tab file.\n"
break
if react is None:
new_node = et.Element("react", id=wellPos)
place = _get_tag_pos(self._node, "react", self.xmlkeys(), 9999999)
self._node.insert(place, new_node)
react = new_node
new_node = et.Element("sample", id=sLin[1])
react.insert(0, new_node)
exp = _get_all_children(react, "data")
for node in exp:
forId = _get_first_child(node, "tar")
if forId is not None and forId.attrib['id'] == sLin[3]:
data = node
break
if data is None:
new_node = et.Element("data")
place = _get_tag_pos(react, "data", ["sample", "data", "partitions"], 9999999)
react.insert(place, new_node)
data = new_node
new_node = et.Element("tar", id=sLin[3])
place = _get_tag_pos(data, "tar",
_getXMLDataType(),
9999999)
data.insert(place, new_node)
if dMode == "amp":
presentAmp = _get_first_child(data, "adp")
if presentAmp is not None:
ret += "Well " + wellPos + " (" + sLin[0] + ") with sample \"" + sLin[1] + " and target \"" + \
sLin[3] + "\" has already amplification data, no data were added.\n"
else:
colCount = 6
for col in sLin[6:]:
new_node = et.Element("adp")
place = _get_tag_pos(data, "adp",
_getXMLDataType(),
9999999)
data.insert(place, new_node)
new_sub = et.Element("cyc")
new_sub.text = head[colCount]
place = _get_tag_pos(new_node, "cyc", ["cyc", "tmp", "fluor"], 9999999)
new_node.insert(place, new_sub)
new_sub = et.Element("fluor")
new_sub.text = col
place = _get_tag_pos(new_node, "fluor", ["cyc", "tmp", "fluor"], 9999999)
new_node.insert(place, new_sub)
colCount += 1
if dMode == "melt":
presentAmp = _get_first_child(data, "mdp")
if presentAmp is not None:
ret += "Well " + wellPos + " (" + sLin[0] + ") with sample \"" + sLin[1] + " and target \"" + \
sLin[3] + "\" has already melting data, no data were added.\n"
else:
colCount = 6
for col in sLin[6:]:
new_node = et.Element("mdp")
place = _get_tag_pos(data, "mdp",
_getXMLDataType(),
9999999)
data.insert(place, new_node)
new_sub = et.Element("tmp")
new_sub.text = head[colCount]
place = _get_tag_pos(new_node, "tmp", ["tmp", "fluor"], 9999999)
new_node.insert(place, new_sub)
new_sub = et.Element("fluor")
new_sub.text = col
place = _get_tag_pos(new_node, "fluor", ["tmp", "fluor"], 9999999)
new_node.insert(place, new_sub)
colCount += 1
return ret
def import_digital_data(self, rootEl, fileformat, filename, filelist, ignoreCh=""):
"""Imports data from a tab seperated table file with digital PCR overview data.
Args:
self: The class self parameter.
rootEl: The rdml root element.
fileformat: The format of the files (RDML, BioRad).
filename: The tab overvie file to open (recommended but optional).
filelist: A list of tab files with fluorescence data (optional, works without filename).
Returns:
A string with the modifications made.
"""
tempList = re.split(r"\D+", ignoreCh)
ignoreList = []
for posNum in tempList:
if re.search(r"\d", posNum):
ignoreList.append(int(posNum))
ret = ""
wellNames = []
uniqueFileNames = []
if filelist is None:
filelist = []
# Get the information for the lookup dictionaries
samTypeLookup = {}
tarTypeLookup = {}
dyeLookup = {}
headerLookup = {}
fileLookup = {}
fileNameSuggLookup = {}
samples = _get_all_children(rootEl._node, "sample")
for sample in samples:
if sample.attrib['id'] != "":
samId = sample.attrib['id']
forType = _get_first_child_text(sample, "type")
if forType != "":
samTypeLookup[samId] = forType
targets = _get_all_children(rootEl._node, "target")
for target in targets:
if target.attrib['id'] != "":
tarId = target.attrib['id']
forType = _get_first_child_text(target, "type")
if forType != "":
tarTypeLookup[tarId] = forType
dyes = _get_all_children(rootEl._node, "dye")
for dye in dyes:
if dye.attrib['id'] != "":
dyeLookup[dye.attrib['id']] = 1
# Work the overview file
if filename is not None:
with open(filename, newline='') as tfile: # add encoding='utf-8' ?
posCount = 0
posWell = 0
posSample = -1
posSampleType = -1
posDye = -1
posDyeCh2 = -1
posDyeCh3 = -1
posTarget = -1
posTargetCh2 = -1
posTargetCh3 = -1
posTargetType = -1
posCopConc = -1
posPositives = -1
posNegatives = -1
posCopConcCh2 = -1
posPositivesCh2 = -1
posNegativesCh2 = -1
posCopConcCh3 = -1
posPositivesCh3 = -1
posNegativesCh3 = -1
posUndefined = -1
posExcluded = -1
posVolume = -1
posFilename = -1
countUpTarget = 1
if fileformat == "RDML":
tabLines = list(csv.reader(tfile, delimiter='\t'))
for hInfo in tabLines[0]:
if hInfo == "Sample":
posSample = posCount
if hInfo == "SampleType":
posSampleType = posCount
if hInfo == "Target":
posTarget = posCount
if hInfo == "TargetType":
posTargetType = posCount
if hInfo == "Dye":
posDye = posCount
if hInfo == "Copies":
posCopConc = posCount
if hInfo == "Positives":
posPositives = posCount
if hInfo == "Negatives":
posNegatives = posCount
if hInfo == "Undefined":
posUndefined = posCount
if hInfo == "Excluded":
posExcluded = posCount
if hInfo == "Volume":
posVolume = posCount
if hInfo == "FileName":
posFilename = posCount
posCount += 1
elif fileformat == "Bio-Rad":
tabLines = list(csv.reader(tfile, delimiter=','))
for hInfo in tabLines[0]:
if hInfo == "Sample":
posSample = posCount
if hInfo in ["TargetType", "TypeAssay"]:
posDye = posCount
if hInfo in ["Target", "Assay"]:
posTarget = posCount
if hInfo == "CopiesPer20uLWell":
posCopConc = posCount
if hInfo == "Positives":
posPositives = posCount
if hInfo == "Negatives":
posNegatives = posCount
posCount += 1
elif fileformat == "Stilla":
posWell = 1
tabLines = list(csv.reader(tfile, delimiter=','))
for hInfo in tabLines[0]:
hInfo = re.sub(r"^ +", '', hInfo)
if hInfo == "SampleName":
posSample = posCount
# This is a hack of the format to allow specification of targets
if hInfo == "Blue_Channel_Target":
posTarget = posCount
if hInfo == "Green_Channel_Target":
posTargetCh2 = posCount
if hInfo == "Red_Channel_Target":
posTargetCh3 = posCount
# End of hack
if hInfo == "Blue_Channel_Concentration":
posCopConc = posCount
if hInfo == "Blue_Channel_NumberOfPositiveDroplets":
posPositives = posCount
if hInfo == "Blue_Channel_NumberOfNegativeDroplets":
posNegatives = posCount
if hInfo == "Green_Channel_Concentration":
posCopConcCh2 = posCount
if hInfo == "Green_Channel_NumberOfPositiveDroplets":
posPositivesCh2 = posCount
if hInfo == "Green_Channel_NumberOfNegativeDroplets":
posNegativesCh2 = posCount
if hInfo == "Red_Channel_Concentration":
posCopConcCh3 = posCount
if hInfo == "Red_Channel_NumberOfPositiveDroplets":
posPositivesCh3 = posCount
if hInfo == "Red_Channel_NumberOfNegativeDroplets":
posNegativesCh3 = posCount
posCount += 1
else:
raise RdmlError('Unknown digital file format.')
if posSample == -1:
raise RdmlError('The overview tab-format is not valid, sample columns are missing.')
if posDye == -1 and fileformat != "Stilla":
raise RdmlError('The overview tab-format is not valid, dye / channel columns are missing.')
if posTarget == -1 and fileformat != "Stilla":
raise RdmlError('The overview tab-format is not valid, target columns are missing.')
if posPositives == -1:
raise RdmlError('The overview tab-format is not valid, positives columns are missing.')
if posNegatives == -1:
raise RdmlError('The overview tab-format is not valid, negatives columns are missing.')
# Process the lines
for rowNr in range(1, len(tabLines)):
emptyLine = True
if len(tabLines[rowNr]) < 7:
continue
for colNr in range(0, len(tabLines[rowNr])):
if tabLines[rowNr][colNr] != "":
emptyLine = False
tabLines[rowNr][colNr] = re.sub(r'^ +', '', tabLines[rowNr][colNr])
tabLines[rowNr][colNr] = re.sub(r' +$', '', tabLines[rowNr][colNr])
if emptyLine is True:
continue
sLin = tabLines[rowNr]
if sLin[posSample] not in samTypeLookup:
posSampleTypeName = "unkn"
if posSampleType != -1:
posSampleTypeName = sLin[posSampleType]
rootEl.new_sample(sLin[posSample], posSampleTypeName)
samTypeLookup[sLin[posSample]] = posSampleTypeName
ret += "Created sample \"" + sLin[posSample] + "\" with type \"" + posSampleTypeName + "\"\n"
# Fix well position
wellPos = re.sub(r"\"", "", sLin[posWell])
if fileformat == "Stilla":
wellPos = re.sub(r'^\d+-', '', wellPos)
# Create nonexisting targets and dyes
if fileformat == "Stilla":
if 1 not in ignoreList:
if posTarget > -1:
crTarName = sLin[posTarget]
else:
crTarName = " Target " + str(countUpTarget) + " Ch1"
countUpTarget += 1
chan = "Ch1"
if crTarName not in tarTypeLookup:
if chan not in dyeLookup:
rootEl.new_dye(chan)
dyeLookup[chan] = 1
ret += "Created dye \"" + chan + "\"\n"
rootEl.new_target(crTarName, "toi")
elem = rootEl.get_target(byid=crTarName)
elem["dyeId"] = chan
tarTypeLookup[crTarName] = "toi"
ret += "Created " + crTarName + " with type \"toi\" and dye \"" + chan + "\"\n"
if wellPos.upper() not in headerLookup:
headerLookup[wellPos.upper()] = {}
headerLookup[wellPos.upper()][chan] = crTarName
if 2 not in ignoreList:
if posTargetCh2 > -1:
crTarName = sLin[posTargetCh2]
else:
crTarName = " Target " + str(countUpTarget) + " Ch2"
countUpTarget += 1
chan = "Ch2"
if crTarName not in tarTypeLookup:
if chan not in dyeLookup:
rootEl.new_dye(chan)
dyeLookup[chan] = 1
ret += "Created dye \"" + chan + "\"\n"
rootEl.new_target(crTarName, "toi")
elem = rootEl.get_target(byid=crTarName)
elem["dyeId"] = chan
tarTypeLookup[crTarName] = "toi"
ret += "Created " + crTarName + " with type \"toi\" and dye \"" + chan + "\"\n"
if wellPos.upper() not in headerLookup:
headerLookup[wellPos.upper()] = {}
headerLookup[wellPos.upper()][chan] = crTarName
if 3 not in ignoreList:
if posTargetCh3 > -1:
crTarName = sLin[posTargetCh3]
else:
crTarName = " Target " + str(countUpTarget) + " Ch3"
countUpTarget += 1
chan = "Ch3"
if crTarName not in tarTypeLookup:
if chan not in dyeLookup:
rootEl.new_dye(chan)
dyeLookup[chan] = 1
ret += "Created dye \"" + chan + "\"\n"
rootEl.new_target(crTarName, "toi")
elem = rootEl.get_target(byid=crTarName)
elem["dyeId"] = chan
tarTypeLookup[crTarName] = "toi"
ret += "Created " + crTarName + " with type \"toi\" and dye \"" + chan + "\"\n"
if wellPos.upper() not in headerLookup:
headerLookup[wellPos.upper()] = {}
headerLookup[wellPos.upper()][chan] = crTarName
else:
if fileformat == "Bio-Rad":
posDyeName = sLin[posDye][:3]
else:
posDyeName = sLin[posDye]
if posTarget > -1 and int(re.sub(r"\D", "", posDyeName)) not in ignoreList:
if sLin[posTarget] not in tarTypeLookup:
if posDyeName not in dyeLookup:
rootEl.new_dye(posDyeName)
dyeLookup[posDyeName] = 1
ret += "Created dye \"" + posDyeName + "\"\n"
posTargetTypeName = "toi"
if posTargetType != -1:
posTargetTypeName = sLin[posTargetType]
rootEl.new_target(sLin[posTarget], posTargetTypeName)
elem = rootEl.get_target(byid=sLin[posTarget])
elem["dyeId"] = posDyeName
tarTypeLookup[sLin[posTarget]] = posTargetTypeName
ret += "Created " + sLin[posTarget] + " with type \"" + posTargetTypeName + "\" and dye \"" + posDyeName + "\"\n"
if wellPos.upper() not in headerLookup:
headerLookup[wellPos.upper()] = {}
headerLookup[wellPos.upper()][posDyeName] = sLin[posTarget]
if posFilename != -1 and sLin[posFilename] != "":
fileNameSuggLookup[wellPos.upper()] = sLin[posFilename]
react = None
partit = None
data = None
# Get the position number if required
wellPosStore = wellPos
if re.search(r"\D\d+", wellPos):
old_letter = ord(re.sub(r"\d", "", wellPos.upper())) - ord("A")
old_nr = int(re.sub(r"\D", "", wellPos))
newId = old_nr + old_letter * int(self["pcrFormat_columns"])
wellPos = str(newId)
exp = _get_all_children(self._node, "react")
for node in exp:
if wellPos == node.attrib['id']:
react = node
forId = _get_first_child_text(react, "sample")
if forId and forId != "" and forId.attrib['id'] != sLin[posSample]:
ret += "Missmatch: Well " + wellPos + " (" + sLin[posWell] + ") has sample \"" + forId.attrib['id'] + \
"\" in RDML file and sample \"" + sLin[posSample] + "\" in tab file.\n"
break
if react is None:
new_node = et.Element("react", id=wellPos)
place = _get_tag_pos(self._node, "react", self.xmlkeys(), 9999999)
self._node.insert(place, new_node)
react = new_node
new_node = et.Element("sample", id=sLin[posSample])
react.insert(0, new_node)
partit = _get_first_child(react, "partitions")
if partit is None:
new_node = et.Element("partitions")
place = _get_tag_pos(react, "partitions", ["sample", "data", "partitions"], 9999999)
react.insert(place, new_node)
partit = new_node
new_node = et.Element("volume")
if fileformat == "RDML":
new_node.text = sLin[posVolume]
elif fileformat == "Bio-Rad":
new_node.text = "0.85"
elif fileformat == "Stilla":
new_node.text = "0.59"
else:
new_node.text = "0.70"
place = _get_tag_pos(partit, "volume", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
if fileformat == "Stilla":
exp = _get_all_children(partit, "data")
for i in range(1, 4):
if i in ignoreList:
continue
data = None
posDyeName = "Ch" + str(i)
stillaTarget = headerLookup[wellPosStore.upper()][posDyeName]
stillaConc = "0"
stillaPos = "0"
stillaNeg = "0"
if i == 1:
stillaConc = sLin[posCopConc]
stillaPos = sLin[posPositives]
stillaNeg = sLin[posNegatives]
if i == 2:
stillaConc = sLin[posCopConcCh2]
stillaPos = sLin[posPositivesCh2]
stillaNeg = sLin[posNegativesCh2]
if i == 3:
stillaConc = sLin[posCopConcCh3]
stillaPos = sLin[posPositivesCh3]
stillaNeg = sLin[posNegativesCh3]
if re.search(r"\.", stillaConc):
stillaConc = re.sub(r"0+$", "", stillaConc)
stillaConc = re.sub(r"\.$", ".0", stillaConc)
for node in exp:
forId = _get_first_child(node, "tar")
if forId is not None and forId.attrib['id'] == stillaTarget:
data = node
break
if data is None:
new_node = et.Element("data")
place = _get_tag_pos(partit, "data", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
data = new_node
new_node = et.Element("tar", id=stillaTarget)
place = _get_tag_pos(data, "tar", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
new_node = et.Element("pos")
new_node.text = stillaPos
place = _get_tag_pos(data, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
new_node = et.Element("neg")
new_node.text = stillaNeg
place = _get_tag_pos(data, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
new_node = et.Element("conc")
new_node.text = stillaConc
place = _get_tag_pos(data, "conc", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
else:
exp = _get_all_children(partit, "data")
for node in exp:
forId = _get_first_child(node, "tar")
if forId is not None and forId.attrib['id'] == sLin[posTarget]:
data = node
break
if data is None:
new_node = et.Element("data")
place = _get_tag_pos(partit, "data", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
data = new_node
new_node = et.Element("tar", id=sLin[posTarget])
place = _get_tag_pos(data, "tar", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
new_node = et.Element("pos")
new_node.text = sLin[posPositives]
place = _get_tag_pos(data, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
new_node = et.Element("neg")
new_node.text = sLin[posNegatives]
place = _get_tag_pos(data, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
if posUndefined != -1 and sLin[posUndefined] != "":
new_node = et.Element("undef")
new_node.text = sLin[posUndefined]
place = _get_tag_pos(data, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
if posExcluded != -1 and sLin[posExcluded] != "":
new_node = et.Element("excl")
new_node.text = sLin[posExcluded]
place = _get_tag_pos(data, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
if posCopConc != -1:
new_node = et.Element("conc")
if int(sLin[posPositives]) == 0:
new_node.text = "0"
else:
if fileformat == "RDML":
new_node.text = sLin[posCopConc]
elif fileformat == "Bio-Rad":
new_node.text = str(float(sLin[posCopConc])/20)
else:
new_node.text = sLin[posCopConc]
place = _get_tag_pos(data, "conc", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
# Read the raw data files
# Extract the well position from file names
constNameChars = 0
if len(filelist) > 0:
charStopCount = False
for i in range(len(filelist[0])):
currChar = None
if charStopCount is False:
for wellFileName in filelist:
if currChar is None:
currChar = wellFileName[i]
else:
if currChar != wellFileName[i]:
charStopCount = True
if charStopCount is False:
constNameChars = i + 1
for wellFileName in filelist:
currName = wellFileName[constNameChars:].upper()
currName = currName.replace(".CSV", "")
currName = currName.replace(".TSV", "")
currName = currName.replace("_AMPLITUDE", "")
currName = currName.replace("_COMPENSATEDDATA", "")
currName = currName.replace("_RAWDATA", "")
currName = re.sub(r"^\d+_", "", currName)
wellNames.append(currName)
fileLookup[currName] = wellFileName
# Propose a filename for raw data
runId = self._node.get('id')
runFix = re.sub(r"[^A-Za-z0-9]", "", runId)
experimentId = self._node.getparent().get('id')
experimentFix = re.sub(r"[^A-Za-z0-9]", "", experimentId)
propFileName = "partitions/" + experimentFix + "_" + runFix
# Get the used unique file names
if zipfile.is_zipfile(self._rdmlFilename):
with zipfile.ZipFile(self._rdmlFilename, 'r') as rdmlObj:
# Get list of files names in rdml zip
allRDMLfiles = rdmlObj.namelist()
for ele in allRDMLfiles:
if re.search("^partitions/", ele):
uniqueFileNames.append(ele.lower())
# Now process the files
warnVolume = ""
for well in wellNames:
outTabFile = ""
keepCh1 = False
keepCh2 = False
keepCh3 = False
header = ""
react = None
partit = None
dataCh1 = None
dataCh2 = None
dataCh3 = None
wellPos = well
if re.search(r"\D\d+", well):
old_letter = ord(re.sub(r"\d", "", well).upper()) - ord("A")
old_nr = int(re.sub(r"\D", "", well))
newId = old_nr + old_letter * int(self["pcrFormat_columns"])
wellPos = str(newId)
exp = _get_all_children(self._node, "react")
for node in exp:
if wellPos == node.attrib['id']:
react = node
break
if react is None:
sampleName = "Sample in " + well
if sampleName not in samTypeLookup:
rootEl.new_sample(sampleName, "unkn")
samTypeLookup[sampleName] = "unkn"
ret += "Created sample \"" + sampleName + "\" with type \"" + "unkn" + "\"\n"
new_node = et.Element("react", id=wellPos)
place = _get_tag_pos(self._node, "react", self.xmlkeys(), 9999999)
self._node.insert(place, new_node)
react = new_node
new_node = et.Element("sample", id=sampleName)
react.insert(0, new_node)
partit = _get_first_child(react, "partitions")
if partit is None:
new_node = et.Element("partitions")
place = _get_tag_pos(react, "partitions", ["sample", "data", "partitions"], 9999999)
react.insert(place, new_node)
partit = new_node
new_node = et.Element("volume")
if fileformat == "RDML":
new_node.text = "0.7"
warnVolume = "No information on partition volume given, used 0.7."
elif fileformat == "Bio-Rad":
new_node.text = "0.85"
elif fileformat == "Stilla":
new_node.text = "0.59"
else:
new_node.text = "0.85"
place = _get_tag_pos(partit, "volume", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
if wellPos in fileNameSuggLookup:
finalFileName = "partitions/" + fileNameSuggLookup[wellPos]
else:
finalFileName = "partitions/" + _get_first_child_text(partit, "endPtTable")
if finalFileName == "partitions/":
finalFileName = propFileName + "_" + wellPos + "_" + well + ".tsv"
triesCount = 0
if finalFileName.lower() in uniqueFileNames:
while triesCount < 100:
finalFileName = propFileName + "_" + wellPos + "_" + well + "_" + str(triesCount) + ".tsv"
if finalFileName.lower() not in uniqueFileNames:
uniqueFileNames.append(finalFileName.lower())
break
# print(finalFileName, flush=True)
with open(fileLookup[well], newline='') as wellfile: # add encoding='utf-8' ?
if fileformat == "RDML":
wellLines = list(csv.reader(wellfile, delimiter='\t'))
wellFileContent = wellfile.read()
_writeFileInRDML(self._rdmlFilename, finalFileName, wellFileContent)
delElem = _get_first_child(partit, "endPtTable")
if delElem is not None:
partit.remove(delElem)
new_node = et.Element("endPtTable")
new_node.text = re.sub(r'^partitions/', '', finalFileName)
place = _get_tag_pos(partit, "endPtTable", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
header = wellLines[0]
for col in range(0, len(header), 2):
cPos = 0
cNeg = 0
cUndef = 0
cExcl = 0
if header[col] != "":
targetName = header[col]
if targetName not in tarTypeLookup:
dye = "Ch" + str(int((col + 1) / 2))
if dye not in dyeLookup:
rootEl.new_dye(dye)
dyeLookup[dye] = 1
ret += "Created dye \"" + dye + "\"\n"
rootEl.new_target(targetName, "toi")
elem = rootEl.get_target(byid=targetName)
elem["dyeId"] = dye
tarTypeLookup[targetName] = "toi"
ret += "Created target " + targetName + " with type \"" + "toi" + "\" and dye \"" + dye + "\"\n"
for line in wellLines[1:]:
splitLine = line.split("\t")
if len(splitLine) - 1 < col + 1:
continue
if splitLine[col + 1] == "p":
cPos += 1
if splitLine[col + 1] == "n":
cNeg += 1
if splitLine[col + 1] == "u":
cUndef += 1
if splitLine[col + 1] == "e":
cExcl += 1
data = None
exp = _get_all_children(partit, "data")
for node in exp:
forId = _get_first_child(node, "tar")
if forId is not None and forId.attrib['id'] == targetName:
data = node
if data is None:
new_node = et.Element("data")
place = _get_tag_pos(partit, "data", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
data = new_node
new_node = et.Element("tar", id=targetName)
place = _get_tag_pos(data, "tar", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
delElem = _get_first_child(partit, "pos")
if delElem is not None:
data.remove(delElem)
new_node = et.Element("pos")
new_node.text = str(cPos)
place = _get_tag_pos(data, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
delElem = _get_first_child(partit, "neg")
if delElem is not None:
data.remove(delElem)
new_node = et.Element("neg")
new_node.text = str(cNeg)
place = _get_tag_pos(data, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
delElem = _get_first_child(partit, "undef")
if delElem is not None:
data.remove(delElem)
if cExcl > 0:
new_node = et.Element("undef")
new_node.text = str(cUndef)
place = _get_tag_pos(data, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
delElem = _get_first_child(partit, "excl")
if delElem is not None:
data.remove(delElem)
if cExcl > 0:
new_node = et.Element("excl")
new_node.text = str(cExcl)
place = _get_tag_pos(data, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
data.insert(place, new_node)
elif fileformat == "Bio-Rad":
wellLines = list(csv.reader(wellfile, delimiter=','))
ch1Pos = "0"
ch1Neg = "0"
ch1sum = 0
ch2Pos = "0"
ch2Neg = "0"
ch2sum = 0
if well in headerLookup:
if "Ch1" in headerLookup[well] and 1 not in ignoreList:
keepCh1 = True
header += headerLookup[well]["Ch1"] + "\t" + headerLookup[well]["Ch1"] + "\t"
if "Ch2" in headerLookup[well] and 2 not in ignoreList:
keepCh2 = True
header += headerLookup[well]["Ch2"] + "\t" + headerLookup[well]["Ch2"] + "\t"
outTabFile += re.sub(r'\t$', '\n', header)
else:
headerLookup[well] = {}
dyes = ["Ch1", "Ch2"]
if len(wellLines) > 1:
ch1Pos = ""
ch1Neg = ""
ch2Pos = ""
ch2Neg = ""
if re.search(r"\d", wellLines[1][0]) and 1 not in ignoreList:
keepCh1 = True
if len(wellLines[1]) > 1 and re.search(r"\d", wellLines[1][1]) and 2 not in ignoreList:
keepCh2 = True
for dye in dyes:
if dye not in dyeLookup:
rootEl.new_dye(dye)
dyeLookup[dye] = 1
ret += "Created dye \"" + dye + "\"\n"
dyeCount = 0
for dye in dyes:
dyeCount += 1
targetName = "Target in " + well + " " + dye
if targetName not in tarTypeLookup:
rootEl.new_target(targetName, "toi")
elem = rootEl.get_target(byid=targetName)
elem["dyeId"] = dye
tarTypeLookup[targetName] = "toi"
ret += "Created target " + targetName + " with type \"" + "toi" + "\" and dye \"" + dye + "\"\n"
headerLookup[well][dye] = targetName
if (dyeCount == 1 and keepCh1) or (dyeCount == 2 and keepCh2):
header += targetName + "\t" + targetName + "\t"
outTabFile += re.sub(r'\t$', '\n', header)
if keepCh1 or keepCh2:
exp = _get_all_children(partit, "data")
for node in exp:
forId = _get_first_child(node, "tar")
if keepCh1 and forId is not None and forId.attrib['id'] == headerLookup[well]["Ch1"]:
dataCh1 = node
ch1Pos = _get_first_child_text(dataCh1, "pos")
ch1Neg = _get_first_child_text(dataCh1, "neg")
ch1sum += int(ch1Pos) + int(ch1Neg)
if keepCh2 and forId is not None and forId.attrib['id'] == headerLookup[well]["Ch2"]:
dataCh2 = node
ch2Pos = _get_first_child_text(dataCh2, "pos")
ch2Neg = _get_first_child_text(dataCh2, "neg")
ch2sum += int(ch2Pos) + int(ch2Neg)
if dataCh1 is None and keepCh1:
new_node = et.Element("data")
place = _get_tag_pos(partit, "data", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
dataCh1 = new_node
new_node = et.Element("tar", id=headerLookup[well]["Ch1"])
place = _get_tag_pos(dataCh1, "tar", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
dataCh1.insert(place, new_node)
ch1Pos = ""
ch1Neg = ""
ch1sum = 2
if dataCh2 is None and keepCh2:
new_node = et.Element("data")
place = _get_tag_pos(partit, "data", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
dataCh2 = new_node
new_node = et.Element("tar", id=headerLookup[well]["Ch2"])
place = _get_tag_pos(dataCh2, "tar", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
dataCh2.insert(place, new_node)
ch2Pos = ""
ch2Neg = ""
ch2sum = 2
if dataCh1 is None and dataCh2 is None:
continue
if ch1sum < 1 and ch2sum < 1:
continue
if ch1Pos == "" and ch1Neg == "" and ch2Pos == "" and ch2Neg == "":
countPart = 0
for splitLine in wellLines[1:]:
if len(splitLine[0]) < 2:
continue
if keepCh1:
outTabFile += splitLine[0] + "\t" + "u"
if keepCh2:
if keepCh1:
outTabFile += "\t"
outTabFile += splitLine[1] + "\t" + "u\n"
else:
outTabFile += "\n"
countPart += 1
if keepCh1:
new_node = et.Element("pos")
new_node.text = "0"
place = _get_tag_pos(dataCh1, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
dataCh1.insert(place, new_node)
new_node = et.Element("neg")
new_node.text = "0"
place = _get_tag_pos(dataCh1, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
dataCh1.insert(place, new_node)
new_node = et.Element("undef")
new_node.text = str(countPart)
place = _get_tag_pos(dataCh1, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"], 9999999)
dataCh1.insert(place, new_node)
if keepCh2:
new_node = et.Element("pos")
new_node.text = "0"
place = _get_tag_pos(dataCh2, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh2.insert(place, new_node)
new_node = et.Element("neg")
new_node.text = "0"
place = _get_tag_pos(dataCh2, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh2.insert(place, new_node)
new_node = et.Element("undef")
new_node.text = str(countPart)
place = _get_tag_pos(dataCh2, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh2.insert(place, new_node)
else:
ch1Arr = []
ch2Arr = []
ch1Cut = 0
ch2Cut = 0
for splitLine in wellLines[1:]:
if len(splitLine) < 2:
continue
if keepCh1:
ch1Arr.append(float(splitLine[0]))
if keepCh2:
ch2Arr.append(float(splitLine[1]))
if keepCh1:
ch1Arr.sort()
if 0 < int(ch1Neg) <= len(ch1Arr):
ch1Cut = ch1Arr[int(ch1Neg) - 1]
if keepCh2:
ch2Arr.sort()
if 0 < int(ch2Neg) <= len(ch2Arr):
ch2Cut = ch2Arr[int(ch2Neg) - 1]
for splitLine in wellLines[1:]:
if len(splitLine) < 2:
continue
if keepCh1:
outTabFile += splitLine[0] + "\t"
if float(splitLine[0]) > ch1Cut:
outTabFile += "p"
else:
outTabFile += "n"
if keepCh2:
if keepCh1:
outTabFile += "\t"
outTabFile += splitLine[1] + "\t"
if float(splitLine[1]) > ch2Cut:
outTabFile += "p\n"
else:
outTabFile += "n\n"
else:
outTabFile += "\n"
_writeFileInRDML(self._rdmlFilename, finalFileName, outTabFile)
new_node = et.Element("endPtTable")
new_node.text = re.sub(r'^partitions/', '', finalFileName)
place = _get_tag_pos(partit, "endPtTable", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
else:
react.remove(partit)
elif fileformat == "Stilla":
wellLines = list(csv.reader(wellfile, delimiter=','))
ch1Pos = "0"
ch1Neg = "0"
ch1sum = 0
ch2Pos = "0"
ch2Neg = "0"
ch2sum = 0
ch3Pos = "0"
ch3Neg = "0"
ch3sum = 0
if well in headerLookup:
if "Ch1" in headerLookup[well] and 1 not in ignoreList:
keepCh1 = True
header += headerLookup[well]["Ch1"] + "\t" + headerLookup[well]["Ch1"] + "\t"
if "Ch2" in headerLookup[well] and 2 not in ignoreList:
keepCh2 = True
header += headerLookup[well]["Ch2"] + "\t" + headerLookup[well]["Ch2"] + "\t"
if "Ch3" in headerLookup[well] and 3 not in ignoreList:
keepCh3 = True
header += headerLookup[well]["Ch3"] + "\t" + headerLookup[well]["Ch3"] + "\t"
outTabFile += re.sub(r'\t$', '\n', header)
else:
headerLookup[well] = {}
dyes = ["Ch1", "Ch2", "Ch3"]
if len(wellLines) > 1:
ch1Pos = ""
ch1Neg = ""
ch2Pos = ""
ch2Neg = ""
ch3Pos = ""
ch3Neg = ""
if re.search(r"\d", wellLines[1][0]) and 1 not in ignoreList:
keepCh1 = True
if len(wellLines[1]) > 1 and re.search(r"\d", wellLines[1][1]) and 2 not in ignoreList:
keepCh2 = True
if len(wellLines[1]) > 2 and re.search(r"\d", wellLines[1][2]) and 3 not in ignoreList:
keepCh3 = True
for dye in dyes:
if dye not in dyeLookup:
rootEl.new_dye(dye)
dyeLookup[dye] = 1
ret += "Created dye \"" + dye + "\"\n"
dyeCount = 0
for dye in dyes:
dyeCount += 1
targetName = "Target in " + well + " " + dye
if targetName not in tarTypeLookup:
rootEl.new_target(targetName, "toi")
elem = rootEl.get_target(byid=targetName)
elem["dyeId"] = dye
tarTypeLookup[targetName] = "toi"
ret += "Created target " + targetName + " with type \"" + "toi" + "\" and dye \"" + dye + "\"\n"
if (dyeCount == 1 and keepCh1) or (dyeCount == 2 and keepCh2) or (dyeCount == 3 and keepCh3):
headerLookup[well][dye] = targetName
header += targetName + "\t" + targetName + "\t"
outTabFile += re.sub(r'\t$', '\n', header)
if keepCh1 or keepCh2 or keepCh3:
exp = _get_all_children(partit, "data")
for node in exp:
forId = _get_first_child(node, "tar")
if keepCh1 and forId is not None and forId.attrib['id'] == headerLookup[well]["Ch1"]:
dataCh1 = node
ch1Pos = _get_first_child_text(dataCh1, "pos")
ch1Neg = _get_first_child_text(dataCh1, "neg")
ch1sum += int(ch1Pos) + int(ch1Neg)
if keepCh2 and forId is not None and forId.attrib['id'] == headerLookup[well]["Ch2"]:
dataCh2 = node
ch2Pos = _get_first_child_text(dataCh2, "pos")
ch2Neg = _get_first_child_text(dataCh2, "neg")
ch2sum += int(ch2Pos) + int(ch2Neg)
if keepCh3 and forId is not None and forId.attrib['id'] == headerLookup[well]["Ch3"]:
dataCh3 = node
ch3Pos = _get_first_child_text(dataCh3, "pos")
ch3Neg = _get_first_child_text(dataCh3, "neg")
ch3sum += int(ch3Pos) + int(ch3Neg)
if dataCh1 is None and keepCh1:
new_node = et.Element("data")
place = _get_tag_pos(partit, "data", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
dataCh1 = new_node
new_node = et.Element("tar", id=headerLookup[well]["Ch1"])
place = _get_tag_pos(dataCh1, "tar", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh1.insert(place, new_node)
ch1Pos = ""
ch1Neg = ""
ch1sum = 2
if dataCh2 is None and keepCh2:
new_node = et.Element("data")
place = _get_tag_pos(partit, "data", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
dataCh2 = new_node
new_node = et.Element("tar", id=headerLookup[well]["Ch2"])
place = _get_tag_pos(dataCh2, "tar", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh2.insert(place, new_node)
ch2Pos = ""
ch2Neg = ""
ch2sum = 2
if dataCh3 is None and keepCh3:
new_node = et.Element("data")
place = _get_tag_pos(partit, "data", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
dataCh3 = new_node
new_node = et.Element("tar", id=headerLookup[well]["Ch3"])
place = _get_tag_pos(dataCh3, "tar", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh3.insert(place, new_node)
ch3Pos = ""
ch3Neg = ""
ch3sum = 2
if dataCh1 is None and dataCh2 is None and dataCh3 is None:
continue
if ch1sum < 1 and ch2sum < 1 and ch3sum < 1:
continue
if ch1Pos == "" and ch1Neg == "" and ch2Pos == "" and ch2Neg == "" and ch3Pos == "" and ch3Neg == "":
countPart = 0
for splitLine in wellLines[1:]:
if len(splitLine[0]) < 2:
continue
if keepCh1:
outTabFile += splitLine[0] + "\t" + "u"
if keepCh2:
if keepCh1:
outTabFile += "\t"
outTabFile += splitLine[1] + "\t" + "u"
if keepCh3:
if keepCh1 or keepCh2:
outTabFile += "\t"
outTabFile += splitLine[2] + "\t" + "u\n"
else:
outTabFile += "\n"
countPart += 1
if keepCh1:
new_node = et.Element("pos")
new_node.text = "0"
place = _get_tag_pos(dataCh1, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh1.insert(place, new_node)
new_node = et.Element("neg")
new_node.text = "0"
place = _get_tag_pos(dataCh1, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh1.insert(place, new_node)
new_node = et.Element("undef")
new_node.text = str(countPart)
place = _get_tag_pos(dataCh1, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh1.insert(place, new_node)
if keepCh2:
new_node = et.Element("pos")
new_node.text = "0"
place = _get_tag_pos(dataCh2, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh2.insert(place, new_node)
new_node = et.Element("neg")
new_node.text = "0"
place = _get_tag_pos(dataCh2, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh2.insert(place, new_node)
new_node = et.Element("undef")
new_node.text = str(countPart)
place = _get_tag_pos(dataCh2, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh2.insert(place, new_node)
if keepCh3:
new_node = et.Element("pos")
new_node.text = "0"
place = _get_tag_pos(dataCh3, "pos", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh3.insert(place, new_node)
new_node = et.Element("neg")
new_node.text = "0"
place = _get_tag_pos(dataCh3, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh3.insert(place, new_node)
new_node = et.Element("undef")
new_node.text = str(countPart)
place = _get_tag_pos(dataCh3, "neg", ["tar", "pos", "neg", "undef", "excl", "conc"],
9999999)
dataCh3.insert(place, new_node)
else:
ch1Arr = []
ch2Arr = []
ch3Arr = []
ch1Cut = 0
ch2Cut = 0
ch3Cut = 0
for splitLine in wellLines[1:]:
if len(splitLine) < 3:
continue
if keepCh1:
ch1Arr.append(float(splitLine[0]))
if keepCh2:
ch2Arr.append(float(splitLine[1]))
if keepCh3:
ch3Arr.append(float(splitLine[2]))
if keepCh1:
ch1Arr.sort()
if 0 < int(ch1Neg) <= len(ch1Arr):
ch1Cut = ch1Arr[int(ch1Neg) - 1]
if keepCh2:
ch2Arr.sort()
if 0 < int(ch2Neg) <= len(ch2Arr):
ch2Cut = ch2Arr[int(ch2Neg) - 1]
if keepCh3:
ch3Arr.sort()
if 0 < int(ch3Neg) <= len(ch3Arr):
ch3Cut = ch3Arr[int(ch3Neg) - 1]
for splitLine in wellLines[1:]:
if len(splitLine) < 2:
continue
if keepCh1:
outTabFile += splitLine[0] + "\t"
if float(splitLine[0]) > ch1Cut:
outTabFile += "p"
else:
outTabFile += "n"
if keepCh2:
if keepCh1:
outTabFile += "\t"
outTabFile += splitLine[1] + "\t"
if float(splitLine[1]) > ch2Cut:
outTabFile += "p"
else:
outTabFile += "n"
if keepCh3:
if keepCh1 or keepCh2:
outTabFile += "\t"
outTabFile += splitLine[2] + "\t"
if float(splitLine[2]) > ch3Cut:
outTabFile += "p\n"
else:
outTabFile += "n\n"
else:
outTabFile += "\n"
_writeFileInRDML(self._rdmlFilename, finalFileName, outTabFile)
new_node = et.Element("endPtTable")
new_node.text = re.sub(r'^partitions/', '', finalFileName)
place = _get_tag_pos(partit, "endPtTable", ["volume", "endPtTable", "data"], 9999999)
partit.insert(place, new_node)
else:
react.remove(partit)
ret += warnVolume
return ret
def get_digital_overview_data(self, rootEl):
"""Provides the digital overview data in tab seperated format.
Args:
self: The class self parameter.
rootEl: The rdml root element.
Returns:
A string with the overview data table.
"""
# 0 1 2 3 4 5 6 7 8 9 10 11 12 13
ret = "Pos\tWell\tSample\tSampleType\tTarget\tTargetType\tDye\tCopies\tPositives\tNegatives\tUndefined\tExcluded\tVolume\tFileName\n"
tabLines = []
# Fill the lookup dics
samTypeLookup = {}
tarTypeLookup = {}
tarDyeLookup = {}
samples = _get_all_children(rootEl._node, "sample")
for sample in samples:
if sample.attrib['id'] != "":
samId = sample.attrib['id']
forType = _get_first_child_text(sample, "type")
if forType != "":
samTypeLookup[samId] = forType
targets = _get_all_children(rootEl._node, "target")
for target in targets:
if target.attrib['id'] != "":
tarId = target.attrib['id']
forType = _get_first_child_text(target, "type")
if forType != "":
tarTypeLookup[tarId] = forType
forId = _get_first_child(target, "dyeId")
if forId is not None and forId.attrib['id'] != "":
tarDyeLookup[tarId] = forId.attrib['id']
reacts = _get_all_children(self._node, "react")
for react in reacts:
pPos = react.attrib['id']
posId = int(react.attrib['id'])
pIdNumber = posId % int(self["pcrFormat_columns"])
pIdLetter = chr(ord("A") + int(posId / int(self["pcrFormat_columns"])))
pWell = pIdLetter + str(pIdNumber)
pSample = ""
pSampleType = ""
pFileName = ""
forId = _get_first_child(react, "sample")
if forId is not None:
if forId.attrib['id'] != "":
pSample = forId.attrib['id']
pSampleType = samTypeLookup[forId.attrib['id']]
partit = _get_first_child(react, "partitions")
if partit is not None:
endPtTable = _get_first_child_text(partit, "endPtTable")
if endPtTable != "":
pFileName = endPtTable
pVolume = _get_first_child_text(partit, "volume")
partit_datas = _get_all_children(partit, "data")
for partit_data in partit_datas:
pTarget = ""
pTargetType = ""
pDye = ""
forId = _get_first_child(partit_data, "tar")
if forId is not None:
if forId.attrib['id'] != "":
pTarget = forId.attrib['id']
pTargetType = tarTypeLookup[pTarget]
pDye = tarDyeLookup[pTarget]
pCopies = _get_first_child_text(partit_data, "conc")
pPositives = _get_first_child_text(partit_data, "pos")
pNegatives = _get_first_child_text(partit_data, "neg")
pUnknown = _get_first_child_text(partit_data, "undef")
pExcluded = _get_first_child_text(partit_data, "excl")
retLine = pPos + "\t"
retLine += pWell + "\t"
retLine += pSample + "\t"
retLine += pSampleType + "\t"
retLine += pTarget + "\t"
retLine += pTargetType + "\t"
retLine += pDye + "\t"
retLine += pCopies + "\t"
retLine += pPositives + "\t"
retLine += pNegatives + "\t"
retLine += pUnknown + "\t"
retLine += pExcluded + "\t"
retLine += pVolume + "\t"
retLine += pFileName + "\n"
tabLines.append(retLine)
tabLines.sort(key=_sort_list_digital_PCR)
for tLine in tabLines:
ret += tLine
return ret
def get_digital_raw_data(self, reactPos):
"""Provides the digital of a react in tab seperated format.
Args:
self: The class self parameter.
reactPos: The react id to get the digital raw data from
Returns:
A string with the raw data table.
"""
react = None
retVal = ""
# Get the position number if required
wellPos = str(reactPos)
if re.search(r"\D\d+", wellPos):
old_letter = ord(re.sub(r"\d", "", wellPos.upper())) - ord("A")
old_nr = int(re.sub(r"\D", "", wellPos))
newId = old_nr + old_letter * int(self["pcrFormat_columns"])
wellPos = str(newId)
exp = _get_all_children(self._node, "react")
for node in exp:
if wellPos == node.attrib['id']:
react = node
break
if react is None:
return ""
partit = _get_first_child(react, "partitions")
if partit is None:
return ""
finalFileName = "partitions/" + _get_first_child_text(partit, "endPtTable")
if finalFileName == "partitions/":
return ""
if zipfile.is_zipfile(self._rdmlFilename):
zf = zipfile.ZipFile(self._rdmlFilename, 'r')
try:
retVal = zf.read(finalFileName).decode('utf-8')
except KeyError:
raise RdmlError('No ' + finalFileName + ' in compressed RDML file found.')
finally:
zf.close()
return retVal
def getreactjson(self):
"""Returns a json of the react data including fluorescence data.
Args:
self: The class self parameter.
Returns:
A json of the data.
"""
all_data = {}
data = []
reacts = _get_all_children(self._node, "react")
adp_cyc_max = 0.0
adp_fluor_min = 99999999
adp_fluor_max = 0.0
mdp_tmp_min = 120.0
mdp_tmp_max = 0.0
mdp_fluor_min = 99999999
mdp_fluor_max = 0.0
max_data = 0
max_partition_data = 0
anyCorrections = 0
for react in reacts:
react_json = {
"id": react.get('id'),
}
forId = _get_first_child(react, "sample")
if forId is not None:
if forId.attrib['id'] != "":
react_json["sample"] = forId.attrib['id']
react_datas = _get_all_children(react, "data")
max_data = max(max_data, len(react_datas))
react_datas_json = []
for react_data in react_datas:
in_react = {}
forId = _get_first_child(react_data, "tar")
if forId is not None:
if forId.attrib['id'] != "":
in_react["tar"] = forId.attrib['id']
_add_first_child_to_dic(react_data, in_react, True, "cq")
_add_first_child_to_dic(react_data, in_react, True, "N0")
_add_first_child_to_dic(react_data, in_react, True, "ampEffMet")
_add_first_child_to_dic(react_data, in_react, True, "ampEff")
_add_first_child_to_dic(react_data, in_react, True, "ampEffSE")
_add_first_child_to_dic(react_data, in_react, True, "corrF")
# Calculate the correction factors
calcCorr = _get_first_child_text(react_data, "corrF")
calcCq = _get_first_child_text(react_data, "cq")
calcN0 = _get_first_child_text(react_data, "N0")
calcEff = _get_first_child_text(react_data, "ampEff")
in_react["corrCq"] = ""
in_react["corrN0"] = ""
if not calcCorr == "":
calcCorr = float(calcCorr)
if not np.isnan(calcCorr):
if 0.0 < calcCorr < 1.0:
if calcEff == "":
calcEff = 2.0
else:
calcEff = float(calcEff)
if not np.isnan(calcEff):
if 0.0 < calcEff < 3.0:
if not calcCq == "":
calcCq = float(calcCq)
if not np.isnan(calcCq):
if calcCq > 0.0:
finalCq = calcCq - np.log10(calcCorr) / np.log10(calcEff)
in_react["corrCq"] = "{:.3f}".format(finalCq)
anyCorrections = 1
else:
in_react["corrCq"] = "-1.0"
if not calcN0 == "":
calcN0 = float(calcN0)
if not np.isnan(calcN0):
if calcCq > 0.0:
finalN0 = calcCorr * calcN0
in_react["corrN0"] = "{:.2e}".format(finalN0)
anyCorrections = 1
else:
in_react["corrN0"] = "-1.0"
if calcCorr == 0.0:
if not calcCq == "":
in_react["corrCq"] = ""
if not calcN0 == "":
in_react["corrN0"] = 0.0
if calcCorr == 1.0:
if not calcCq == "":
in_react["corrCq"] = calcCq
if not calcN0 == "":
in_react["corrN0"] = calcN0
_add_first_child_to_dic(react_data, in_react, True, "meltTemp")
_add_first_child_to_dic(react_data, in_react, True, "excl")
_add_first_child_to_dic(react_data, in_react, True, "note")
_add_first_child_to_dic(react_data, in_react, True, "endPt")
_add_first_child_to_dic(react_data, in_react, True, "bgFluor")
_add_first_child_to_dic(react_data, in_react, True, "bgFluorSlp")
_add_first_child_to_dic(react_data, in_react, True, "quantFluor")
adps = _get_all_children(react_data, "adp")
adps_json = []
for adp in adps:
cyc = _get_first_child_text(adp, "cyc")
fluor = _get_first_child_text(adp, "fluor")
adp_cyc_max = max(adp_cyc_max, float(cyc))
adp_fluor_min = min(adp_fluor_min, float(fluor))
adp_fluor_max = max(adp_fluor_max, float(fluor))
in_adp = [cyc, fluor, _get_first_child_text(adp, "tmp")]
adps_json.append(in_adp)
in_react["adps"] = adps_json
mdps = _get_all_children(react_data, "mdp")
mdps_json = []
for mdp in mdps:
tmp = _get_first_child_text(mdp, "tmp")
fluor = _get_first_child_text(mdp, "fluor")
mdp_tmp_min = min(mdp_tmp_min, float(tmp))
mdp_tmp_max = max(mdp_tmp_max, float(tmp))
mdp_fluor_min = min(mdp_fluor_min, float(fluor))
mdp_fluor_max = max(mdp_fluor_max, float(fluor))
in_mdp = [tmp, fluor]
mdps_json.append(in_mdp)
in_react["mdps"] = mdps_json
react_datas_json.append(in_react)
react_json["datas"] = react_datas_json
partit = _get_first_child(react, "partitions")
if partit is not None:
in_partitions = {}
endPtTable = _get_first_child_text(partit, "endPtTable")
if endPtTable != "":
in_partitions["endPtTable"] = endPtTable
partit_datas = _get_all_children(partit, "data")
max_partition_data = max(max_partition_data, len(partit_datas))
partit_datas_json = []
for partit_data in partit_datas:
in_partit = {}
forId = _get_first_child(partit_data, "tar")
if forId is not None:
if forId.attrib['id'] != "":
in_partit["tar"] = forId.attrib['id']
_add_first_child_to_dic(partit_data, in_partit, False, "pos")
_add_first_child_to_dic(partit_data, in_partit, False, "neg")
_add_first_child_to_dic(partit_data, in_partit, True, "undef")
_add_first_child_to_dic(partit_data, in_partit, True, "excl")
_add_first_child_to_dic(partit_data, in_partit, True, "conc")
partit_datas_json.append(in_partit)
in_partitions["datas"] = partit_datas_json
react_json["partitions"] = in_partitions
data.append(react_json)
all_data["reacts"] = data
all_data["adp_cyc_max"] = adp_cyc_max
all_data["anyCalcCorrections"] = anyCorrections
all_data["adp_fluor_min"] = adp_fluor_min
all_data["adp_fluor_max"] = adp_fluor_max
all_data["mdp_tmp_min"] = mdp_tmp_min
all_data["mdp_tmp_max"] = mdp_tmp_max
all_data["mdp_fluor_min"] = mdp_fluor_min
all_data["mdp_fluor_max"] = mdp_fluor_max
all_data["max_data_len"] = max_data
all_data["max_partition_data_len"] = max_partition_data
return all_data
def setExclNote(self, vReact, vTar, vExcl, vNote):
"""Saves the note and excl string for one react/data combination.
Args:
self: The class self parameter.
vReact: The reaction id.
vTar: The target id.
vExcl: The exclusion string to save.
vNote: The note string to save.
Returns:
Nothing, updates RDML data.
"""
expParent = self._node.getparent()
rootPar = expParent.getparent()
ver = rootPar.get('version')
dataXMLelements = _getXMLDataType()
reacts = _get_all_children(self._node, "react")
for react in reacts:
if int(react.get('id')) == int(vReact):
react_datas = _get_all_children(react, "data")
for react_data in react_datas:
forId = _get_first_child(react_data, "tar")
if forId is not None:
if forId.attrib['id'] == vTar:
_change_subelement(react_data, "excl", dataXMLelements, vExcl, True, "string")
if ver == "1.3":
_change_subelement(react_data, "note", dataXMLelements, vNote, True, "string")
return
def webAppLinRegPCR(self, pcrEfficiencyExl=0.05, updateRDML=False, excludeNoPlateau=True, excludeEfficiency="outlier"):
"""Performs LinRegPCR on the run. Modifies the cq values and returns a json with additional data.
Args:
self: The class self parameter.
pcrEfficiencyExl: Exclude samples with an efficiency outside the given range (0.05).
updateRDML: If true, update the RDML data with the calculated values.
excludeNoPlateau: If true, samples without plateau are excluded from mean PCR efficiency calculation.
excludeEfficiency: Choose "outlier", "mean", "include" to exclude based on indiv PCR eff.
Returns:
A dictionary with the resulting data, presence and format depending on input.
rawData: A 2d array with the raw fluorescence values
baselineCorrectedData: A 2d array with the baseline corrected raw fluorescence values
resultsList: A 2d array object.
resultsCSV: A csv string.
"""
allData = self.getreactjson()
res = self.linRegPCR(pcrEfficiencyExl=pcrEfficiencyExl,
updateRDML=updateRDML,
excludeNoPlateau=excludeNoPlateau,
excludeEfficiency=excludeEfficiency,
saveRaw=False,
saveBaslineCorr=True,
saveResultsList=True,
saveResultsCSV=False,
verbose=False)
if "baselineCorrectedData" in res:
bas_cyc_max = len(res["baselineCorrectedData"][0]) - 5
bas_fluor_min = 99999999
bas_fluor_max = 0.0
for row in range(1, len(res["baselineCorrectedData"])):
bass_json = []
for col in range(5, len(res["baselineCorrectedData"][row])):
cyc = res["baselineCorrectedData"][0][col]
fluor = res["baselineCorrectedData"][row][col]
if not (np.isnan(fluor) or fluor <= 0.0):
bas_fluor_min = min(bas_fluor_min, float(fluor))
bas_fluor_max = max(bas_fluor_max, float(fluor))
in_bas = [cyc, fluor, ""]
bass_json.append(in_bas)
# Fixme do not loop over all, use sorted data and clever moving
for react in allData["reacts"]:
if react["id"] == res["baselineCorrectedData"][row][0]:
for data in react["datas"]:
if data["tar"] == res["baselineCorrectedData"][row][3]:
data["bass"] = list(bass_json)
allData["bas_cyc_max"] = bas_cyc_max
allData["bas_fluor_min"] = bas_fluor_min
allData["bas_fluor_max"] = bas_fluor_max
if "resultsList" in res:
header = res["resultsList"].pop(0)
resList = sorted(res["resultsList"], key=_sort_list_int)
for rRow in range(0, len(resList)):
for rCol in range(0, len(resList[rRow])):
if isinstance(resList[rRow][rCol], np.float64) and np.isnan(resList[rRow][rCol]):
resList[rRow][rCol] = ""
if isinstance(resList[rRow][rCol], float) and math.isnan(resList[rRow][rCol]):
resList[rRow][rCol] = ""
allData["LinRegPCR_Result_Table"] = json.dumps([header] + resList, cls=NpEncoder)
if "noRawData" in res:
allData["error"] = res["noRawData"]
return allData
def linRegPCR(self, pcrEfficiencyExl=0.05, updateRDML=False, excludeNoPlateau=True, excludeEfficiency="outlier",
commaConv=False, ignoreExclusion=False,
saveRaw=False, saveBaslineCorr=False, saveResultsList=False, saveResultsCSV=False,
timeRun=False, verbose=False):
"""Performs LinRegPCR on the run. Modifies the cq values and returns a json with additional data.
Args:
self: The class self parameter.
pcrEfficiencyExl: Exclude samples with an efficiency outside the given range (0.05).
updateRDML: If true, update the RDML data with the calculated values.
excludeNoPlateau: If true, samples without plateau are excluded from mean PCR efficiency calculation.
excludeEfficiency: Choose "outlier", "mean", "include" to exclude based on indiv PCR eff.
commaConv: If true, convert comma separator to dot.
ignoreExclusion: If true, ignore the RDML exclusion strings.
saveRaw: If true, no raw values are given in the returned data
saveBaslineCorr: If true, no baseline corrected values are given in the returned data
saveResultsList: If true, return a 2d array object.
saveResultsCSV: If true, return a csv string.
timeRun: If true, print runtime for baseline and total.
verbose: If true, comment every performed step.
Returns:
A dictionary with the resulting data, presence and format depending on input.
rawData: A 2d array with the raw fluorescence values
baselineCorrectedData: A 2d array with the baseline corrected raw fluorescence values
resultsList: A 2d array object.
resultsCSV: A csv string.
"""
expParent = self._node.getparent()
rootPar = expParent.getparent()
dataVersion = rootPar.get('version')
if dataVersion == "1.0":
raise RdmlError('LinRegPCR requires RDML version > 1.0.')
##############################
# Collect the data in arrays #
##############################
# res is a 2 dimensional array accessed only by
# variables, so columns might be added here
header = [["id", # 0
"well", # 1
"sample", # 2
"sample type", # 3
"sample nucleotide", # 4
"target", # 5
"target chemistry", # 6
"excluded", # 7
"note", # 8
"baseline", # 9
"lower limit", # 10
"upper limit", # 11
"common threshold", # 12
"group threshold", # 13
"n in log phase", # 14
"last log cycle", # 15
"n included", # 16
"log lin cycle", # 17
"log lin fluorescence", # 18
"indiv PCR eff", # 19
"R2", # 20
"N0 (indiv eff - for debug use)", # 21
"Cq (indiv eff - for debug use)", # 22
"Cq with group threshold (indiv eff - for debug use)", # 23
"mean PCR eff", # 24
"standard error of the mean PCR eff", # 25
"N0 (mean eff)", # 26
"Cq (mean eff)", # 27
"mean PCR eff - no plateau", # 28
"standard error of the mean PCR eff - no plateau", # 29
"N0 (mean eff) - no plateau", # 30
"Cq (mean eff) - no plateau", # 31
"mean PCR eff - mean efficiency", # 32
"standard error of the mean PCR eff - mean efficiency", # 33
"N0 (mean eff) - mean efficiency", # 34
"Cq (mean eff) - mean efficiency", # 35
"mean PCR eff - no plateau - mean efficiency", # 36
"standard error of the mean PCR eff - no plateau - mean efficiency", # 37
"N0 (mean eff) - no plateau - mean efficiency", # 38
"Cq (mean eff) - no plateau - mean efficiency", # 39
"mean PCR eff - stat efficiency", # 40
"standard error of the mean PCR eff - stat efficiency", # 41
"N0 (mean eff) - stat efficiency", # 42
"Cq (mean eff) - stat efficiency", # 43
"mean PCR eff - no plateau - stat efficiency", # 44
"standard error of the stat PCR eff - no plateau - stat efficiency", # 45
"N0 (mean eff) - no plateau - stat efficiency", # 46
"Cq (mean eff) - no plateau - stat efficiency", # 47
"amplification", # 48
"baseline error", # 49
"plateau", # 50
"noisy sample", # 51
"PCR efficiency outside mean rage", # 52
"PCR efficiency outside mean rage - no plateau", # 53
"PCR efficiency outlier", # 54
"PCR efficiency outlier - no plateau", # 55
"short log lin phase", # 56
"Cq is shifting", # 57
"too low Cq eff", # 58
"too low Cq N0", # 59
"used for W-o-L setting"]] # 60
rar_id = 0
rar_well = 1
rar_sample = 2
rar_sample_type = 3
rar_sample_nucleotide = 4
rar_tar = 5
rar_tar_chemistry = 6
rar_excl = 7
rar_note = 8
rar_baseline = 9
rar_lower_limit = 10
rar_upper_limit = 11
rar_threshold_common = 12
rar_threshold_group = 13
rar_n_log = 14
rar_stop_log = 15
rar_n_included = 16
rar_log_lin_cycle = 17
rar_log_lin_fluorescence = 18
rar_indiv_PCR_eff = 19
rar_R2 = 20
rar_N0_indiv_eff = 21
rar_Cq_common = 22
rar_Cq_grp = 23
rar_meanEff_Skip = 24
rar_stdEff_Skip = 25
rar_meanN0_Skip = 26
rar_Cq_Skip = 27
rar_meanEff_Skip_Plat = 28
rar_stdEff_Skip_Plat = 29
rar_meanN0_Skip_Plat = 30
rar_Cq_Skip_Plat = 31
rar_meanEff_Skip_Mean = 32
rar_stdEff_Skip_Mean = 33
rar_meanN0_Skip_Mean = 34
rar_Cq_Skip_Mean = 35
rar_meanEff_Skip_Plat_Mean = 36
rar_stdEff_Skip_Plat_Mean = 37
rar_meanN0_Skip_Plat_Mean = 38
rar_Cq_Skip_Plat_Mean = 39
rar_meanEff_Skip_Out = 40
rar_stdEff_Skip_Out = 41
rar_meanN0_Skip_Out = 42
rar_Cq_Skip_Out = 43
rar_meanEff_Skip_Plat_Out = 44
rar_stdEff_Skip_Plat_Out = 45
rar_meanN0_Skip_Plat_Out = 46
rar_Cq_Skip_Plat_Out = 47
rar_amplification = 48
rar_baseline_error = 49
rar_plateau = 50
rar_noisy_sample = 51
rar_effOutlier_Skip_Mean = 52
rar_effOutlier_Skip_Plat_Mean = 53
rar_effOutlier_Skip_Out = 54
rar_effOutlier_Skip_Plat_Out = 55
rar_shortLogLinPhase = 56
rar_CqIsShifting = 57
rar_tooLowCqEff = 58
rar_tooLowCqN0 = 59
rar_isUsedInWoL = 60
res = []
finalData = {}
adp_cyc_max = 0
pcrEfficiencyExl = float(pcrEfficiencyExl)
if excludeEfficiency not in ["outlier", "mean", "include"]:
excludeEfficiency = "outlier"
reacts = _get_all_children(self._node, "react")
# First get the max number of cycles and create the numpy array
for react in reacts:
react_datas = _get_all_children(react, "data")
for react_data in react_datas:
adps = _get_all_children(react_data, "adp")
for adp in adps:
cyc = _get_first_child_text(adp, "cyc")
adp_cyc_max = max(adp_cyc_max, float(cyc))
adp_cyc_max = math.ceil(adp_cyc_max)
# spFl is the shape for all fluorescence numpy data arrays
spFl = (len(reacts), int(adp_cyc_max))
rawFluor = np.zeros(spFl, dtype=np.float64)
rawFluor[rawFluor <= 0.00000001] = np.nan
# Create a matrix with the cycle for each rawFluor value
vecCycles = np.tile(np.arange(1, (spFl[1] + 1), dtype=np.int64), (spFl[0], 1))
# Initialization of the vecNoAmplification vector
vecExcludedByUser = np.zeros(spFl[0], dtype=np.bool_)
rdmlElemData = []
# Now process the data for numpy and create results array
rowCount = 0
for react in reacts:
posId = react.get('id')
pIdNumber = (int(posId) - 1) % int(self["pcrFormat_columns"]) + 1
pIdLetter = chr(ord("A") + int((int(posId) - 1) / int(self["pcrFormat_columns"])))
pWell = pIdLetter + str(pIdNumber)
sample = ""
forId = _get_first_child(react, "sample")
if forId is not None:
if forId.attrib['id'] != "":
sample = forId.attrib['id']
react_datas = _get_all_children(react, "data")
for react_data in react_datas:
forId = _get_first_child(react_data, "tar")
target = ""
if forId is not None:
if forId.attrib['id'] != "":
target = forId.attrib['id']
if ignoreExclusion:
excl = ""
else:
excl = _get_first_child_text(react_data, "excl")
excl = _cleanErrorString(excl, "amp")
excl = re.sub(r'^;|;$', '', excl)
if not excl == "":
vecExcludedByUser[rowCount] = True
noteVal = _get_first_child_text(react_data, "note")
noteVal = _cleanErrorString(noteVal, "amp")
noteVal = re.sub(r'^;|;$', '', noteVal)
rdmlElemData.append(react_data)
res.append([posId, pWell, sample, "", "", target, "", excl, noteVal, "",
"", "", "", "", "", "", "", "", "", "",
"", "", "", "", "", "", "", "", "", "",
"", "", "", "", "", "", "", "", "", "",
"", "", "", "", "", "", "", "", "", "",
"", "", "", "", "", "", "", "", "", "",
""]) # Must match header length
adps = _get_all_children(react_data, "adp")
for adp in adps:
cyc = int(math.ceil(float(_get_first_child_text(adp, "cyc")))) - 1
fluor = _get_first_child_text(adp, "fluor")
if commaConv:
noDot = fluor.replace(".", "")
fluor = noDot.replace(",", ".")
rawFluor[rowCount, cyc] = float(fluor)
rowCount += 1
# Look up sample and target information
parExp = self._node.getparent()
parRoot = parExp.getparent()
dicLU_dyes = {}
luDyes = _get_all_children(parRoot, "dye")
for lu_dye in luDyes:
lu_chemistry = _get_first_child_text(lu_dye, "dyeChemistry")
if lu_chemistry == "":
lu_chemistry = "non-saturating DNA binding dye"
if lu_dye.attrib['id'] != "":
dicLU_dyes[lu_dye.attrib['id']] = lu_chemistry
dicLU_targets = {}
luTargets = _get_all_children(parRoot, "target")
for lu_target in luTargets:
forId = _get_first_child(lu_target, "dyeId")
lu_dyeId = ""
if forId is not None:
if forId.attrib['id'] != "":
lu_dyeId = forId.attrib['id']
if lu_dyeId == "" or lu_dyeId not in dicLU_dyes:
dicLU_targets[lu_target.attrib['id']] = "non-saturating DNA binding dye"
if lu_target.attrib['id'] != "":
dicLU_targets[lu_target.attrib['id']] = dicLU_dyes[lu_dyeId]
dicLU_samSpecType = {}
dicLU_samGenType = {}
dicLU_samNucl = {}
luSamples = _get_all_children(parRoot, "sample")
for lu_sample in luSamples:
lu_Nucl = ""
forUnit = _get_first_child(lu_sample, "templateQuantity")
if forUnit is not None:
lu_Nucl = _get_first_child_text(forUnit, "nucleotide")
if lu_Nucl == "":
lu_Nucl = "cDNA"
if lu_sample.attrib['id'] != "":
dicLU_TypeData = {}
typesList = _get_all_children(lu_sample, "type")
for node in typesList:
if "targetId" in node.attrib:
dicLU_TypeData[node.attrib["targetId"]] = node.text
else:
dicLU_samGenType[lu_sample.attrib['id']] = node.text
dicLU_samSpecType[lu_sample.attrib['id']] = dicLU_TypeData
dicLU_samNucl[lu_sample.attrib['id']] = lu_Nucl
# Update the table with dictionary help
for oRow in range(0, spFl[0]):
if res[oRow][rar_sample] != "":
# Try to get specific type information else general else "unkn"
if res[oRow][rar_tar] in dicLU_samSpecType[res[oRow][rar_sample]]:
res[oRow][rar_sample_type] = dicLU_samSpecType[res[oRow][rar_sample]][res[oRow][rar_tar]]
elif res[oRow][rar_sample] in dicLU_samGenType:
res[oRow][rar_sample_type] = dicLU_samGenType[res[oRow][rar_sample]]
else:
res[oRow][rar_sample_type] = "unkn"
res[oRow][rar_sample_nucleotide] = dicLU_samNucl[res[oRow][rar_sample]]
if res[oRow][rar_tar] != "":
res[oRow][rar_tar_chemistry] = dicLU_targets[res[oRow][rar_tar]]
if saveRaw:
rawTable = [[header[0][rar_id], header[0][rar_well], header[0][rar_sample], header[0][rar_tar], header[0][rar_excl]]]
for oCol in range(0, spFl[1]):
rawTable[0].append(oCol + 1)
for oRow in range(0, spFl[0]):
rawTable.append([res[oRow][rar_id], res[oRow][rar_well], res[oRow][rar_sample], res[oRow][rar_tar], res[oRow][rar_excl]])
for oCol in range(0, spFl[1]):
rawTable[oRow + 1].append(float(rawFluor[oRow, oCol]))
finalData["rawData"] = rawTable
# Count the targets and create the target variables
# Position 0 is for the general over all window without targets
vecTarget = np.zeros(spFl[0], dtype=np.int64)
vecTarget[vecTarget <= 0] = -1
targetsCount = 1
tarWinLookup = {}
for oRow in range(0, spFl[0]):
if res[oRow][rar_tar] not in tarWinLookup:
tarWinLookup[res[oRow][rar_tar]] = targetsCount
targetsCount += 1
vecTarget[oRow] = tarWinLookup[res[oRow][rar_tar]]
upWin = np.zeros(targetsCount, dtype=np.float64)
lowWin = np.zeros(targetsCount, dtype=np.float64)
threshold = np.ones(targetsCount, dtype=np.float64)
# Initialization of the error vectors
vecNoAmplification = np.zeros(spFl[0], dtype=np.bool_)
vecBaselineError = np.zeros(spFl[0], dtype=np.bool_)
vecNoPlateau = np.zeros(spFl[0], dtype=np.bool_)
vecNoisySample = np.zeros(spFl[0], dtype=np.bool_)
vecSkipSample = np.zeros(spFl[0], dtype=np.bool_)
vecShortLogLin = np.zeros(spFl[0], dtype=np.bool_)
vecCtIsShifting = np.zeros(spFl[0], dtype=np.bool_)
vecIsUsedInWoL = np.zeros(spFl[0], dtype=np.bool_)
vecEffOutlier_Skip_Mean = np.zeros(spFl[0], dtype=np.bool_)
vecEffOutlier_Skip_Plat_Mean = np.zeros(spFl[0], dtype=np.bool_)
vecEffOutlier_Skip_Out = np.zeros(spFl[0], dtype=np.bool_)
vecEffOutlier_Skip_Plat_Out = np.zeros(spFl[0], dtype=np.bool_)
vecTooLowCqEff = np.zeros(spFl[0], dtype=np.bool_)
vecTooLowCqN0 = np.zeros(spFl[0], dtype=np.bool_)
# Start and stop cycles of the log lin phase
stopCyc = np.zeros(spFl[0], dtype=np.int64)
startCyc = np.zeros(spFl[0], dtype=np.int64)
startCycFix = np.zeros(spFl[0], dtype=np.int64)
# Initialization of the PCR efficiency vectors
pcrEff = np.ones(spFl[0], dtype=np.float64)
nNulls = np.ones(spFl[0], dtype=np.float64)
nInclu = np.zeros(spFl[0], dtype=np.int64)
correl = np.zeros(spFl[0], dtype=np.float64)
meanEff_Skip = np.zeros(spFl[0], dtype=np.float64)
meanEff_Skip_Plat = np.zeros(spFl[0], dtype=np.float64)
meanEff_Skip_Mean = np.zeros(spFl[0], dtype=np.float64)
meanEff_Skip_Plat_Mean = np.zeros(spFl[0], dtype=np.float64)
meanEff_Skip_Out = np.zeros(spFl[0], dtype=np.float64)
meanEff_Skip_Plat_Out = np.zeros(spFl[0], dtype=np.float64)
stdEff_Skip = np.zeros(spFl[0], dtype=np.float64)
stdEff_Skip_Plat = np.zeros(spFl[0], dtype=np.float64)
stdEff_Skip_Mean = np.zeros(spFl[0], dtype=np.float64)
stdEff_Skip_Plat_Mean = np.zeros(spFl[0], dtype=np.float64)
stdEff_Skip_Out = np.zeros(spFl[0], dtype=np.float64)
stdEff_Skip_Plat_Out = np.zeros(spFl[0], dtype=np.float64)
indMeanX = np.zeros(spFl[0], dtype=np.float64)
indMeanY = np.zeros(spFl[0], dtype=np.float64)
indivCq = np.zeros(spFl[0], dtype=np.float64)
indivCq_Grp = np.zeros(spFl[0], dtype=np.float64)
meanNnull_Skip = np.zeros(spFl[0], dtype=np.float64)
meanNnull_Skip_Plat = np.zeros(spFl[0], dtype=np.float64)
meanNnull_Skip_Mean = np.zeros(spFl[0], dtype=np.float64)
meanNnull_Skip_Plat_Mean = np.zeros(spFl[0], dtype=np.float64)
meanNnull_Skip_Out = np.zeros(spFl[0], dtype=np.float64)
meanNnull_Skip_Plat_Out = np.zeros(spFl[0], dtype=np.float64)
meanCq_Skip = np.zeros(spFl[0], dtype=np.float64)
meanCq_Skip_Plat = np.zeros(spFl[0], dtype=np.float64)
meanCq_Skip_Mean = np.zeros(spFl[0], dtype=np.float64)
meanCq_Skip_Plat_Mean = np.zeros(spFl[0], dtype=np.float64)
meanCq_Skip_Out = np.zeros(spFl[0], dtype=np.float64)
meanCq_Skip_Plat_Out = np.zeros(spFl[0], dtype=np.float64)
# Set all to nan
indMeanX[:] = np.nan
indMeanY[:] = np.nan
indivCq[:] = np.nan
indivCq_Grp[:] = np.nan
meanNnull_Skip[:] = np.nan
meanNnull_Skip_Plat[:] = np.nan
meanNnull_Skip_Mean[:] = np.nan
meanNnull_Skip_Plat_Mean[:] = np.nan
meanNnull_Skip_Out[:] = np.nan
meanNnull_Skip_Plat_Out[:] = np.nan
meanCq_Skip[:] = np.nan
meanCq_Skip_Plat[:] = np.nan
meanCq_Skip_Mean[:] = np.nan
meanCq_Skip_Plat_Mean[:] = np.nan
meanCq_Skip_Out[:] = np.nan
meanCq_Skip_Plat_Out[:] = np.nan
# Basic Variables
pointsInWoL = 4
baseCorFluor = rawFluor.copy()
########################
# Baseline correction #
########################
start_time = datetime.datetime.now()
###########################################################################
# First quality check : Is there enough amplification during the reaction #
###########################################################################
# Slope calculation per react/target - the intercept is never used for now
rawMod = rawFluor.copy()
# There should be no negative values in uncorrected raw data
absMinFluor = np.nanmin(rawMod)
if absMinFluor < 0.0:
finalData["noRawData"] = "Error: Fluorescence data have negative values. Use raw data without baseline correction!"
rawMod[np.isnan(rawMod)] = 0
rawMod[rawMod <= 0.00000001] = np.nan
[slopeAmp, _unused] = _lrp_linReg(vecCycles, np.log10(rawMod))
# Calculate the minimum of fluorescence values per react/target, store it as background
# and substract it from the raw fluorescence values
vecMinFluor = np.nanmin(rawMod, axis=1)
vecBackground = 0.99 * vecMinFluor
vecDefBackgrd = vecBackground.copy()
minCorFluor = rawMod - vecBackground[:, np.newaxis]
minCorFluor[np.isnan(minCorFluor)] = 0
minCorFluor[minCorFluor <= 0.00000001] = np.nan
minFluCount = np.ones(minCorFluor.shape, dtype=np.int64)
minFluCount[np.isnan(minCorFluor)] = 0
minFluCountSum = np.sum(minFluCount, axis=1)
[minSlopeAmp, _unused] = _lrp_linReg(vecCycles, np.log10(minCorFluor))
for oRow in range(0, spFl[0]):
# Check to detect the negative slopes and the PCR reactions that have an
# amplification less than seven the minimum fluorescence
if slopeAmp[oRow] < 0 or minSlopeAmp[oRow] < (np.log10(7.0) / minFluCountSum[oRow]):
vecNoAmplification[oRow] = True
# Get the right positions ignoring nan values
posCount = 0
posZero = 0
posOne = 0
posEight = 0
posNine = 0
for realPos in range(0, spFl[1]):
if not np.isnan(minCorFluor[oRow, realPos]):
if posCount == 0:
posZero = realPos
if posCount == 1:
posOne = realPos
if posCount == 8:
posEight = realPos
if posCount == 9:
posNine = realPos
if posCount > 9:
break
posCount += 1
# There must be an increase in fluorescence after the amplification.
if ((minCorFluor[oRow, posEight] + minCorFluor[oRow, posNine]) / 2) / \
((minCorFluor[oRow, posZero] + minCorFluor[oRow, posOne]) / 2) < 1.2:
if minCorFluor[oRow, -1] / np.nanmean(minCorFluor[oRow, posZero:posNine + 1]) < 7:
vecNoAmplification[oRow] = True
if not vecNoAmplification[oRow]:
stopCyc[oRow] = _lrp_findStopCyc(minCorFluor, oRow)
[startCyc[oRow], startCycFix[oRow]] = _lrp_findStartCyc(minCorFluor, oRow, stopCyc[oRow])
else:
vecSkipSample[oRow] = True
stopCyc[oRow] = minCorFluor.shape[1]
startCyc[oRow] = 1
startCycFix[oRow] = 1
# Get the positions ignoring nan values
posCount = 0
posMinOne = 0
posMinTwo = 0
for realPos in range(stopCyc[oRow] - 2, 0, -1):
if not np.isnan(minCorFluor[oRow, realPos - 1]):
if posCount == 0:
posMinOne = realPos + 1
if posCount > 0:
posMinTwo = realPos + 1
break
posCount += 1
if not (minCorFluor[oRow, stopCyc[oRow] - 1] > minCorFluor[oRow, posMinOne - 1] > minCorFluor[oRow, posMinTwo - 1]):
vecNoAmplification[oRow] = True
vecSkipSample[oRow] = True
if vecNoAmplification[oRow] or vecBaselineError[oRow] or stopCyc[oRow] == minCorFluor.shape[1]:
vecNoPlateau[oRow] = True
# Set an initial window already for WOL calculation
lastCycMeanMax = _lrp_lastCycMeanMax(minCorFluor, vecSkipSample, vecNoPlateau)
upWin[0] = 0.1 * lastCycMeanMax
lowWin[0] = 0.1 * lastCycMeanMax / 16.0
##################################################
# Main loop : Calculation of the baseline values #
##################################################
# The for loop go through all the react/target table and make calculations one by one
for oRow in range(0, spFl[0]):
if verbose:
print('React: ' + str(oRow))
# If there is a "no amplification" error, there is no baseline value calculated and it is automatically the
# minimum fluorescence value assigned as baseline value for the considered reaction :
if not vecNoAmplification[oRow]:
# Make sure baseline is overestimated, without using slope criterion
# increase baseline per cycle till eff > 2 or remaining log lin points < pointsInWoL
# fastest when vecBackground is directly set to 5 point below stopCyc
start = stopCyc[oRow]
# Find the first value that is not NaN
firstNotNaN = 1 # Cycles so +1 to array
while np.isnan(baseCorFluor[oRow, firstNotNaN - 1]) and firstNotNaN < stopCyc[oRow]:
firstNotNaN += 1
subtrCount = 5
while subtrCount > 0 and start > firstNotNaN:
start -= 1
if not np.isnan(rawFluor[oRow, start - 1]):
subtrCount -= 1
vecBackground[oRow] = 0.99 * rawFluor[oRow, start - 1]
baseCorFluor[oRow] = rawFluor[oRow] - vecBackground[oRow]
baseCorFluor[np.isnan(baseCorFluor)] = 0
baseCorFluor[baseCorFluor <= 0.00000001] = np.nan
# baseline is now certainly too high
# 1. extend line downwards from stopCyc[] till slopeLow < slopeHigh of vecBackground[] < vecMinFluor[]
countTrials = 0
slopeHigh = 0.0
slopeLow = 0.0
while True:
countTrials += 1
stopCyc[oRow] = _lrp_findStopCyc(baseCorFluor, oRow)
[startCyc[oRow], startCycFix[oRow]] = _lrp_findStartCyc(baseCorFluor, oRow, stopCyc[oRow])
if stopCyc[oRow] - startCycFix[oRow] > 0:
# Calculate a slope for the upper and the lower half between startCycFix and stopCyc
[slopeLow, slopeHigh] = _lrp_testSlopes(baseCorFluor, oRow, stopCyc, startCycFix)
vecDefBackgrd[oRow] = vecBackground[oRow]
else:
break
if slopeLow >= slopeHigh:
vecBackground[oRow] *= 0.99
baseCorFluor[oRow] = rawFluor[oRow] - vecBackground[oRow]
baseCorFluor[np.isnan(baseCorFluor)] = 0
baseCorFluor[baseCorFluor <= 0.00000001] = np.nan
if (slopeLow < slopeHigh or
vecBackground[oRow] < 0.95 * vecMinFluor[oRow] or
countTrials > 1000):
break
if vecBackground[oRow] < 0.95 * vecMinFluor[oRow]:
vecBaselineError[oRow] = True
# 2. fine tune slope of total line
stepVal = 0.005 * vecBackground[oRow]
baseStep = 1.0
countTrials = 0
trialsToShift = 0
curSlopeDiff = 10
curSignDiff = 0
SlopeHasShifted = False
while True:
countTrials += 1
trialsToShift += 1
if trialsToShift > 10 and not SlopeHasShifted:
baseStep *= 2
trialsToShift = 0
lastSignDiff = curSignDiff
lastSlopeDiff = curSlopeDiff
vecDefBackgrd[oRow] = vecBackground[oRow]
# apply baseline
baseCorFluor[oRow] = rawFluor[oRow] - vecBackground[oRow]
baseCorFluor[np.isnan(baseCorFluor)] = 0
baseCorFluor[baseCorFluor <= 0.00000001] = np.nan
# find start and stop of log lin phase
stopCyc[oRow] = _lrp_findStopCyc(baseCorFluor, oRow)
[startCyc[oRow], startCycFix[oRow]] = _lrp_findStartCyc(baseCorFluor, oRow, stopCyc[oRow])
if stopCyc[oRow] - startCycFix[oRow] > 0:
[slopeLow, slopeHigh] = _lrp_testSlopes(baseCorFluor, oRow, stopCyc, startCycFix)
curSlopeDiff = np.abs(slopeLow - slopeHigh)
if (slopeLow - slopeHigh) > 0.0:
curSignDiff = 1
else:
curSignDiff = -1
# start with baseline that is too low: slopeLow is low
if slopeLow < slopeHigh:
# increase baseline
vecBackground[oRow] += baseStep * stepVal
else:
# crossed right baseline
# go two steps back
vecBackground[oRow] -= baseStep * stepVal * 2
# decrease stepsize
baseStep /= 2
SlopeHasShifted = True
else:
break
if (((np.abs(curSlopeDiff - lastSlopeDiff) < 0.00001) and
(curSignDiff == lastSignDiff) and SlopeHasShifted) or
(np.abs(curSlopeDiff) < 0.0001) or
(countTrials > 1000)):
break
# reinstate samples that reach the slope diff criterion within 0.9 * vecMinFluor
if curSlopeDiff < 0.0001 and vecDefBackgrd[oRow] > 0.9 * vecMinFluor[oRow]:
vecBaselineError[oRow] = False
# 3: skip sample when fluor[stopCyc]/fluor[startCyc] < 20
loglinlen = 20.0 # RelaxLogLinLengthRG in Pascal may choose 10.0
if baseCorFluor[oRow, stopCyc[oRow] - 1] / baseCorFluor[oRow, startCycFix[oRow] - 1] < loglinlen:
vecShortLogLin[oRow] = True
pcrEff[oRow] = np.power(10, slopeHigh)
else:
vecSkipSample[oRow] = True
vecDefBackgrd[oRow] = 0.99 * vecMinFluor[oRow]
baseCorFluor[oRow] = rawFluor[oRow] - vecDefBackgrd[oRow]
baseCorFluor[np.isnan(baseCorFluor)] = 0
baseCorFluor[baseCorFluor <= 0.00000001] = np.nan
# This values are used for the table
stopCyc[oRow] = spFl[1]
startCyc[oRow] = spFl[1] + 1
startCycFix[oRow] = spFl[1] + 1
pcrEff[oRow] = np.nan
if vecBaselineError[oRow]:
vecSkipSample[oRow] = True
vecBackground = vecDefBackgrd
baselineCorrectedData = baseCorFluor
# Check if cq values are stable with a modified baseline
checkFluor = np.zeros(spFl, dtype=np.float64)
[meanPcrEff, _unused] = _lrp_meanPcrEff(None, [], pcrEff, vecSkipSample, vecNoPlateau, vecShortLogLin)
# The baseline is only used for this check
checkBaseline = np.log10(upWin[0]) - np.log10(meanPcrEff)
for oRow in range(0, spFl[0]):
if vecShortLogLin[oRow] and not vecNoAmplification[oRow]:
# Recalculate it separately from the good values
checkFluor[oRow] = rawFluor[oRow] - 1.05 * vecBackground[oRow]
checkFluor[np.isnan(checkFluor)] = 0.0
checkFluor[checkFluor <= 0.00000001] = np.nan
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
maxFlour = np.nanmax(checkFluor)
if np.isnan(maxFlour):
tempMeanX, tempMeanY, tempPcrEff, _unused, _unused2, _unused3 = _lrp_paramInWindow(baseCorFluor,
oRow,
upWin[0],
lowWin[0])
else:
tempMeanX, tempMeanY, tempPcrEff, _unused, _unused2, _unused3 = _lrp_paramInWindow(checkFluor,
oRow,
upWin[0],
lowWin[0])
if tempPcrEff > 1.000000000001:
CtShiftUp = tempMeanX + (checkBaseline - tempMeanY) / np.log10(tempPcrEff)
else:
CtShiftUp = 0.0
checkFluor[oRow] = rawFluor[oRow] - 0.95 * vecBackground[oRow]
checkFluor[np.isnan(checkFluor)] = 0
checkFluor[checkFluor <= 0.00000001] = np.nan
tempMeanX, tempMeanY, tempPcrEff, _unused, _unused2, _unused3 = _lrp_paramInWindow(checkFluor,
oRow,
upWin[0],
lowWin[0])
if tempPcrEff > 1.000000000001:
CtShiftDown = tempMeanX + (checkBaseline - tempMeanY) / np.log10(tempPcrEff)
else:
CtShiftDown = 0.0
if np.abs(CtShiftUp - CtShiftDown) > 1.0:
vecBaselineError[oRow] = True
vecSkipSample[oRow] = True
vecCtIsShifting[oRow] = True
else:
if not vecBaselineError[oRow]:
vecSkipSample[oRow] = False
vecSkipSample[vecExcludedByUser] = True
# Update the window
lastCycMeanMax = _lrp_lastCycMeanMax(baseCorFluor, vecSkipSample, vecNoPlateau)
upWin[0] = 0.1 * lastCycMeanMax
lowWin[0] = 0.1 * lastCycMeanMax / 16.0
maxFluorTotal = np.nanmax(baseCorFluor)
minFluorTotal = np.nanmin(baseCorFluor)
if minFluorTotal < maxFluorTotal / 10000:
minFluorTotal = maxFluorTotal / 10000
# Fixme: Per group
# CheckNoisiness
skipGroup = False
maxLim = _lrp_meanStopFluor(baseCorFluor, None, None, stopCyc, vecSkipSample, vecNoPlateau)
if maxLim > 0.0:
maxLim = np.log10(maxLim)
else:
skipGroup = True
checkMeanEff = 1.0
if not skipGroup:
step = pointsInWoL * _lrp_logStepStop(baseCorFluor, None, [], stopCyc, vecSkipSample, vecNoPlateau)
upWin, lowWin = _lrp_setLogWin(None, maxLim, step, upWin, lowWin, maxFluorTotal, minFluorTotal)
# checkBaseline = np.log10(0.5 * np.round(1000 * np.power(10, upWin[0])) / 1000)
_unused, _unused2, tempPcrEff, _unused3, _unused4, _unused5 = _lrp_allParamInWindow(baseCorFluor,
None, [],
indMeanX, indMeanY,
pcrEff, nNulls,
nInclu, correl,
upWin, lowWin,
vecNoAmplification,
vecBaselineError)
checkMeanEff, _unused = _lrp_meanPcrEff(None, [], tempPcrEff, vecSkipSample, vecNoPlateau, vecShortLogLin)
if checkMeanEff < 1.001:
skipGroup = True
if not skipGroup:
foldWidth = np.log10(np.power(checkMeanEff, pointsInWoL))
upWin, lowWin = _lrp_setLogWin(None, maxLim, foldWidth, upWin, lowWin, maxFluorTotal, minFluorTotal)
# compare to Log(1.01*lowLim) to compensate for
# the truncation in cuplimedit with + 0.0043
lowLim = maxLim - foldWidth + 0.0043
for oRow in range(0, spFl[0]):
if not vecSkipSample[oRow]:
startWinCyc, stopWinCyc, _unused = _lrp_startStopInWindow(baseCorFluor, oRow, upWin[0], lowWin[0])
minStartCyc = startWinCyc - 1
# Handle possible NaN
while np.isnan(baseCorFluor[oRow, minStartCyc - 1]) and minStartCyc > 1:
minStartCyc -= 1
minStopCyc = stopWinCyc - 1
while np.isnan(baseCorFluor[oRow, minStopCyc - 1]) and minStopCyc > 2:
minStopCyc -= 1
minStartFlour = baseCorFluor[oRow, minStartCyc - 1]
if np.isnan(minStartFlour):
minStartFlour = 0.00001
startStep = np.log10(baseCorFluor[oRow, startWinCyc - 1]) - np.log10(minStartFlour)
stopStep = np.log10(baseCorFluor[oRow, stopWinCyc - 1]) - np.log10(baseCorFluor[oRow, minStopCyc - 1])
if (np.log10(minStartFlour) > lowLim and not
((minStartFlour < baseCorFluor[oRow, startWinCyc - 1] and startStep < 1.2 * stopStep) or
(startWinCyc - minStartCyc > 1.2))):
vecNoisySample[oRow] = True
vecSkipSample[oRow] = True
if saveBaslineCorr:
rawTable = [[header[0][rar_id], header[0][rar_well], header[0][rar_sample], header[0][rar_tar], header[0][rar_excl]]]
for oCol in range(0, spFl[1]):
rawTable[0].append(oCol + 1)
for oRow in range(0, spFl[0]):
rawTable.append([res[oRow][rar_id], res[oRow][rar_well], res[oRow][rar_sample], res[oRow][rar_tar], res[oRow][rar_excl]])
for oCol in range(0, spFl[1]):
rawTable[oRow + 1].append(float(baselineCorrectedData[oRow, oCol]))
finalData["baselineCorrectedData"] = rawTable
if timeRun:
stop_time = datetime.datetime.now() - start_time
print("Done Baseline: " + str(stop_time) + "sec")
###########################################################
# Calculation of the Window of Linearity (WOL) per target #
###########################################################
# Set a starting window for all groups
for tar in range(1, targetsCount):
upWin[tar] = upWin[0]
lowWin[tar] = lowWin[0]
for oRow in range(0, spFl[0]):
if vecNoAmplification[oRow] or vecBaselineError[oRow] or stopCyc[oRow] == spFl[1]:
vecNoPlateau[oRow] = True
else:
vecNoPlateau[oRow] = False
for tar in range(1, targetsCount):
indMeanX, indMeanY, pcrEff, nNulls, nInclu, correl, upWin, lowWin, threshold, vecIsUsedInWoL = _lrp_setWoL(baseCorFluor, tar, vecTarget, pointsInWoL,
indMeanX, indMeanY, pcrEff, nNulls, nInclu,
correl, upWin, lowWin, maxFluorTotal,
minFluorTotal, stopCyc, startCyc, threshold,
vecNoAmplification, vecBaselineError,
vecSkipSample, vecNoPlateau, vecShortLogLin,
vecIsUsedInWoL)
indMeanX, indMeanY, pcrEff, nNulls, nInclu, correl, upWin, lowWin, threshold, vecIsUsedInWoL, vecNoPlateau = _lrp_assignNoPlateau(baseCorFluor, tar, vecTarget,
pointsInWoL, indMeanX, indMeanY,
pcrEff, nNulls, nInclu, correl,
upWin, lowWin, maxFluorTotal,
minFluorTotal, stopCyc, startCyc,
threshold, vecNoAmplification,
vecBaselineError, vecSkipSample,
vecNoPlateau, vecShortLogLin,
vecIsUsedInWoL)
# Median values calculation
vecSkipSample_Plat = vecSkipSample.copy()
vecSkipSample_Plat[vecNoPlateau] = True
logThreshold = np.log10(threshold[1:])
threshold[0] = np.power(10, np.mean(logThreshold))
# Create the warnings for the different chemistries
# Chem Arr 0 1 2 3 4 5 6 7 8 9 10
critCqEff = [28.0, 28.0, 19.0, 16.0, 14.0, 12.0, 11.0, 11.0, 10.0, 10.0, 9.0] # For error Eff < 0.01
critCqN0 = [40.0, 40.0, 27.0, 19.0, 16.0, 13.0, 12.0, 11.0, 10.0, 9.0, 9.0] # For bias N0 < 0.95
for oRow in range(0, spFl[0]):
if res[oRow][rar_tar_chemistry] in ["hydrolysis probe", "labelled reverse primer", "DNA-zyme probe"]:
critCqOffset = 0.0
if (res[oRow][rar_tar_chemistry] == "labelled reverse primer" and
res[oRow][rar_sample_nucleotide] in ["DNA", "genomic DNA"]):
critCqOffset = 1.0
if (res[oRow][rar_tar_chemistry] == "DNA-zyme probe" and
res[oRow][rar_sample_nucleotide] in ["DNA", "genomic DNA"]):
critCqOffset = 4.0
if (res[oRow][rar_tar_chemistry] == "DNA-zyme probe" and
res[oRow][rar_sample_nucleotide] in ["cDNA", "RNA"]):
critCqOffset = 6.0
if (not np.isnan(pcrEff[oRow]) and pcrEff[oRow] > 1.0001 and
threshold[vecTarget[oRow]] > 0.0001 and not (vecNoAmplification[oRow] or vecBaselineError[oRow])):
effIndex = int(np.trunc(10 * pcrEff[oRow] + 1 - 10))
if effIndex < 0:
effIndex = 0
if effIndex > 10:
effIndex = 10
tempCq_Grp = indMeanX[oRow] + (np.log10(threshold[0]) - indMeanY[oRow]) / np.log10(pcrEff[oRow])
if tempCq_Grp > 0.0:
if tempCq_Grp < (critCqEff[effIndex] + critCqOffset):
vecTooLowCqEff[oRow] = True
if tempCq_Grp < (critCqN0[effIndex] + critCqOffset):
vecTooLowCqN0[oRow] = True
pcreff_NoNaN = pcrEff.copy()
pcreff_NoNaN[np.isnan(pcrEff)] = 0.0
for tar in range(1, targetsCount):
# Calculating all choices takes less time then to recalculate
pcreff_Skip = pcrEff.copy()
pcreff_Skip[vecTooLowCqEff] = np.nan
pcreff_Skip[vecSkipSample] = np.nan
pcreff_Skip[pcreff_NoNaN < 1.001] = np.nan
pcreff_Skip[~(vecTarget == tar)] = np.nan
pcreff_Skip_Plat = pcreff_Skip.copy()
pcreff_Skip_Plat[vecSkipSample_Plat] = np.nan
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
pcreffMedian_Skip = np.nanmedian(pcreff_Skip)
pcreffMedian_Skip_Plat = np.nanmedian(pcreff_Skip_Plat)
for oRow in range(0, spFl[0]):
if tar == vecTarget[oRow]:
if not np.isnan(pcrEff[oRow]):
if (np.isnan(pcreffMedian_Skip) or
not (pcreffMedian_Skip - pcrEfficiencyExl <= pcrEff[oRow] <= pcreffMedian_Skip + pcrEfficiencyExl)):
vecEffOutlier_Skip_Mean[oRow] = True
if (np.isnan(pcreffMedian_Skip_Plat) or
not (pcreffMedian_Skip_Plat - pcrEfficiencyExl <= pcrEff[oRow] <= pcreffMedian_Skip_Plat + pcrEfficiencyExl)):
vecEffOutlier_Skip_Plat_Mean[oRow] = True
pcreff_Skip_Mean = pcreff_Skip.copy()
pcreff_Skip_Mean[vecEffOutlier_Skip_Mean] = np.nan
pcreff_Skip_Plat_Mean = pcreff_Skip_Plat.copy()
pcreff_Skip_Plat_Mean[vecEffOutlier_Skip_Plat_Mean] = np.nan
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
pcreffMedian_Skip = np.nanmedian(pcreff_Skip_Mean)
pcreffMedian_Skip_Plat = np.nanmedian(pcreff_Skip_Plat_Mean)
for oRow in range(0, spFl[0]):
if tar is None or tar == vecTarget[oRow]:
if not np.isnan(pcrEff[oRow]):
if (np.isnan(pcreffMedian_Skip) or
not (pcreffMedian_Skip - pcrEfficiencyExl <= pcrEff[oRow] <= pcreffMedian_Skip + pcrEfficiencyExl)):
vecEffOutlier_Skip_Mean[oRow] = True
else:
vecEffOutlier_Skip_Mean[oRow] = False
if (np.isnan(pcreffMedian_Skip_Plat) or
not (pcreffMedian_Skip_Plat - pcrEfficiencyExl <= pcrEff[oRow] <= pcreffMedian_Skip_Plat + pcrEfficiencyExl)):
vecEffOutlier_Skip_Plat_Mean[oRow] = True
else:
vecEffOutlier_Skip_Plat_Mean[oRow] = False
else:
vecEffOutlier_Skip_Mean[oRow] = True
vecEffOutlier_Skip_Plat_Mean[oRow] = True
pcreff_Skip_Mean = pcreff_Skip.copy()
pcreff_Skip_Mean[vecEffOutlier_Skip_Mean] = np.nan
pcreff_Skip_Plat_Mean = pcreff_Skip_Plat.copy()
pcreff_Skip_Plat_Mean[vecEffOutlier_Skip_Plat_Mean] = np.nan
vecEffOutlier_Skip_Out[_lrp_removeOutlier(pcreff_Skip, vecNoPlateau)] = True
vecEffOutlier_Skip_Plat_Out[_lrp_removeOutlier(pcreff_Skip_Plat, vecNoPlateau)] = True
pcreff_Skip_Out = pcreff_Skip.copy()
pcreff_Skip_Out[vecEffOutlier_Skip_Out] = np.nan
pcreff_Skip_Plat_Out = pcreff_Skip_Plat.copy()
pcreff_Skip_Plat_Out[vecEffOutlier_Skip_Plat_Out] = np.nan
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
tempMeanEff_Skip = np.nanmean(pcreff_Skip)
tempMeanEff_Skip_Plat = np.nanmean(pcreff_Skip_Plat)
tempMeanEff_Skip_Mean = np.nanmean(pcreff_Skip_Mean)
tempMeanEff_Skip_Plat_Mean = np.nanmean(pcreff_Skip_Plat_Mean)
tempMeanEff_Skip_Out = np.nanmean(pcreff_Skip_Out)
tempMeanEff_Skip_Plat_Out = np.nanmean(pcreff_Skip_Plat_Out)
tempStdEff_Skip = np.nanstd(pcreff_Skip)
tempStdEff_Skip_Plat = np.nanstd(pcreff_Skip_Plat)
tempStdEff_Skip_Mean = np.nanstd(pcreff_Skip_Mean)
tempStdEff_Skip_Plat_Mean = np.nanstd(pcreff_Skip_Plat_Mean)
tempStdEff_Skip_Out = np.nanstd(pcreff_Skip_Out)
tempStdEff_Skip_Plat_Out = np.nanstd(pcreff_Skip_Plat_Out)
for oRow in range(0, spFl[0]):
if tar == vecTarget[oRow]:
meanEff_Skip[oRow] = tempMeanEff_Skip
meanEff_Skip_Plat[oRow] = tempMeanEff_Skip_Plat
meanEff_Skip_Mean[oRow] = tempMeanEff_Skip_Mean
meanEff_Skip_Plat_Mean[oRow] = tempMeanEff_Skip_Plat_Mean
meanEff_Skip_Out[oRow] = tempMeanEff_Skip_Out
meanEff_Skip_Plat_Out[oRow] = tempMeanEff_Skip_Plat_Out
stdEff_Skip[oRow] = tempStdEff_Skip
stdEff_Skip_Plat[oRow] = tempStdEff_Skip_Plat
stdEff_Skip_Mean[oRow] = tempStdEff_Skip_Mean
stdEff_Skip_Plat_Mean[oRow] = tempStdEff_Skip_Plat_Mean
stdEff_Skip_Out[oRow] = tempStdEff_Skip_Out
stdEff_Skip_Plat_Out[oRow] = tempStdEff_Skip_Plat_Out
# Correction of the different chemistries
cqCorrection = 0.0
if res[oRow][rar_tar_chemistry] in ["hydrolysis probe", "labelled reverse primer", "DNA-zyme probe"]:
cqCorrection = -1.0
if not np.isnan(pcrEff[oRow]) and pcrEff[oRow] > 1.0001 and threshold[tar] > 0.0001 and not (vecNoAmplification[oRow] or vecBaselineError[oRow]):
if res[oRow][rar_tar_chemistry] == "DNA-zyme probe":
cqCorrection = -1.0 + np.log10(1 / (1 - (1 / pcrEff[oRow]))) / np.log10(pcrEff[oRow])
indivCq[oRow] = indMeanX[oRow] + (np.log10(threshold[0]) - indMeanY[oRow]) / np.log10(pcrEff[oRow]) + cqCorrection
indivCq_Grp[oRow] = indMeanX[oRow] + (np.log10(threshold[tar]) - indMeanY[oRow]) / np.log10(pcrEff[oRow]) + cqCorrection
if not np.isnan(pcrEff[oRow]) and pcrEff[oRow] > 1.0:
if not np.isnan(meanEff_Skip[oRow]) and meanEff_Skip[oRow] > 1.001:
if res[oRow][rar_tar_chemistry] == "DNA-zyme probe":
cqCorrection = -1.0 + np.log10(1 / (1 - (1 / meanEff_Skip[oRow]))) / np.log10(meanEff_Skip[oRow])
meanCq_Skip[oRow] = indMeanX[oRow] + (np.log10(threshold[0]) - indMeanY[oRow]) / np.log10(meanEff_Skip[oRow]) + cqCorrection
if not np.isnan(meanEff_Skip_Plat[oRow]) and meanEff_Skip_Plat[oRow] > 1.001:
if res[oRow][rar_tar_chemistry] == "DNA-zyme probe":
cqCorrection = -1.0 + np.log10(1 / (1 - (1 / meanEff_Skip_Plat[oRow]))) / np.log10(meanEff_Skip_Plat[oRow])
meanCq_Skip_Plat[oRow] = indMeanX[oRow] + (np.log10(threshold[0]) - indMeanY[oRow]) / np.log10(meanEff_Skip_Plat[oRow]) + cqCorrection
if not np.isnan(meanEff_Skip_Mean[oRow]) and meanEff_Skip_Mean[oRow] > 1.001:
if res[oRow][rar_tar_chemistry] == "DNA-zyme probe":
cqCorrection = -1.0 + np.log10(1 / (1 - (1 / meanEff_Skip_Mean[oRow]))) / np.log10(meanEff_Skip_Mean[oRow])
meanCq_Skip_Mean[oRow] = indMeanX[oRow] + (np.log10(threshold[0]) - indMeanY[oRow]) / np.log10(meanEff_Skip_Mean[oRow]) + cqCorrection
if not np.isnan(meanEff_Skip_Plat_Mean[oRow]) and meanEff_Skip_Plat_Mean[oRow] > 1.001:
if res[oRow][rar_tar_chemistry] == "DNA-zyme probe":
cqCorrection = -1.0 + np.log10(1 / (1 - (1 / meanEff_Skip_Plat_Mean[oRow]))) / np.log10(meanEff_Skip_Plat_Mean[oRow])
meanCq_Skip_Plat_Mean[oRow] = indMeanX[oRow] + (np.log10(threshold[0]) - indMeanY[oRow]) / np.log10(meanEff_Skip_Plat_Mean[oRow]) + cqCorrection
if not np.isnan(meanEff_Skip_Out[oRow]) and meanEff_Skip_Out[oRow] > 1.001:
if res[oRow][rar_tar_chemistry] == "DNA-zyme probe":
cqCorrection = -1.0 + np.log10(1 / (1 - (1 / meanEff_Skip_Out[oRow]))) / np.log10(meanEff_Skip_Out[oRow])
meanCq_Skip_Out[oRow] = indMeanX[oRow] + (np.log10(threshold[0]) - indMeanY[oRow]) / np.log10(meanEff_Skip_Out[oRow]) + cqCorrection
if not np.isnan(meanEff_Skip_Plat_Out[oRow]) and meanEff_Skip_Plat_Out[oRow] > 1.001:
if res[oRow][rar_tar_chemistry] == "DNA-zyme probe":
cqCorrection = -1.0 + np.log10(1 / (1 - (1 / meanEff_Skip_Plat_Out[oRow]))) / np.log10(meanEff_Skip_Plat_Out[oRow])
meanCq_Skip_Plat_Out[oRow] = indMeanX[oRow] + (np.log10(threshold[0]) - indMeanY[oRow]) / np.log10(meanEff_Skip_Plat_Out[oRow]) + cqCorrection
if not np.isnan(pcrEff[oRow]) and pcrEff[oRow] > 1.0 and 0.0 < indivCq[oRow] < 2 * spFl[1]:
if not np.isnan(meanEff_Skip[oRow]) and meanEff_Skip[oRow] > 1.001:
meanNnull_Skip[oRow] = threshold[0] / np.power(meanEff_Skip[oRow], meanCq_Skip[oRow])
if not np.isnan(meanEff_Skip_Plat[oRow]) and meanEff_Skip_Plat[oRow] > 1.001:
meanNnull_Skip_Plat[oRow] = threshold[0] / np.power(meanEff_Skip_Plat[oRow], meanCq_Skip_Plat[oRow])
if not np.isnan(meanEff_Skip_Mean[oRow]) and meanEff_Skip_Mean[oRow] > 1.001:
meanNnull_Skip_Mean[oRow] = threshold[0] / np.power(meanEff_Skip_Mean[oRow], meanCq_Skip_Mean[oRow])
if not | np.isnan(meanEff_Skip_Plat_Mean[oRow]) | numpy.isnan |
#!/usr/bin/env python3
from collections import defaultdict
from warnings import warn
import numpy as np
from pandas import DataFrame
from scipy.linalg import eig
from pgmpy.factors.discrete import State
from pgmpy.utils import sample_discrete
from pgmpy.extern import six
from pgmpy.extern.six.moves import range, zip
class MarkovChain(object):
"""
Class to represent a Markov Chain with multiple kernels for factored state space,
along with methods to simulate a run.
Public Methods:
---------------
set_start_state(state)
add_variable(variable, cardinality)
add_variables_from(vars_list, cards_list)
add_transition_model(variable, transition_dict)
sample(start_state, size)
Examples:
---------
Create an empty Markov Chain:
>>> from pgmpy.models import MarkovChain as MC
>>> model = MC()
And then add variables to it
>>> model.add_variables_from(['intel', 'diff'], [2, 3])
Or directly create a Markov Chain from a list of variables and their cardinalities
>>> model = MC(['intel', 'diff'], [2, 3])
Add transition models
>>> intel_tm = {0: {0: 0.25, 1: 0.75}, 1: {0: 0.5, 1: 0.5}}
>>> model.add_transition_model('intel', intel_tm)
>>> diff_tm = {0: {0: 0.1, 1: 0.5, 2: 0.4}, 1: {0: 0.2, 1: 0.2, 2: 0.6 }, 2: {0: 0.7, 1: 0.15, 2: 0.15}}
>>> model.add_transition_model('diff', diff_tm)
Set a start state
>>> from pgmpy.factors.discrete import State
>>> model.set_start_state([State('intel', 0), State('diff', 2)])
Sample from it
>>> model.sample(size=5)
intel diff
0 0 2
1 1 0
2 0 1
3 1 0
4 0 2
"""
def __init__(self, variables=None, card=None, start_state=None):
"""
Parameters:
-----------
variables: array-like iterable object
A list of variables of the model.
card: array-like iterable object
A list of cardinalities of the variables.
start_state: array-like iterable object
List of tuples representing the starting states of the variables.
"""
if variables is None:
variables = []
if card is None:
card = []
if not hasattr(variables, "__iter__") or isinstance(
variables, six.string_types
):
raise ValueError("variables must be a non-string iterable.")
if not hasattr(card, "__iter__") or isinstance(card, six.string_types):
raise ValueError("card must be a non-string iterable.")
self.variables = variables
self.cardinalities = {v: c for v, c in zip(variables, card)}
self.transition_models = {var: {} for var in variables}
if start_state is None or self._check_state(start_state):
self.state = start_state
def set_start_state(self, start_state):
"""
Set the start state of the Markov Chain. If the start_state is given as a array-like iterable, its contents
are reordered in the internal representation.
Parameters:
-----------
start_state: dict or array-like iterable object
Dict (or list) of tuples representing the starting states of the variables.
Examples:
---------
>>> from pgmpy.models import MarkovChain as MC
>>> from pgmpy.factors.discrete import State
>>> model = MC(['a', 'b'], [2, 2])
>>> model.set_start_state([State('a', 0), State('b', 1)])
"""
if start_state is not None:
if not hasattr(start_state, "__iter__") or isinstance(
start_state, six.string_types
):
raise ValueError("start_state must be a non-string iterable.")
# Must be an array-like iterable. Reorder according to self.variables.
state_dict = {var: st for var, st in start_state}
start_state = [State(var, state_dict[var]) for var in self.variables]
if start_state is None or self._check_state(start_state):
self.state = start_state
def _check_state(self, state):
"""
Checks if a list representing the state of the variables is valid.
"""
if not hasattr(state, "__iter__") or isinstance(state, six.string_types):
raise ValueError("Start state must be a non-string iterable object.")
state_vars = {s.var for s in state}
if not state_vars == set(self.variables):
raise ValueError(
"Start state must represent a complete assignment to all variables."
"Expected variables in state: {svar}, Got: {mvar}.".format(
svar=state_vars, mvar=set(self.variables)
)
)
for var, val in state:
if val >= self.cardinalities[var]:
raise ValueError(
"Assignment {val} to {var} invalid.".format(val=val, var=var)
)
return True
def add_variable(self, variable, card=0):
"""
Add a variable to the model.
Parameters:
-----------
variable: any hashable python object
card: int
Representing the cardinality of the variable to be added.
Examples:
---------
>>> from pgmpy.models import MarkovChain as MC
>>> model = MC()
>>> model.add_variable('x', 4)
"""
if variable not in self.variables:
self.variables.append(variable)
else:
warn("Variable {var} already exists.".format(var=variable))
self.cardinalities[variable] = card
self.transition_models[variable] = {}
def add_variables_from(self, variables, cards):
"""
Add several variables to the model at once.
Parameters:
-----------
variables: array-like iterable object
List of variables to be added.
cards: array-like iterable object
List of cardinalities of the variables to be added.
Examples:
---------
>>> from pgmpy.models import MarkovChain as MC
>>> model = MC()
>>> model.add_variables_from(['x', 'y'], [3, 4])
"""
for var, card in zip(variables, cards):
self.add_variable(var, card)
def add_transition_model(self, variable, transition_model):
"""
Adds a transition model for a particular variable.
Parameters:
-----------
variable: any hashable python object
must be an existing variable of the model.
transition_model: dict or 2d array
dict representing valid transition probabilities defined for every possible state of the variable.
array represent a square matrix where every row sums to 1,
array[i,j] indicates the transition probalities from State i to State j
Examples:
---------
>>> from pgmpy.models import MarkovChain as MC
>>> model = MC()
>>> model.add_variable('grade', 3)
>>> grade_tm = {0: {0: 0.1, 1: 0.5, 2: 0.4}, 1: {0: 0.2, 1: 0.2, 2: 0.6 }, 2: {0: 0.7, 1: 0.15, 2: 0.15}}
>>> grade_tm_matrix = np.array([[0.1, 0.5, 0.4], [0.2, 0.2, 0.6], [0.7, 0.15, 0.15]])
>>> model.add_transition_model('grade', grade_tm)
>>> model.add_transition_model('grade', grade_tm_matrix)
"""
if isinstance(transition_model, list):
transition_model = np.array(transition_model)
# check if the transition model is valid
if not isinstance(transition_model, dict):
if not isinstance(transition_model, np.ndarray):
raise ValueError("Transition model must be a dict or numpy array")
elif len(transition_model.shape) != 2:
raise ValueError(
"Transition model must be 2d array.given {t}".format(
t=transition_model.shape
)
)
elif transition_model.shape[0] != transition_model.shape[1]:
raise ValueError(
"Dimension mismatch {d1}!={d2}".format(
d1=transition_model.shape[0], d2=transition_model.shape[1]
)
)
else:
# convert the matrix to dict
size = transition_model.shape[0]
transition_model = dict(
(
i,
dict(
(j, float(transition_model[i][j])) for j in range(0, size)
),
)
for i in range(0, size)
)
exp_states = set(range(self.cardinalities[variable]))
tm_states = set(transition_model.keys())
if not exp_states == tm_states:
raise ValueError(
"Transitions must be defined for all states of variable {v}. "
"Expected states: {es}, Got: {ts}.".format(
v=variable, es=exp_states, ts=tm_states
)
)
for _, transition in transition_model.items():
if not isinstance(transition, dict):
raise ValueError("Each transition must be a dict.")
prob_sum = 0
for _, prob in transition.items():
if prob < 0 or prob > 1:
raise ValueError(
"Transitions must represent valid probability weights."
)
prob_sum += prob
if not np.allclose(prob_sum, 1):
raise ValueError("Transition probabilities must sum to 1.")
self.transition_models[variable] = transition_model
def sample(self, start_state=None, size=1):
"""
Sample from the Markov Chain.
Parameters:
-----------
start_state: dict or array-like iterable
Representing the starting states of the variables. If None is passed, a random start_state is chosen.
size: int
Number of samples to be generated.
Return Type:
------------
pandas.DataFrame
Examples:
---------
>>> from pgmpy.models import MarkovChain as MC
>>> from pgmpy.factors.discrete import State
>>> model = MC(['intel', 'diff'], [2, 3])
>>> model.set_start_state([State('intel', 0), State('diff', 2)])
>>> intel_tm = {0: {0: 0.25, 1: 0.75}, 1: {0: 0.5, 1: 0.5}}
>>> model.add_transition_model('intel', intel_tm)
>>> diff_tm = {0: {0: 0.1, 1: 0.5, 2: 0.4}, 1: {0: 0.2, 1: 0.2, 2: 0.6 }, 2: {0: 0.7, 1: 0.15, 2: 0.15}}
>>> model.add_transition_model('diff', diff_tm)
>>> model.sample(size=5)
intel diff
0 0 2
1 1 0
2 0 1
3 1 0
4 0 2
"""
if start_state is None:
if self.state is None:
self.state = self.random_state()
# else use previously-set state
else:
self.set_start_state(start_state)
sampled = DataFrame(index=range(size), columns=self.variables)
sampled.loc[0] = [st for var, st in self.state]
var_states = defaultdict(dict)
var_values = defaultdict(dict)
samples = defaultdict(dict)
for var in self.transition_models.keys():
for st in self.transition_models[var]:
var_states[var][st] = list(self.transition_models[var][st].keys())
var_values[var][st] = list(self.transition_models[var][st].values())
samples[var][st] = sample_discrete(
var_states[var][st], var_values[var][st], size=size
)
for i in range(size - 1):
for j, (var, st) in enumerate(self.state):
next_st = samples[var][st][i]
self.state[j] = State(var, next_st)
sampled.loc[i + 1] = [st for var, st in self.state]
return sampled
def prob_from_sample(self, state, sample=None, window_size=None):
"""
Given an instantiation (partial or complete) of the variables of the model,
compute the probability of observing it over multiple windows in a given sample.
If 'sample' is not passed as an argument, generate the statistic by sampling from the
Markov Chain, starting with a random initial state.
Examples:
---------
>>> from pgmpy.models.MarkovChain import MarkovChain as MC
>>> from pgmpy.factors.discrete import State
>>> model = MC(['intel', 'diff'], [3, 2])
>>> intel_tm = {0: {0: 0.2, 1: 0.4, 2:0.4}, 1: {0: 0, 1: 0.5, 2: 0.5}, 2: {2: 0.5, 1:0.5}}
>>> model.add_transition_model('intel', intel_tm)
>>> diff_tm = {0: {0: 0.5, 1: 0.5}, 1: {0: 0.25, 1:0.75}}
>>> model.add_transition_model('diff', diff_tm)
>>> model.prob_from_sample([State('diff', 0)])
array([ 0.27, 0.4 , 0.18, 0.23, ..., 0.29])
"""
if sample is None:
# generate sample of size 10000
sample = self.sample(self.random_state(), size=10000)
if window_size is None:
window_size = len(sample) // 100 # default window size is 100
windows = len(sample) // window_size
probabilities = np.zeros(windows)
for i in range(windows):
for j in range(window_size):
ind = i * window_size + j
state_eq = [sample.loc[ind, v] == s for v, s in state]
if all(state_eq):
probabilities[i] += 1
return probabilities / window_size
def generate_sample(self, start_state=None, size=1):
"""
Generator version of self.sample
Return Type:
------------
List of State namedtuples, representing the assignment to all variables of the model.
Examples:
---------
>>> from pgmpy.models.MarkovChain import MarkovChain
>>> from pgmpy.factors.discrete import State
>>> model = MarkovChain()
>>> model.add_variables_from(['intel', 'diff'], [3, 2])
>>> intel_tm = {0: {0: 0.2, 1: 0.4, 2:0.4}, 1: {0: 0, 1: 0.5, 2: 0.5}, 2: {0: 0.3, 1: 0.3, 2: 0.4}}
>>> model.add_transition_model('intel', intel_tm)
>>> diff_tm = {0: {0: 0.5, 1: 0.5}, 1: {0: 0.25, 1:0.75}}
>>> model.add_transition_model('diff', diff_tm)
>>> gen = model.generate_sample([State('intel', 0), State('diff', 0)], 2)
>>> [sample for sample in gen]
[[State(var='intel', state=2), State(var='diff', state=1)],
[State(var='intel', state=2), State(var='diff', state=0)]]
"""
if start_state is None:
if self.state is None:
self.state = self.random_state()
# else use previously-set state
else:
self.set_start_state(start_state)
# sampled.loc[0] = [self.state[var] for var in self.variables]
for i in range(size):
for j, (var, st) in enumerate(self.state):
next_st = sample_discrete(
list(self.transition_models[var][st].keys()),
list(self.transition_models[var][st].values()),
)[0]
self.state[j] = State(var, next_st)
yield self.state[:]
def is_stationarity(self, tolerance=0.2, sample=None):
"""
Checks if the given markov chain is stationary and checks the steady state
probablity values for the state are consistent.
Parameters:
-----------
tolerance: float
represents the diff between actual steady state value and the computed value
sample: [State(i,j)]
represents the list of state which the markov chain has sampled
Return Type:
------------
Boolean
True, if the markov chain converges to steady state distribution within the tolerance
False, if the markov chain does not converge to steady state distribution within tolerance
Examples:
---------
>>> from pgmpy.models.MarkovChain import MarkovChain
>>> from pgmpy.factors.discrete import State
>>> model = MarkovChain()
>>> model.add_variables_from(['intel', 'diff'], [3, 2])
>>> intel_tm = {0: {0: 0.2, 1: 0.4, 2:0.4}, 1: {0: 0, 1: 0.5, 2: 0.5}, 2: {0: 0.3, 1: 0.3, 2: 0.4}}
>>> model.add_transition_model('intel', intel_tm)
>>> diff_tm = {0: {0: 0.5, 1: 0.5}, 1: {0: 0.25, 1:0.75}}
>>> model.add_transition_model('diff', diff_tm)
>>> model.is_stationarity()
True
"""
keys = self.transition_models.keys()
return_val = True
for k in keys:
# convert dict to numpy matrix
transition_mat = np.array(
[
np.array(list(self.transition_models[k][i].values()))
for i in self.transition_models[k].keys()
],
dtype=np.float,
)
S, U = eig(transition_mat.T)
stationary = np.array(U[:, np.where(np.abs(S - 1.0) < 1e-8)[0][0]].flat)
stationary = (stationary / np.sum(stationary)).real
probabilites = []
window_size = 10000 if sample is None else len(sample)
for i in range(0, transition_mat.shape[0]):
probabilites.extend(
self.prob_from_sample([State(k, i)], window_size=window_size)
)
if any(
np.abs(i) > tolerance for i in np.subtract(probabilites, stationary)
):
return_val = return_val and False
else:
return_val = return_val and True
return return_val
def random_state(self):
"""
Generates a random state of the Markov Chain.
Return Type:
------------
List of namedtuples, representing a random assignment to all variables of the model.
Examples:
---------
>>> from pgmpy.models import MarkovChain as MC
>>> model = MC(['intel', 'diff'], [2, 3])
>>> model.random_state()
[State('diff', 2), State('intel', 1)]
"""
return [
State(var, | np.random.randint(self.cardinalities[var]) | numpy.random.randint |
"""
<NAME>, CSHL, 2020-05-17
"""
import pandas as pd
import numpy as np
import matplotlib as mpl
from matplotlib import pyplot as plt
import seaborn as sns
from patsy import dmatrices
from datetime import datetime
import statsmodels.api as sm
# layout
sns.set(style="ticks", context="paper")
sns.despine(trim=True)
mpl.rcParams['pdf.fonttype'] = 42
mpl.rcParams['ps.fonttype'] = 42
# ====================================== #
# read data from <NAME>
# ====================================== #
# original spreadsheet from <NAME>: https://stevenson.lab.uconn.edu/scaling/
# df = pd.read_csv('https://docs.google.com/spreadsheet/pub?hl=en_US&hl=en_US&key=0Ai7vcDJIlD6AdF9vQWlNRDh2S1dub09jMWRvTFRpemc&single=true&gid=0&output=csv')
# instead, use my own sheet with additional datapoints for imaging
df = pd.read_csv('https://docs.google.com/spreadsheets/d/e/2PACX-1vQdv2uGPz4zSZmfpiIUrHvpB90Cz6cs8rgObbAqNQmsaLb5moGg8sYlIvfSZvXhoh1R1id8lZFyASkC/pub?gid=1390826946&single=true&output=csv')
print(df.describe())
# add some things - like the date for the x-axis
df['date'] = pd.to_datetime(df['Year'].astype(str) + '-' + df['Month'].astype(str) + '-' + '01')
df['years'] = (df['date'] - datetime(1950, 1, 1)).dt.days / 365
df['date_num'] = df['Year'] + (df['Month']-1)/12
df['neurons_log'] = np.log(df['Neurons']) # take log
# ====================================== #
# refit the curve from Stevenson et al. 2011
# ====================================== #
# separate out data for fit to original papers
fit_data = df[(df['Source'] == 'S&K')].copy()
# from https://github.com/ihstevenson/scaling/blob/master/scaling.py:
# Only keep first M papers to record >=N neurons
tmp = fit_data.groupby(['Neurons'])['DOI'].nunique().reset_index()
assert(all(tmp['DOI'] <= 10))
# use patsy
y, X = dmatrices('neurons_log ~ date_num', data=fit_data, return_type='dataframe')
mod = sm.OLS(y, X) # Describe model
res = mod.fit() # Fit model
print(res.summary()) # Summarize model
# what's the doubling time from this model? log(2) / a
doubling_time = np.log(2) / res.params['date_num']
print('Doubling time S&K: %f years'%doubling_time)
# extrapolate to whenever
xvec1 = np.linspace(2000, 2500, 100)
yvec1 = res.predict(sm.add_constant(xvec1))
# ====================================== #
# also fit on all data, including imaging
# ====================================== #
fit_data2 = df[(df['Method'] == 'Imaging')].copy()
# use patsy
y2, X2 = dmatrices('neurons_log ~ date_num', data=fit_data2, return_type='dataframe')
mod2 = sm.OLS(y2, X2) # Describe model
res2 = mod2.fit() # Fit model
print(res2.summary()) # Summarize model
# what's the doubling time from this model? log(2) / a
doubling_time2 = np.log(2) / res2.params['date_num']
print('Doubling time imaging: %f years'%doubling_time2)
# extrapolate to whenever
yvec2 = res2.predict(sm.add_constant(xvec1))
# ====================================== #
# SHOW SOME TARGET NUMBERS FOR NEURONS IN DIFFERENT SPECIES
# ====================================== #
# Herculano-Houzel et al. 2015, 10.1159/000437413
nneurons = [{'species':'Caenorhabditis elegans', 'name':'C. elegans',
'nneurons_low':302, 'nneurons_high':302},
{'species': 'Dan<NAME> (larvae)', 'name': 'Zebrafish (larva)', # https://elifesciences.org/articles/28158
'nneurons_low': 100000, 'nneurons_high': 100000},
# {'species':'Drosophila melanogaster', 'name':'Drosophila', # https://doi.org/10.1016/j.cub.2010.11.056
# 'nneurons_low':135000, 'nneurons_high':135000},
# https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3597383/
{'species':'Mus musculus', 'name':'Mouse', # Vincent et al 2010: 7.5x10^7
'nneurons_low':67873741-10406194, 'nneurons_high':67873741+10406194},
# {'species':'Rattus norvegicus', 'name':'Rat',
# 'nneurons_low':188867832-12622383, 'nneurons_high':188867832+12622383},
{'species': 'Macaca mulatta', 'name': 'Macaque',
'nneurons_low': 6376160000, 'nneurons_high': 6376160000},
{'species': 'Homo sapiens', 'name': 'Human',
'nneurons_low': 86060000000-8120000000, 'nneurons_high': 86060000000+8120000000},
]
# ====================================== #
# for each species, when will record
# from all their neurons?
# ====================================== #
for sp in nneurons:
avg_log = np.log((sp['nneurons_low'] + sp['nneurons_high']) / 2)
max_year = xvec1[np.abs(yvec1-avg_log).argmin()]
min_year = xvec1[np.abs(yvec2-avg_log).argmin()]
print('%s: expected %d - %d'%(sp['name'], min_year, max_year))
# ====================================== #
# make the plot
# ====================================== #
fig, ax = plt.subplots(1, 1, figsize=[5, 3.5])
sns.scatterplot(data=df, x='date_num', y='neurons_log', style='Source',
hue='Method', zorder=0, s=10, linewidths=0.5, alpha=0.5,
palette=sns.color_palette(["firebrick", "midnightblue"]),
hue_order=['Imaging', 'Ephys'],
markers={'S&K':'s', 'Stevenson':'o', 'Urai':'o',
'Rupprecht':'o', 'Charles':'o', 'Meijer':'o',
'Svoboda':'o'}, legend=False)
# write labels in plot, instead of legend
ax.text(2004, np.log(2), 'Electrophysiology',
{'color':"midnightblue", 'fontsize':9, 'fontstyle':'italic'})
ax.text(1985, np.log(1000), 'Optical\nimaging',
{'color':"firebrick", 'fontsize':9, 'fontstyle':'italic'})
# plot Stevenson curve on top
ax.plot(X['date_num'], res.predict(), color='k')
# then show extrapolation beyond 2011; to now
xvec = df[df['date_num'] > 1960]['date_num']
yvec = res.predict(sm.add_constant(xvec))
ax.plot(xvec, yvec, color='k', linestyle='--')
# and finally, all the way out into the future
xvec = | np.linspace(2020, 2025, 100) | numpy.linspace |
# coding:utf-8
import torch.nn.functional as F
import torch
import torch.nn as nn
import cv2
import numpy as np
import matplotlib.pyplot as plt
def dice_loss(pred, target, smooth=1.):
pred = pred.contiguous()
target = target.contiguous()
intersection = (pred * target).sum(dim=2).sum(dim=2)
loss = (1 - ((2. * intersection + smooth) / (pred.sum(dim=2).sum(dim=2) + target.sum(dim=2).sum(dim=2) + smooth)))
return loss.mean()
def calc_loss (pred, target, metrics, bce_weight=0.5):
bce = F.binary_cross_entropy_with_logits(pred, target)
pred = torch.sigmoid(pred)
dice = dice_loss(pred, target)
loss = bce * bce_weight + dice * (1 - bce_weight)
metrics['bce'] += bce.data.cpu().numpy()
metrics['dice'] += dice.data.cpu().numpy()
metrics['loss'] += loss.data.cpu().numpy()
return loss, metrics
def calc_loss_aux (pred, auxiliary, target, metrics, bce_weight=0.5):
bce = F.binary_cross_entropy_with_logits(pred, target)
pred = torch.sigmoid(pred)
dice = dice_loss(pred, target)
auxiliary_bce = nn.BCEWithLogitsLoss()
auxiliary_loss = auxiliary_bce(auxiliary, target[:, 1, :, :].unsqueeze(1))
loss = bce * bce_weight + dice * (1 - bce_weight) + 0.5*auxiliary_loss
metrics['bce'] += bce.data.cpu().numpy()
metrics['dice'] += dice.data.cpu().numpy()
metrics['aux'] += auxiliary_loss.data.cpu().numpy()
metrics['loss'] += loss.data.cpu().numpy()
return loss, metrics
def print_metrics(metrics, epoch_samples, phase):
outputs = []
for k in metrics.keys():
outputs.append("{}: {:4f}".format(k, metrics[k] / epoch_samples))
print("{}: {}".format(phase, ", ".join(outputs)))
def line_level_estimator(pred, labels, batch_size, iou_threshold=0.5):
img_recall_tp = []
img_recall_gt = []
pred = pred.data.cpu().numpy()
labels = labels.data.cpu().numpy()
for batch_idx in range(batch_size):
pred_ = ((pred[batch_idx, 1, :, :] > 0.5) * 255).astype('uint8')
label_ = (labels[batch_idx, 1, :, :] * 255).astype('uint8')
cnts_gt, _ = cv2.findContours(label_, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE)
gt = 0 # the number of gt lines
tp = 0
for blob in cnts_gt:
# 9 is minimum number of pixels to assume a power line
if len(blob) > 9:
gt += 1
maxIOU = 0.01
# img1: gt image containing a power line / img2 = intersection of gt and prediction
blank = np.zeros(pred_.shape[0:2])
img1 = cv2.drawContours(blank.copy(), [blob], -1, 1, thickness=-1)
img2 = img1 * pred_
intersection = img2 == 255
union = img1 > 0
if maxIOU < intersection.sum() / union.sum():
maxIOU = intersection.sum() / union.sum()
if maxIOU > iou_threshold:
tp += 1
continue
img_recall_tp.append(tp)
img_recall_gt.append(gt)
return img_recall_tp, img_recall_gt
def iou_estimator(pred, labels, batch_size, img_merge=False, iou_threshold=0.5):
pred = pred.data.cpu().numpy()
labels = labels.data.cpu().numpy()
if img_merge:
# Calculate IoU score after reconstruction into 512 x 512 image
com_pred = com_lable =np.zeros([512, 512])
com_pred[:256, :256] = pred[0, 1, :, :]
com_pred[:256, 256:] = pred[1, 1, :, :]
com_pred[256:, :256] = pred[2, 1, :, :]
com_pred[256:, 256:] = pred[3, 1, :, :]
com_lable[:256, :256] = labels[0, 1, :, :]
com_lable[:256, 256:] = labels[1, 1, :, :]
com_lable[256:, :256] = labels[2, 1, :, :]
com_lable[256:, 256:] = labels[3, 1, :, :]
pred_ = ((com_pred > iou_threshold) * 255).astype('uint8')
label_ = (com_lable * 255).astype('uint8')
gt = (label_ > 0).astype('int32')
seg = (pred_ > 0).astype('int32')
iou = np.sum(seg[gt == 1]) / ( | np.sum(seg) | numpy.sum |
"""
Author: <NAME>
Email: <EMAIL>
Sub threshold Signal Detection
------------------------------
Computes the cross correlation coefficient between the output
of ChaosNet (normalized firing time) and input signal for
varying noise intensties.
"""
import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import KFold
from sklearn.metrics import confusion_matrix as cm
import os
from sklearn.metrics import (precision_score, recall_score,f1_score, accuracy_score,mean_squared_error,mean_absolute_error)
from sklearn.svm import LinearSVC
import ChaosFEX.feature_extractor as CFX
# Input periodic signal
A = 0.2
t = | np.arange(0, 1, 0.001) | numpy.arange |
import numpy as np
import time
from astropy import wcs
from tabulate import tabulate
import astropy.io.fits as fits
import pandas as pd
def setdiff_nd(a1, a2):
"""
python 使用numpy求二维数组的差集
:param a1:
:param a2:
:return:
"""
# a1 = index_value
# a2 = np.array([point_ii_xy])
a1_rows = a1.view([('', a1.dtype)] * a1.shape[1])
a2_rows = a2.view([('', a2.dtype)] * a2.shape[1])
a3 = np.setdiff1d(a1_rows, a2_rows).view(a1.dtype).reshape(-1, a1.shape[1])
return a3
def get_xyz(data):
"""
:param data: 3D data
:return: 3D data coordinates
第1,2,3维数字依次递增
:param data: 2D data
:return: 2D data coordinates
第1,2维数字依次递增
"""
nim = data.ndim
if nim == 3:
size_x, size_y, size_z = data.shape
x_arange = np.arange(1, size_x+1)
y_arange = np.arange(1, size_y+1)
z_arange = np.arange(1, size_z+1)
[xx, yy, zz] = np.meshgrid(x_arange, y_arange, z_arange, indexing='ij')
xyz = np.column_stack([zz.flatten(), yy.flatten(), xx.flatten()])
else:
size_x, size_y = data.shape
x_arange = np.arange(1, size_x + 1)
y_arange = np.arange(1, size_y + 1)
[xx, yy] = np.meshgrid(x_arange, y_arange, indexing='ij')
xyz = np.column_stack([yy.flatten(), xx.flatten()])
return xyz
def kc_coord_3d(point_ii_xy, xm, ym, zm, r):
"""
:param point_ii_xy: 当前点坐标(x,y,z)
:param xm: size_x
:param ym: size_y
:param zm: size_z
:param r: 2 * r + 1
:return:
返回delta_ii_xy点r邻域的点坐标
"""
it = point_ii_xy[0]
jt = point_ii_xy[1]
kt = point_ii_xy[2]
xyz_min = np.array([[1, it - r], [1, jt - r], [1, kt - r]])
xyz_min = xyz_min.max(axis=1)
xyz_max = np.array([[xm, it + r], [ym, jt + r], [zm, kt + r]])
xyz_max = xyz_max.min(axis=1)
x_arange = np.arange(xyz_min[0], xyz_max[0] + 1)
y_arange = np.arange(xyz_min[1], xyz_max[1] + 1)
v_arange = np.arange(xyz_min[2], xyz_max[2] + 1)
[p_k, p_i, p_j] = np.meshgrid(x_arange, y_arange, v_arange, indexing='ij')
Index_value = np.column_stack([p_k.flatten(), p_i.flatten(), p_j.flatten()])
Index_value = setdiff_nd(Index_value, np.array([point_ii_xy]))
ordrho_jj = np.matmul(Index_value - 1, np.array([[1], [xm], [ym * xm]]))
ordrho_jj.reshape([1, ordrho_jj.shape[0]])
return ordrho_jj[:, 0], Index_value
def kc_coord_2d(point_ii_xy, xm, ym, r):
"""
:param point_ii_xy: 当前点坐标(x,y)
:param xm: size_x
:param ym: size_y
:param r: 2 * r + 1
:return:
返回point_ii_xy点r邻域的点坐标
"""
it = point_ii_xy[0]
jt = point_ii_xy[1]
xyz_min = np.array([[1, it - r], [1, jt - r]])
xyz_min = xyz_min.max(axis=1)
xyz_max = np.array([[xm, it + r], [ym, jt + r]])
xyz_max = xyz_max.min(axis=1)
x_arrange = np.arange(xyz_min[0], xyz_max[0] + 1)
y_arrange = np.arange(xyz_min[1], xyz_max[1] + 1)
[p_k, p_i] = | np.meshgrid(x_arrange, y_arrange, indexing='ij') | numpy.meshgrid |
"""
Statistical functions
"""
from __future__ import absolute_import, division
import numpy as np
from scipy.special import gammaln
from uncertainties import unumpy as unp
from pisa import FTYPE
from pisa.utils.comparisons import FTYPE_PREC, isbarenumeric
from pisa.utils.log import logging
from pisa.utils import likelihood_functions
__all__ = ['SMALL_POS', 'CHI2_METRICS', 'LLH_METRICS', 'ALL_METRICS',
'maperror_logmsg',
'chi2', 'llh', 'log_poisson', 'log_smear', 'conv_poisson',
'norm_conv_poisson', 'conv_llh', 'barlow_llh', 'mod_chi2', 'mcllh_mean', 'mcllh_eff']
__author__ = '<NAME>, <NAME>, <NAME>'
__license__ = '''Copyright (c) 2014-2017, The IceCube Collaboration
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.'''
SMALL_POS = 1e-10 #if FTYPE == np.float64 else FTYPE_PREC
"""A small positive number with which to replace numbers smaller than it"""
CHI2_METRICS = ['chi2', 'mod_chi2']
"""Metrics defined that result in measures of chi squared"""
LLH_METRICS = ['llh', 'conv_llh', 'barlow_llh', 'mcllh_mean', 'mcllh_eff']
"""Metrics defined that result in measures of log likelihood"""
ALL_METRICS = LLH_METRICS + CHI2_METRICS
"""All metrics defined"""
METRICS_TO_MAXIMIZE = LLH_METRICS
"""Metrics that must be maximized to obtain a better fit"""
METRICS_TO_MINIMIZE = CHI2_METRICS
"""Metrics that must be minimized to obtain a better fit"""
# TODO(philippeller):
# * unit tests to ensure these don't break
def maperror_logmsg(m):
"""Create message with thorough info about a map for logging purposes"""
with np.errstate(invalid='ignore'):
msg = ''
msg += ' min val : %s\n' %np.nanmin(m)
msg += ' max val : %s\n' %np.nanmax(m)
msg += ' mean val: %s\n' %np.nanmean(m)
msg += ' num < 0 : %s\n' %np.sum(m < 0)
msg += ' num == 0: %s\n' %np.sum(m == 0)
msg += ' num > 0 : %s\n' %np.sum(m > 0)
msg += ' num nan : %s\n' %np.sum(np.isnan(m))
return msg
def chi2(actual_values, expected_values):
"""Compute the chi-square between each value in `actual_values` and
`expected_values`.
Parameters
----------
actual_values, expected_values : numpy.ndarrays of same shape
Returns
-------
chi2 : numpy.ndarray of same shape as inputs
chi-squared values corresponding to each pair of elements in the inputs
Notes
-----
* Uncertainties are not propagated through this calculation.
* Values in each input are clipped to the range [SMALL_POS, inf] prior to
the calculation to avoid infinities due to the divide function.
"""
if actual_values.shape != expected_values.shape:
raise ValueError(
'Shape mismatch: actual_values.shape = %s,'
' expected_values.shape = %s'
% (actual_values.shape, expected_values.shape)
)
# Convert to simple numpy arrays containing floats
if not isbarenumeric(actual_values):
actual_values = unp.nominal_values(actual_values)
if not isbarenumeric(expected_values):
expected_values = unp.nominal_values(expected_values)
with np.errstate(invalid='ignore'):
# Mask off any nan expected values (these are assumed to be ok)
actual_values = np.ma.masked_invalid(actual_values)
expected_values = np.ma.masked_invalid(expected_values)
# TODO: this check (and the same for `actual_values`) should probably
# be done elsewhere... maybe?
if np.any(actual_values < 0):
msg = ('`actual_values` must all be >= 0...\n'
+ maperror_logmsg(actual_values))
raise ValueError(msg)
if np.any(expected_values < 0):
msg = ('`expected_values` must all be >= 0...\n'
+ maperror_logmsg(expected_values))
raise ValueError(msg)
# TODO: Is this okay to do? Mathematically suspect at best, and can
# still destroy a minimizer's hopes and dreams...
# Replace 0's with small positive numbers to avoid inf in division
np.clip(actual_values, a_min=SMALL_POS, a_max=np.inf,
out=actual_values)
np.clip(expected_values, a_min=SMALL_POS, a_max=np.inf,
out=expected_values)
delta = actual_values - expected_values
if np.all(np.abs(delta) < 5*FTYPE_PREC):
return np.zeros_like(delta, dtype=FTYPE)
assert np.all(actual_values > 0), str(actual_values)
#chi2_val = np.square(delta) / actual_values
chi2_val = np.square(delta) / expected_values
assert np.all(chi2_val >= 0), str(chi2_val[chi2_val < 0])
return chi2_val
def llh(actual_values, expected_values):
"""Compute the log-likelihoods (llh) that each count in `actual_values`
came from the the corresponding expected value in `expected_values`.
Parameters
----------
actual_values, expected_values : numpy.ndarrays of same shape
Returns
-------
llh : numpy.ndarray of same shape as the inputs
llh corresponding to each pair of elements in `actual_values` and
`expected_values`.
Notes
-----
* Uncertainties are not propagated through this calculation.
* Values in `expected_values` are clipped to the range [SMALL_POS, inf]
prior to the calculation to avoid infinities due to the log function.
"""
assert actual_values.shape == expected_values.shape
# Convert to simple numpy arrays containing floats
if not isbarenumeric(actual_values):
actual_values = unp.nominal_values(actual_values)
if not isbarenumeric(expected_values):
expected_values = unp.nominal_values(expected_values)
with np.errstate(invalid='ignore'):
# Mask off any nan expected values (these are assumed to be ok)
actual_values = np.ma.masked_invalid(actual_values)
expected_values = np.ma.masked_invalid(expected_values)
# Check that new array contains all valid entries
if np.any(actual_values < 0):
msg = ('`actual_values` must all be >= 0...\n'
+ maperror_logmsg(actual_values))
raise ValueError(msg)
# TODO: How should we handle nan / masked values in the "data"
# (actual_values) distribution? How about negative numbers?
# Make sure actual values (aka "data") are valid -- no infs, no nans,
# etc.
if np.any((actual_values < 0) | ~np.isfinite(actual_values)):
msg = ('`actual_values` must be >= 0 and neither inf nor nan...\n'
+ maperror_logmsg(actual_values))
raise ValueError(msg)
# Check that new array contains all valid entries
if np.any(expected_values < 0.0):
msg = ('`expected_values` must all be >= 0...\n'
+ maperror_logmsg(expected_values))
raise ValueError(msg)
# Replace 0's with small positive numbers to avoid inf in log
np.clip(expected_values, a_min=SMALL_POS, a_max=np.inf,
out=expected_values)
llh_val = actual_values*np.log(expected_values) - expected_values
# Do following to center around 0
llh_val -= actual_values*np.log(actual_values) - actual_values
return llh_val
def mcllh_mean(actual_values, expected_values):
"""Compute the log-likelihood (llh) based on LMean in table 2 - https://doi.org/10.1007/JHEP06(2019)030
accounting for finite MC statistics.
This is the second most recommended likelihood in the paper.
Parameters
----------
actual_values, expected_values : numpy.ndarrays of same shape
Returns
-------
llh : numpy.ndarray of same shape as the inputs
llh corresponding to each pair of elements in `actual_values` and
`expected_values`.
Notes
-----
*
"""
assert actual_values.shape == expected_values.shape
# Convert to simple numpy arrays containing floats
actual_values = unp.nominal_values(actual_values).ravel()
sigma = unp.std_devs(expected_values).ravel()
expected_values = unp.nominal_values(expected_values).ravel()
with np.errstate(invalid='ignore'):
# Mask off any nan expected values (these are assumed to be ok)
actual_values = np.ma.masked_invalid(actual_values)
expected_values = np.ma.masked_invalid(expected_values)
# Check that new array contains all valid entries
if np.any(actual_values < 0):
msg = ('`actual_values` must all be >= 0...\n'
+ maperror_logmsg(actual_values))
raise ValueError(msg)
# TODO: How should we handle nan / masked values in the "data"
# (actual_values) distribution? How about negative numbers?
# Make sure actual values (aka "data") are valid -- no infs, no nans,
# etc.
if np.any((actual_values < 0) | ~np.isfinite(actual_values)):
msg = ('`actual_values` must be >= 0 and neither inf nor nan...\n'
+ maperror_logmsg(actual_values))
raise ValueError(msg)
# Check that new array contains all valid entries
if np.any(expected_values < 0.0):
msg = ('`expected_values` must all be >= 0...\n'
+ maperror_logmsg(expected_values))
raise ValueError(msg)
llh_val = likelihood_functions.poisson_gamma(actual_values, expected_values, sigma**2, a=0, b=0)
return llh_val
def mcllh_eff(actual_values, expected_values):
"""Compute the log-likelihood (llh) based on eq. 3.16 - https://doi.org/10.1007/JHEP06(2019)030
accounting for finite MC statistics.
This is the most recommended likelihood in the paper.
Parameters
----------
actual_values, expected_values : numpy.ndarrays of same shape
Returns
-------
llh : numpy.ndarray of same shape as the inputs
llh corresponding to each pair of elements in `actual_values` and
`expected_values`.
Notes
-----
*
"""
assert actual_values.shape == expected_values.shape
# Convert to simple numpy arrays containing floats
actual_values = unp.nominal_values(actual_values).ravel()
sigma = unp.std_devs(expected_values).ravel()
expected_values = unp.nominal_values(expected_values).ravel()
with np.errstate(invalid='ignore'):
# Mask off any nan expected values (these are assumed to be ok)
actual_values = np.ma.masked_invalid(actual_values)
expected_values = np.ma.masked_invalid(expected_values)
# Check that new array contains all valid entries
if np.any(actual_values < 0):
msg = ('`actual_values` must all be >= 0...\n'
+ maperror_logmsg(actual_values))
raise ValueError(msg)
# TODO: How should we handle nan / masked values in the "data"
# (actual_values) distribution? How about negative numbers?
# Make sure actual values (aka "data") are valid -- no infs, no nans,
# etc.
if np.any((actual_values < 0) | ~np.isfinite(actual_values)):
msg = ('`actual_values` must be >= 0 and neither inf nor nan...\n'
+ maperror_logmsg(actual_values))
raise ValueError(msg)
# Check that new array contains all valid entries
if np.any(expected_values < 0.0):
msg = ('`expected_values` must all be >= 0...\n'
+ maperror_logmsg(expected_values))
raise ValueError(msg)
llh_val = likelihood_functions.poisson_gamma(actual_values, expected_values, sigma**2, a=1, b=0)
return llh_val
def log_poisson(k, l):
r"""Calculate the log of a poisson pdf
.. math::
p(k,l) = \log\left( l^k \cdot e^{-l}/k! \right)
Parameters
----------
k : float
l : float
Returns
-------
log of poisson
"""
return k*np.log(l) -l - gammaln(k+1)
def log_smear(x, sigma):
r"""Calculate the log of a normal pdf
.. math::
p(x, \sigma) = \log\left( (\sigma \sqrt{2\pi})^{-1} \exp( -x^2 / 2\sigma^2 ) \right)
Parameters
----------
x : float
sigma : float
Returns
-------
log of gaussian
"""
return (
-np.log(sigma) - 0.5*np.log(2*np.pi) - x**2 / (2*sigma**2)
)
def conv_poisson(k, l, s, nsigma=3, steps=50):
r"""Poisson pdf
.. math::
p(k,l) = l^k \cdot e^{-l}/k!
Parameters
----------
k : float
l : float
s : float
sigma for smearing term (= the uncertainty to be accounted for)
nsigma : int
The ange in sigmas over which to do the convolution, 3 sigmas is > 99%,
so should be enough
steps : int
Number of steps to do the intergration in (actual steps are 2*steps + 1,
so this is the steps to each side of the gaussian smearing term)
Returns
-------
float
convoluted poissson likelihood
"""
# Replace 0's with small positive numbers to avoid inf in log
l = max(SMALL_POS, l)
st = 2*(steps + 1)
conv_x = np.linspace(-nsigma*s, +nsigma*s, st)[:-1]+nsigma*s/(st-1.)
conv_y = log_smear(conv_x, s)
f_x = conv_x + l
#f_x = conv_x + k
# Avoid zero values for lambda
idx = np.argmax(f_x > 0)
f_y = log_poisson(k, f_x[idx:])
#f_y = log_poisson(f_x[idx:], l)
if np.isnan(f_y).any():
logging.error('`NaN values`:')
logging.error('idx = %d', idx)
logging.error('s = %s', s)
logging.error('l = %s', l)
logging.error('f_x = %s', f_x)
logging.error('f_y = %s', f_y)
f_y = np.nan_to_num(f_y)
conv = np.exp(conv_y[idx:] + f_y)
norm = np.sum( | np.exp(conv_y) | numpy.exp |
from __future__ import division, with_statement
from scipy.constants import pi
import scipy.constants as cons
import numpy as np
import scipy.optimize as optimize
import matplotlib.pyplot as plt
import scipy.linalg as LA
# print at line 396
__author__ = 'sbt'
# -*- coding: utf-8 -*-
"""
Contains the ModeAnalysis class, which can simulate the positions of ions in a crystal
of desired size. The class contains methods for the generation of a crystal,
relaxation to a minimum potential energy state, and determination of axial and (eventually) planar modes of motion
by methods derived by Wang, Keith, and Freericks in 2013.
Translated from MATLAB code written by <NAME> by <NAME>.
Standardized and slightly revised by <NAME>.
Be careful. Sometimes when using the exact same parameters this
code will make different crystals with the same potential energy. That is,
crystal are degenerate when reflecting over the axes.
"""
class ModeAnalysis:
"""
Simulates a 2-dimensional ion crystal, determining an equilibrium plane configuration given
Penning trap parameters, and then calculates the eigenvectors and eigenmodes.
For reference the following ion number correspond the closed shells:
1 2 3 4 5 6 7 8 9 10 11 12 13 14
7 19 37 61 91 127 169 217 271 331 397 469 547 631...
"""
#Establish fundamental physical constants as class variables
q = 1.602176565E-19
amu = 1.66057e-27
# m_Be = 9.012182 * amu
k_e = 8.9875517873681764E9 # electrostatic constant k_e = 1 / (4.0 pi epsilon_0)
def __init__(self, N=19, XR=1, Vtrap=(0.0, -1750.0, -1970.0), Ctrap=1.0,
omega_z = 1.58e6, ionmass=None, B=4.4588, frot=180., Vwall=1.,
wall_order=2, quiet=True, precision_solving=True,
method = 'bfgs'):
"""
:param N: integer, number of ions
:param shells: integer, number of shells to instantiate the plasma with
:param Vtrap: array of 3 elements, defines the [end, middle, center] voltages on the trap electrodes.
:param Ctrap: float, constant coefficient on trap potentials
:param B: float, defines strength of axial magnetic field.
:param frot: float, frequency of rotation
:param Vwall: float, strength of wall potential in volts
:param wall_order: integer, defines the order of the rotating wall potential
:param mult: float, mutliplicative factor for simplifying numerical calculations
:param quiet: will print some things if False
:param precision_solving: Determines if perturbations will be made to the crystal to find
a low energy state with a number of attempts based on the
number of ions.
Disable for speed, but recommended.
"""
self.method = method
self.ionmass = ionmass
self.m_Be = self.ionmass * self.amu
self.quiet = quiet
self.precision_solving = precision_solving
# Initialize basic variables such as physical constants
self.Nion = N
# self.shells = shells
# self.Nion = 1 + 6 * np.sum(range(1, shells + 1))
# if no input masses, assume all ions are beryllium
self.m = self.m_Be * np.ones(self.Nion)
# mass order is irrelevant and don't assume it will be fixed
# FUTURE: heavier (than Be) ions will be added to outer shells
# for array of ion positions first half is x, last is y
self.u0 = np.empty(2 * self.Nion) # initial lattice
self.u = np.empty(2 * self.Nion) # equilibrium positions
# trap definitions
self.B = B
self.wcyc = self.q * B / self.m_Be # Beryllium cyclotron frequency
# axial trap coefficients; see Teale's final paper
self.C = Ctrap * np.array([[0.0756, 0.5157, 0.4087],
[-0.0001, -0.005, 0.005],
[1.9197e3, 3.7467e3, -5.6663e3],
[0.6738e7, -5.3148e7, 4.641e7]])
# wall order
if wall_order == 2:
self.Cw3 = 0
if wall_order == 3:
self.Cw2 = 0
self.Cw3 = self.q * Vwall * 3e4
self.relec = 0.01 # rotating wall electrode distance in meters
self.Vtrap = np.array(Vtrap) # [Vend, Vmid, Vcenter] for trap electrodes
self.Coeff = np.dot(self.C, self.Vtrap) # Determine the 0th, first, second, and fourth order
# potentials at trap center
#self.wz = 4.9951e6 # old trapping frequency
#self.wz = np.sqrt(2 * self.q * self.Coeff[2] / self.m_Be) # Compute axial frequency
# print('axial freq=',self.wz/(2e6*np.pi),'MHz')
self.omega_z = omega_z
self.wz = self.omega_z
self.wrot = 2 * pi * frot * 1e3 # Rotation frequency in units of angular fre quency
# Not used vvv
#self.wmag = 0.5 * (self.wcyc - np.sqrt(self.wcyc ** 2 - 2 * self.wz ** 2))
self.wmag=0 # a hack for now
self.V0 = (0.5 * self.m_Be * self.wz ** 2) / self.q # Find quadratic voltage at trap center
#self.Cw = 0.045 * Vwall / 1000 # old trap
self.XR=XR
self.Cw = self.XR*Vwall * 1612 / self.V0 # dimensionless coefficient in front
self.delta = self.Cw
# of rotating wall terms in potential
self.dimensionless() # Make system dimensionless
self.beta = (self.wr*self.wc - self.wr ** 2) -1/2
self.axialEvals = [] # Axial eigenvalues
self.axialEvects = [] # Axial eigenvectors
self.planarEvals = [] # Planar eigenvalues
self.planarEvects = [] # Planar Eigenvectors
self.axialEvalsE = [] # Axial eigenvalues in experimental units
self.planarEvalsE = [] # Planar eigenvalues in experimental units
self.p0 = 0 # dimensionless potential energy of equilibrium crystal
self.r = []
self.rsep = []
self.dx = []
self.dy = []
self.hasrun = False
def dimensionless(self):
"""Calculate characteristic quantities and convert to a dimensionless
system
"""
# characteristic length
self.l0 = ((self.k_e * self.q ** 2) / (.5 * self.m_Be * self.wz ** 2)) ** (1 / 3)
self.t0 = 1 / self.wz # characteristic time
self.v0 = self.l0 / self.t0 # characteristic velocity
self.E0 = 0.5*self.m_Be*(self.wz**2)*self.l0**2 # characteristic energy
self.wr = self.wrot / self.wz # dimensionless rotation
self.wc = self.wcyc / self.wz # dimensionless cyclotron
self.md = np.ones(self.Nion)#self.m / self.m_Be # dimensionless mass
def expUnits(self):
"""Convert dimensionless outputs to experimental units"""
self.u0E = self.l0 * self.u0 # Seed lattice
self.uE = self.l0 * self.u # Equilibrium positions
self.axialEvalsE_raw = self.wz * self.axialEvals_raw
self.axialEvalsE = self.wz * self.axialEvals
self.planarEvalsE = self.wz * self.planarEvals
# eigenvectors are dimensionless anyway
def run(self):
"""
Generates a crystal from the generate_crystal method (by the find_scalled_lattice_guess method,
adjusts it into an eqilibirium position by find_eq_pos method)
and then computes the eigenvalues and eigenvectors of the axial modes by calc_axial_modes.
Sorts the eigenvalues and eigenvectors and stores them in self.Evals, self.Evects.
Stores the radial separations as well.
"""
# print('this is the local mode_analysis.')
if self.wmag > self.wrot:
print("Warning: Rotation frequency", self.wrot/(2*pi),
" is below magnetron frequency of", float(self.wrot/(2*pi)))
return 0
self.generate_crystal()
print(np.shape(self.u))
self.axialEvals_raw, self.axialEvals, self.axialEvects = self.calc_axial_modes(self.u)
self.planarEvals, self.planarEvects, self.V = self.calc_planar_modes(self.u)
self.expUnits() # make variables of outputs in experimental units
self.axial_hessian = -self.calc_axial_hessian(self.u)
self.planar_hessian= -self.V/2
self.axial_Mmat = np.diag(self.md)
self.planar_Mmat = np.diag(np.tile(self.md,2))
self.hasrun = True
def generate_crystal(self):
"""
The run method already is a "start-to-finish" implementation of crystal generation and
eigenmode determination, so this simply contains the comopnents which generate a crystal.
:return: Returns a crystal's position vector while also saving it to the class.
"""
# This check hasn't been working properly, and so wmag has been set to
# 0 for the time being (July 2015, SBT)
if self.wmag > self.wrot:
print("Warning: Rotation frequency", self.wrot/(2*pi),
" is below magnetron frequency of", float(self.wrot/(2*pi)))
return 0
#Generate a lattice in dimensionless units
self.u0 = self.find_scaled_lattice_guess(mins=1, res=50)
# self.u0 = self.generate_2D_hex_lattice(2)
# if masses are not all beryllium, force heavier ions to be boundary
# ions, and lighter ions to be near center
# ADD self.addDefects()
#Solve for the equilibrium position
self.u = self.find_eq_pos(self.u0,self.method)
# Will attempt to nudge the crystal to a slightly lower energy state via some
# random perturbation.
# Only changes the positions if the perturbed potential energy was reduced.
#Will perturb less for bigger crystals, as it takes longer depending on how many ions
#there are.
if self.precision_solving is True:
if self.quiet is False:
print("Perturbing crystal...")
if self.Nion <= 62:
for attempt in np.linspace(.05, .5, 50):
self.u = self.perturb_position(self.u, attempt)
if 62 < self.Nion <= 126:
for attempt in np.linspace(.05, .5, 25):
self.u = self.perturb_position(self.u, attempt)
if 127 <= self.Nion <= 200:
for attempt in np.linspace(.05, .5, 10):
self.u = self.perturb_position(self.u, attempt)
if 201 <= self.Nion:
for attempt in np.linspace(.05, .3, 5):
self.u = self.perturb_position(self.u, attempt)
if self.quiet is False:
pass
#print("Perturbing complete")
self.r, self.dx, self.dy, self.rsep = self.find_radial_separation(self.u)
self.p0 = self.pot_energy(self.u)
return self.u
def generate_lattice(self):
"""Generate lattice for an arbitrary number of ions (self.Nion)
:return: a flattened xy position vector defining the 2d hexagonal
lattice
"""
# number of closed shells
S = int((np.sqrt(9 - 12 * (1 - self.Nion)) - 3) / 6)
u0 = self.generate_2D_hex_lattice(S)
N0 = int(u0.size / 2)
x0 = u0[0:N0]
y0 = u0[N0:]
Nadd = self.Nion - N0 # Number of ions left to add
self.Nion = N0
pair = self.add_hex_shell(S + 1) # generate next complete shell
xadd = pair[0::2]
yadd = pair[1::2]
for i in range(Nadd):
# reset number of ions to do this calculation
self.Nion += 1
# make masses all one (add defects later)
self.md = np.ones(self.Nion)
V = [] # list to store potential energies from calculation
# for each ion left to add, calculate potential energy if that
# ion is added
for j in range(len(xadd)):
V.append(self.pot_energy(np.hstack((x0, xadd[j], y0,
yadd[j]))))
ind = np.argmin(V) # ion added with lowest increase in potential
# permanently add to existing crystal
x0 = np.append(x0, xadd[ind])
y0 = np.append(y0, yadd[ind])
# remove ion from list to add
xadd = np.delete(xadd, ind)
yadd = np.delete(yadd, ind)
# Restore mass array
self.md = self.m / self.m_Be # dimensionless mass
return np.hstack((x0, y0))
def pot_energy(self, pos_array):
"""
Computes the potential energy of the ion crystal,
taking into consideration:
Coulomb repulsion
qv x B forces
Trapping potential
and some other things (#todo to be fully analyzed; june 10 2015)
:param pos_array: The position vector of the crystal to be analyzed.
:return: The scalar potential energy of the crystal configuration.
"""
# Frequency of rotation, mass and the number of ions in the array
# the x positions are the first N elements of the position array
x = pos_array[0:self.Nion]
# The y positions are the last N elements of the position array
y = pos_array[self.Nion:]
# dx flattens the array into a row vector
dx = x.reshape((x.size, 1)) - x
dy = y.reshape((y.size, 1)) - y
# rsep is the distances between
rsep = np.sqrt(dx ** 2 + dy ** 2)
with np.errstate(divide='ignore'):
Vc = np.where(rsep != 0., 1 / rsep, 0)
"""
#Deprecated version below which takes into account anharmonic effects, to be used later
V = 0.5 * (-m * wr ** 2 - q * self.Coeff[2] + q * B * wr) * np.sum((x ** 2 + y ** 2)) \
- q * self.Coeff[3] * np.sum((x ** 2 + y ** 2) ** 2) \
+ np.sum(self.Cw2 * (x ** 2 - y ** 2)) \
+ np.sum(self.Cw3 * (x ** 3 - 3 * x * y ** 2)) \
+ 0.5 * k_e * q ** 2 * np.sum(Vc)
"""
V = -np.sum((self.md * self.wr ** 2 + 0.5 * self.md - self.wr * self.wc) * (x ** 2 + y ** 2)) \
+ np.sum(self.md * self.Cw * (x ** 2 - y ** 2)) + 0.5 * np.sum(Vc)
return V
def force_penning(self, pos_array):
"""
Computes the net forces acting on each ion in the crystal;
used as the jacobian by find_eq_pos to minimize the potential energy
of a crystal configuration.
:param pos_array: crystal to find forces of.
:return: a vector of size 2N describing the x forces and y forces.
"""
x = pos_array[0:self.Nion]
y = pos_array[self.Nion:]
dx = x.reshape((x.size, 1)) - x
dy = y.reshape((y.size, 1)) - y
rsep = np.sqrt(dx ** 2 + dy ** 2)
# Calculate coulomb force on each ion
with np.errstate(divide='ignore'):
Fc = np.where(rsep != 0., rsep ** (-2), 0)
with np.errstate(divide='ignore', invalid='ignore'):
fx = np.where(rsep != 0., np.float64((dx / rsep) * Fc), 0)
fy = np.where(rsep != 0., np.float64((dy / rsep) * Fc), 0)
# total force on each ion
""" Deprecated version below which uses anharmonic trap potentials
Ftrapx = (-m * wr ** 2 - q * self.Coeff[2] + q * B * wr + 2 * self.Cw2) * x \
- 4 * q * self.Coeff[3] * (x ** 3 + x * y ** 2) + 3 * self.Cw3 * (x ** 2 - y ** 2)
Ftrapy = (-m * wr ** 2 - q * self.Coeff[2] + q * B * wr - 2 * self.Cw2) * y \
- 4 * q * self.Coeff[3] * (y ** 3 + y * x ** 2) - 6 * self.Cw3 * x * y
# Ftrap = (m*w**2 + q*self.V0 - 2*q*self.Vw - q*self.B* w) * pos_array
"""
Ftrapx = -2 * self.md * (self.wr ** 2 - self.wr * self.wc + 0.5 -
self.Cw) * x
Ftrapy = -2 * self.md * (self.wr ** 2 - self.wr * self.wc + 0.5 +
self.Cw) * y
Fx = -np.sum(fx, axis=1) + Ftrapx
Fy = -np.sum(fy, axis=1) + Ftrapy
return np.array([Fx, Fy]).flatten()
def hessian_penning(self, pos_array):
"""Calculate Hessian of potential"""
x = pos_array[0:self.Nion]
y = pos_array[self.Nion:]
dx = x.reshape((x.size, 1)) - x
dy = y.reshape((y.size, 1)) - y
rsep = np.sqrt(dx ** 2 + dy ** 2)
with np.errstate(divide='ignore'):
rsep5 = np.where(rsep != 0., rsep ** (-5), 0)
dxsq = dx ** 2
dysq = dy ** 2
# X derivatives, Y derivatives for alpha != beta
Hxx = np.mat((rsep ** 2 - 3 * dxsq) * rsep5)
Hyy = np.mat((rsep ** 2 - 3 * dysq) * rsep5)
# Above, for alpha == beta
# np.diag usa diagnoal value to form a matrix
Hxx += np.mat(np.diag(-2 * self.md * (self.wr ** 2 - self.wr * self.wc + .5 -
self.Cw) -
np.sum((rsep ** 2 - 3 * dxsq) * rsep5, axis=0)))
Hyy += np.mat(np.diag(-2 * self.md * (self.wr ** 2 - self.wr * self.wc + .5 +
self.Cw) -
np.sum((rsep ** 2 - 3 * dysq) * rsep5, axis=0)))
# print(self.V0)
# print('Cw=',self.Cw)
# print('wr=',self.wr)
# print('wc=',self.wc)
# print('wz=',self.wz)
# Mixed derivatives
Hxy = np.mat(-3 * dx * dy * rsep5)
Hxy += np.mat(np.diag(3 * np.sum(dx * dy * rsep5, axis=0)))
H = np.bmat([[Hxx, Hxy], [Hxy, Hyy]])
H = np.asarray(H)
return H
def find_scaled_lattice_guess(self, mins, res):
"""
Will generate a 2d hexagonal lattice based on the shells intialiization parameter.
Guesses initial minimum separation of mins and then increases spacing until a local minimum of
potential energy is found.
This doesn't seem to do anything. Needs a fixin' - AK
:param mins: the minimum separation to begin with.
:param res: the resizing parameter added onto the minimum spacing.
:return: the lattice with roughly minimized potential energy (via spacing alone).
"""
# Make a 2d lattice; u represents the position
uthen = self.generate_lattice()
uthen = uthen * mins
# Figure out the lattice's initial potential energy
pthen = self.pot_energy(uthen)
# Iterate through the range of minimum spacing in steps of res/resolution
for scale in np.linspace(mins, 10, res):
# Quickly make a 2d hex lattice; perhaps with some stochastic procedure?
uguess = uthen * scale
# Figure out the potential energy of that newly generated lattice
# print(uguess)
pnow = self.pot_energy(uguess)
# And if the program got a lattice that was less favorably distributed, conclude
# that we had a pretty good guess and return the lattice.
if pnow >= pthen:
# print("find_scaled_lattice: Minimum found")
# print "initial scale guess: " + str(scale)
# self.scale = scale
# print(scale)
return uthen
# If not, then we got a better guess, so store the energy score and current arrangement
# and try again for as long as we have mins and resolution to iterate through.
uthen = uguess
pthen = pnow
# If you're this far it means we've given up
# self.scale = scale
# print "find_scaled_lattice: no minimum found, returning last guess"
return uthen
def find_eq_pos(self, u0, method="bfgs"):
"""
Runs optimization code to tweak the position vector defining the crystal to a minimum potential energy
configuration.
:param u0: The position vector which defines the crystal.
:return: The equilibrium position vector.
"""
newton_tolerance = 1e-34
bfgs_tolerance = 1e-34
if method == "newton":
out = optimize.minimize(self.pot_energy, u0, method='Newton-CG', jac=self.force_penning,
hess=self.hessian_penning,
options={'xtol': newton_tolerance, 'disp': not self.quiet})
if method == 'bfgs':
out = optimize.minimize(self.pot_energy, u0, method='BFGS', jac=self.force_penning,
options={'gtol': bfgs_tolerance, 'disp': False}) # not self.quiet})
if (method != 'bfgs') & (method != 'newton'):
print('method, '+method+', not recognized')
exit()
return out.x
def calc_axial_hessian(self, pos_array):
"""
Calculate the axial hessian matrix for a crystal defined
by pos_array.
THIS MAY NEED TO BE EDITED FOR NONHOMOGENOUS MASSES
:param pos_array: Position vector which defines the crystal
to be analyzed.
:return: Array of eigenvalues, Array of eigenvectors
"""
x = pos_array[0:self.Nion]
y = pos_array[self.Nion:]
dx = x.reshape((x.size, 1)) - x
dy = y.reshape((y.size, 1)) - y
rsep = np.sqrt(dx ** 2 + dy ** 2)
with np.errstate(divide='ignore'):
rsep3 = np.where(rsep != 0., rsep ** (-3), 0)
K = np.diag((-1 + 0.5 * np.sum(rsep3, axis=0)))
K -= 0.5 * rsep3
return K
def calc_axial_modes(self, pos_array):
"""
Calculate the modes of axial vibration for a crystal defined
by pos_array.
THIS MAY NEED TO BE EDITED FOR NONHOMOGENOUS MASSES
:param pos_array: Position vector which defines the crystal
to be analyzed.
:return: Array of eigenvalues, Array of eigenvectors
"""
x = pos_array[0:self.Nion]
y = pos_array[self.Nion:]
dx = x.reshape((x.size, 1)) - x
dy = y.reshape((y.size, 1)) - y
rsep = np.sqrt(dx ** 2 + dy ** 2)
with np.errstate(divide='ignore'):
rsep3 = np.where(rsep != 0., rsep ** (-3), 0)
K = np.diag((-1 + 0.5 * np.sum(rsep3, axis=0)))
K -= 0.5 * rsep3
# Make first order system by making space twice as large
Zn = np.zeros((self.Nion, self.Nion))
eyeN = np.identity(self.Nion)
Mmat = np.diag(self.md)
Minv = np.linalg.inv(Mmat)
firstOrder = np.bmat([[Zn, eyeN], [np.dot(Minv,K), Zn]])
Eval, Evect = np.linalg.eig(firstOrder)
Eval_raw = Eval
# Convert 2N imaginary eigenvalues to N real eigenfrequencies
ind = np.argsort(np.absolute(np.imag(Eval)))
# print('ind=',ind)
Eval = np.imag(Eval[ind])
Eval = Eval[Eval >= 0] # toss the negative eigenvalues
Evect = Evect[:, ind] # sort eigenvectors accordingly
# Normalize by energy of mode
for i in range(2*self.Nion):
pos_part = Evect[:self.Nion, i]
vel_part = Evect[self.Nion:, i]
norm = vel_part.H*Mmat*vel_part - pos_part.H*K*pos_part
with np.errstate(divide='ignore',invalid='ignore'):
Evect[:, i] = np.where(np.sqrt(norm) != 0., Evect[:, i]/np.sqrt(norm), 0)
#Evect[:, i] = Evect[:, i]/np.sqrt(norm)
Evect = np.asarray(Evect)
return Eval_raw, Eval, Evect
def calc_planar_modes(self, pos_array):
"""Calculate Planar Mode Eigenvalues and Eigenvectors
THIS MAY NEED TO BE EDITED FOR NONHOMOGENOUS MASSES
:param pos_array: Position vector which defines the crystal
to be analyzed.
:return: Array of eigenvalues, Array of eigenvectors
"""
V = -self.hessian_penning(pos_array) # -Hessian
Zn = np.zeros((self.Nion, self.Nion)) #Nion, number of ions
Z2n = np.zeros((2 * self.Nion, 2 * self.Nion))
offdiag = (2 * self.wr - self.wc) * np.identity(self.Nion) # np.identity: unitary matrix
A = np.bmat([[Zn, offdiag], [-offdiag, Zn]])
Mmat = np.diag(np.concatenate((self.md,self.md))) #md =1
Minv = np.linalg.inv(Mmat)
firstOrder = np.bmat([[Z2n, np.identity(2 * self.Nion)], [np.dot(Minv,V/2), A]])
#mp.dps = 25
#firstOrder = mp.matrix(firstOrder)
#Eval, Evect = mp.eig(firstOrder)
Eval, Evect = np.linalg.eig(firstOrder)
# currently giving too many zero modes (increase numerical precision?)
# make eigenvalues real.
ind = np.argsort(np.absolute( | np.imag(Eval) | numpy.imag |
# Copyright (c) 2003-2019 by <NAME>
#
# TreeCorr is free software: redistribution and use in source and binary forms,
# with or without modification, are permitted provided that the following
# conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
# list of conditions, and the disclaimer given in the accompanying LICENSE
# file.
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions, and the disclaimer given in the documentation
# and/or other materials provided with the distribution.
from __future__ import print_function
import numpy as np
import os
import coord
import time
import fitsio
import treecorr
from test_helper import assert_raises, do_pickle, timer, get_from_wiki, CaptureLog, clear_save
from test_helper import profile
def generate_shear_field(npos, nhalo, rng=None):
# We do something completely different here than we did for 2pt patch tests.
# A straight Gaussian field with a given power spectrum has no significant 3pt power,
# so it's not a great choice for simulating a field for 3pt tests.
# Instead we place N SIS "halos" randomly in the grid.
# Then we translate that to a shear field via FFT.
if rng is None:
rng = np.random.RandomState()
# Generate x,y values for the real-space field
x = rng.uniform(0,1000, size=npos)
y = rng.uniform(0,1000, size=npos)
nh = rng.poisson(nhalo)
# Fill the kappa values with SIS halo profiles.
xc = rng.uniform(0,1000, size=nh)
yc = rng.uniform(0,1000, size=nh)
scale = rng.uniform(20,50, size=nh)
mass = rng.uniform(0.01, 0.05, size=nh)
# Avoid making huge nhalo * nsource arrays. Loop in blocks of 64 halos
nblock = (nh-1) // 64 + 1
kappa = np.zeros_like(x)
gamma = np.zeros_like(x, dtype=complex)
for iblock in range(nblock):
i = iblock*64
j = (iblock+1)*64
dx = x[:,np.newaxis]-xc[np.newaxis,i:j]
dy = y[:,np.newaxis]-yc[np.newaxis,i:j]
dx[dx==0] = 1 # Avoid division by zero.
dy[dy==0] = 1
dx /= scale[i:j]
dy /= scale[i:j]
rsq = dx**2 + dy**2
r = rsq**0.5
k = mass[i:j] / r # "Mass" here is really just a dimensionless normalization propto mass.
kappa += np.sum(k, axis=1)
# gamma_t = kappa for SIS.
g = -k * (dx + 1j*dy)**2 / rsq
gamma += np.sum(g, axis=1)
return x, y, np.real(gamma), np.imag(gamma), kappa
@timer
def test_kkk_jk():
# Test jackknife and other covariance estimates for kkk correlations.
# Note: This test takes a while!
# The main version I think is a pretty decent test of the code correctness.
# It shows that bootstrap in particular easily gets to within 50% of the right variance.
# Sometimes within 20%, but because of the randomness there, it varies a bit.
# Jackknife isn't much worse. Just a little below 50%. But still pretty good.
# Sample and Marked are not great for this test. I think they will work ok when the
# triangles of interest are mostly within single patches, but that's not the case we
# have here, and it would take a lot more points to get to that regime. So the
# accuracy tests for those two are pretty loose.
if __name__ == '__main__':
# This setup takes about 740 sec to run.
nhalo = 3000
nsource = 5000
npatch = 32
tol_factor = 1
elif False:
# This setup takes about 180 sec to run.
nhalo = 2000
nsource = 2000
npatch = 16
tol_factor = 2
elif False:
# This setup takes about 51 sec to run.
nhalo = 1000
nsource = 1000
npatch = 16
tol_factor = 3
else:
# This setup takes about 20 sec to run.
# So we use this one for regular unit test runs.
# It's pretty terrible in terms of testing the accuracy, but it works for code coverage.
# But whenever actually working on this part of the code, definitely need to switch
# to one of the above setups. Preferably run the name==main version to get a good
# test of the code correctness.
nhalo = 500
nsource = 500
npatch = 16
tol_factor = 4
file_name = 'data/test_kkk_jk_{}.npz'.format(nsource)
print(file_name)
if not os.path.isfile(file_name):
nruns = 1000
all_kkks = []
rng1 = np.random.RandomState()
for run in range(nruns):
x, y, _, _, k = generate_shear_field(nsource, nhalo, rng1)
print(run,': ',np.mean(k),np.std(k))
cat = treecorr.Catalog(x=x, y=y, k=k)
kkk = treecorr.KKKCorrelation(nbins=3, min_sep=30., max_sep=100.,
min_u=0.9, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.1, nvbins=1)
kkk.process(cat)
print(kkk.ntri.ravel().tolist())
print(kkk.zeta.ravel().tolist())
all_kkks.append(kkk)
mean_kkk = np.mean([kkk.zeta.ravel() for kkk in all_kkks], axis=0)
var_kkk = np.var([kkk.zeta.ravel() for kkk in all_kkks], axis=0)
np.savez(file_name, all_kkk=np.array([kkk.zeta.ravel() for kkk in all_kkks]),
mean_kkk=mean_kkk, var_kkk=var_kkk)
data = np.load(file_name)
mean_kkk = data['mean_kkk']
var_kkk = data['var_kkk']
print('mean = ',mean_kkk)
print('var = ',var_kkk)
rng = np.random.RandomState(12345)
x, y, _, _, k = generate_shear_field(nsource, nhalo, rng)
cat = treecorr.Catalog(x=x, y=y, k=k)
kkk = treecorr.KKKCorrelation(nbins=3, min_sep=30., max_sep=100.,
min_u=0.9, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.1, nvbins=1, rng=rng)
kkk.process(cat)
print(kkk.ntri.ravel())
print(kkk.zeta.ravel())
print(kkk.varzeta.ravel())
kkkp = kkk.copy()
catp = treecorr.Catalog(x=x, y=y, k=k, npatch=npatch)
# Do the same thing with patches.
kkkp.process(catp)
print('with patches:')
print(kkkp.ntri.ravel())
print(kkkp.zeta.ravel())
print(kkkp.varzeta.ravel())
np.testing.assert_allclose(kkkp.ntri, kkk.ntri, rtol=0.05 * tol_factor)
np.testing.assert_allclose(kkkp.zeta, kkk.zeta, rtol=0.1 * tol_factor, atol=1e-3 * tol_factor)
np.testing.assert_allclose(kkkp.varzeta, kkk.varzeta, rtol=0.05 * tol_factor, atol=3.e-6)
print('jackknife:')
cov = kkkp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.diagonal(cov), var_kkk, rtol=0.6 * tol_factor)
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.5*tol_factor)
print('sample:')
cov = kkkp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.diagonal(cov), var_kkk, rtol=0.7 * tol_factor)
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.7*tol_factor)
print('marked:')
cov = kkkp.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.diagonal(cov), var_kkk, rtol=0.7 * tol_factor)
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.7*tol_factor)
print('bootstrap:')
cov = kkkp.estimate_cov('bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.diagonal(cov), var_kkk, rtol=0.5 * tol_factor)
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.3*tol_factor)
# Now as a cross correlation with all 3 using the same patch catalog.
print('with 3 patched catalogs:')
kkkp.process(catp, catp, catp)
print(kkkp.zeta.ravel())
np.testing.assert_allclose(kkkp.zeta, kkk.zeta, rtol=0.1 * tol_factor, atol=1e-3 * tol_factor)
print('jackknife:')
cov = kkkp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.5*tol_factor)
print('sample:')
cov = kkkp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('marked:')
cov = kkkp.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('bootstrap:')
cov = kkkp.estimate_cov('bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.3*tol_factor)
# Repeat this test with different combinations of patch with non-patch catalogs:
# All the methods work best when the patches are used for all 3 catalogs. But there
# are probably cases where this kind of cross correlation with only some catalogs having
# patches could be desired. So this mostly just checks that the code runs properly.
# Patch on 1 only:
print('with patches on 1 only:')
kkkp.process(catp, cat)
print(kkkp.zeta.ravel())
np.testing.assert_allclose(kkkp.zeta, kkk.zeta, rtol=0.1 * tol_factor, atol=1e-3 * tol_factor)
print('jackknife:')
cov = kkkp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('sample:')
cov = kkkp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('marked:')
cov = kkkp.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('bootstrap:')
cov = kkkp.estimate_cov('bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
# Patch on 2 only:
print('with patches on 2 only:')
kkkp.process(cat, catp, cat)
print(kkkp.zeta.ravel())
np.testing.assert_allclose(kkkp.zeta, kkk.zeta, rtol=0.1 * tol_factor, atol=1e-3 * tol_factor)
print('jackknife:')
cov = kkkp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.diagonal(cov), var_kkk, rtol=0.9 * tol_factor)
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('sample:')
cov = kkkp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('marked:')
cov = kkkp.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('bootstrap:')
cov = kkkp.estimate_cov('bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
# Patch on 3 only:
print('with patches on 3 only:')
kkkp.process(cat, cat, catp)
print(kkkp.zeta.ravel())
np.testing.assert_allclose(kkkp.zeta, kkk.zeta, rtol=0.1 * tol_factor, atol=1e-3 * tol_factor)
print('jackknife:')
cov = kkkp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('sample:')
cov = kkkp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('marked:')
cov = kkkp.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('bootstrap:')
cov = kkkp.estimate_cov('bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
# Patch on 1,2
print('with patches on 1,2:')
kkkp.process(catp, catp, cat)
print(kkkp.zeta.ravel())
np.testing.assert_allclose(kkkp.zeta, kkk.zeta, rtol=0.1 * tol_factor, atol=1e-3 * tol_factor)
print('jackknife:')
cov = kkkp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.3*tol_factor)
print('sample:')
cov = kkkp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('marked:')
cov = kkkp.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('bootstrap:')
cov = kkkp.estimate_cov('bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.4*tol_factor)
# Patch on 2,3
print('with patches on 2,3:')
kkkp.process(cat, catp)
print(kkkp.zeta.ravel())
np.testing.assert_allclose(kkkp.zeta, kkk.zeta, rtol=0.1 * tol_factor, atol=1e-3 * tol_factor)
print('jackknife:')
cov = kkkp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.3*tol_factor)
print('sample:')
cov = kkkp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.7*tol_factor)
print('marked:')
cov = kkkp.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('bootstrap:')
cov = kkkp.estimate_cov('bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.3*tol_factor)
# Patch on 1,3
print('with patches on 1,3:')
kkkp.process(catp, cat, catp)
print(kkkp.zeta.ravel())
np.testing.assert_allclose(kkkp.zeta, kkk.zeta, rtol=0.1 * tol_factor, atol=1e-3 * tol_factor)
print('jackknife:')
cov = kkkp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.3*tol_factor)
print('sample:')
cov = kkkp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('marked:')
cov = kkkp.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.8*tol_factor)
print('bootstrap:')
cov = kkkp.estimate_cov('bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_kkk))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_kkk), atol=0.3*tol_factor)
# Finally a set (with all patches) using the KKKCrossCorrelation class.
kkkc = treecorr.KKKCrossCorrelation(nbins=3, min_sep=30., max_sep=100.,
min_u=0.9, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.1, nvbins=1, rng=rng)
print('CrossCorrelation:')
kkkc.process(catp, catp, catp)
for k1 in kkkc._all:
print(k1.ntri.ravel())
print(k1.zeta.ravel())
print(k1.varzeta.ravel())
np.testing.assert_allclose(k1.ntri, kkk.ntri, rtol=0.05 * tol_factor)
np.testing.assert_allclose(k1.zeta, kkk.zeta, rtol=0.1 * tol_factor, atol=1e-3 * tol_factor)
np.testing.assert_allclose(k1.varzeta, kkk.varzeta, rtol=0.05 * tol_factor, atol=3.e-6)
print('jackknife:')
cov = kkkc.estimate_cov('jackknife')
print(np.diagonal(cov))
for i in range(6):
v = np.diagonal(cov)[i*6:(i+1)*6]
print('max log(ratio) = ',np.max(np.abs(np.log(v)-np.log(var_kkk))))
np.testing.assert_allclose(np.log(v), np.log(var_kkk), atol=0.5*tol_factor)
print('sample:')
cov = kkkc.estimate_cov('sample')
print(np.diagonal(cov))
for i in range(6):
v = np.diagonal(cov)[i*6:(i+1)*6]
print('max log(ratio) = ',np.max(np.abs(np.log(v)-np.log(var_kkk))))
np.testing.assert_allclose(np.log(v), np.log(var_kkk), atol=0.8*tol_factor)
print('marked:')
cov = kkkc.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
for i in range(6):
v = np.diagonal(cov)[i*6:(i+1)*6]
print('max log(ratio) = ',np.max(np.abs(np.log(v)-np.log(var_kkk))))
np.testing.assert_allclose(np.log(v), np.log(var_kkk), atol=0.8*tol_factor)
print('bootstrap:')
cov = kkkc.estimate_cov('bootstrap')
print(np.diagonal(cov))
for i in range(6):
v = np.diagonal(cov)[i*6:(i+1)*6]
print('max log(ratio) = ',np.max(np.abs(np.log(v)-np.log(var_kkk))))
np.testing.assert_allclose(np.log(v), np.log(var_kkk), atol=0.5*tol_factor)
# All catalogs need to have the same number of patches
catq = treecorr.Catalog(x=x, y=y, k=k, npatch=2*npatch)
with assert_raises(RuntimeError):
kkkp.process(catp, catq)
with assert_raises(RuntimeError):
kkkp.process(catp, catq, catq)
with assert_raises(RuntimeError):
kkkp.process(catq, catp, catq)
with assert_raises(RuntimeError):
kkkp.process(catq, catq, catp)
@timer
def test_ggg_jk():
# Test jackknife and other covariance estimates for ggg correlations.
if __name__ == '__main__':
# This setup takes about 590 sec to run.
nhalo = 5000
nsource = 5000
npatch = 32
tol_factor = 1
elif False:
# This setup takes about 160 sec to run.
nhalo = 2000
nsource = 2000
npatch = 16
tol_factor = 2
elif False:
# This setup takes about 50 sec to run.
nhalo = 1000
nsource = 1000
npatch = 16
tol_factor = 3
else:
# This setup takes about 13 sec to run.
nhalo = 500
nsource = 500
npatch = 8
tol_factor = 3
# I couldn't figure out a way to get reasonable S/N in the shear field. I thought doing
# discrete halos would give some significant 3pt shear pattern, at least for equilateral
# triangles, but the signal here is still consistent with zero. :(
# The point is the variance, which is still calculated ok, but I would have rathered
# have something with S/N > 0.
# For these tests, I set up the binning to just accumulate all roughly equilateral triangles
# in a small separation range. The binning always uses two bins for each to get + and - v
# bins. So this function averages these two values to produce 1 value for each gamma.
f = lambda g: np.array([np.mean(g.gam0), np.mean(g.gam1), np.mean(g.gam2), np.mean(g.gam3)])
file_name = 'data/test_ggg_jk_{}.npz'.format(nsource)
print(file_name)
if not os.path.isfile(file_name):
nruns = 1000
all_gggs = []
rng1 = np.random.RandomState()
for run in range(nruns):
x, y, g1, g2, _ = generate_shear_field(nsource, nhalo, rng1)
# For some reason std(g2) is coming out about 1.5x larger than std(g1).
# Probably a sign of some error in the generate function, but I don't see it.
# For this purpose I think it doesn't really matter, but it's a bit odd.
print(run,': ',np.mean(g1),np.std(g1),np.mean(g2),np.std(g2))
cat = treecorr.Catalog(x=x, y=y, g1=g1, g2=g2)
ggg = treecorr.GGGCorrelation(nbins=1, min_sep=20., max_sep=40.,
min_u=0.6, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.6, nvbins=1)
ggg.process(cat)
print(ggg.ntri.ravel())
print(f(ggg))
all_gggs.append(ggg)
all_ggg = np.array([f(ggg) for ggg in all_gggs])
mean_ggg = np.mean(all_ggg, axis=0)
var_ggg = np.var(all_ggg, axis=0)
np.savez(file_name, mean_ggg=mean_ggg, var_ggg=var_ggg)
data = np.load(file_name)
mean_ggg = data['mean_ggg']
var_ggg = data['var_ggg']
print('mean = ',mean_ggg)
print('var = ',var_ggg)
rng = np.random.RandomState(12345)
x, y, g1, g2, _ = generate_shear_field(nsource, nhalo, rng)
cat = treecorr.Catalog(x=x, y=y, g1=g1, g2=g2)
ggg = treecorr.GGGCorrelation(nbins=1, min_sep=20., max_sep=40.,
min_u=0.6, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.6, nvbins=1, rng=rng)
ggg.process(cat)
print(ggg.ntri.ravel())
print(ggg.gam0.ravel())
print(ggg.gam1.ravel())
print(ggg.gam2.ravel())
print(ggg.gam3.ravel())
gggp = ggg.copy()
catp = treecorr.Catalog(x=x, y=y, g1=g1, g2=g2, npatch=npatch)
# Do the same thing with patches.
gggp.process(catp)
print('with patches:')
print(gggp.ntri.ravel())
print(gggp.vargam0.ravel())
print(gggp.vargam1.ravel())
print(gggp.vargam2.ravel())
print(gggp.vargam3.ravel())
print(gggp.gam0.ravel())
print(gggp.gam1.ravel())
print(gggp.gam2.ravel())
print(gggp.gam3.ravel())
np.testing.assert_allclose(gggp.ntri, ggg.ntri, rtol=0.05 * tol_factor)
np.testing.assert_allclose(gggp.gam0, ggg.gam0, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(gggp.gam1, ggg.gam1, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(gggp.gam2, ggg.gam2, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(gggp.gam3, ggg.gam3, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(gggp.vargam0, ggg.vargam0, rtol=0.1 * tol_factor)
np.testing.assert_allclose(gggp.vargam1, ggg.vargam1, rtol=0.1 * tol_factor)
np.testing.assert_allclose(gggp.vargam2, ggg.vargam2, rtol=0.1 * tol_factor)
np.testing.assert_allclose(gggp.vargam3, ggg.vargam3, rtol=0.1 * tol_factor)
print('jackknife:')
cov = gggp.estimate_cov('jackknife', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.4*tol_factor)
print('sample:')
cov = gggp.estimate_cov('sample', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
print('marked:')
cov = gggp.estimate_cov('marked_bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.9*tol_factor)
print('bootstrap:')
cov = gggp.estimate_cov('bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.3*tol_factor)
# Now as a cross correlation with all 3 using the same patch catalog.
print('with 3 patched catalogs:')
gggp.process(catp, catp, catp)
print(gggp.gam0.ravel())
np.testing.assert_allclose(gggp.gam0, ggg.gam0, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(gggp.gam1, ggg.gam1, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(gggp.gam2, ggg.gam2, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(gggp.gam3, ggg.gam3, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
print('jackknife:')
cov = gggp.estimate_cov('jackknife', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.4*tol_factor)
print('sample:')
cov = gggp.estimate_cov('sample', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.6*tol_factor)
print('marked:')
cov = gggp.estimate_cov('marked_bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
print('bootstrap:')
cov = gggp.estimate_cov('bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.4*tol_factor)
# The separate patch/non-patch combinations aren't that interesting, so skip them
# for GGG unless running from main.
if __name__ == '__main__':
# Patch on 1 only:
print('with patches on 1 only:')
gggp.process(catp, cat)
print('jackknife:')
cov = gggp.estimate_cov('jackknife', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
print('sample:')
cov = gggp.estimate_cov('sample', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.7*tol_factor)
print('marked:')
cov = gggp.estimate_cov('marked_bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
print('bootstrap:')
cov = gggp.estimate_cov('bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
# Patch on 2 only:
print('with patches on 2 only:')
gggp.process(cat, catp, cat)
print('jackknife:')
cov = gggp.estimate_cov('jackknife', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
print('sample:')
cov = gggp.estimate_cov('sample', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.7*tol_factor)
print('marked:')
cov = gggp.estimate_cov('marked_bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
print('bootstrap:')
cov = gggp.estimate_cov('bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
# Patch on 3 only:
print('with patches on 3 only:')
gggp.process(cat, cat, catp)
print('jackknife:')
cov = gggp.estimate_cov('jackknife', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
print('sample:')
cov = gggp.estimate_cov('sample', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.7*tol_factor)
print('marked:')
cov = gggp.estimate_cov('marked_bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
print('bootstrap:')
cov = gggp.estimate_cov('bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.9*tol_factor)
# Patch on 1,2
print('with patches on 1,2:')
gggp.process(catp, catp, cat)
print('jackknife:')
cov = gggp.estimate_cov('jackknife', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.6*tol_factor)
print('sample:')
cov = gggp.estimate_cov('sample', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.6*tol_factor)
print('marked:')
cov = gggp.estimate_cov('marked_bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
print('bootstrap:')
cov = gggp.estimate_cov('bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.5*tol_factor)
# Patch on 2,3
print('with patches on 2,3:')
gggp.process(cat, catp)
print('jackknife:')
cov = gggp.estimate_cov('jackknife', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.6*tol_factor)
print('sample:')
cov = gggp.estimate_cov('sample', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.8*tol_factor)
print('marked:')
cov = gggp.estimate_cov('marked_bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=1.0*tol_factor)
print('bootstrap:')
cov = gggp.estimate_cov('bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.3*tol_factor)
# Patch on 1,3
print('with patches on 1,3:')
gggp.process(catp, cat, catp)
print('jackknife:')
cov = gggp.estimate_cov('jackknife', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.6*tol_factor)
print('sample:')
cov = gggp.estimate_cov('sample', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.6*tol_factor)
print('marked:')
cov = gggp.estimate_cov('marked_bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.7*tol_factor)
print('bootstrap:')
cov = gggp.estimate_cov('bootstrap', func=f)
print(np.diagonal(cov).real)
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_ggg))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_ggg), atol=0.5*tol_factor)
# Finally a set (with all patches) using the GGGCrossCorrelation class.
gggc = treecorr.GGGCrossCorrelation(nbins=1, min_sep=20., max_sep=40.,
min_u=0.6, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.6, nvbins=1, rng=rng)
print('CrossCorrelation:')
gggc.process(catp, catp, catp)
for g in gggc._all:
print(g.ntri.ravel())
print(g.gam0.ravel())
print(g.vargam0.ravel())
np.testing.assert_allclose(g.ntri, ggg.ntri, rtol=0.05 * tol_factor)
np.testing.assert_allclose(g.gam0, ggg.gam0, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(g.vargam0, ggg.vargam0, rtol=0.05 * tol_factor)
np.testing.assert_allclose(g.gam1, ggg.gam1, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(g.vargam1, ggg.vargam1, rtol=0.05 * tol_factor)
np.testing.assert_allclose(g.gam2, ggg.gam2, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(g.vargam2, ggg.vargam2, rtol=0.05 * tol_factor)
np.testing.assert_allclose(g.gam3, ggg.gam3, rtol=0.3 * tol_factor, atol=0.3 * tol_factor)
np.testing.assert_allclose(g.vargam3, ggg.vargam3, rtol=0.05 * tol_factor)
fc = lambda gggc: np.concatenate([
[np.mean(g.gam0), np.mean(g.gam1), np.mean(g.gam2), np.mean(g.gam3)]
for g in gggc._all])
print('jackknife:')
cov = gggc.estimate_cov('jackknife', func=fc)
print(np.diagonal(cov).real)
for i in range(6):
v = np.diagonal(cov)[i*4:(i+1)*4]
print('max log(ratio) = ',np.max(np.abs(np.log(v)-np.log(var_ggg))))
np.testing.assert_allclose(np.log(v), np.log(var_ggg), atol=0.4*tol_factor)
print('sample:')
cov = gggc.estimate_cov('sample', func=fc)
print(np.diagonal(cov).real)
for i in range(6):
v = np.diagonal(cov)[i*4:(i+1)*4]
print('max log(ratio) = ',np.max(np.abs(np.log(v)-np.log(var_ggg))))
np.testing.assert_allclose(np.log(v), np.log(var_ggg), atol=0.6*tol_factor)
print('marked:')
cov = gggc.estimate_cov('marked_bootstrap', func=fc)
print(np.diagonal(cov).real)
for i in range(6):
v = np.diagonal(cov)[i*4:(i+1)*4]
print('max log(ratio) = ',np.max(np.abs(np.log(v)-np.log(var_ggg))))
np.testing.assert_allclose(np.log(v), np.log(var_ggg), atol=0.8*tol_factor)
print('bootstrap:')
cov = gggc.estimate_cov('bootstrap', func=fc)
print(np.diagonal(cov).real)
for i in range(6):
v = np.diagonal(cov)[i*4:(i+1)*4]
print('max log(ratio) = ',np.max(np.abs(np.log(v)-np.log(var_ggg))))
np.testing.assert_allclose(np.log(v), np.log(var_ggg), atol=0.3*tol_factor)
# Without func, don't check the accuracy, but make sure it returns something the right shape.
cov = gggc.estimate_cov('jackknife')
assert cov.shape == (48, 48)
@timer
def test_nnn_jk():
# Test jackknife and other covariance estimates for nnn correlations.
if __name__ == '__main__':
# This setup takes about 1200 sec to run.
nhalo = 300
nsource = 2000
npatch = 16
source_factor = 50
rand_factor = 3
tol_factor = 1
elif False:
# This setup takes about 250 sec to run.
nhalo = 200
nsource = 1000
npatch = 16
source_factor = 50
rand_factor = 2
tol_factor = 2
else:
# This setup takes about 44 sec to run.
nhalo = 100
nsource = 500
npatch = 8
source_factor = 30
rand_factor = 1
tol_factor = 3
file_name = 'data/test_nnn_jk_{}.npz'.format(nsource)
print(file_name)
if not os.path.isfile(file_name):
rng = np.random.RandomState()
nruns = 1000
all_nnns = []
all_nnnc = []
t0 = time.time()
for run in range(nruns):
t2 = time.time()
x, y, _, _, k = generate_shear_field(nsource * source_factor, nhalo, rng)
p = k**3
p /= np.sum(p)
ns = rng.poisson(nsource)
select = rng.choice(range(len(x)), size=ns, replace=False, p=p)
print(run,': ',np.mean(k),np.std(k),np.min(k),np.max(k))
cat = treecorr.Catalog(x=x[select], y=y[select])
ddd = treecorr.NNNCorrelation(nbins=3, min_sep=50., max_sep=100., bin_slop=0.2,
min_u=0.8, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.2, nvbins=1)
rx = rng.uniform(0,1000, rand_factor*nsource)
ry = rng.uniform(0,1000, rand_factor*nsource)
rand_cat = treecorr.Catalog(x=rx, y=ry)
rrr = treecorr.NNNCorrelation(nbins=3, min_sep=50., max_sep=100., bin_slop=0.2,
min_u=0.8, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.2, nvbins=1)
rrr.process(rand_cat)
rdd = ddd.copy()
drr = ddd.copy()
ddd.process(cat)
rdd.process(rand_cat, cat)
drr.process(cat, rand_cat)
zeta_s, _ = ddd.calculateZeta(rrr)
zeta_c, _ = ddd.calculateZeta(rrr, drr, rdd)
print('simple: ',zeta_s.ravel())
print('compensated: ',zeta_c.ravel())
all_nnns.append(zeta_s.ravel())
all_nnnc.append(zeta_c.ravel())
t3 = time.time()
print('time: ',round(t3-t2),round((t3-t0)/60),round((t3-t0)*(nruns/(run+1)-1)/60))
mean_nnns = np.mean(all_nnns, axis=0)
var_nnns = np.var(all_nnns, axis=0)
mean_nnnc = np.mean(all_nnnc, axis=0)
var_nnnc = np.var(all_nnnc, axis=0)
np.savez(file_name, mean_nnns=mean_nnns, var_nnns=var_nnns,
mean_nnnc=mean_nnnc, var_nnnc=var_nnnc)
data = np.load(file_name)
mean_nnns = data['mean_nnns']
var_nnns = data['var_nnns']
mean_nnnc = data['mean_nnnc']
var_nnnc = data['var_nnnc']
print('mean simple = ',mean_nnns)
print('var simple = ',var_nnns)
print('mean compensated = ',mean_nnnc)
print('var compensated = ',var_nnnc)
# Make a random catalog with 2x as many sources, randomly distributed .
rng = np.random.RandomState(1234)
rx = rng.uniform(0,1000, rand_factor*nsource)
ry = rng.uniform(0,1000, rand_factor*nsource)
rand_cat = treecorr.Catalog(x=rx, y=ry)
rrr = treecorr.NNNCorrelation(nbins=3, min_sep=50., max_sep=100., bin_slop=0.2,
min_u=0.8, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.2, nvbins=1)
t0 = time.time()
rrr.process(rand_cat)
t1 = time.time()
print('Time to process rand cat = ',t1-t0)
print('RRR:',rrr.tot)
print(rrr.ntri.ravel())
# Make the data catalog
x, y, _, _, k = generate_shear_field(nsource * source_factor, nhalo, rng=rng)
print('mean k = ',np.mean(k))
print('min,max = ',np.min(k),np.max(k))
p = k**3
p /= np.sum(p)
select = rng.choice(range(len(x)), size=nsource, replace=False, p=p)
cat = treecorr.Catalog(x=x[select], y=y[select])
ddd = treecorr.NNNCorrelation(nbins=3, min_sep=50., max_sep=100., bin_slop=0.2,
min_u=0.8, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.2, nvbins=1, rng=rng)
rdd = ddd.copy()
drr = ddd.copy()
ddd.process(cat)
rdd.process(rand_cat, cat)
drr.process(cat, rand_cat)
zeta_s1, var_zeta_s1 = ddd.calculateZeta(rrr)
zeta_c1, var_zeta_c1 = ddd.calculateZeta(rrr, drr, rdd)
print('DDD:',ddd.tot)
print(ddd.ntri.ravel())
print('simple: ')
print(zeta_s1.ravel())
print(var_zeta_s1.ravel())
print('DRR:',drr.tot)
print(drr.ntri.ravel())
print('RDD:',rdd.tot)
print(rdd.ntri.ravel())
print('compensated: ')
print(zeta_c1.ravel())
print(var_zeta_c1.ravel())
# Make the patches with a large random catalog to make sure the patches are uniform area.
big_rx = rng.uniform(0,1000, 100*nsource)
big_ry = rng.uniform(0,1000, 100*nsource)
big_catp = treecorr.Catalog(x=big_rx, y=big_ry, npatch=npatch, rng=rng)
patch_centers = big_catp.patch_centers
# Do the same thing with patches on D, but not yet on R.
dddp = treecorr.NNNCorrelation(nbins=3, min_sep=50., max_sep=100., bin_slop=0.2,
min_u=0.8, max_u=1.0, nubins=1,
min_v=0.0, max_v=0.2, nvbins=1, rng=rng)
rddp = dddp.copy()
drrp = dddp.copy()
catp = treecorr.Catalog(x=x[select], y=y[select], patch_centers=patch_centers)
print('Patch\tNtot')
for p in catp.patches:
print(p.patch,'\t',p.ntot,'\t',patch_centers[p.patch])
print('with patches on D:')
dddp.process(catp)
rddp.process(rand_cat, catp)
drrp.process(catp, rand_cat)
# Need to run calculateZeta to get patch-based covariance
with assert_raises(RuntimeError):
dddp.estimate_cov('jackknife')
zeta_s2, var_zeta_s2 = dddp.calculateZeta(rrr)
print('DDD:',dddp.tot)
print(dddp.ntri.ravel())
print('simple: ')
print(zeta_s2.ravel())
print(var_zeta_s2.ravel())
np.testing.assert_allclose(zeta_s2, zeta_s1, rtol=0.05 * tol_factor)
np.testing.assert_allclose(var_zeta_s2, var_zeta_s1, rtol=0.05 * tol_factor)
# Check the _calculate_xi_from_pairs function. Using all pairs, should get total xi.
ddd1 = dddp.copy()
ddd1._calculate_xi_from_pairs(dddp.results.keys())
np.testing.assert_allclose(ddd1.zeta, dddp.zeta)
# None of these are very good without the random using patches.
# I think this is basically just that the approximations used for estimating the area_frac
# to figure out the appropriate altered RRR counts isn't accurate enough when the total
# counts are as low as this. I think (hope) that it should be semi-ok when N is much larger,
# but this is probably saying that for 3pt using patches for R is even more important than
# for 2pt.
# Ofc, it could also be that this is telling me I still have a bug somewhere that I haven't
# managed to find... :(
print('jackknife:')
cov = dddp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_nnns))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_nnns), atol=2.3*tol_factor)
print('sample:')
cov = dddp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_nnns))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_nnns), atol=1.2*tol_factor)
print('marked:')
cov = dddp.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_nnns))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_nnns), atol=1.3*tol_factor)
print('bootstrap:')
cov = dddp.estimate_cov('bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_nnns))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_nnns), atol=2.2*tol_factor)
zeta_c2, var_zeta_c2 = dddp.calculateZeta(rrr, drrp, rddp)
print('compensated: ')
print('DRR:',drrp.tot)
print(drrp.ntri.ravel())
print('RDD:',rddp.tot)
print(rddp.ntri.ravel())
print(zeta_c2.ravel())
print(var_zeta_c2.ravel())
np.testing.assert_allclose(zeta_c2, zeta_c1, rtol=0.05 * tol_factor, atol=1.e-3 * tol_factor)
np.testing.assert_allclose(var_zeta_c2, var_zeta_c1, rtol=0.05 * tol_factor)
print('jackknife:')
cov = dddp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_nnnc))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_nnnc), atol=2.6*tol_factor)
print('sample:')
cov = dddp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_nnnc))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_nnnc), atol=3.8*tol_factor)
print('marked:')
cov = dddp.estimate_cov('marked_bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_nnnc))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_nnnc), atol=2.3*tol_factor)
print('bootstrap:')
cov = dddp.estimate_cov('bootstrap')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_nnnc))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_nnnc), atol=2.6*tol_factor)
# Now with the random also using patches
# These are a lot better than the above tests. But still not nearly as good as we were able
# to get in 2pt. I'm pretty sure this is just due to the fact that we need to have much
# smaller catalogs to make it feasible to run this in a reasonable amount of time. I don't
# think this is a sign of any bug in the code.
print('with patched random catalog:')
rand_catp = treecorr.Catalog(x=rx, y=ry, patch_centers=patch_centers)
rrrp = rrr.copy()
rrrp.process(rand_catp)
drrp.process(catp, rand_catp)
rddp.process(rand_catp, catp)
print('simple: ')
zeta_s2, var_zeta_s2 = dddp.calculateZeta(rrrp)
print('DDD:',dddp.tot)
print(dddp.ntri.ravel())
print(zeta_s2.ravel())
print(var_zeta_s2.ravel())
np.testing.assert_allclose(zeta_s2, zeta_s1, rtol=0.05 * tol_factor)
np.testing.assert_allclose(var_zeta_s2, var_zeta_s1, rtol=0.05 * tol_factor)
ddd1 = dddp.copy()
ddd1._calculate_xi_from_pairs(dddp.results.keys())
np.testing.assert_allclose(ddd1.zeta, dddp.zeta)
t0 = time.time()
print('jackknife:')
cov = dddp.estimate_cov('jackknife')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_nnns))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_nnns), atol=0.9*tol_factor)
t1 = time.time()
print('t = ',t1-t0)
t0 = time.time()
print('sample:')
cov = dddp.estimate_cov('sample')
print(np.diagonal(cov))
print('max log(ratio) = ',np.max(np.abs(np.log(np.diagonal(cov))-np.log(var_nnns))))
np.testing.assert_allclose(np.log(np.diagonal(cov)), np.log(var_nnns), atol=0.7*tol_factor)
t1 = time.time()
print('t = ',t1-t0)
t0 = time.time()
print('marked:')
cov = dddp.estimate_cov('marked_bootstrap')
print( | np.diagonal(cov) | numpy.diagonal |
"""Testing the setup of the payoff distributions."""
from collections import OrderedDict
import pytest
import numpy as np
from sp_experiment.define_payoff_settings import (get_payoff_settings,
get_payoff_dict,
get_random_payoff_settings,
)
@pytest.mark.parametrize('ev_diff', [0.1, 0.9, 7.])
def test_get_payoff_settings(ev_diff):
"""Test the setup of payoff distributions."""
payoff_settings = get_payoff_settings(ev_diff)
assert payoff_settings.ndim == 2
assert payoff_settings.shape[-1] == 8
assert payoff_settings.shape[0] >= 1
for probability in payoff_settings[0, [2, 3, 6, 7]]:
assert probability in np.round(np.arange(0.1, 1, 0.1), 1)
mags = list()
for magnitude in payoff_settings[0, [0, 1, 4, 5]]:
assert magnitude in range(1, 10)
mags.append(magnitude)
assert len(np.unique(mags)) == 4
def test_get_payoff_dict():
"""Test getting a payoff_dict off a setup."""
payoff_settings = get_payoff_settings(0.1)
setting = payoff_settings[0, :]
payoff_dict = get_payoff_dict(setting)
# Should be a dict
assert isinstance(payoff_dict, OrderedDict)
assert len(list(payoff_dict.values())[0]) == 10
assert len(list(payoff_dict.values())[1]) == 10
def _simulate_run(rand_payoff_settings, n_samples=12, seed=None):
"""Simulate a participant with 50% 50% left right tendency."""
rng = np.random.RandomState(seed)
actions = list()
outcomes = list()
for setting in rand_payoff_settings:
payoff_dict = get_payoff_dict(setting)
for sample in range(n_samples):
action = rng.choice((0, 1))
actions.append(action)
outcome = rng.choice(payoff_dict[action])
outcomes.append(outcome)
actions = np.array(actions)
outcomes = np.array(outcomes)
# combine actions and outcomes to code outcomes on the left with negative
# sign outcomes on the right with positive sign ... will end up with stim
# classes: - sign for "left", + sign for "right"
stim_classes = outcomes * (actions*2-1)
return stim_classes
def _make_class_hist(stim_classes):
"""Turn stim_classes into hist."""
# Make a histogram of which stimulus_classes we have collected so far
bins = np.hstack((np.arange(-9, 0), np.arange(1, 11)))
stim_class_hist = np.histogram(stim_classes, bins)
# Make an array from the hist and sort it
stim_class_arr = np.vstack((stim_class_hist[0], stim_class_hist[1][:-1])).T
stim_class_arr_sorted = stim_class_arr[stim_class_arr[:, 0].argsort()]
return stim_class_arr_sorted
def test_balancing():
"""Test that we can get a balanced stimulus selection."""
seed = 1
max_ntrls = 100
ev_diff = 0.9
payoff_settings = get_payoff_settings(ev_diff)
# No balancing at all, this will lead to a few stim_classes never
# being shown
rand_payoff_settings = payoff_settings.copy()
rng = np.random.RandomState(seed)
perm = rng.permutation(max_ntrls)
rand_payoff_settings = rand_payoff_settings[perm, :]
stim_classes = _simulate_run(rand_payoff_settings, n_samples=12, seed=seed)
hist = _make_class_hist(stim_classes)
diff1 = np.diff(hist[[0, -1], 0])
# some balancing
rand_payoff_settings = get_random_payoff_settings(max_ntrls,
payoff_settings,
-1,
seed)
stim_classes = _simulate_run(rand_payoff_settings, n_samples=12, seed=seed)
hist = _make_class_hist(stim_classes)
diff2 = | np.diff(hist[[0, -1], 0]) | numpy.diff |
# This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
# See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
# Author(s): <NAME>
#
# Copyright (C) 2018-2019 Inria
#
# Modification(s):
# - YYYY/MM Author: Description of the modification
import numpy as np
from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.preprocessing import StandardScaler
from sklearn.utils import validation
#############################################
# Preprocessing #############################
#############################################
class BirthPersistenceTransform(BaseEstimator, TransformerMixin):
"""
This is a class for the affine transformation (x,y) -> (x,y-x) to be applied on persistence diagrams.
"""
def __init__(self):
"""
Constructor for BirthPersistenceTransform class.
"""
return None
def fit(self, X, y=None):
"""
Fit the BirthPersistenceTransform class on a list of persistence diagrams (this function actually does nothing but is useful when BirthPersistenceTransform is included in a scikit-learn Pipeline).
Parameters:
X (list of n x 2 numpy array): input persistence diagrams.
y (n x 1 array): persistence diagram labels (unused).
"""
return self
def transform(self, X):
"""
Apply the BirthPersistenceTransform function on the persistence diagrams.
Parameters:
X (list of n x 2 numpy array): input persistence diagrams.
Returns:
list of n x 2 numpy array: transformed persistence diagrams.
"""
Xfit = []
for diag in X:
#new_diag = np.empty(diag.shape)
#np.copyto(new_diag, diag)
new_diag = np.copy(diag)
new_diag[:,1] = new_diag[:,1] - new_diag[:,0]
Xfit.append(new_diag)
return Xfit
def __call__(self, diag):
"""
Apply BirthPersistenceTransform on a single persistence diagram and outputs the result.
Parameters:
diag (n x 2 numpy array): input persistence diagram.
Returns:
n x 2 numpy array: transformed persistence diagram.
"""
return self.fit_transform([diag])[0]
class Clamping(BaseEstimator, TransformerMixin):
"""
This is a class for clamping values. It can be used as a parameter for the DiagramScaler class, for instance if you want to clamp abscissae or ordinates of persistence diagrams.
"""
def __init__(self, minimum=-np.inf, maximum=np.inf):
"""
Constructor for the Clamping class.
Parameters:
limit (double): clamping value (default np.inf).
"""
self.minimum = minimum
self.maximum = maximum
def fit(self, X, y=None):
"""
Fit the Clamping class on a list of values (this function actually does nothing but is useful when Clamping is included in a scikit-learn Pipeline).
Parameters:
X (numpy array of size n): input values.
y (n x 1 array): value labels (unused).
"""
return self
def transform(self, X):
"""
Clamp list of values.
Parameters:
X (numpy array of size n): input list of values.
Returns:
numpy array of size n: output list of values.
"""
Xfit = np.clip(X, self.minimum, self.maximum)
return Xfit
class DiagramScaler(BaseEstimator, TransformerMixin):
"""
This is a class for preprocessing persistence diagrams with a given list of scalers, such as those included in scikit-learn.
"""
def __init__(self, use=False, scalers=[]):
"""
Constructor for the DiagramScaler class.
Parameters:
use (bool): whether to use the class or not (default False).
scalers (list of classes): list of scalers to be fit on the persistence diagrams (default []). Each element of the list is a tuple with two elements: the first one is a list of coordinates, and the second one is a scaler (i.e. a class with fit() and transform() methods) that is going to be applied to these coordinates. Common scalers can be found in the scikit-learn library (such as MinMaxScaler for instance).
"""
self.scalers = scalers
self.use = use
def fit(self, X, y=None):
"""
Fit the DiagramScaler class on a list of persistence diagrams: persistence diagrams are concatenated in a big numpy array, and scalers are fit (by calling their fit() method) on their corresponding coordinates in this big array.
Parameters:
X (list of n x 2 or n x 1 numpy arrays): input persistence diagrams.
y (n x 1 array): persistence diagram labels (unused).
"""
if self.use:
if len(X) == 1:
P = X[0]
else:
P = np.concatenate(X,0)
for (indices, scaler) in self.scalers:
scaler.fit(np.reshape(P[:,indices], [-1, 1]))
return self
def transform(self, X):
"""
Apply the DiagramScaler function on the persistence diagrams. The fitted scalers are applied (by calling their transform() method) to their corresponding coordinates in each persistence diagram individually.
Parameters:
X (list of n x 2 or n x 1 numpy arrays): input persistence diagrams.
Returns:
list of n x 2 or n x 1 numpy arrays: transformed persistence diagrams.
"""
Xfit = [np.copy(d) for d in X]
if self.use:
for i in range(len(Xfit)):
if Xfit[i].shape[0] > 0:
for (indices, scaler) in self.scalers:
for I in indices:
Xfit[i][:,I] = np.squeeze(scaler.transform(np.reshape(Xfit[i][:,I], [-1,1])))
return Xfit
def __call__(self, diag):
"""
Apply DiagramScaler on a single persistence diagram and outputs the result.
Parameters:
diag (n x 2 numpy array): input persistence diagram.
Returns:
n x 2 numpy array: transformed persistence diagram.
"""
return self.fit_transform([diag])[0]
class Padding(BaseEstimator, TransformerMixin):
"""
This is a class for padding a list of persistence diagrams with dummy points, so that all persistence diagrams end up with the same number of points.
"""
def __init__(self, use=False):
"""
Constructor for the Padding class.
Parameters:
use (bool): whether to use the class or not (default False).
"""
self.use = use
def fit(self, X, y=None):
"""
Fit the Padding class on a list of persistence diagrams (this function actually does nothing but is useful when Padding is included in a scikit-learn Pipeline).
Parameters:
X (list of n x 2 or n x 1 numpy arrays): input persistence diagrams.
y (n x 1 array): persistence diagram labels (unused).
"""
self.max_pts = max([len(diag) for diag in X])
return self
def transform(self, X):
"""
Add dummy points to each persistence diagram so that they all have the same cardinality. All points are given an additional coordinate indicating if the point was added after padding (0) or already present before (1).
Parameters:
X (list of n x 2 or n x 1 numpy arrays): input persistence diagrams.
Returns:
list of n x 3 or n x 2 numpy arrays: padded persistence diagrams.
"""
if self.use:
Xfit, num_diag = [], len(X)
for diag in X:
diag_pad = np.pad(diag, ((0,max(0, self.max_pts - diag.shape[0])), (0,1)), "constant", constant_values=((0,0),(0,0)))
diag_pad[:diag.shape[0],2] = np.ones(diag.shape[0])
Xfit.append(diag_pad)
else:
Xfit = X
return Xfit
def __call__(self, diag):
"""
Apply Padding on a single persistence diagram and outputs the result.
Parameters:
diag (n x 2 numpy array): input persistence diagram.
Returns:
n x 2 numpy array: padded persistence diagram.
"""
return self.fit_transform([diag])[0]
class ProminentPoints(BaseEstimator, TransformerMixin):
"""
This is a class for removing points that are close or far from the diagonal in persistence diagrams. If persistence diagrams are n x 2 numpy arrays (i.e. persistence diagrams with ordinary features), points are ordered and thresholded by distance-to-diagonal. If persistence diagrams are n x 1 numpy arrays (i.e. persistence diagrams with essential features), points are not ordered and thresholded by first coordinate.
"""
def __init__(self, use=False, num_pts=10, threshold=-1, location="upper"):
"""
Constructor for the ProminentPoints class.
Parameters:
use (bool): whether to use the class or not (default False).
location (string): either "upper" or "lower" (default "upper"). Whether to keep the points that are far away ("upper") or close ("lower") to the diagonal.
num_pts (int): cardinality threshold (default 10). If location == "upper", keep the top **num_pts** points that are the farthest away from the diagonal. If location == "lower", keep the top **num_pts** points that are the closest to the diagonal.
threshold (double): distance-to-diagonal threshold (default -1). If location == "upper", keep the points that are at least at a distance **threshold** from the diagonal. If location == "lower", keep the points that are at most at a distance **threshold** from the diagonal.
"""
self.num_pts = num_pts
self.threshold = threshold
self.use = use
self.location = location
def fit(self, X, y=None):
"""
Fit the ProminentPoints class on a list of persistence diagrams (this function actually does nothing but is useful when ProminentPoints is included in a scikit-learn Pipeline).
Parameters:
X (list of n x 2 or n x 1 numpy arrays): input persistence diagrams.
y (n x 1 array): persistence diagram labels (unused).
"""
return self
def transform(self, X):
"""
If location == "upper", first select the top **num_pts** points that are the farthest away from the diagonal, then select and return from these points the ones that are at least at distance **threshold** from the diagonal for each persistence diagram individually. If location == "lower", first select the top **num_pts** points that are the closest to the diagonal, then select and return from these points the ones that are at most at distance **threshold** from the diagonal for each persistence diagram individually.
Parameters:
X (list of n x 2 or n x 1 numpy arrays): input persistence diagrams.
Returns:
list of n x 2 or n x 1 numpy arrays: thresholded persistence diagrams.
"""
if self.use:
Xfit, num_diag = [], len(X)
for i in range(num_diag):
diag = X[i]
if diag.shape[1] >= 2:
if diag.shape[0] > 0:
pers = np.abs(diag[:,1] - diag[:,0])
idx_thresh = pers >= self.threshold
thresh_diag, thresh_pers = diag[idx_thresh], pers[idx_thresh]
sort_index = np.flip(np.argsort(thresh_pers, axis=None), 0)
if self.location == "upper":
new_diag = thresh_diag[sort_index[:min(self.num_pts, thresh_diag.shape[0])],:]
if self.location == "lower":
new_diag = np.concatenate( [ thresh_diag[sort_index[min(self.num_pts, thresh_diag.shape[0]):],:], diag[~idx_thresh] ], axis=0)
else:
new_diag = diag
else:
if diag.shape[0] > 0:
birth = diag[:,:1]
idx_thresh = birth >= self.threshold
thresh_diag, thresh_birth = diag[idx_thresh], birth[idx_thresh]
if self.location == "upper":
new_diag = thresh_diag[:min(self.num_pts, thresh_diag.shape[0]),:]
if self.location == "lower":
new_diag = np.concatenate( [ thresh_diag[min(self.num_pts, thresh_diag.shape[0]):,:], diag[~idx_thresh] ], axis=0)
else:
new_diag = diag
Xfit.append(new_diag)
else:
Xfit = X
return Xfit
def __call__(self, diag):
"""
Apply ProminentPoints on a single persistence diagram and outputs the result.
Parameters:
diag (n x 2 numpy array): input persistence diagram.
Returns:
n x 2 numpy array: thresholded persistence diagram.
"""
return self.fit_transform([diag])[0]
class DiagramSelector(BaseEstimator, TransformerMixin):
"""
This is a class for extracting finite or essential points in persistence diagrams.
"""
def __init__(self, use=False, limit=np.inf, point_type="finite"):
"""
Constructor for the DiagramSelector class.
Parameters:
use (bool): whether to use the class or not (default False).
limit (double): second coordinate value that is the criterion for being an essential point (default numpy.inf).
point_type (string): either "finite" or "essential". The type of the points that are going to be extracted.
"""
self.use, self.limit, self.point_type = use, limit, point_type
def fit(self, X, y=None):
"""
Fit the DiagramSelector class on a list of persistence diagrams (this function actually does nothing but is useful when DiagramSelector is included in a scikit-learn Pipeline).
Parameters:
X (list of n x 2 or n x 1 numpy arrays): input persistence diagrams.
y (n x 1 array): persistence diagram labels (unused).
"""
return self
def transform(self, X):
"""
Extract and return the finite or essential points of each persistence diagram individually.
Parameters:
X (list of n x 2 or n x 1 numpy arrays): input persistence diagrams.
Returns:
list of n x 2 or n x 1 numpy arrays: extracted persistence diagrams.
"""
if self.use:
Xfit, num_diag = [], len(X)
if self.point_type == "finite":
Xfit = [ diag[diag[:,1] < self.limit] if diag.shape[0] != 0 else diag for diag in X]
else:
Xfit = [ diag[diag[:,1] >= self.limit, 0:1] if diag.shape[0] != 0 else diag for diag in X]
else:
Xfit = X
return Xfit
def __call__(self, diag):
"""
Apply DiagramSelector on a single persistence diagram and outputs the result.
Parameters:
diag (n x 2 numpy array): input persistence diagram.
Returns:
n x 2 numpy array: extracted persistence diagram.
"""
return self.fit_transform([diag])[0]
def _sample(X, max_points=None, weight_function=None, random_state=None):
"""
Helper function, samples points from given set X.
Parameters:
X: numpy array
max_point: number of points to sample.
weight_function: if given used to calculate probabilities of sampling each point.
random_state: PRNG seed.
"""
rnd = validation.check_random_state(random_state)
rows = X.shape[0]
if max_points is None or rows <= max_points:
return X
p = None
if weight_function:
p = np.zeros(rows)
for row in range(rows):
p[row] = weight_function(X[row])
p /= np.sum(p)
return X[rnd.choice(rows, max_points, p=p, replace=False)]
class RandomPDSampler(BaseEstimator, TransformerMixin):
"""
Used to consolidate and take random samples from list of persistence diagrams.
"""
def __init__(self, max_points=None, weight_function=None, random_state=None):
"""
Constructor for the RandomPDSampler class.
Parameters:
max_point: number of points to sample from consolidated PD's.
weight_function: if given used to calculate probabilities of sampling each point.
random_state: PRNG seed.
"""
self.max_points = max_points
self.weight_function = weight_function
self.random_state = random_state
def fit(self, X, y=None):
"""
Fit the RandomPDSampler class on a list of values (For pipeline compatibility - does nothing).
Parameters:
X (list of n x 2 numpy arrays): input persistence diagrams.
y (n x 1 array): persistence diagram labels (unused).
"""
return self
def transform(self, X):
"""
Concatenate and sample points from persistence diagrams list.
Parameters:
X (list of n x 2 numpy arrays): input persistence diagrams.
Returns:
Array with single PD (np.array of size max_points).
"""
if not X:
return []
return [_sample(
np.concatenate(X),
self.max_points,
self.weight_function,
self.random_state
)]
def fit_transform(self, X, y=None):
return self.transform(X)
class GridPDSampler(BaseEstimator, TransformerMixin):
"""
This class will consolidate list od persistence diagrams, divide consolidated diagram into smaller cells, distribute uniformly number of samples between them, and finally randomly sample from each cell, and consolidate samples back into diagram.
"""
def __init__(self, grid_shape, max_points, weight_function=None, random_state=None):
"""
Constructor for the GridPDSampler class.
Parameters:
grid_shape: 2d array with number of grid cells in vertical and horizontal direction [Y_cell_number, X_cell_number].
max_point: number of points to sample from consolidated PD's.
weight_function: if given used to calculate probabilities of sampling each point.
random_state: PRNG seed.
"""
self.grid_shape = grid_shape
self.max_points = max_points
self.weight_function = weight_function
self.random_state = random_state
def _grid_generator(self, X, y_points, x_points):
"""Iterate over grid cells"""
for y in range(1, len(y_points)):
if y == 1:
mask = y_points[y - 1] <= X[:, 1]
else:
mask = y_points[y - 1] < X[:, 1]
mask &= X[:, 1] <= y_points[y]
y_split = X[mask]
for x in range(1, len(x_points)):
if x == 1:
mask = x_points[x - 1] <= y_split[:, 0]
else:
mask = x_points[x - 1] < y_split[:, 0]
mask &= y_split[:, 0] <= x_points[x]
yield y_split[mask]
def fit(self, X, y=None):
"""
Fit the GridPDSampler class on a list of values (For pipeline compatibility - does nothing).
Parameters:
X (list of n x 2 numpy arrays): input persistence diagrams.
y (n x 1 array): persistence diagram labels (unused).
"""
return self
def transform(self, X):
"""
Concatenate, compute cells and randomly sample from each one.
Parameters:
X (list of n x 2 numpy arrays): input persistence diagrams.
Returns:
Array with single PD (np.array of size max_points).
"""
out = []
if not X:
return out
X = np.concatenate(X)
y_points = np.linspace(np.min(X[:, 1]), np.max(X[:, 1]), self.grid_shape[0] + 1)
x_points = np.linspace(np.min(X[:, 0]), np.max(X[:, 0]), self.grid_shape[1] + 1)
cells_populations, _, _ = np.histogram2d(x=X[:,0], y=X[:,1], bins=(x_points, y_points))
cells_populations = cells_populations.T
samples_to_take = | np.zeros(cells_populations.shape, dtype=np.int32) | numpy.zeros |
import pandas as pd
import numpy as np
import math
import time
import pickle
_DEBUG = False
# _DEBUG = True
| np.random.seed(42) | numpy.random.seed |
import numpy as np
import os
import re
import requests
import sys
import time
from netCDF4 import Dataset
import pandas as pd
from bs4 import BeautifulSoup
from tqdm import tqdm
# setup constants used to access the data from the different M2M interfaces
BASE_URL = 'https://ooinet.oceanobservatories.org/api/m2m/' # base M2M URL
SENSOR_URL = '12576/sensor/inv/' # Sensor Information
# setup access credentials
AUTH = ['OOIAPI-853A3LA6QI3L62', '<KEY>']
def M2M_Call(uframe_dataset_name, start_date, end_date):
options = '?beginDT=' + start_date + '&endDT=' + end_date + '&format=application/netcdf'
r = requests.get(BASE_URL + SENSOR_URL + uframe_dataset_name + options, auth=(AUTH[0], AUTH[1]))
if r.status_code == requests.codes.ok:
data = r.json()
else:
return None
# wait until the request is completed
print('Waiting for OOINet to process and prepare data request, this may take up to 20 minutes')
url = [url for url in data['allURLs'] if re.match(r'.*async_results.*', url)][0]
check_complete = url + '/status.txt'
with tqdm(total=400, desc='Waiting') as bar:
for i in range(400):
r = requests.get(check_complete)
bar.update(1)
if r.status_code == requests.codes.ok:
bar.n = 400
bar.last_print_n = 400
bar.refresh()
print('\nrequest completed in %f minutes.' % elapsed)
break
else:
time.sleep(3)
elapsed = (i * 3) / 60
return data
def M2M_Files(data, tag=''):
"""
Use a regex tag combined with the results of the M2M data request to collect the data from the THREDDS catalog.
Collected data is gathered into an xarray dataset for further processing.
:param data: JSON object returned from M2M data request with details on where the data is to be found for download
:param tag: regex tag to use in discriminating the data files, so we only collect the correct ones
:return: the collected data as an xarray dataset
"""
# Create a list of the files from the request above using a simple regex as a tag to discriminate the files
url = [url for url in data['allURLs'] if re.match(r'.*thredds.*', url)][0]
files = list_files(url, tag)
return files
def list_files(url, tag=''):
"""
Function to create a list of the NetCDF data files in the THREDDS catalog created by a request to the M2M system.
:param url: URL to user's THREDDS catalog specific to a data request
:param tag: regex pattern used to distinguish files of interest
:return: list of files in the catalog with the URL path set relative to the catalog
"""
page = requests.get(url).text
soup = BeautifulSoup(page, 'html.parser')
pattern = re.compile(tag)
return [node.get('href') for node in soup.find_all('a', text=pattern)]
def M2M_Data(nclist,variables):
thredds = 'https://opendap.oceanobservatories.org/thredds/dodsC/ooi/'
#nclist is going to contain more than one url eventually
for jj in range(len(nclist)):
url=nclist[jj]
url=url[25:]
dap_url = thredds + url + '#fillmismatch'
openFile = Dataset(dap_url,'r')
for ii in range(len(variables)):
dum = openFile.variables[variables[ii].name]
variables[ii].data = np.append(variables[ii].data, dum[:].data)
tmp = variables[0].data/60/60/24
time_converted = pd.to_datetime(tmp, unit='D', origin=pd.Timestamp('1900-01-01'))
return variables, time_converted
class var(object):
def __init__(self):
"""A Class that generically holds data with a variable name
and the units as attributes"""
self.name = ''
self.data = np.array([])
self.units = ''
def __repr__(self):
return_str = "name: " + self.name + '\n'
return_str += "units: " + self.units + '\n'
return_str += "data: size: " + str(self.data.shape)
return return_str
class structtype(object):
def __init__(self):
""" A class that imitates a Matlab structure type
"""
self._data = []
def __getitem__(self, index):
"""implement index behavior in the struct"""
if index == len(self._data):
self._data.append(var())
return self._data[index]
def __len__(self):
return len(self._data)
def M2M_URLs(platform_name,node,instrument_class,method):
var_list = structtype()
#MOPAK
if platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/SBD17/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/SBD11/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/SBD11/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/SBD17/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/SBD11/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/SBD11/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
elif platform_name == 'CE09OSPM' and node == 'BUOY' and instrument_class == 'MOPAK' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSPM/SBS01/01-MOPAK0000/telemetered/mopak_o_dcl_accel'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
#METBK
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/SBD11/06-METBKA000/telemetered/metbk_a_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
elif platform_name == 'CE04OSSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/SBD11/06-METBKA000/telemetered/metbk_a_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
elif platform_name == 'CE07SHSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/SBD11/06-METBKA000/telemetered/metbk_a_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
elif platform_name == 'CE09OSSM' and node == 'BUOY' and instrument_class == 'METBK1' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/SBD11/06-METBKA000/telemetered/metbk_a_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'sea_surface_temperature'
var_list[2].name = 'sea_surface_conductivity'
var_list[3].name = 'met_salsurf'
var_list[4].name = 'met_windavg_mag_corr_east'
var_list[5].name = 'met_windavg_mag_corr_north'
var_list[6].name = 'barometric_pressure'
var_list[7].name = 'air_temperature'
var_list[8].name = 'relative_humidity'
var_list[9].name = 'longwave_irradiance'
var_list[10].name = 'shortwave_irradiance'
var_list[11].name = 'precipitation'
var_list[12].name = 'met_heatflx_minute'
var_list[13].name = 'met_latnflx_minute'
var_list[14].name = 'met_netlirr_minute'
var_list[15].name = 'met_sensflx_minute'
var_list[16].name = 'eastward_velocity'
var_list[17].name = 'northward_velocity'
var_list[18].name = 'met_spechum'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[7].data = np.array([])
var_list[8].data = np.array([])
var_list[9].data = np.array([])
var_list[10].data = np.array([])
var_list[11].data = np.array([])
var_list[12].data = np.array([])
var_list[13].data = np.array([])
var_list[14].data = np.array([])
var_list[15].data = np.array([])
var_list[16].data = np.array([])
var_list[17].data = np.array([])
var_list[18].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'degC'
var_list[2].units = 'S/m'
var_list[3].units = 'unitless'
var_list[4].units = 'm/s'
var_list[5].units = 'm/s'
var_list[6].units = 'mbar'
var_list[7].units = 'degC'
var_list[8].units = '#'
var_list[9].units = 'W/m'
var_list[10].units = 'W/m'
var_list[11].units = 'mm'
var_list[12].units = 'W/m'
var_list[13].units = 'W/m'
var_list[14].units = 'W/m'
var_list[15].units = 'W/m'
var_list[16].units = 'm/s'
var_list[17].units = 'm/s'
var_list[18].units = 'g/kg'
#FLORT
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE01ISSM' and node == 'BUOY' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/SBD17/06-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE06ISSM' and node == 'BUOY' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/SBD17/06-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID27/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID27/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID27/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID27/02-FLORTD000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
elif platform_name == 'CE09OSPM' and node == 'PROFILER' and instrument_class == 'FLORT' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSPM/WFP01/04-FLORTK000/telemetered/flort_sample'
var_list[0].name = 'time'
var_list[1].name = 'seawater_scattering_coefficient'
var_list[2].name = 'fluorometric_chlorophyll_a'
var_list[3].name = 'fluorometric_cdom'
var_list[4].name = 'total_volume_scattering_coefficient'
var_list[5].name = 'optical_backscatter'
var_list[6].name = 'int_ctd_pressure'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[5].data = np.array([])
var_list[6].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'm-1'
var_list[2].units = 'ug/L'
var_list[3].units = 'ppb'
var_list[4].units = 'm-1 sr-1'
var_list[5].units = 'm-1'
var_list[6].units = 'dbar'
#FDCHP
elif platform_name == 'CE02SHSM' and node == 'BUOY' and instrument_class == 'FDCHP' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/SBD12/08-FDCHPA000/telemetered/fdchp_a_dcl_instrument'
var_list[0].name = 'time'
var_list[0].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
#DOSTA
elif platform_name == 'CE01ISSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/RID16/03-DOSTAD000/telemetered/dosta_abcdjm_ctdbp_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE02SHSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE02SHSM/RID27/04-DOSTAD000/telemetered/dosta_abcdjm_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE04OSSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE04OSSM/RID27/04-DOSTAD000/telemetered/dosta_abcdjm_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE06ISSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/RID16/03-DOSTAD000/telemetered/dosta_abcdjm_ctdbp_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE07SHSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE07SHSM/RID27/04-DOSTAD000/telemetered/dosta_abcdjm_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE09OSSM' and node == 'NSIF' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE09OSSM/RID27/04-DOSTAD000/telemetered/dosta_abcdjm_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'estimated_oxygen_concentration'
var_list[3].name = 'optode_temperature'
var_list[4].name = 'dosta_abcdjm_cspp_tc_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[3].data = np.array([])
var_list[4].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
var_list[3].units = 'degC'
var_list[4].units = 'umol/L'
elif platform_name == 'CE01ISSM' and node == 'MFN' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE01ISSM/MFD37/03-DOSTAD000/telemetered/dosta_abcdjm_ctdbp_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = np.array([])
var_list[1].data = np.array([])
var_list[2].data = np.array([])
var_list[0].units = 'seconds since 1900-01-01'
var_list[1].units = 'umol/kg'
var_list[2].units = 'umol/L'
elif platform_name == 'CE06ISSM' and node == 'MFN' and instrument_class == 'DOSTA' and method == 'Telemetered':
uframe_dataset_name = 'CE06ISSM/MFD37/03-DOSTAD000/telemetered/dosta_abcdjm_ctdbp_dcl_instrument'
var_list[0].name = 'time'
var_list[1].name = 'dissolved_oxygen'
var_list[2].name = 'dosta_ln_optode_oxygen'
var_list[0].data = | np.array([]) | numpy.array |
__author__ = '<NAME>'
__all__ = ['EulerianGrid']
import os
import numpy as np
class EulerianGrid(object):
def __repr__(self):
return f'{self.__class__.__name__}()'
def __init__(self):
"""
Класс реализует общие методы,
для расчетов в газодинамической постановке
"""
self.tau = 0
# Длина ячейки на пред. шаге. 3необходимо для расчета веторов q
self._previous_cell_lenght = 0
def _velocity_parameters(self):
self.c_interface = (self.c_cell[1:] + self.c_cell[:-1]) / 2
self.mah_cell_minus = \
(self.v_cell[:-1] - self.v_interface) / self.c_interface
self.mah_cell_plus = \
(self.v_cell[1:] - self.v_interface) / self.c_interface
def _get_mah_press_interface(self):
self.mah_interface = self._fetta_plus() + self._fetta_mines()
self.press_interface = \
self._getta_plus() * self.press_cell[:-1] \
+ self._getta_mines() * self.press_cell[1:]
def _calculate_tau(self):
buffer_ = \
(self.x_interface[1:] - self.x_interface[:-1]) \
/ (abs(self.v_cell[1:-1]) + self.c_cell[1:-1])
self.tau = self.gun.kurant * min(buffer_)
def _new_x_interfaces(self, last_x_interface):
self.x_interface = np.linspace(0, last_x_interface, self.nodes - 1)
def _fetta_plus(self):
"""
Параметр в пересчете давления на границе для индекса +
"""
answer = np.zeros_like(self.mah_cell_minus)
if_cond = np.abs(self.mah_cell_minus) >= 1
else_cond = | np.abs(self.mah_cell_minus) | numpy.abs |
# Visualization function
import numpy as np
import matplotlib.pyplot as plt
from math import ceil
from PIL import Image
from scipy.ndimage.filters import gaussian_filter
def img_combine(img, ncols=5, size=1, path=False):
"""
Draw the images with array
img: image array to plot - size = n x im_w x im_h x 3
"""
nimg= img.shape[0]
nrows=int(ceil(nimg/ncols))
fig, axes = plt.subplots(nrows=nrows, ncols=ncols, sharex=True, sharey=True, figsize=(ncols*size,nrows*size))
if nrows==0:
return
elif ncols == 1:
for r, ax in zip( | np.arange(nrows) | numpy.arange |
# Copyright (c) Microsoft Corporation. All rights reserved.
# Licensed under the MIT License.
"""
Class to visualize raster mask labels and hardmax or softmax model predictions, for semantic segmentation tasks.
"""
import json
import os
from io import BytesIO
from typing import Union, Tuple
import matplotlib
matplotlib.use('Agg')
import matplotlib.colors as mcolors
import matplotlib.pyplot as plt
import numpy as np
from PIL import Image, ImageColor
class RasterLabelVisualizer(object):
"""Visualizes raster mask labels and predictions."""
def __init__(self, label_map: Union[str, dict]):
"""Constructs a raster label visualizer.
Args:
label_map: a path to a JSON file containing a dict, or a dict. The dict needs to have two fields:
num_to_name {
numerical category (str or int) : display name (str)
}
num_to_color {
numerical category (str or int) : color representation (an object that matplotlib.colors recognizes
as a color; additionally a (R, G, B) tuple or list with uint8 values will also be parsed)
}
"""
if isinstance(label_map, str):
assert os.path.exists(label_map)
with open(label_map) as f:
label_map = json.load(f)
assert 'num_to_name' in label_map
assert isinstance(label_map['num_to_name'], dict)
assert 'num_to_color' in label_map
assert isinstance(label_map['num_to_color'], dict)
self.num_to_name = RasterLabelVisualizer._dict_key_to_int(label_map['num_to_name'])
self.num_to_color = RasterLabelVisualizer._dict_key_to_int(label_map['num_to_color'])
assert len(self.num_to_color) == len(self.num_to_name)
self.num_classes = len(self.num_to_name)
# check for duplicate names or colors
assert len(set(self.num_to_color.values())) == self.num_classes, 'There are duplicate colors in the colormap'
assert len(set(self.num_to_name.values())) == self.num_classes, \
'There are duplicate class names in the colormap'
self.num_to_color = RasterLabelVisualizer.standardize_colors(self.num_to_color)
# create the custom colormap according to colors defined in label_map
required_colors = []
# key is originally a string
for num, color_name in sorted(self.num_to_color.items(), key=lambda x: x[0]): # num already cast to int
rgb = mcolors.to_rgb(mcolors.CSS4_COLORS[color_name])
# mcolors.to_rgb is to [0, 1] values; ImageColor.getrgb gets [1, 255] values
required_colors.append(rgb)
self.colormap = mcolors.ListedColormap(required_colors)
# vmin and vmax appear to be inclusive,
# so if there are a total of 34 classes, class 0 to class 33 each maps to a color
self.normalizer = mcolors.Normalize(vmin=0, vmax=self.num_classes - 1)
self.color_matrix = self._make_color_matrix()
@staticmethod
def _dict_key_to_int(d: dict) -> dict:
return {int(k): v for k, v in d.items()}
def _make_color_matrix(self) -> np.ndarray:
"""Creates a color matrix of dims (num_classes, 3), where a row corresponds to the RGB values of each class.
"""
matrix = []
for num, color in sorted(self.num_to_color.items(), key=lambda x: x[0]):
rgb = RasterLabelVisualizer.matplotlib_color_to_uint8_rgb(color)
matrix.append(rgb)
matrix = np.array(matrix)
assert matrix.shape == (self.num_classes, 3)
return matrix
@staticmethod
def standardize_colors(num_to_color: dict) -> dict:
"""Return a new dict num_to_color with colors verified. uint8 RGB tuples are converted to a hex string
as matplotlib.colors do not accepted uint8 intensity values"""
new = {}
for num, color in num_to_color.items():
if mcolors.is_color_like(color):
new[num] = color
else:
# try to see if it's a (r, g, b) tuple or list of uint8 values
assert len(color) == 3 or len(
color) == 4, f'Color {color} is specified as a tuple or list but is not of length 3 or 4'
for c in color:
assert isinstance(c, int) and 0 < c < 256, f'RGB value {c} is out of range'
new[num] = RasterLabelVisualizer.uint8_rgb_to_hex(color[0], color[1], color[3]) # drop any alpha values
assert len(new) == len(num_to_color)
return new
@staticmethod
def uint8_rgb_to_hex(r: int, g: int, b: int) -> str:
"""Convert RGB values in uint8 to a hex color string
Reference
https://codereview.stackexchange.com/questions/229282/performance-for-simple-code-that-converts-a-rgb-tuple-to-hex-string
"""
return f'#{r:02x}{g:02x}{b:02x}'
@staticmethod
def matplotlib_color_to_uint8_rgb(color: Union[str, tuple, list]) -> Tuple[int, int, int]:
"""Converts any matplotlib recognized color representation to (R, G, B) uint intensity values
Need to use matplotlib, which recognizes different color formats, to convert to hex,
then use PIL to convert to uint8 RGB. matplotlib does not support the uint8 RGB format
"""
color_hex = mcolors.to_hex(color)
color_rgb = ImageColor.getcolor(color_hex, 'RGB') # '#DDA0DD' to (221, 160, 221); alpha silently dropped
return color_rgb
def get_tiff_colormap(self) -> dict:
"""Returns the object to pass to rasterio dataset object's write_colormap() function,
which is a dict mapping int values to a tuple of (R, G, B)
See https://rasterio.readthedocs.io/en/latest/topics/color.html for writing the TIFF colormap
"""
colormap = {}
for num, color in self.num_to_color.items():
# uint8 RGB required by TIFF
colormap[num] = RasterLabelVisualizer.matplotlib_color_to_uint8_rgb(color)
return colormap
def get_tool_colormap(self) -> str:
"""Returns a string that is a JSON of a list of items specifying the name and color
of classes. Example:
"[
{"name": "Water", "color": "#0000FF"},
{"name": "Tree Canopy", "color": "#008000"},
{"name": "Field", "color": "#80FF80"},
{"name": "Built", "color": "#806060"}
]"
"""
classes = []
for num, name in sorted(self.num_to_name.items(), key=lambda x: int(x[0])):
color = self.num_to_color[num]
color_hex = mcolors.to_hex(color)
classes.append({
'name': name,
'color': color_hex
})
classes = json.dumps(classes, indent=4)
return classes
@staticmethod
def plot_colortable(name_to_color: dict, title: str, sort_colors: bool = False, emptycols: int = 0) -> plt.Figure:
"""
function taken from https://matplotlib.org/3.1.0/gallery/color/named_colors.html
"""
cell_width = 212
cell_height = 22
swatch_width = 70
margin = 12
topmargin = 40
# Sort name_to_color by hue, saturation, value and name.
if sort_colors is True:
by_hsv = sorted((tuple(mcolors.rgb_to_hsv(mcolors.to_rgb(color))),
name)
for name, color in name_to_color.items())
names = [name for hsv, name in by_hsv]
else:
names = list(name_to_color)
n = len(names)
ncols = 4 - emptycols
nrows = n // ncols + int(n % ncols > 0)
width = cell_width * 4 + 2 * margin
height = cell_height * nrows + margin + topmargin
dpi = 80 # other numbers don't seem to work well
fig, ax = plt.subplots(figsize=(width / dpi, height / dpi), dpi=dpi)
fig.subplots_adjust(margin / width, margin / height,
(width - margin) / width, (height - topmargin) / height)
ax.set_xlim(0, cell_width * 4)
ax.set_ylim(cell_height * (nrows - 0.5), -cell_height / 2.)
ax.yaxis.set_visible(False)
ax.xaxis.set_visible(False)
ax.set_axis_off()
ax.set_title(title, fontsize=24, loc='left', pad=10)
for i, name in enumerate(names):
row = i % nrows
col = i // nrows
y = row * cell_height
swatch_start_x = cell_width * col
swatch_end_x = cell_width * col + swatch_width
text_pos_x = cell_width * col + swatch_width + 7
ax.text(text_pos_x, y, name, fontsize=14,
horizontalalignment='left',
verticalalignment='center')
ax.hlines(y, swatch_start_x, swatch_end_x,
color=name_to_color[name], linewidth=18)
return fig
def plot_color_legend(self, legend_title: str = 'Categories') -> plt.Figure:
"""Builds a legend of color block, numerical categories and names of the categories.
Returns:
a matplotlib.pyplot Figure
"""
label_map = {}
for num, color in self.num_to_color.items():
label_map['{} {}'.format(num, self.num_to_name[num])] = color
fig = RasterLabelVisualizer.plot_colortable(label_map, legend_title, sort_colors=False, emptycols=3)
return fig
def show_label_raster(self, label_raster: Union[Image.Image, np.ndarray],
size: Tuple[int, int] = (10, 10)) -> Tuple[Image.Image, BytesIO]:
"""Visualizes a label mask or hardmax predictions of a model, according to the category color map
provided when the class was initialized.
The label_raster provided needs to contain values in [0, num_classes].
Args:
label_raster: 2D numpy array or PIL Image where each number indicates the pixel's class
size: matplotlib size in inches (h, w)
Returns:
(im, buf) - PIL image of the matplotlib figure, and a BytesIO buf containing the matplotlib Figure
saved as a PNG
"""
if not isinstance(label_raster, np.ndarray):
label_raster = | np.asarray(label_raster) | numpy.asarray |
# import required libraries
import numpy as np
import cv2
print('OpenCV version: '+cv2.__version__)
import matplotlib.pyplot as plt
import pandas as pd
import datetime
import os
from collections import Counter
# Set source folder
SRC_FOLDER = "C:/Users/raksh/OneDrive - The Pennsylvania State University/PhD Research/Paper-4/SysID Experiment/OL Test 3/"
# open and read file containing start and end timestamps of the videos
df_vidTimes = pd.read_excel(SRC_FOLDER + "Video_Timestamps_1.xlsx")
df_vidTimes.drop(df_vidTimes.columns[0],axis=1,inplace=True)
################ ALL FUNCTIONS DEFINITIONS ################
def perspCorrection(img,pt1,pt2,pt3,pt4,scale_width,scale_height):
# Create a copy of the image
img_copy = np.copy(img)
# Convert to RGB so as to display via matplotlib
# Using Matplotlib we can easily find the coordinates of the 4 points that is essential for finding then transformation matrix
#img = cv2.cvtColor(img,cv2.COLOR_BGR2RGB)
# to calculate the transformation matrix
input_pts = np.float32([pt1,pt2,pt3,pt4])
output_pts = np.float32([[0,0],[scale_width-1,0],[0,scale_height-1],[scale_width-1,scale_height-1]])
# Compute the perspective transform M
M = cv2.getPerspectiveTransform(input_pts,output_pts)
# Apply the perspective transformation to the image
imgPersp = cv2.warpPerspective(img,M,(scale_width, scale_height)) #,flags=cv2.INTER_LINEAR) cv2.INTER_CUBIC is also an option
imgGrayPersp = cv2.cvtColor(imgPersp, cv2.COLOR_BGR2GRAY)
# visulaize corners using cv2 circles
for x in range (0,4):
cv2.circle(img_copy,(round(input_pts[x][0]),round(input_pts[x][1])),5,(0,0,255),cv2.FILLED)
return [img_copy,imgPersp,imgGrayPersp]
def extractTopBottom(img,tStart,tEnd,bStart,bEnd):
img_top = img[tStart[1]:tEnd[1],tStart[0]:tEnd[0]]
img_bottom = img[bStart[1]:bEnd[1],bStart[0]:bEnd[0]]
return [img_top,img_bottom]
def gaussianBlur(img,fsize):
# gaussian blur
gblur = cv2.GaussianBlur(img,(fsize,fsize),0)
return gblur
def medianBlur(img,fsize=3):
# median blur - effective at removing salt and pepper noise
mblur = cv2.medianBlur(img,fsize)
return mblur
def bilateralFilter(img):
# Bilateral filter preserves edges while removing noise
bfblur = cv2.bilateralFilter(img,9,75,75)
return bfblur
def gAdaptiveThresholding(img):
# median filtering
adaptive_gaussian = cv2.adaptiveThreshold(img,255,cv2.ADAPTIVE_THRESH_GAUSSIAN_C,\
cv2.THRESH_BINARY,11,2)
return adaptive_gaussian
def morphOps(img,kernel1,kernel2,k1_num_passes=2):
# Closing = Dilation + Erosion
# dilation
mask_dil = cv2.dilate(img,kernel1,iterations = k1_num_passes)
# erosion
mask_erode = cv2.erode(mask_dil,kernel2,iterations = 1)
return mask_erode
def computeW_Rev(img,img_debug):
avg_num_pixels = 159
scaling_factor = 1.0
mm_per_pixel = ((1/32)*25.4)/(scaling_factor*avg_num_pixels)
edge_length_threshold = 55
min_L_edge_threshold = False
min_R_edge_threshold = False
# Predefine arrays for data storage
approx_edges = 10
num_edges = np.zeros(img.shape[0]) #,dtype=np.uint16)
edge_start = np.zeros([img.shape[0],approx_edges])#,dtype=np.uint16)
edge_end = np.zeros([img.shape[0],approx_edges])#,dtype=np.uint16)
edge_count = 0
k=0
sse = False
tse = False
# start scanning from (0,0) until black pixel is found
# go across columns first
for i in range(img.shape[0]):
found_edge = False
temp_edge_count = 0
k=0
for j in range(img.shape[1]):
if(img[i,j]<=50):
# Black pixel found - edge
if(found_edge==False):
found_edge = True
temp_edge_count += 1
num_edges[i] = temp_edge_count
edge_start[i][k] = j
k += 1
else:
if(found_edge):
edge_end[i][k-1] = j-1
found_edge = False
x = Counter(num_edges)
y = {z:count for z, count in x.items() if count >= edge_length_threshold and z > 1}
#print(y)
if(len(y)!=0):
edge_condition = sorted(y,key=y.get)[0]
else:
print('num_edges > 1 and length(num_edges) >= threshold not satisfied . . . Lowering threshold to identify matches')
w = {z:count for z, count in x.items() if count < edge_length_threshold and z > 1}
if(len(w)!=0):
print('Found num_edges > 1 and length(num_edges) < threshold!')
edge_condition = sorted(w,key=w.get)[0]
else:
print('Unable to find edge condition . . . check image')
edge_condition = -1
if img_debug:
print('edge condition: ' + str(edge_condition))
if edge_condition == 2: #max(num_edges)==2:
# max num_edges = 2
L1_edge_start = edge_start[:,0][np.argwhere(num_edges==2)][np.logical_and(edge_start[:,0][np.argwhere(num_edges==2)]>60,edge_start[:,0][np.argwhere(num_edges==2)]<300)]
L1_edge_end = edge_end[:,0][np.argwhere(num_edges==2)][np.logical_and(edge_end[:,0][np.argwhere(num_edges==2)]>60,edge_end[:,0][np.argwhere(num_edges==2)]<300)]
if(np.max(L1_edge_start)-np.min(L1_edge_start)>13):
L1_edge_start = L1_edge_start[L1_edge_start >= (np.max(L1_edge_start)-10)]
if(np.max(L1_edge_end)-np.min(L1_edge_end)>15):
L1_edge_end = L1_edge_end[L1_edge_end >= (np.max(L1_edge_end)-10)]
trueLedge_start = L1_edge_start
trueLedge_end = L1_edge_end
R1_edge_start = edge_start[:,1][np.argwhere(num_edges==2)][edge_start[:,1][np.argwhere(num_edges==2)]>350]
R1_edge_end = edge_end[:,1][np.argwhere(num_edges==2)][edge_end[:,1][np.argwhere(num_edges==2)]>350]
if(np.max(R1_edge_start)-np.min(R1_edge_start)>13):
R1_edge_start = R1_edge_start[R1_edge_start <= (np.min(R1_edge_start)+10)]
if(np.max(R1_edge_end)-np.min(R1_edge_end)>13):
R1_edge_end = R1_edge_end[R1_edge_end <= (np.min(R1_edge_end)+10)]
trueRedge_start = R1_edge_start
trueRedge_end = R1_edge_end
if(len(trueLedge_start)>len(trueLedge_end)):
trueLedge_start = np.array([trueLedge_start[i] for i in range(len(trueLedge_end))])
if(len(trueLedge_start)<len(trueLedge_end)):
trueLedge_end = np.array([trueLedge_end[i] for i in range(len(trueLedge_start))])
if(len(trueRedge_start)>len(trueRedge_end)):
trueRedge_start = np.array([trueRedge_start[i] for i in range(len(trueRedge_end))])
if(len(trueRedge_start)<len(trueRedge_end)):
trueRedge_end = np.array([trueRedge_end[i] for i in range(len(trueRedge_start))])
line1_start = (round(np.mean((trueLedge_start+trueLedge_end)/2)),0)
line1_end = (round(np.mean((trueLedge_start+trueLedge_end)/2)),img.shape[0])
line2_start = (round(np.mean((trueRedge_start+trueRedge_end)/2)),0)
line2_end = (round(np.mean((trueRedge_start+trueRedge_end)/2)),img.shape[0])
edge_count = 2
case_cond = 1
elif edge_condition == 3: #max(num_edges)==3:
# max num_edges = 3
# logic for finding true left edge
L2_edge_start = edge_start[:,1][np.argwhere(num_edges==3)][edge_start[:,1][np.argwhere(num_edges==3)]<250]
if(len(L2_edge_start)>=edge_length_threshold):
trueLedge_start = L2_edge_start
trueLedge_end = edge_end[:,1][np.argwhere(num_edges==3)][edge_end[:,1][np.argwhere(num_edges==3)]<250]
else:
if(len(edge_start[:,0][np.argwhere(num_edges==3)][np.logical_and(edge_start[:,0][np.argwhere(num_edges==3)]<250,edge_start[:,0][np.argwhere(num_edges==3)]>60)])!=0):
L1_edge_start = edge_start[:,0][np.argwhere(num_edges==3)][np.logical_and(edge_start[:,0][np.argwhere(num_edges==3)]<250,edge_start[:,0][np.argwhere(num_edges==3)]>60)]
if(len(L2_edge_start)!=0):
L1_edge_start = np.hstack((L1_edge_start,L2_edge_start))
if(np.max(L1_edge_start)-np.min(L1_edge_start)>13):
L1_edge_start = L1_edge_start[L1_edge_start >= (np.max(L1_edge_start)-10)]
else:
L1_edge_start = edge_start[:,0][np.argwhere(num_edges==2)][edge_start[:,0][np.argwhere(num_edges==2)]<250]
if(len(L1_edge_start)>=edge_length_threshold):
trueLedge_start = L1_edge_start
if(len(edge_start[:,0][np.argwhere(num_edges==3)][np.logical_and(edge_start[:,0][np.argwhere(num_edges==3)]<250,edge_start[:,0][np.argwhere(num_edges==3)]>60)])!=0):
trueLedge_end = edge_end[:,0][np.argwhere(num_edges==3)][np.logical_and(edge_end[:,0][np.argwhere(num_edges==3)]<250,edge_end[:,0][np.argwhere(num_edges==3)]>60)]
if(len(L2_edge_start)!=0):
trueLedge_end = np.hstack((trueLedge_end,edge_end[:,1][np.argwhere(num_edges==3)][edge_end[:,1][np.argwhere(num_edges==3)]<250]))
if(np.max(trueLedge_end)-np.min(trueLedge_end)>13):
trueLedge_end = trueLedge_end[trueLedge_end >= (np.max(trueLedge_end)-10)]
else:
trueLedge_end = edge_end[:,0][np.argwhere(num_edges==2)][edge_end[:,0][np.argwhere(num_edges==2)]<250]
elif(len(L1_edge_start)!=0 and len(L1_edge_start)<edge_length_threshold):
trueLedge_start = L1_edge_start
trueLedge_end = edge_end[:,0][np.argwhere(num_edges==3)][edge_end[:,0][np.argwhere(num_edges==3)]<250]
trueLedge_end = np.hstack((trueLedge_end,edge_end[:,0][np.argwhere(num_edges==2)][edge_end[:,0][np.argwhere(num_edges==2)]<250]))
min_L_edge_threshold = True
else:
print('max(num_edges)=3 invalid true left edge condition encountered . . . check code')
# logic for finding true right edge
R2_edge_start = edge_start[:,1][np.argwhere(num_edges==3)][edge_start[:,1][np.argwhere(num_edges==3)]>350]
if(len(R2_edge_start)>=edge_length_threshold):
trueRedge_start = R2_edge_start
trueRedge_end = edge_end[:,1][np.argwhere(num_edges==3)][edge_end[:,1][np.argwhere(num_edges==3)]>350]
else:
R1_edge_start = edge_start[:,1][np.argwhere(num_edges==2)][edge_start[:,1][np.argwhere(num_edges==2)]>350]
if(len(R1_edge_start)==0):
# three definite edges
trueRedge_start = edge_start[:,2][np.argwhere(num_edges==3)][edge_start[:,2][np.argwhere(num_edges==3)]>350]
trueRedge_end = edge_end[:,2][np.argwhere(num_edges==3)][edge_end[:,2][np.argwhere(num_edges==3)]>350]
elif(len(R1_edge_start)>=edge_length_threshold):
trueRedge_start = R1_edge_start
trueRedge_end = edge_end[:,1][np.argwhere(num_edges==2)][edge_end[:,1][np.argwhere(num_edges==2)]>350]
elif(len(R1_edge_start)!=0 and len(R1_edge_start)<edge_length_threshold):
# there are some elements but edge length is minimal
trueRedge_start = R1_edge_start
trueRedge_end = edge_end[:,1][np.argwhere(num_edges==2)][edge_end[:,1][np.argwhere(num_edges==2)]>350]
min_R_edge_threshold = True
else:
print('max(num_edges)=3 invalid true right edge condition encountered . . . check code')
if(np.max(trueRedge_start)-np.min(trueRedge_start)>13):
trueRedge_start = trueRedge_start[trueRedge_start <= (np.min(trueRedge_start)+10)]
if(np.max(trueRedge_end)-np.min(trueRedge_end)>13):
trueRedge_end = trueRedge_end[trueRedge_end <= (np.min(trueRedge_end)+10)]
if(len(trueLedge_start)>len(trueLedge_end)):
trueLedge_start = np.array([trueLedge_start[i] for i in range(len(trueLedge_end))])
if(len(trueLedge_start)<len(trueLedge_end)):
trueLedge_end = np.array([trueLedge_end[i] for i in range(len(trueLedge_start))])
if(len(trueRedge_start)>len(trueRedge_end)):
trueRedge_start = np.array([trueRedge_start[i] for i in range(len(trueRedge_end))])
if(len(trueRedge_start)<len(trueRedge_end)):
trueRedge_end = np.array([trueRedge_end[i] for i in range(len(trueRedge_start))])
if(len(trueLedge_start)<edge_length_threshold):
min_L_edge_threshold = True
if(len(trueRedge_start)<edge_length_threshold):
min_R_edge_threshold = True
if(min_L_edge_threshold or min_R_edge_threshold):
line1_start = (round(np.mean((trueLedge_start + trueLedge_end)/2)),0)
line1_end = (round(np.mean((trueLedge_start + trueLedge_end)/2)),img.shape[0])
line2_start = (round(np.mean((trueRedge_start + trueRedge_end)/2)),0)
line2_end = (round(np.mean((trueRedge_start + trueRedge_end)/2)),img.shape[0])
edge_count = 3
case_cond = 2
elif(np.logical_and(len(trueLedge_start)>=edge_length_threshold,len(trueRedge_start)>=edge_length_threshold)):
line1_start = (round(np.mean((trueLedge_start + trueLedge_end)/2)),0)
line1_end = (round(np.mean((trueLedge_start + trueLedge_end)/2)),img.shape[0])
line2_start = (round(np.mean((trueRedge_start + trueRedge_end)/2)),0)
line2_end = (round(np.mean((trueRedge_start + trueRedge_end)/2)),img.shape[0])
edge_count = 3
case_cond = 3
else:
print('max(num_edges)=3 with no matching condition reached . . . check code')
elif edge_condition == 4: #max(num_edges)==4:
# max num_edges = 4
# logic for finding true left edge
L3_edge_start = edge_start[:,2][np.argwhere(num_edges==4)][edge_start[:,2][np.argwhere(num_edges==4)]<250]
if(len(L3_edge_start)>=edge_length_threshold):
trueLedge_start = L3_edge_start
trueLedge_end = edge_end[:,2][np.argwhere(num_edges==4)][edge_end[:,2][np.argwhere(num_edges==4)]<250]
else:
L2_edge_start = edge_start[:,1][np.argwhere(num_edges==4)][np.logical_and(edge_start[:,1][np.argwhere(num_edges==4)]<250,edge_start[:,1][np.argwhere(num_edges==4)]>60)]
L2_edge_start = np.hstack((L2_edge_start,edge_start[:,1][np.argwhere(num_edges==3)][edge_start[:,1][np.argwhere(num_edges==3)]<250]))
if(len(L2_edge_start)>=edge_length_threshold):
trueLedge_start = L2_edge_start
trueLedge_end = edge_end[:,1][np.argwhere(num_edges==4)][np.logical_and(edge_end[:,1][np.argwhere(num_edges==4)]<250,edge_end[:,1][np.argwhere(num_edges==4)]>60)]
trueLedge_end = np.hstack((trueLedge_end,edge_end[:,1][np.argwhere(num_edges==3)][edge_end[:,1][np.argwhere(num_edges==3)]<250]))
else:
L1_edge_start = edge_start[:,0][np.argwhere(num_edges==2)][edge_start[:,0][np.argwhere(num_edges==2)]<250]
L1_edge_start = np.hstack((L1_edge_start,edge_start[:,0][np.argwhere(num_edges==3)][edge_start[:,0][np.argwhere(num_edges==3)]<250]))
L1_edge_start = np.hstack((L1_edge_start,edge_start[:,0][np.argwhere(num_edges==4)][edge_start[:,0][np.argwhere(num_edges==4)]<250]))
if(len(L1_edge_start)>= edge_length_threshold):
trueLedge_start = L1_edge_start
trueLedge_end = edge_end[:,0][np.argwhere(num_edges==2)][edge_end[:,0][np.argwhere(num_edges==2)]<250]
trueLedge_end = np.hstack((trueLedge_end,edge_end[:,0][np.argwhere(num_edges==3)][edge_end[:,0][np.argwhere(num_edges==3)]<250]))
trueLedge_end = np.hstack((trueLedge_end,edge_end[:,0][np.argwhere(num_edges==4)][edge_end[:,0][np.argwhere(num_edges==4)]<250]))
else:
print('max(num_edges)=4 invalid true left edge condition encountered . . . check code')
# logic for finding true right edge
R3_edge_start = edge_start[:,1][np.argwhere(num_edges==4)][edge_start[:,1][np.argwhere(num_edges==4)]>350]
if(len(R3_edge_start)>=edge_length_threshold):
trueRedge_start = R3_edge_start
trueRedge_end = edge_end[:,1][np.argwhere(num_edges==4)][edge_end[:,1][np.argwhere(num_edges==4)]>350]
else:
R2_edge_start = edge_start[:,2][np.argwhere(num_edges==4)][edge_start[:,2][np.argwhere(num_edges==4)]>350]
R2_edge_start = np.hstack((R2_edge_start,edge_start[:,1][np.argwhere(num_edges==3)][edge_start[:,1][np.argwhere(num_edges==3)]>350]))
if(len(R2_edge_start)>=edge_length_threshold):
trueRedge_start = R2_edge_start
trueRedge_end = edge_end[:,2][np.argwhere(num_edges==4)][edge_end[:,2][np.argwhere(num_edges==4)]>350]
trueRedge_end = np.hstack((trueRedge_end,edge_end[:,1][np.argwhere(num_edges==3)][edge_end[:,1][np.argwhere(num_edges==3)]>350]))
else:
R1_edge_start = edge_start[:,1][np.argwhere(num_edges==2)][edge_start[:,1][np.argwhere(num_edges==2)]>350]
R1_edge_start = np.hstack((R1_edge_start,edge_start[:,2][np.argwhere(num_edges==3)][edge_start[:,2][np.argwhere(num_edges==3)]>350]))
R1_edge_start = np.hstack((R1_edge_start,edge_start[:,3][np.argwhere(num_edges==4)][edge_start[:,3][np.argwhere(num_edges==4)]>350]))
if(len(R1_edge_start)>= edge_length_threshold):
trueRedge_start = R1_edge_start
trueRedge_end = edge_end[:,1][np.argwhere(num_edges==2)][edge_end[:,1][np.argwhere(num_edges==2)]>350]
trueRedge_end = np.hstack((trueRedge_end,edge_end[:,2][np.argwhere(num_edges==3)][edge_end[:,2][np.argwhere(num_edges==3)]>350]))
trueRedge_end = np.hstack((trueRedge_end,edge_end[:,3][np.argwhere(num_edges==4)][edge_end[:,3][np.argwhere(num_edges==4)]>350]))
else:
print('max(num_edges)=4 invalid true right edge condition encountered . . . check code')
if(len(trueLedge_start)>len(trueLedge_end)):
trueLedge_start = np.array([trueLedge_start[i] for i in range(len(trueLedge_end))])
if(len(trueLedge_start)<len(trueLedge_end)):
trueLedge_end = np.array([trueLedge_end[i] for i in range(len(trueLedge_start))])
if(len(trueRedge_start)>len(trueRedge_end)):
trueRedge_start = np.array([trueRedge_start[i] for i in range(len(trueRedge_end))])
if(len(trueRedge_start)<len(trueRedge_end)):
trueRedge_end = np.array([trueRedge_end[i] for i in range(len(trueRedge_start))])
if(np.logical_and(len(trueLedge_start)>=edge_length_threshold,len(trueRedge_start)>=edge_length_threshold)):
line1_start = (round(np.mean((trueLedge_start + trueLedge_end)/2)),0)
line1_end = (round(np.mean((trueLedge_start + trueLedge_end)/2)),img.shape[0])
line2_start = (round(np.mean((trueRedge_start + trueRedge_end)/2)),0)
line2_end = (round(np.mean((trueRedge_start + trueRedge_end)/2)),img.shape[0])
edge_count = 4
case_cond = 4
else:
print('max(num_edges)=4 with no matching condition reached . . . check code')
elif edge_condition > 4:
# greater than 4 max edges case is typically - stringing or rother artifact causing psuedo edges
# Identify true left edge
L4_edge_start = edge_start[:,3][np.argwhere(num_edges==5)][edge_start[:,3][np.argwhere(num_edges==5)]<250]
if(len(L4_edge_start)>=edge_length_threshold):
trueLedge_start = L4_edge_start
trueLedge_end = edge_end[:,3][np.argwhere(num_edges==5)][edge_end[:,3][np.argwhere(num_edges==5)]<250]
else:
L3_edge_start = edge_start[:,2][np.argwhere(num_edges==5)][edge_start[:,2][np.argwhere(num_edges==5)]<250]
L3_edge_start = np.hstack((L3_edge_start,edge_start[:,2][np.argwhere(num_edges==4)][edge_start[:,2][np.argwhere(num_edges==4)]<250]))
L3_edge_start = np.hstack((L3_edge_start,edge_start[:,1][np.argwhere(num_edges==3)][np.logical_and(edge_start[:,1][np.argwhere(num_edges==3)]<250,edge_start[:,1][np.argwhere(num_edges==3)]>60)]))
if(len(L3_edge_start)>=edge_length_threshold):
trueLedge_start = L3_edge_start
trueLedge_end = edge_end[:,2][np.argwhere(num_edges==5)][edge_end[:,2][np.argwhere(num_edges==5)]<250]
trueLedge_end = np.hstack((trueLedge_end,edge_end[:,2][np.argwhere(num_edges==4)][edge_end[:,2][np.argwhere(num_edges==4)]<250]))
trueLedge_end = np.hstack((trueLedge_end,edge_end[:,1][np.argwhere(num_edges==3)][edge_end[:,1][np.argwhere(num_edges==3)]<250]))
elif(len(L3_edge_start)!= 0 and len(L3_edge_start)<edge_length_threshold):
trueLedge_start = L3_edge_start
trueLedge_end = edge_end[:,2][np.argwhere(num_edges==5)][edge_end[:,2][np.argwhere(num_edges==5)]<250]
trueLedge_end = np.hstack((trueLedge_end,edge_end[:,2][np.argwhere(num_edges==4)][edge_end[:,2][np.argwhere(num_edges==4)]<250]))
trueLedge_end = np.hstack((trueLedge_end,edge_end[:,1][np.argwhere(num_edges==3)][edge_end[:,1][np.argwhere(num_edges==3)]<250]))
min_L_edge_threshold = True
else:
# L2_edge_start = edge_start[:,1][np.argwhere(num_edges==3)][edge_start[:,1][np.argwhere(num_edges==3)]<250]
# L2_edge_start = np.hstack((L2_edge_start,edge_start[:,0][np.argwhere(num_edges==3)][edge_start[:,0][np.argwhere(num_edges==3)]<250]))
# if(len(L2_edge_start)>=edge_length_threshold):
# trueLedge_start = L2_edge_start
# trueLedge_end = edge_end[:,1][np.argwhere(num_edges==3)][edge_end[:,1][np.argwhere(num_edges==3)]<250]
# trueLedge_end = np.hstack((trueLedge_end,edge_end[:,0][np.argwhere(num_edges==3)][edge_end[:,0][np.argwhere(num_edges==3)]<250]))
# else:
print('max(num_edges)>4 invalid true left edge condition encountered . . . check code')
# Identify true right edge
sse_Redge_start = edge_start[:,3][np.argwhere(num_edges==5)][edge_start[:,3][np.argwhere(num_edges==5)]>350]
sse_Redge_start = np.hstack((sse_Redge_start,edge_start[:,2][np.argwhere(num_edges==4)][edge_start[:,2][np.argwhere(num_edges==4)]>350]))
if(len(sse_Redge_start)>=edge_length_threshold):
trueRedge_start = sse_Redge_start
trueRedge_end = edge_end[:,3][np.argwhere(num_edges==5)][edge_end[:,3][np.argwhere(num_edges==5)]>350]
trueRedge_end = np.hstack((trueRedge_end,edge_end[:,2][np.argwhere(num_edges==4)][edge_end[:,2][np.argwhere(num_edges==4)]>350]))
elif(len(sse_Redge_start)!= 0 and len(sse_Redge_start)<edge_length_threshold):
trueRedge_start = sse_Redge_start
trueRedge_end = edge_end[:,3][np.argwhere(num_edges==5)][edge_end[:,3][ | np.argwhere(num_edges==5) | numpy.argwhere |
# Dual annealing unit tests implementation.
# Copyright (c) 2018 <NAME> <<EMAIL>>,
# <NAME> <<EMAIL>>
# Author: <NAME>, PMP S.A.
"""
Unit tests for the dual annealing global optimizer
"""
from scipy.optimize import dual_annealing
from scipy.optimize._dual_annealing import VisitingDistribution
from scipy.optimize._dual_annealing import ObjectiveFunWrapper
from scipy.optimize._dual_annealing import EnergyState
from scipy.optimize._dual_annealing import LocalSearchWrapper
from scipy.optimize import rosen, rosen_der
import numpy as np
from numpy.testing import (assert_equal, TestCase, assert_allclose,
assert_array_less)
from pytest import raises as assert_raises
from scipy._lib._util import check_random_state
class TestDualAnnealing(TestCase):
def setUp(self):
# A function that returns always infinity for initialization tests
self.weirdfunc = lambda x: np.inf
# 2-D bounds for testing function
self.ld_bounds = [(-5.12, 5.12)] * 2
# 4-D bounds for testing function
self.hd_bounds = self.ld_bounds * 4
# Number of values to be generated for testing visit function
self.nbtestvalues = 5000
self.high_temperature = 5230
self.low_temperature = 0.1
self.qv = 2.62
self.seed = 1234
self.rs = check_random_state(self.seed)
self.nb_fun_call = 0
self.ngev = 0
def tearDown(self):
pass
def callback(self, x, f, context):
# For testing callback mechanism. Should stop for e <= 1 as
# the callback function returns True
if f <= 1.0:
return True
def func(self, x, args=()):
# Using Rastrigin function for performing tests
if args:
shift = args
else:
shift = 0
y = np.sum((x - shift) ** 2 - 10 * np.cos(2 * np.pi * (
x - shift))) + 10 * np.size(x) + shift
self.nb_fun_call += 1
return y
def rosen_der_wrapper(self, x, args=()):
self.ngev += 1
return rosen_der(x, *args)
def test_visiting_stepping(self):
lu = list(zip(*self.ld_bounds))
lower = np.array(lu[0])
upper = np.array(lu[1])
dim = lower.size
vd = VisitingDistribution(lower, upper, self.qv, self.rs)
values = np.zeros(dim)
x_step_low = vd.visiting(values, 0, self.high_temperature)
# Make sure that only the first component is changed
assert_equal(np.not_equal(x_step_low, 0), True)
values = np.zeros(dim)
x_step_high = vd.visiting(values, dim, self.high_temperature)
# Make sure that component other than at dim has changed
assert_equal(np.not_equal(x_step_high[0], 0), True)
def test_visiting_dist_high_temperature(self):
lu = list(zip(*self.ld_bounds))
lower = np.array(lu[0])
upper = np.array(lu[1])
vd = VisitingDistribution(lower, upper, self.qv, self.rs)
# values = np.zeros(self.nbtestvalues)
# for i in np.arange(self.nbtestvalues):
# values[i] = vd.visit_fn(self.high_temperature)
values = vd.visit_fn(self.high_temperature, self.nbtestvalues)
# Visiting distribution is a distorted version of Cauchy-Lorentz
# distribution, and as no 1st and higher moments (no mean defined,
# no variance defined).
# Check that big tails values are generated
assert_array_less(np.min(values), 1e-10)
assert_array_less(1e+10, | np.max(values) | numpy.max |
# -*- coding: utf-8 -*-
"""
Poop analysis
Created 2020
@author: PClough
"""
import pandas as pd
import numpy as np
import chart_studio
import plotly.graph_objects as go
from plotly.offline import plot
from plotly.subplots import make_subplots
from scipy import stats
import datetime as dt
from time import strptime
import calendar
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
import vlc
df = pd.read_excel("Poo Data.xlsx", engine='openpyxl')
chart_studio.tools.set_credentials_file(username='YOUR USERNAME HERE', api_key='YOUR API HERE')
#%% Histogram of size of poos
# Replace sizes of 1, 2, and 3 in "size of poo?" heading to be small, medium and large
df['Size of poo? '].replace([1, 2, 3], ['Small', 'Medium', 'Poonarmi'], inplace = True)
fig = go.Figure()
fig.add_trace(go.Histogram(x = df['Size of poo? '],
name = 'Poop',
xbins = dict(
start = "Small",
),
marker_color = ('rgb(166,86,50)')))
fig.update_layout(
title_text = "Size of the poo poo's",
yaxis_title = "Count",
font = dict(size = 16))
plot(fig)
#%% Violin plot for day of week on x axis and type of poo on y axis
fig2 = go.Figure()
days = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun']
# Remove 'Type ' before the number
df['Type of poop 💩? '] = df['Type of poop 💩? '].str.replace('Type ', '')
Date_column = df['When did the poo occur? '].dt.strftime("%a")
for day in days:
fig2.add_trace(go.Violin(x = Date_column[Date_column == day],
y = df['Type of poop 💩? '][Date_column == day],
name = day,
box_visible = True,
meanline_visible = True,
showlegend = False,
fillcolor = 'chocolate',
line = dict(color = 'DarkSalmon')))
fig2.update_layout(yaxis = dict(range=[0.5,7.5]), title = "Average poo type over whole year", font = dict(size = 16))
fig2.update_yaxes(ticks="inside", tick0 = 1, dtick = 1, title = "Bristol stool scale index")
plot(fig2)
# %% Ridgeline plot for day of week on x axis and type of poo on y axis
# 12 rows of data, one for each month
# 7 columns of data, averaging that months poo types
months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']
# Remove 'Type ' before the number
df['Type of poop 💩? '] = df['Type of poop 💩? '].str.replace('Type ', '')
New_Date_column = df['When did the poo occur? '].dt.strftime("%b")
i = 0
max_val = 0
data = np.zeros([12,100]) # the value of 100 is just massively oversizing it, assuming there will be less than 100 poo's of a single type in one month
for month in months:
for j in range(1,8):
data[i, np.sum(df['Type of poop 💩? '][New_Date_column == month] == str(j))] = j-1
if max_val < np.sum(df['Type of poop 💩? '][New_Date_column == month] == str(j)):
max_val = np.sum(df['Type of poop 💩? '][New_Date_column == month] == str(j))
i += 1
# Find where the furthest right hand datapoint is and then cut everything off after that
idx = np.arange(max_val+1, 100)
data = np.delete(data, idx, axis=1)
data[data == 0] = 'nan'
fig3 = go.Figure()
for data_line in data:
fig3.add_trace(go.Violin(x=data_line))
fig3.update_traces(orientation='h', side='positive', width=2, points=False)
fig3.update_layout(xaxis_showgrid=False,
xaxis_zeroline=False,
xaxis=dict(range=[0,8]),
title = "Average poo type over whole year",
font = dict(size = 16))
plot(fig3)
#%% Violin plot for day of week on x axis and type of poo on y axis broken out month by month
days = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun']
months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']
fig4 = make_subplots(rows=2, cols=6, shared_yaxes=True, subplot_titles=(months))
# Remove 'Type ' before the number
df['Type of poop 💩? '] = df['Type of poop 💩? '].str.replace('Type ', '')
Date_column = df['When did the poo occur? '].dt.strftime("%a")
row_num = 1
col_num = 0
for month in months:
col_num += 1
if col_num > 6:
col_num = 1
row_num = 2
for day in days:
fig4.add_trace(go.Violin(x = Date_column[Date_column == day][New_Date_column == month],
y = df['Type of poop 💩? '][Date_column == day][New_Date_column == month],
name = month + day,
box_visible = True,
meanline_visible = True,
showlegend = False,
fillcolor = 'chocolate',
line = dict(color = 'DarkSalmon')),
row = row_num, col = col_num)
fig4.update_layout(yaxis = dict(range=[0.5,7.5]), title = "Average poo type, broken down month-by-month", font = dict(size = 16))
fig4.update_yaxes(ticks="inside", col = 1, tick0 = 1, dtick = 1, title = "Bristol stool scale index")
fig4.update_xaxes(ticks="inside")
plot(fig4)
#%% scatter plot x axis = Time since last poo (delta t), y axis (Size of poo)
# Return the number of hours from a timedelta
def days_hours_minutes(td):
return td.days*24 + td.seconds//3600 + (td.seconds//60)%60/60
d = {'When did the poo occur?': df['When did the poo occur? '], 'Size of poo?': df['Size of poo? '], 'time_since_last_poo': pd.Timedelta(0, unit='h')}
scatterplot_df = pd.DataFrame(data=d)
scatterplot_df = scatterplot_df.sort_values(by = ['When did the poo occur?']).reset_index(drop=True)
for i in range(1, len(df['When did the poo occur? '])-1):
scatterplot_df.loc[i, 'time_since_last_poo'] = days_hours_minutes(scatterplot_df['When did the poo occur?'][i] - scatterplot_df['When did the poo occur?'][i-1])
scatterplot_df.loc[0, 'time_since_last_poo'] = 0
scatterplot_df.loc[scatterplot_df['time_since_last_poo'].last_valid_index(), 'time_since_last_poo'] = 0
# Correlation line
dataforfitline = np.zeros([np.size(scatterplot_df,0), 1])
j = 0
for i in scatterplot_df['Size of poo?']:
if i == 'Small':
dataforfitline[j] = 1
if i == 'Medium':
dataforfitline[j] = 2
if i == 'Poonarmi':
dataforfitline[j] = 3
j += 1
dataforfitline2 = pd.DataFrame(data = scatterplot_df['time_since_last_poo'])
dataforfitline2[1] = dataforfitline
dataforfitline2 = dataforfitline2.sort_values(by = ['time_since_last_poo']).reset_index(drop=True)
slope, intercept, r_value, p_value, std_err = stats.linregress(dataforfitline2.astype(float))
line = slope*scatterplot_df['time_since_last_poo'] + intercept
fig5 = go.Figure(data=go.Scatter(x = scatterplot_df['time_since_last_poo'],
# y = scatterplot_df['Size of poo?'],
y = dataforfitline2[1],
mode = 'markers',
text = scatterplot_df['When did the poo occur?'],
name = 'Poops',
hovertemplate = "%{text}"))
fig5.add_trace(go.Scatter(x = scatterplot_df['time_since_last_poo'], y = line, mode = 'lines', name = 'R\u00b2 = ' + round(r_value**2,2).astype(str)))
fig5.update_xaxes(title_text="Hours since last poop")
fig5.update_yaxes(title_text="Size of poop")
fig5.update_layout(title = "Correlation between time since last poo and size of poo", font = dict(size = 16))
plot(fig5)
#%% scatter plot x axis = Time since las poo (delta t), y axis (Type of poo)
d2 = {'When did the poo occur?': df['When did the poo occur? '], 'Type of poo?': df['Type of poop 💩? '], 'time_since_last_poo': pd.Timedelta(0, unit='h')}
scatterplot_df2 = pd.DataFrame(data=d2)
scatterplot_df2 = scatterplot_df2.sort_values(by = ['When did the poo occur?']).reset_index(drop=True)
for i in range(1, len(df['When did the poo occur? '])-1):
scatterplot_df2.loc[i, 'time_since_last_poo'] = days_hours_minutes(scatterplot_df2['When did the poo occur?'][i] - scatterplot_df2['When did the poo occur?'][i-1])
scatterplot_df2.loc[0, 'time_since_last_poo'] = 0
scatterplot_df2.loc[scatterplot_df2['time_since_last_poo'].last_valid_index(), 'time_since_last_poo'] = 0
# Correlation line
dataforfitline3 = pd.DataFrame(data = scatterplot_df2['time_since_last_poo'])
dataforfitline3[1] = scatterplot_df2['Type of poo?']
dataforfitline3 = dataforfitline3.sort_values(by = ['time_since_last_poo']).reset_index(drop=True)
slope, intercept, r_value, p_value, std_err = stats.linregress(dataforfitline3.astype(float))
line = slope*scatterplot_df2['time_since_last_poo'] + intercept
fig6 = go.Figure(data=go.Scatter(x = scatterplot_df2['time_since_last_poo'],
y = scatterplot_df2['Type of poo?'],
mode = 'markers',
text = scatterplot_df2['When did the poo occur?'],
hovertemplate = "%{text}"))
fig6.add_trace(go.Scatter(x = scatterplot_df2['time_since_last_poo'], y = line, mode = 'lines', name = 'R\u00b2 = ' + round(r_value**2,2).astype(str)))
fig6.update_xaxes(title_text = "Hours since last poop")
fig6.update_yaxes(title_text = "Type of poop")
fig6.update_layout(title = "Correlation between time since last poo and type of poo", font = dict(size = 16))
plot(fig6)
# %% Calendar plot of each day and number of poos, darker colour for more poos
# Number of poos for each day
Num_of_poos = pd.DataFrame()
j = 0
for i in df['When did the poo occur? '].dt.strftime("%x").unique():
Num_of_poos.loc[j, 'Date'] = i
Num_of_poos.loc[j, 'Day'] = pd.to_datetime(i).strftime("%d")
Num_of_poos.loc[j, 'Month'] = pd.to_datetime(i).strftime("%b")
Num_of_poos.loc[j, 'Count'] = (df['When did the poo occur? '].dt.strftime("%x") == i).sum()
j += 1
days = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun']
months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']
total_poos_in_month = []
plot_titles = []
j = 0
for i in months:
total_poos_in_month.append(int(Num_of_poos['Count'][Num_of_poos['Month'] == i].sum()))
plot_titles.append(i + '<br>Total poopies = ' + str(total_poos_in_month[j]))
j += 1
fig7 = make_subplots(rows = 2, cols = 6, shared_yaxes = True, subplot_titles = plot_titles)
year = 2020
row_num = 1
col_num = 0
for month in months:
col_num += 1
if col_num > 6:
col_num = 1
row_num = 2
MyMonthData = calendar.monthcalendar(2020, strptime(month, '%b').tm_mon)
z = MyMonthData[::-1]
m = 0
for i in z:
n = 0
for j in i:
if j == 0:
z[m].pop(n)
z[m].insert(n, '')
elif any((Num_of_poos['Day'] == str(j).zfill(2)) & (Num_of_poos['Month'] == month)) == False:
z[m].pop(n)
z[m].insert(n, 0)
else:
z[m].pop(n)
z[m].insert(n, int(Num_of_poos.loc[(Num_of_poos['Day'] == str(j).zfill(2)) & (Num_of_poos['Month'] == month), 'Count']))
n += 1
m += 1
name = []
for a in calendar.Calendar().monthdatescalendar(year, strptime(month, '%b').tm_mon):
for b in a:
name.append(b.strftime("%d %b %Y"))
name = np.reshape([inner for inner in name], (len(MyMonthData), 7))
name = name[::-1]
fig7.add_trace(go.Heatmap(
x = days,
y = list(range(len(MyMonthData), 0)),
z = z,
meta = name,
hovertemplate = 'Date: %{meta} <br>Number of poos: %{z}<extra></extra>',
xgap = 1, ygap = 1,
zmin = 0, zmax = max(Num_of_poos['Count']),
# colorscale = "turbid"),
colorscale = [
[0, 'rgb(249, 238, 229)'], # 0 for the prettiness
[0.14, 'rgb(249, 230, 217)'], # 0
[0.29, 'rgb(204, 153, 102)'], # 1
[0.43, 'rgb(153, 102, 51)'], # 2
[0.57, 'rgb(115, 77, 38)'], # 3
[0.71, 'rgb(77, 51, 25)'], # 4
[1, 'rgb(38, 26, 13)']]), # 5
row = row_num, col = col_num)
fig7['layout'].update(plot_bgcolor = 'white',
title_text = "Poopy calendar",
yaxis_showticklabels = False,
yaxis7_showticklabels = False,
font = dict(size = 16))
plot(fig7)
# add % of that months poos for each day in hovertemplate
# %% Calendar plot of each day and a function of type/number/size of poos, darker colour for worse poos
# Correlation line
dataforfitline = np.zeros([np.size(scatterplot_df,0), 1])
j = 0
for i in scatterplot_df['Size of poo?']:
if i == 'Small':
dataforfitline[j] = 1
if i == 'Medium':
dataforfitline[j] = 2
if i == 'Poonarmi':
dataforfitline[j] = 3
j += 1
# Number of poos for each day
Num_type_of_poos = pd.DataFrame()
j = 0
for i in df['When did the poo occur? '].dt.strftime("%x").unique():
Num_type_of_poos.loc[j, 'Date'] = i
Num_type_of_poos.loc[j, 'Day'] = pd.to_datetime(i).strftime("%d")
Num_type_of_poos.loc[j, 'Month'] = pd.to_datetime(i).strftime("%b")
Num_type_of_poos.loc[j, 'Count'] = (df['When did the poo occur? '].dt.strftime("%x") == i).sum()
Num_type_of_poos.loc[j, 'Type'] = np.abs(int(df['Type of poop 💩? '][j]) - 4)
Num_type_of_poos.loc[j, 'Size'] = dataforfitline[j]
# Num_type_of_poos.loc[j, 'Size'] = df['Size of poo? '][j]
Num_type_of_poos.loc[j, 'Func_data'] = (Num_type_of_poos.loc[j, 'Count'] + Num_type_of_poos.loc[j, 'Type']) * Num_type_of_poos.loc[j, 'Size']
j += 1
days = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun']
months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']
#
#total_poos_in_month = []
#plot_titles = []
#j = 0
#for i in months:
# total_poos_in_month.append(int(Num_type_of_poos['Count'][Num_type_of_poos['Month'] == i].sum()))
# plot_titles.append(i + '<br>Total poopies = ' + str(total_poos_in_month[j]))
# j += 1
fig8 = make_subplots(rows = 2, cols = 6, shared_yaxes = True, subplot_titles = months)
year = 2020
row_num = 1
col_num = 0
for month in months:
col_num += 1
if col_num > 6:
col_num = 1
row_num = 2
MyMonthData = calendar.monthcalendar(2020, strptime(month, '%b').tm_mon)
z = MyMonthData[::-1]
m = 0
for i in z:
n = 0
for j in i:
if j == 0:
z[m].pop(n)
z[m].insert(n, '')
elif any((Num_type_of_poos['Day'] == str(j).zfill(2)) & (Num_type_of_poos['Month'] == month)) == False:
z[m].pop(n)
z[m].insert(n, 0)
else:
z[m].pop(n)
z[m].insert(n, int(Num_type_of_poos.loc[(Num_type_of_poos['Day'] == str(j).zfill(2)) & (Num_type_of_poos['Month'] == month), 'Func_data']))
n += 1
m += 1
name = []
for a in calendar.Calendar().monthdatescalendar(year, strptime(month, '%b').tm_mon):
for b in a:
name.append(b.strftime("%d %b %Y"))
name = np.reshape([inner for inner in name], (len(MyMonthData), 7))
name = name[::-1]
fig8.add_trace(go.Heatmap(
x = days,
y = list(range(len(MyMonthData), 0)),
z = z,
meta = name,
hovertemplate = 'Date: %{meta} <br>Poo impact: %{z}<extra></extra>',
xgap = 1, ygap = 1,
zmin = 0, zmax = max(Num_type_of_poos['Func_data']),
# colorscale = "turbid"),
colorscale = [
[0, 'rgb(249, 230, 217)'], # 0
[0.2, 'rgb(204, 153, 102)'], # 1
[0.4, 'rgb(153, 102, 51)'], # 2
[0.6, 'rgb(115, 77, 38)'], # 3
[0.8, 'rgb(80, 54, 28)'], # 4
[1, 'rgb(38, 26, 13)']]), # 5
row = row_num, col = col_num)
fig8['layout'].update(plot_bgcolor = 'white',
title_text = "Poopy calendar - Function of number of, size of, and type of poos",
yaxis_showticklabels = False,
yaxis7_showticklabels = False,
font = dict(size = 16))
plot(fig8)
# %% Distribution of poos on stool scale per day
days = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun']
# Remove 'Type ' before the number
df['Type of poop 💩? '] = df['Type of poop 💩? '].str.replace('Type ', '')
Date_column = df['When did the poo occur? '].dt.strftime("%a")
Total_poos = len(df['Type of poop 💩? '])
ydata = []
for day in days:
ydata.append((len(df['Type of poop 💩? '][Date_column == day])/Total_poos)*100)
fig9 = go.Figure()
fig9.add_trace(go.Bar(x = days,
y = ydata,
hovertemplate = '%{y:.1f}%<extra></extra>',
name = day,
showlegend = False,
marker_color = ('rgb(166,86,50)')))
fig9.update_layout(title = "Poo distribution by day", font = dict(size = 16))
fig9.update_yaxes(range=[0, 20], ticks = "inside", title = "Percentage of poos / %")
fig9.update_xaxes(title = "Day of week")
plot(fig9)
#should make this a stacked bar chart of type of poo stacked with the total number of poos as the overall height.
#%% Most frequent time of day
timerange = ['00', '01', '02', '03', '04', '05', '06', '07', '08', '09', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19', '20', '21', '22', '23']
X_titles = [t + ':00' for t in timerange]
# Remove 'Type ' before the number
df['Type of poop 💩? '] = df['Type of poop 💩? '].str.replace('Type ', '')
Time_column = df['When did the poo occur? '].dt.strftime("%H")
Total_poos = len(df['Type of poop 💩? '])
ydata = []
for t in timerange:
ydata.append((len(df['Type of poop 💩? '][Time_column == t])/Total_poos)*100)
fig10 = go.Figure()
fig10.add_trace(go.Bar(x = timerange,
y = ydata,
hovertemplate = '%{y:.1f}%<extra></extra>',
showlegend = False,
marker_color = ('rgb(166,86,50)')))
fig10.update_layout(title = "Poo distribution by time", font = dict(size = 16))
fig10.update_yaxes(range=[0, 20], ticks = "inside", title = "Percentage of poos / %")
fig10.update_xaxes(ticks = "inside", title = "Time of day", tickmode = 'array', tickvals = [int(t) for t in timerange], ticktext = X_titles)
plot(fig10)
# %% Distribution by type
Type_of_poop = [str(i) for i in range(1,8)] # 1 to 7
# Remove 'Type ' before the number
df['Type of poop 💩? '] = df['Type of poop 💩? '].str.replace('Type ', '')
Total_poos = len(df['Type of poop 💩? '])
ydata = []
for poo in Type_of_poop:
ydata.append((sum(df['Type of poop 💩? '] == poo)/Total_poos)*100)
fig11 = go.Figure()
fig11.add_trace(go.Bar(x = Type_of_poop,
y = ydata,
hovertemplate = '%{y:.1f}%<extra></extra>',
showlegend = False,
marker_color = ('rgb(166,86,50)')))
fig11.update_layout(title = "Poo distribution by type", font = dict(size = 16))
fig11.update_yaxes(range=[0, 60], ticks = "inside", title = "Percentage of poos / %")
fig11.update_xaxes(title = "Type of poo")
plot(fig11)
# %% Distribution by type excluding Jan and Feb
Type_of_poop = [str(i) for i in range(1,8)] # 1 to 7
months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']
# Remove 'Type ' before the number
df['Type of poop 💩? '] = df['Type of poop 💩? '].str.replace('Type ', '')
Total_poos = len(df['Type of poop 💩? '])
ydata = []
for poo in Type_of_poop:
ydata.append(sum(np.logical_and(df['Type of poop 💩? '] == poo, df['When did the poo occur? '].dt.strftime("%m") > '02')/Total_poos)*100)
fig12 = go.Figure()
fig12.add_trace(go.Bar(x = Type_of_poop,
y = ydata,
hovertemplate = '%{y:.1f}%<extra></extra>',
showlegend = False,
marker_color = ('rgb(166,86,50)')))
fig12.update_layout(title = "Poo distribution by type (excluding Jan and Feb)", font = dict(size = 16))
fig12.update_yaxes(range=[0, 60], ticks = "inside", title = "Percentage of poos / %")
fig12.update_xaxes(title = "Type of poo")
plot(fig12)
# %% Poo: The Musical
# 1812 Overture
p = vlc.MediaPlayer("1812 overture - Cut2.mp3")
p.play()
# Use Rain drop style visulisation
#def plot_the_poos():
# Remove 'Type ' before the number
df['Type of poop 💩? '] = df['Type of poop 💩? '].str.replace('Type ', '')
if df['Size of poo? '][0] != 1 and df['Size of poo? '][0] != 2 and df['Size of poo? '][0] != 3:
df['Size of poo? '].replace(['Small', 'Medium', 'Poonarmi'], [1, 2, 3], inplace = True)
df = df.sort_values(by=['When did the poo occur? '], ascending = True)
# Number of poos for each day
Overture_of_poos = pd.DataFrame()
j = 0
for i in df['When did the poo occur? '].dt.strftime("%x").unique():
Overture_of_poos.loc[j, 'Date'] = i
Overture_of_poos.loc[j, 'Count'] = (df['When did the poo occur? '].dt.strftime("%x") == i).sum()
Overture_of_poos.loc[j, 'Poo impact'] = 1
Poo_type = df['Type of poop 💩? '][df['When did the poo occur? '].dt.strftime("%x") == i]
Poo_size = df['Size of poo? '][df['When did the poo occur? '].dt.strftime("%x") == i]
for a in Poo_type.index:
Overture_of_poos.loc[j, 'Poo impact'] += abs(int(Poo_type[a])-4) * Poo_size[a]
j += 1
# Fixing random state for reproducibility
np.random.seed(3)
# Create new Figure and an Axes which fills it.
fig = plt.figure(figsize=(7, 6))
ax = fig.add_axes([0, 0, 1, 1], frameon=False)
ax.set_xlim(0, 1), ax.set_xticks([])
ax.set_ylim(0, 1), ax.set_yticks([])
# Create rain data
n_drops = len(Overture_of_poos)
rain_drops = np.zeros(n_drops, dtype=[('position', float, 2),
('size', float, 1),
('growth', float, 1),
('color', float, 4)])
# Initialize the raindrops in random positions and with random growth rates.
rain_drops['position'] = np.random.uniform(0, 1, (n_drops, 2))
# Construct the scatter which we will update during animation
# as the raindrops develop.
scat = ax.scatter(rain_drops['position'][:, 0], rain_drops['position'][:, 1],
s = rain_drops['size'], lw = 0.5, edgecolors = 'white', facecolors = 'white')
#rain_drops['growth'] = 50 # np.random.uniform(50, 200, n_drops)
rain_drops['color'] = (102/255, 51/255, 0, 1)
def update(frame_number):
# Get an index which we can use to re-spawn the oldest raindrop.
current_index = frame_number % n_drops
# Make all colors more transparent as time progresses.
rain_drops['color'][:, 3] -= 0.05 # 1.0/len(rain_drops)
rain_drops['color'][:, 3] = np.clip(rain_drops['color'][:, 3], 0, 1)
# Make all circles bigger.
rain_drops['size'] += rain_drops['growth']
# Pick a new position for oldest rain drop, resetting its size, color and growth factor.
rain_drops['position'][current_index] = np.random.uniform(0, 1, 2)
rain_drops['size'][current_index] = Overture_of_poos['Poo impact'][current_index] * 200
rain_drops['color'][current_index] = (102/255, 51/255, 0, 1)
rain_drops['growth'][current_index] = rain_drops['size'][current_index]/10 # np.random.uniform(50, 200)
# Update the scatter collection, with the new colors, sizes and positions.
scat.set_edgecolors(rain_drops['color'])
scat.set_facecolors(rain_drops['color'])
scat.set_sizes(rain_drops['size'])
scat.set_offsets(rain_drops['position'])
# New text
style = dict(size = 20, color = 'black')
day_of_month = dt.datetime.strptime(Overture_of_poos['Date'][current_index], '%m/%d/%y').strftime("%d")
month = dt.datetime.strptime(Overture_of_poos['Date'][current_index], '%m/%d/%y').strftime("%B")
my_text = ax.text(0.8, 0.05, str(day_of_month) + " " + str(month), ha='center', **style)
plt.pause(0.2) # 54 bpm at 4/4
# Clear old text
my_text.remove()
# Construct the animation, using the update function as the animation director.
animation = FuncAnimation(fig, update, interval = 30)
plt.show()
#%%
p.stop()
#%% Poo stats
# Remove 'Type ' before the number
df['Type of poop 💩? '] = df['Type of poop 💩? '].str.replace('Type ', '')
# Number of poos for each day
Num_type_of_poos = pd.DataFrame()
j = 0
for i in df['When did the poo occur? '].dt.strftime("%x").unique():
Num_type_of_poos.loc[j, 'Date'] = i
Num_type_of_poos.loc[j, 'Day'] = pd.to_datetime(i).strftime("%d")
Num_type_of_poos.loc[j, 'Month'] = pd.to_datetime(i).strftime("%b")
Num_type_of_poos.loc[j, 'Count'] = (df['When did the poo occur? '].dt.strftime("%x") == i).sum()
Num_type_of_poos.loc[j, 'Type'] = np.abs(int(df['Type of poop 💩? '][j]) - 4)
Num_type_of_poos.loc[j, 'Size'] = int(df['Size of poo? '][j])
Num_type_of_poos.loc[j, 'Func_data'] = (Num_type_of_poos.loc[j, 'Count'] + Num_type_of_poos.loc[j, 'Type']) * Num_type_of_poos.loc[j, 'Size']
j += 1
# Max number of poos in a day, week, month
Max_poopys = np.max(Num_type_of_poos['Count'])
print('Max poos in a day =', Max_poopys)
# Number of sloppy poonarmi's in the year
Num_sloppy_poonarmis = | np.logical_and(Num_type_of_poos['Type'] == 3, Num_type_of_poos['Size'] == 3) | numpy.logical_and |
""" Features for optically imaging of samples
Contains features which performs physical simulations of optical devices to
create camera images of samples.
Classes
-------
Microscope
Image a sample using an optical system.
Optics
Abstract base optics class.
Fluorescence
Optical device for fluorescenct imaging.
Brightfield
Images coherently illuminated samples.
"""
from pint.quantity import Quantity
from deeptrack.backend.units import ConversionTable
from deeptrack.properties import propagate_data_to_dependencies
import numpy as np
from .features import DummyFeature, Feature, StructuralFeature
from .image import Image, pad_image_to_fft
from .types import ArrayLike, PropertyLike
from scipy.ndimage import convolve
from . import units as u
from deeptrack import image
class Microscope(StructuralFeature):
"""Image a sample using an optical system.
Wraps a feature-set defining a sample and a feature-set defining the optics.
Parameters
----------
sample : Feature
A feature-set resolving a list of images describing the sample to be imaged
objective : Feature
A feature-set defining the optical device that images the sample
"""
__distributed__ = False
def __init__(self, sample: Feature, objective: Feature, **kwargs):
super().__init__(**kwargs)
self._sample = self.add_feature(sample)
self._objective = self.add_feature(objective)
def get(self, image, **kwargs):
# Grab properties from the objective to pass to the sample
additional_sample_kwargs = self._objective.properties()
propagate_data_to_dependencies(self._sample, **additional_sample_kwargs)
list_of_scatterers = self._sample()
if not isinstance(list_of_scatterers, list):
list_of_scatterers = [list_of_scatterers]
volume_samples = [
scatterer
for scatterer in list_of_scatterers
if not scatterer.get_property("is_field", default=False)
]
field_samples = [
scatterer
for scatterer in list_of_scatterers
if scatterer.get_property("is_field", default=False)
]
sample_volume, limits = _create_volume(
volume_samples, **additional_sample_kwargs
)
sample_volume = Image(sample_volume)
for scatterer in volume_samples + field_samples:
sample_volume.merge_properties_from(scatterer)
propagate_data_to_dependencies(
self._objective,
limits=limits,
fields=field_samples,
)
imaged_sample = self._objective.resolve(sample_volume)
# Merge with input
if not image:
return imaged_sample
if not isinstance(image, list):
image = [image]
for i in range(len(image)):
image[i].merge_properties_from(imaged_sample)
return image
# OPTICAL SYSTEMS
class Optics(Feature):
"""Abstract base optics class.
Provides structure and methods common for most optical devices.
Parameters
----------
NA : float
The NA of the limiting aperature.
wavelength : float
The wavelength of the scattered light in meters.
magnification : float
The magnification of the optical system.
resolution : array_like[float (, float, float)]
The distance between pixels in the camera. A third value can be
included to define the resolution in the z-direction.
refractive_index_medium : float
The refractive index of the medium.
padding : array_like[int, int, int, int]
Pads the sample volume with zeros to avoid edge effects.
output_region : array_like[int, int, int, int]
The region of the image to output (x,y,width,height). Default
None returns entire image.
pupil : Feature
A feature-set resolving the pupil function at focus. The feature-set
receive an unaberrated pupil as input.
"""
__conversion_table__ = ConversionTable(
wavelength=(u.meter, u.meter),
resolution=(u.meter, u.meter),
voxel_size=(u.meter, u.meter),
)
def __init__(
self,
NA: PropertyLike[float] = 0.7,
wavelength: PropertyLike[float] = 0.66e-6,
magnification: PropertyLike[float] = 10,
resolution: PropertyLike[float or ArrayLike[float]] = 1e-6,
refractive_index_medium: PropertyLike[float] = 1.33,
padding: PropertyLike[ArrayLike[int]] = (10, 10, 10, 10),
output_region: PropertyLike[ArrayLike[int]] = (0, 0, 128, 128),
pupil: Feature = None,
illumination: Feature = None,
**kwargs
):
def get_voxel_size(resolution, magnification):
return np.ones((3,)) * resolution / magnification
def get_pixel_size(resolution, magnification):
pixel_size = resolution / magnification
if isinstance(pixel_size, Quantity):
return pixel_size.to(u.meter).magnitude
else:
return pixel_size
super().__init__(
NA=NA,
wavelength=wavelength,
refractive_index_medium=refractive_index_medium,
magnification=magnification,
resolution=resolution,
padding=padding,
output_region=output_region,
voxel_size=get_voxel_size,
pixel_size=get_pixel_size,
limits=None,
fields=None,
**kwargs
)
self.pupil = self.add_feature(pupil) if pupil else DummyFeature()
self.illumination = (
self.add_feature(illumination) if illumination else DummyFeature()
)
def _pupil(
self,
shape,
NA,
wavelength,
refractive_index_medium,
voxel_size,
include_aberration=True,
defocus=0,
**kwargs
):
# Calculates the pupil at each z-position in defocus.
shape = np.array(shape)
# Pupil radius
R = NA / wavelength * np.array(voxel_size)[:2]
x_radius = R[0] * shape[0]
y_radius = R[1] * shape[1]
x = (np.linspace(-(shape[0] / 2), shape[0] / 2 - 1, shape[0])) / x_radius + 1e-8
y = (np.linspace(-(shape[1] / 2), shape[1] / 2 - 1, shape[1])) / y_radius + 1e-8
W, H = np.meshgrid(y, x)
RHO = W ** 2 + H ** 2
RHO[RHO > 1] = 1
pupil_function = ((RHO < 1) * 1.0).astype(np.complex)
# Defocus
z_shift = (
2
* np.pi
* refractive_index_medium
/ wavelength
* voxel_size[2]
* np.sqrt(1 - (NA / refractive_index_medium) ** 2 * RHO)
)
# Downsample the upsampled pupil
pupil_function[np.isnan(pupil_function)] = 0
pupil_function[np.isinf(pupil_function)] = 0
pupil_function_is_nonzero = pupil_function != 0
if include_aberration:
pupil = self.pupil
if isinstance(pupil, Feature):
pupil_function = pupil(pupil_function)
elif isinstance(pupil, np.ndarray):
pupil_function *= pupil
pupil_functions = []
for z in defocus:
pupil_at_z = Image(pupil_function)
pupil_at_z[pupil_function_is_nonzero] *= np.exp(
1j * z_shift[pupil_function_is_nonzero] * z
)
pupil_functions.append(pupil_at_z)
return pupil_functions
def _pad_volume(
self, volume, limits=None, padding=None, output_region=None, **kwargs
):
if limits is None:
limits = np.zeros((3, 2))
new_limits = np.array(limits)
output_region = np.array(output_region)
# Replace None entries with current limit
output_region[0] = (
output_region[0] if not output_region[0] is None else new_limits[0, 0]
)
output_region[1] = (
output_region[1] if not output_region[1] is None else new_limits[0, 1]
)
output_region[2] = (
output_region[2] if not output_region[2] is None else new_limits[1, 0]
)
output_region[3] = (
output_region[3] if not output_region[3] is None else new_limits[1, 1]
)
for i in range(2):
new_limits[i, :] = (
np.min([new_limits[i, 0], output_region[i] - padding[1]]),
np.max(
[
new_limits[i, 1],
output_region[i + 2] + padding[i + 2],
]
),
)
new_volume = np.zeros(
np.diff(new_limits, axis=1)[:, 0].astype(np.int32),
dtype=np.complex,
)
old_region = (limits - new_limits).astype(np.int32)
limits = limits.astype(np.int32)
new_volume[
old_region[0, 0] : old_region[0, 0] + limits[0, 1] - limits[0, 0],
old_region[1, 0] : old_region[1, 0] + limits[1, 1] - limits[1, 0],
old_region[2, 0] : old_region[2, 0] + limits[2, 1] - limits[2, 0],
] = volume
return new_volume, new_limits
def __call__(self, sample, **kwargs):
return Microscope(sample, self, **kwargs)
class Fluorescence(Optics):
"""Optical device for fluorescenct imaging
Images samples by creating a discretized volume, where each pixel
represents the intensity of the light emitted by fluorophores in
the the voxel.
Parameters
----------
NA : float
The NA of the limiting aperature.
wavelength : float
The wavelength of the scattered light in meters.
magnification : float
The magnification of the optical system.
resolution : array_like[float (, float, float)]
The distance between pixels in the camera. A third value can be
included to define the resolution in the z-direction.
refractive_index_medium : float
The refractive index of the medium.
padding : array_like[int, int, int, int]
Pads the sample volume with zeros to avoid edge effects.
output_region : array_like[int, int, int, int]
The region of the image to output (x,y,width,height). Default
None returns entire image.
pupil : Feature
A feature-set resolving the pupil function at focus. The feature-set
receive an unaberrated pupil as input.
"""
def get(self, illuminated_volume, limits, **kwargs):
"""Convolves the image with a pupil function"""
# Pad volume
padded_volume, limits = self._pad_volume(
illuminated_volume, limits=limits, **kwargs
)
# Extract indexes of the output region
pad = kwargs.get("padding", (0, 0, 0, 0))
output_region = np.array(kwargs.get("output_region", (None, None, None, None)))
output_region[0] = (
None
if output_region[0] is None
else int(output_region[0] - limits[0, 0] - pad[0])
)
output_region[1] = (
None
if output_region[1] is None
else int(output_region[1] - limits[1, 0] - pad[1])
)
output_region[2] = (
None
if output_region[2] is None
else int(output_region[2] - limits[0, 0] + pad[2])
)
output_region[3] = (
None
if output_region[3] is None
else int(output_region[3] - limits[1, 0] + pad[3])
)
padded_volume = padded_volume[
output_region[0] : output_region[2],
output_region[1] : output_region[3],
:,
]
z_limits = limits[2, :]
output_image = Image(np.zeros((*padded_volume.shape[0:2], 1)))
index_iterator = range(padded_volume.shape[2])
# Get planes in volume where not all values are 0.
z_iterator = np.linspace(
z_limits[0],
z_limits[1],
num=padded_volume.shape[2],
endpoint=False,
)
zero_plane = np.all(padded_volume == 0, axis=(0, 1), keepdims=False)
z_values = z_iterator[~zero_plane]
# Further pad image to speed up fft
volume = pad_image_to_fft(padded_volume, axes=(0, 1))
pupils = self._pupil(volume.shape[:2], defocus=z_values, **kwargs)
pupil_iterator = iter(pupils)
# Loop through voluma and convole sample with pupil function
for i, z in zip(index_iterator, z_iterator):
if zero_plane[i]:
continue
image = volume[:, :, i]
pupil = Image(next(pupil_iterator))
psf = np.square(np.abs(np.fft.ifft2(np.fft.fftshift(pupil))))
optical_transfer_function = np.fft.fft2(psf)
fourier_field = np.fft.fft2(image)
convolved_fourier_field = fourier_field * optical_transfer_function
field = Image(np.fft.ifft2(convolved_fourier_field))
# Discard remaining imaginary part (should be 0 up to rounding error)
field = np.real(field)
output_image[:, :, 0] += field[
: padded_volume.shape[0], : padded_volume.shape[1]
]
output_image = output_image[pad[0] : -pad[2], pad[1] : -pad[3]]
try:
output_image.properties = illuminated_volume.properties + pupil.properties
except UnboundLocalError:
output_image.properties = illuminated_volume.properties
return output_image
class Brightfield(Optics):
"""Images coherently illuminated samples.
Images samples by creating a discretized volume, where each pixel
represents the effective refractive index of that pixel. Light is
propagated through the sample iteratively by first propagating the
light in the fourier space, followed by a refractive index correction
in the real space.
Parameters
----------
illumination : Feature
Feature-set resolving the complex field entering the sample. Default
is a field with all values 1.
NA : float
The NA of the limiting aperature.
wavelength : float
The wavelength of the scattered light in meters.
magnification : float
The magnification of the optical system.
resolution : array_like[float (, float, float)]
The distance between pixels in the camera. A third value can be
included to define the resolution in the z-direction.
refractive_index_medium : float
The refractive index of the medium.
padding : array_like[int, int, int, int]
Pads the sample volume with zeros to avoid edge effects.
output_region : array_like[int, int, int, int]
The region of the image to output (x,y,width,height). Default
None returns entire image.
pupil : Feature
A feature-set resolving the pupil function at focus. The feature-set
receive an unaberrated pupil as input.
"""
__gpu_compatible__ = True
def get(self, illuminated_volume, limits, fields, **kwargs):
"""Convolves the image with a pupil function"""
# Pad volume
padded_volume, limits = self._pad_volume(
illuminated_volume, limits=limits, **kwargs
)
# Extract indexes of the output region
pad = kwargs.get("padding", (0, 0, 0, 0))
output_region = np.array(kwargs.get("output_region", (None, None, None, None)))
output_region[0] = (
None
if output_region[0] is None
else int(output_region[0] - limits[0, 0] - pad[0])
)
output_region[1] = (
None
if output_region[1] is None
else int(output_region[1] - limits[1, 0] - pad[1])
)
output_region[2] = (
None
if output_region[2] is None
else int(output_region[2] - limits[0, 0] + pad[2])
)
output_region[3] = (
None
if output_region[3] is None
else int(output_region[3] - limits[1, 0] + pad[3])
)
padded_volume = padded_volume[
output_region[0] : output_region[2],
output_region[1] : output_region[3],
:,
]
z_limits = limits[2, :]
output_image = Image(image.maybe_cupy(np.zeros((*padded_volume.shape[0:2], 1))))
index_iterator = range(padded_volume.shape[2])
z_iterator = np.linspace(
z_limits[0],
z_limits[1],
num=padded_volume.shape[2],
endpoint=False,
)
zero_plane = np.all(padded_volume == 0, axis=(0, 1), keepdims=False)
# z_values = z_iterator[~zero_plane]
volume = pad_image_to_fft(padded_volume, axes=(0, 1))
voxel_size = kwargs["voxel_size"]
pupils = self._pupil(
volume.shape[:2], defocus=[1], include_aberration=False, **kwargs
) + self._pupil(
volume.shape[:2], defocus=[-z_limits[1]], include_aberration=True, **kwargs
)
pupil_step = np.fft.fftshift(pupils[0])
light_in = image.maybe_cupy(np.ones(volume.shape[:2], dtype=np.complex))
light_in = self.illumination.resolve(light_in)
light_in = np.fft.fft2(light_in)
K = 2 * np.pi / kwargs["wavelength"]
field_z = [field.get_property("z") for field in fields]
field_offsets = [field.get_property("offset_z", default=0) for field in fields]
z = z_limits[1]
for i, z in zip(index_iterator, z_iterator):
light_in = light_in * pupil_step
to_remove = []
for idx, fz in enumerate(field_z):
if fz < z:
propagation_matrix = image.maybe_cupy(
self._pupil(
fields[idx].shape,
defocus=[z - fz - field_offsets[idx] / voxel_size[-1]],
include_aberration=False,
**kwargs
)[0]
)
propagation_matrix = propagation_matrix * np.exp(
1j
* voxel_size[-1]
* 2
* np.pi
/ kwargs["wavelength"]
* kwargs["refractive_index_medium"]
* (z - fz)
)
light_in += np.fft.fft2(fields[idx][:, :, 0]) * np.fft.fftshift(
propagation_matrix
)
to_remove.append(idx)
for idx in reversed(to_remove):
fields.pop(idx)
field_z.pop(idx)
field_offsets.pop(idx)
if zero_plane[i]:
continue
ri_slice = volume[:, :, i]
light = np.fft.ifft2(light_in)
light_out = light * np.exp(1j * ri_slice * voxel_size[-1] * K)
light_in = np.fft.fft2(light_out)
# Add remaining fields
for idx, fz in enumerate(field_z):
prop_dist = z - fz - field_offsets[idx] / voxel_size[-1]
propagation_matrix = image.maybe_cupy(
self._pupil(
fields[idx].shape,
defocus=[prop_dist],
include_aberration=False,
**kwargs
)[0]
)
propagation_matrix = propagation_matrix * np.exp(
-1j
* voxel_size[-1]
* 2
* np.pi
/ kwargs["wavelength"]
* kwargs["refractive_index_medium"]
* prop_dist
)
light_in += np.fft.fft2(fields[idx][:, :, 0]) * np.fft.fftshift(
propagation_matrix
)
light_in_focus = light_in * image.maybe_cupy(np.fft.fftshift(pupils[-1]))
output_image = np.fft.ifft2(light_in_focus)[
: padded_volume.shape[0], : padded_volume.shape[1]
]
output_image = np.expand_dims(output_image, axis=-1)
output_image = Image(output_image[pad[0] : -pad[2], pad[1] : -pad[3]])
if not kwargs.get("return_field", False):
output_image = np.square(np.abs(output_image))
output_image.properties = illuminated_volume.properties
return output_image
class IlluminationGradient(Feature):
"""Adds a gradient in the illumination
Parameters
----------
gradient : array_like[float, float]
Gradient of the plane to add to the amplitude of the field in pixels.
constant : float
Constant value to add to the amplitude of the field.
vmin : float
clips the amplitude of the field to be at least this value
vmax : float
clips the amplitude of the field to be at most this value
"""
def __init__(
self,
gradient: PropertyLike[ArrayLike[float]] = (0, 0),
constant: PropertyLike[float] = 0,
vmin: PropertyLike[float] = 0,
vmax: PropertyLike[float] = np.inf,
**kwargs
):
super().__init__(
gradient=gradient, constant=constant, vmin=vmin, vmax=vmax, **kwargs
)
def get(self, image, gradient, constant, vmin, vmax, **kwargs):
x = np.arange(image.shape[0])
y = np.arange(image.shape[1])
X, Y = np.meshgrid(y, x)
amplitude = X * gradient[0] + Y * gradient[1]
if image.ndim == 3:
amplitude = np.expand_dims(amplitude, axis=-1)
amplitude = np.clip(np.abs(image) + amplitude + constant, vmin, vmax)
image = amplitude * image / np.abs(image)
image[np.isnan(image)] = 0
return image
def _get_position(image, mode="corner", return_z=False):
# Extracts the position of the upper left corner of a scatterer
num_outputs = 2 + return_z
if mode == "corner" and image.size > 0:
import scipy.ndimage
shift = scipy.ndimage.measurements.center_of_mass(np.abs(image))
if np.isnan(shift).any():
shift = np.array(image.shape) / 2
else:
shift = np.zeros((num_outputs))
position = np.array(image.get_property("position", default=None))
# position[:2] = position[:2]
if position is None:
return position
if len(position) == 3:
if return_z:
return position - shift
else:
return position[0:2] - shift[0:2]
elif len(position) == 2:
if return_z:
outp = (
np.array([position[0], position[1], image.get_property("z", default=0)])
- shift
)
return outp
else:
return position - shift[0:2]
return position
def _create_volume(
list_of_scatterers,
pad=(0, 0, 0, 0),
output_region=(None, None, None, None),
refractive_index_medium=1.33,
**kwargs
):
# Converts a list of scatterers into a volume.
if not isinstance(list_of_scatterers, list):
list_of_scatterers = [list_of_scatterers]
volume = np.zeros((1, 1, 1), dtype=np.complex)
limits = None
OR = np.zeros((4,))
OR[0] = np.inf if output_region[0] is None else int(output_region[0] - pad[0])
OR[1] = -np.inf if output_region[1] is None else int(output_region[1] - pad[1])
OR[2] = np.inf if output_region[2] is None else int(output_region[2] + pad[2])
OR[3] = -np.inf if output_region[3] is None else int(output_region[3] + pad[3])
for scatterer in list_of_scatterers:
position = _get_position(scatterer, mode="corner", return_z=True)
if scatterer.get_property("intensity", None) is not None:
scatterer_value = scatterer.get_property("intensity")
elif scatterer.get_property("refractive_index", None) is not None:
scatterer_value = (
scatterer.get_property("refractive_index") - refractive_index_medium
)
else:
scatterer_value = scatterer.get_property("value")
scatterer = scatterer * scatterer_value
if limits is None:
limits = np.zeros((3, 2), dtype=np.int32)
limits[:, 0] = np.floor(position).astype(np.int32)
limits[:, 1] = np.floor(position).astype(np.int32) + 1
if (
position[0] + scatterer.shape[0] < OR[0]
or position[0] > OR[2]
or position[1] + scatterer.shape[1] < OR[1]
or position[1] > OR[3]
):
continue
padded_scatterer = Image(
np.pad(
scatterer,
[(2, 2), (2, 2), (2, 2)],
"constant",
constant_values=0,
)
)
padded_scatterer.merge_properties_from(scatterer)
scatterer = padded_scatterer
position = _get_position(scatterer, mode="corner", return_z=True)
shape = np.array(scatterer.shape)
if position is None:
RuntimeWarning(
"Optical device received an image without a position property. It will be ignored."
)
continue
splined_scatterer = | np.zeros_like(scatterer) | numpy.zeros_like |
import argparse
import csv
import datetime
import math
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import numpy as np
import os
import pandas as pd
import pickle
import shutil
import sys
import time
import warnings
import yaml
import torch
import torch.backends.cudnn as cudnn
import torch.distributed as distributed
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
import torchvision.datasets as dset
import torchvision.utils as vutils
from multiprocessing import Process
from torch.utils.data import TensorDataset
from tqdm import tqdm
try:
from torchvision.transforms.functional import resize, InterpolationMode
interp = InterpolationMode.NEAREST
except:
from torchvision.transforms.functional import resize
interp = 0
import dist_utils
import lib.utils as utils
from lib import layers
from lib.dataloader import get_dataloaders
from lib.multiscale import CNFMultiscale
from lib.regularization import get_regularization, append_regularization_to_log
from lib.regularization import append_regularization_keys_header, append_regularization_csv_dict
from lib.utils import logit_logpx_to_image_bpd, convert_base_from_10, vis_imgs_laps, convert_time_stamp_to_hrs, logpx_to_bpd
from misc import set_cnf_options, count_nfe, count_training_parameters, count_parameters
cudnn.benchmark = True
SOLVERS = ["dopri5", "bdf", "rk4", "midpoint", 'adams', 'explicit_adams', 'adaptive_heun', 'bosh3']
def get_args():
parser = argparse.ArgumentParser("Multi-Resolution Continuous Normalizing Flow")
# Mode
parser.add_argument("--mode", type=str, default="image", choices=["wavelet", "mrcnf"])
# Multi-res
parser.add_argument("--normal_resolution", type=int, default=64, help="Resolution at which z is standard normal. (def: 64)")
parser.add_argument('--std_scale', type=eval, default=True, choices=[True, False], help="Add AffineTx layer at end of CNF to scale output acc to z_std")
# Data
parser.add_argument("--data", type=str, default="mnist", choices=["mnist", "svhn", "cifar10", "lsun_church", "celebahq", "imagenet", "imagenet64_cf", "zap50k", "fashion_mnist"])
parser.add_argument("--data_path", default="./data/", help="mnist: `./data/`, cifar10: `./data/CIFAR10`, imagenet: `./data/ilsvrc2012.hdf5`")
parser.add_argument("--imagenet_classes", type=str, default="")
parser.add_argument("--nworkers", type=int, default=8)
parser.add_argument("--im_size", type=int, default=32)
parser.add_argument('--ds_idx_mod', type=int, default=None, help="In case we want to train on only subset of images, e.g. mod=10 => images [0, 1, ..., 9]")
parser.add_argument('--ds_idx_skip', type=int, default=0, help="In case we want to train on only subset of images, e.g. mod=10 and skip=10 => images [10, 11, ..., 19]")
parser.add_argument('--ds_length', type=int, default=None, help="Total length of dataset, to decide number of batches per epoch")
parser.add_argument('--test_ds_idx_mod', type=int, default=None, help="In case we want to test on only subset of images, e.g. mod=10 => images [0, 1, ..., 9]")
parser.add_argument('--test_ds_idx_skip', type=int, default=0, help="In case we want to test on only subset of images, e.g. mod=10 and skip=10 => images [10, 11, ..., 19]")
parser.add_argument('--test_ds_length', type=int, default=None, help="Total length of test dataset, to decide number of batches per epoch")
# Save
parser.add_argument("--save_path", type=str, default="experiments/cnf")
# Model
parser.add_argument("--dims", type=str, default="64,64,64")
parser.add_argument("--strides", type=str, default="1,1,1,1")
parser.add_argument("--num_blocks", type=str, default="2,2", help='Number of stacked CNFs, per scale. Should have 1 item, or max_scales number of items.')
parser.add_argument('--bn', type=eval, default=False, choices=[True, False], help="Add BN to coarse")
parser.add_argument("--layer_type", type=str, default="concat", choices=["ignore", "concat"])
parser.add_argument("--nonlinearity", type=str, default="softplus", choices=["tanh", "relu", "softplus", "elu", "swish", "square", "identity"])
parser.add_argument('--zero_last', type=eval, default=True, choices=[True, False])
# Data characteristics
parser.add_argument("--nbits", type=int, default=8)
parser.add_argument('--max_scales', type=int, default=2, help="# of scales for image pyramid")
parser.add_argument('--scale', type=int, default=0, help='freeze all parameters but this scale; start evaluating loss from this scale')
parser.add_argument("--add_noise", type=eval, default=True, choices=[True, False])
parser.add_argument("--tau", type=float, default=0.5)
parser.add_argument('--logit', type=eval, default=True, choices=[True, False])
parser.add_argument("--alpha", type=float, default=0.05, help="if logit is true, alpha is used to convert from pixel to logit (and back)")
parser.add_argument('--concat_input', type=eval, default=True, choices=[True, False], help="To concat the image input to odefunc or not.")
# ODE Solver
parser.add_argument('--solver', type=str, default='dopri5', choices=SOLVERS)
parser.add_argument('--atol', type=float, default=1e-5, help='only for adaptive solvers')
parser.add_argument('--rtol', type=float, default=1e-5, help='only for adaptive solvers')
parser.add_argument('--step_size', type=float, default=0.25, help='only for fixed step size solvers')
parser.add_argument('--first_step', type=float, default=0.166667, help='only for adaptive solvers')
# ODE Solver for test
parser.add_argument('--test_solver', type=str, default=None, choices=SOLVERS + [None])
parser.add_argument('--test_atol', type=float, default=None)
parser.add_argument('--test_rtol', type=float, default=None)
parser.add_argument('--test_step_size', type=float, default=None)
parser.add_argument('--test_first_step', type=float, default=None)
# ODE stop time
parser.add_argument('--time_length', type=float, default=1.0)
parser.add_argument('--train_T', type=eval, default=False)
parser.add_argument('--steer_b', type=float, default=0.0)
# Train
parser.add_argument('--joint', type=eval, default=False, choices=[True, False], help="Joint training of all scales (else train each scale separately)")
parser.add_argument("--num_epochs", type=int, default=100, help="# of epochs in case of JOINT training only.")
parser.add_argument("--batch_size", type=int, default=4)
parser.add_argument('--epochs_per_scale', type=str, default=None, help="# of epochs per scale in case NOT JOINT training; if not specified, will default to `num_epochs/max_scales`. Eg. `100` or `40,30,30`")
parser.add_argument("--batch_size_per_scale", type=str, default=None, help="Batch sizes to use for every scale. # mentioned can be 1, or must match max_scales. Will default to batch_size if not specified. Eg. `256` or `1024,512,256`")
parser.add_argument("--test_batch_size", type=int, default=-1)
parser.add_argument("--lr", type=float, default=0.001, help="LR of different scales")
parser.add_argument("--lr_per_scale", type=str, default=None, help="LR of different scales; if not specified, will default to `lr")
parser.add_argument("--lr_warmup_iters", type=int, default=1000)
parser.add_argument('--lr_gamma', type=float, default=0.999)
parser.add_argument('--lr_scheduler', type=str, choices=["plateau", "step", "multiplicative"], default="plateau")
parser.add_argument('--plateau_factor', type=float, default=0.1)
parser.add_argument('--plateau_patience', type=int, default=4)
parser.add_argument('--plateau_threshold', type=float, default=0.0001)
parser.add_argument('--plateau_threshold_mode', type=str, choices=["abs", "rel"], default="abs")
parser.add_argument('--lr_step', type=int, default=10, help="Not valid for plateau or multiplicative")
parser.add_argument('--min_lr', type=float, default=1.01e-8, help="Min LR")
parser.add_argument('--min_lr_max_iters', type=int, default=100, help="Max iters to run at min_lr")
parser.add_argument('--optimizer', type=str, default='adam', choices=['adam', 'sgd'])
parser.add_argument("--weight_decay", type=float, default=0.0)
parser.add_argument("--max_grad_norm", type=float, default=100.0, help="Max norm of gradients")
parser.add_argument("--grad_norm_patience", type=int, default=10, help="Max norm of gradients")
# Regularizations
parser.add_argument('--kinetic-energy', type=float, default=None, help="int_t ||f||_2^2")
parser.add_argument('--jacobian-norm2', type=float, default=None, help="int_t ||df/dx||_F^2")
parser.add_argument('--div_samples',type=int, default=1)
parser.add_argument("--divergence_fn", type=str, default="approximate", choices=["brute_force", "approximate"])
# Distributed training
parser.add_argument('--distributed', action='store_true', help='Run distributed training')
parser.add_argument('--dist-url', default='env://', type=str,
help='url used to set up distributed training')
parser.add_argument('--dist-backend', default='nccl', type=str, help='distributed backend')
parser.add_argument('--local_rank', default=0, type=int,
help='Used for multi-process training. Can either be manually set ' +
'or automatically set by using \'python -m multiproc\'.')
parser.add_argument("--resume", type=str, default=None, help='path to saved check point')
parser.add_argument("--ckpt_to_load", type=str, nargs='?', default="", help='path to saved check point to load but not resume training from.')
parser.add_argument("--val_freq", type=int, default=1)
parser.add_argument("--save_freq_within_epoch", type=int, default=0, help="(>=0) Number of ITERATIONS(!) within an epoch in which to save model, calc metrics, visualize samples")
parser.add_argument('--disable_viz', action='store_true', help="Disable viz")
parser.add_argument("--plot_freq", type=int, default=1)
parser.add_argument("--log_freq", type=int, default=10)
parser.add_argument("--vis_n_images", type=int, default=100)
parser.add_argument('--disable_cuda', action='store_true')
parser.add_argument('--inference', type=eval, default=False, choices=[True, False])
parser.add_argument('--disable_date', action='store_true')
parser.add_argument('--copy_scripts', type=eval, default=True, choices=[True, False], help="Copy this and other scripts to save directory.")
parser.add_argument('--seed', type=int, default=42)
parser.add_argument('-f', help="DUMMY arg for Jupyter")
try:
args = parser.parse_args()
except:
args = parser.parse_args(args=[])
args.command = 'python ' + ' '.join(sys.argv)
args.conv = True
args.im_ch = 1 if args.data == 'mnist' else 3
if args.inference:
args.copy_scripts = False
assert args.steer_b < args.time_length
args.imagenet_classes = list(map(int, args.imagenet_classes.split(","))) if len(args.imagenet_classes) > 0 else []
if args.data == 'mnist':
args.alpha = 1e-6
else:
args.alpha = 0.05
if not args.disable_date:
args.save_path = os.path.join(os.path.dirname(args.save_path), f'{datetime.datetime.now():%Y%m%d_%H%M%S}_{os.path.basename(args.save_path)}')
args.num_blocks = [int(args.num_blocks)] * args.max_scales if ',' not in args.num_blocks else list(map(int, args.num_blocks.split(",")))
d, dl, st = args.dims.split(',')[0], len(args.dims.split(',')), args.strides.split(',')[0]
args.save_path = f'{args.save_path}_M{args.mode[0]}_b{args.nbits}_sc{args.max_scales}_{args.scale}_d{d}_{dl}_st{st}_bl' + (f"{args.num_blocks}" if ',' not in args.num_blocks else "_".join(args.num_blocks.split(",")))
args.save_path += f'_S{args.solver[0]+args.solver[-1]}_{args.optimizer}_ke{args.kinetic_energy}_jf{args.jacobian_norm2}_st{args.steer_b}_n{str(args.add_noise)[0]}_GN{args.max_grad_norm}'
args.save_path += f'_nres{args.normal_resolution}'
if args.std_scale:
args.save_path += f"std"
if args.joint:
args.save_path += f'_j{str(args.joint)[0]}_e{args.num_epochs}_bs{args.batch_size}_lr{args.lr}'
if args.test_batch_size == -1:
args.test_batch_size = args.batch_size
else:
# epochs
if args.epochs_per_scale is None:
args.save_path += f'_j{str(args.joint)[0]}_ep{int(args.num_epochs / args.max_scales)}'
args.epochs_per_scale = [int(args.num_epochs / args.max_scales)] * args.max_scales
else:
args.save_path += f'_j{str(args.joint)[0]}_es{"_".join(args.epochs_per_scale.split(","))}'
args.epochs_per_scale = [int(args.epochs_per_scale)] * args.max_scales if ',' not in args.epochs_per_scale else list(map(int, args.epochs_per_scale.split(",")))
assert len(args.epochs_per_scale) == args.max_scales, f"Specify 1 or max_scales # of epochs_per_scale! Given {args.epochs_per_scale}, max_scales {args.max_scales}"
args.num_epochs = sum(args.epochs_per_scale)
# batch size
if args.batch_size_per_scale is None:
args.save_path += f'_bs{args.batch_size}'
args.batch_size_per_scale = [args.batch_size] * args.max_scales
else:
args.save_path += f'_bs{"_".join(args.batch_size_per_scale.split(","))}'
args.batch_size_per_scale = [int(args.batch_size_per_scale)] * args.max_scales if ',' not in args.batch_size_per_scale else list(map(int, args.batch_size_per_scale.split(",")))
assert len(args.batch_size_per_scale) == args.max_scales, f"Specify 1 or max_scales # of batch_size_per_scale! Given {args.batch_size_per_scale}, max_scales {args.max_scales}"
if args.test_batch_size == -1:
args.test_batch_size = min(args.batch_size_per_scale)
# LR
if args.lr_per_scale is None:
args.save_path += f'_lr{args.lr}'
args.lr_per_scale = [args.lr] * args.max_scales
else:
# args.save_path += f'_lr{"_".join(args.lr_per_scale.split(","))}'
args.lr_per_scale = [float(args.lr_per_scale)] * args.max_scales if ',' not in args.lr_per_scale else list(map(float, args.lr_per_scale.split(",")))
assert len(args.lr_per_scale) == args.max_scales, f"Specify 1 or max_scales # of lr_per_scale! Given {args.lr_per_scale}, max_scales {args.max_scales}"
# ckpt_to_load
if args.ckpt_to_load is not "" and args.ckpt_to_load is not None:
args.resume = None
return args
class MSFlow():
def __init__(self, args=None, train_im_dataset=None):
if args is None:
self.args = get_args()
else:
self.args = args
self.train_im_dataset = train_im_dataset
torch.manual_seed(self.args.seed)
# Get device
self.args.device = "cuda:%d"%torch.cuda.current_device() if torch.cuda.is_available() and not args.disable_cuda else "cpu"
self.device = torch.device(self.args.device)
self.cuda = self.device != torch.device('cpu')
self.cvt = lambda x: x.type(torch.float32).to(self.device, non_blocking=True)
# Build model
self.model = CNFMultiscale(**vars(args),
regs=argparse.Namespace(kinetic_energy=args.kinetic_energy,
jacobian_norm2=args.jacobian_norm2))
self.image_shapes = self.model.image_shapes
self.input_shapes = self.model.input_shapes
if self.args.mode == '1d' or self.args.mode == '2d' or 'wavelet' in self.args.mode:
self.z_stds = self.model.z_stds
self.num_scales = self.model.num_scales
for cnf in self.model.scale_models:
set_cnf_options(self.args, cnf)
# if self.args.mode == 'wavelet':
# self.wavelet_shapes = self.model.wavelet_tx.wavelet_shapes
# Distributed model
if self.args.distributed:
torch.cuda.set_device(self.args.local_rank)
distributed.init_process_group(backend=self.args.dist_backend, init_method=self.args.dist_url, world_size=dist_utils.env_world_size(), rank=dist_utils.env_rank())
assert(dist_utils.env_world_size() == distributed.get_world_size())
self.model = self.model.cuda()
self.model = dist_utils.DDP(self.model,
device_ids=[self.args.local_rank],
output_device=self.args.local_rank)
# Model to device, set to scale
else:
self.model = self.model.to(self.device)
# Load (possibly partial) ckpt
if self.args.ckpt_to_load:
print(f"Loading weights from {self.args.ckpt_to_load}")
assert os.path.exists(self.args.ckpt_to_load), f"ckpt_to_load does not exist! Given {self.args.ckpt_to_load}"
ckpt = torch.load(self.args.ckpt_to_load, map_location=self.device)
self.model.load_state_dict(ckpt['state_dict'], strict=False)
else:
# If save_path exists, then resume from it
if os.path.exists(self.args.save_path) and self.args.resume is None:
self.args.resume = os.path.join(self.args.save_path, 'checkpoints', 'ckpt.pth')
if not self.args.joint:
# Turn off updates for parameters in other scale models
if self.args.distributed:
self.model.module.scale = self.args.scale
else:
self.model.scale = self.args.scale
# Optimizer
self.define_optimizer()
# Meters
self.init_meters()
# Other variables
if not self.args.resume:
self.itr = 0
self.begin_batch = 0
self.train_time_total = 0.
self.best_train_loss = float("inf")
self.best_val_loss = float("inf")
self.scale = self.args.scale
self.begin_epoch = 1 if (self.scale == 0 or self.args.joint) else np.cumsum(self.args.epochs_per_scale[:self.scale])[-1] + 1
# Restore parameters
else:
print(f"RESUMING {self.args.resume}")
self.args.save_path = os.path.dirname(os.path.dirname(self.args.resume))
checkpt = torch.load(self.args.resume, map_location=self.device)
# Model
self.model.load_state_dict(checkpt["state_dict"], strict=False)
# self.load_my_state_dict(checkpt["state_dict"])
# Optimizer
if "optim_state_dict" in checkpt.keys():
self.optimizer.load_state_dict(checkpt["optim_state_dict"])
# Manually move optimizer state to device.
for state in self.optimizer.state.values():
for k, v in state.items():
if torch.is_tensor(v):
state[k] = self.cvt(v)
# Scale
self.scale = checkpt['scale']
if not self.args.joint:
print(f"Setting to Scale {checkpt['scale']}")
# Turn off updates for parameters in other scale models
if self.args.distributed:
self.model.module.scale = checkpt["scale"]
else:
self.model.scale = checkpt["scale"]
# Fixed_z
self.fixed_z = checkpt['fixed_z']
self.fixed_strict_z = checkpt['fixed_strict_z']
# Epoch
try:
self.begin_epoch = checkpt['epoch']
except:
self.begin_epoch = np.cumsum(self.args.epochs_per_scale[:self.scale])[-1] + 1
# Logs
chkdir = os.path.join(os.path.dirname(self.args.resume), "../")
trdf = pd.read_csv(os.path.join(chkdir, 'train_log.csv'))
try:
self.itr = checkpt['itr'] + 1
except:
self.itr = trdf['itr'].to_numpy()[-1]
try:
self.begin_batch = checkpt['batch'] + 1
except:
self.begin_batch = trdf['batch'].to_numpy()[-1]
try:
self.train_time_total = checkpt['train_time']
except:
self.train_time_total = trdf['train_time'].to_numpy()[-1]
tedf = pd.read_csv(os.path.join(chkdir, 'test_log.csv'))
self.best_train_loss = float("inf")
self.best_val_loss = tedf['val_loss'].min()
# self.lr_meter.update(checkpt['lr_meter_val'], epoch=self.begin_epoch-1)
loaded = self.load_meters()
if not loaded:
try:
self.lr_meter.update(checkpt['lr_meter_val'], epoch=self.begin_epoch-1)
except:
self.lr_meter.update(self.args.lr, epoch=self.begin_epoch-1)
# Print
print(f"Scale {self.model.scale}, Epoch {self.begin_epoch}, Batch {self.begin_batch}, Itr {self.itr}, train time {self.train_time_total}, best val loss {self.best_val_loss}")
# Only want master rank logging
is_master = (not self.args.distributed) or (dist_utils.env_rank()==0)
is_rank0 = self.args.local_rank == 0
self.write_log = is_rank0 and is_master
# Dirs, scripts
if os.path.exists(self.args.save_path):
# self.args.inference = True
self.args.copy_scripts = False
else:
self.args.inference = False
print(f"Making dir {self.args.save_path}")
utils.makedirs(self.args.save_path)
if args.copy_scripts: utils.copy_scripts(os.path.dirname(os.path.abspath(__file__)), self.args.save_path)
utils.makedirs(os.path.join(self.args.save_path, "checkpoints"))
utils.makedirs(os.path.join(self.args.save_path, "samples"))
# utils.makedirs(os.path.join(self.args.save_path, "samples","temp0.9"))
# utils.makedirs(os.path.join(self.args.save_path, "samples","temp0.8"))
# utils.makedirs(os.path.join(self.args.save_path, "samples","temp0.7"))
utils.makedirs(os.path.join(self.args.save_path, "plots"))
# Args
with open(os.path.join(self.args.save_path, 'args.yaml'), 'w') as f:
yaml.dump(vars(self.args), f, default_flow_style=False)
if self.write_log:
self.init_logg()
def find_moving_avg(self, vals, momentum=0.99):
avg = vals[0]
for val in vals[1:]:
avg = avg * momentum + val * (1 - momentum)
return avg
def update_meter(self, meter, vals):
meter.vals = vals
meter.val = vals[-1]
meter.avg = self.find_moving_avg(vals, meter.momentum)
return meter
# Meters
def init_meters(self):
self.lr_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.elapsed_meter = utils.RunningAverageMeter(0.97, save_seq=True)
# Train
self.itr_time_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.train_time_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.loss_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.nll_loss_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.bpd_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.reg_loss_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.nfe_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.grad_meter = utils.RunningAverageMeter(0.97, save_seq=True)
# bpd
self.bpd_mean_dict_meters = {}
self.bpd_std_dict_meters = {}
# logpz
self.logpz_mean_dict_meters = {}
self.logpz_std_dict_meters = {}
# deltalogp
self.deltalogp_mean_dict_meters = {}
self.deltalogp_std_dict_meters = {}
for sc in range(self.args.max_scales):
# bpd
self.bpd_mean_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
self.bpd_std_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
# logpz
self.logpz_mean_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
self.logpz_std_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
# deltalogp
self.deltalogp_mean_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
self.deltalogp_std_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
# Val
self.val_time_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.val_loss_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.val_bpd_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.val_nfe_meter = utils.RunningAverageMeter(0.97, save_seq=True)
# bpd
self.val_bpd_mean_dict_meters = {}
self.val_bpd_std_dict_meters = {}
# logpz
self.val_logpz_mean_dict_meters = {}
self.val_logpz_std_dict_meters = {}
# deltalogp
self.val_deltalogp_mean_dict_meters = {}
self.val_deltalogp_std_dict_meters = {}
for sc in range(self.args.max_scales):
# bpd
self.val_bpd_mean_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
self.val_bpd_std_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
# logpz
self.val_logpz_mean_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
self.val_logpz_std_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
# deltalogp
self.val_deltalogp_mean_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
self.val_deltalogp_std_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
# Noisy Val
self.noisy_val_loss_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.noisy_val_bpd_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.noisy_val_nfe_meter = utils.RunningAverageMeter(0.97, save_seq=True)
# bpd
self.noisy_val_bpd_mean_dict_meters = {}
self.noisy_val_bpd_std_dict_meters = {}
# logpz
self.noisy_val_logpz_mean_dict_meters = {}
self.noisy_val_logpz_std_dict_meters = {}
# deltalogp
self.noisy_val_deltalogp_mean_dict_meters = {}
self.noisy_val_deltalogp_std_dict_meters = {}
for sc in range(self.args.max_scales):
# bpd
self.noisy_val_bpd_mean_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
self.noisy_val_bpd_std_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
# logpz
self.noisy_val_logpz_mean_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
self.noisy_val_logpz_std_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
# deltalogp
self.noisy_val_deltalogp_mean_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
self.noisy_val_deltalogp_std_dict_meters[sc] = utils.RunningAverageMeter(0.97, save_seq=True)
# IS, FID
self.isc_mean_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.isc_std_meter = utils.RunningAverageMeter(0.97, save_seq=True)
self.fid_meter = utils.RunningAverageMeter(0.97, save_seq=True)
def save_meters(self):
meters_pkl = os.path.join(self.args.save_path, 'meters.pkl')
with open(meters_pkl, "wb") as f:
pickle.dump({
'lr_meter': self.lr_meter,
'elapsed_meter': self.elapsed_meter,
'itr_time_meter': self.itr_time_meter,
'train_time_meter': self.train_time_meter,
'loss_meter': self.loss_meter,
'nll_loss_meter': self.nll_loss_meter,
'bpd_meter': self.bpd_meter,
'reg_loss_meter': self.reg_loss_meter,
'nfe_meter': self.nfe_meter,
'grad_meter': self.grad_meter,
'bpd_mean_dict_meters': self.bpd_mean_dict_meters,
'bpd_std_dict_meters': self.bpd_std_dict_meters,
'logpz_mean_dict_meters': self.logpz_mean_dict_meters,
'logpz_std_dict_meters': self.logpz_std_dict_meters,
'deltalogp_mean_dict_meters': self.deltalogp_mean_dict_meters,
'deltalogp_std_dict_meters': self.deltalogp_std_dict_meters,
'val_time_meter': self.val_time_meter,
'val_loss_meter': self.val_loss_meter,
'val_bpd_meter': self.val_bpd_meter,
'val_nfe_meter': self.val_nfe_meter,
'val_bpd_mean_dict_meters': self.val_bpd_mean_dict_meters,
'val_bpd_std_dict_meters': self.val_bpd_std_dict_meters,
'val_logpz_mean_dict_meters': self.val_logpz_mean_dict_meters,
'val_logpz_std_dict_meters': self.val_logpz_std_dict_meters,
'val_deltalogp_mean_dict_meters': self.val_deltalogp_mean_dict_meters,
'val_deltalogp_std_dict_meters': self.val_deltalogp_std_dict_meters,
'noisy_val_loss_meter': self.noisy_val_loss_meter,
'noisy_val_bpd_meter': self.noisy_val_bpd_meter,
'noisy_val_nfe_meter': self.noisy_val_nfe_meter,
'noisy_val_bpd_mean_dict_meters': self.noisy_val_bpd_mean_dict_meters,
'noisy_val_bpd_std_dict_meters': self.noisy_val_bpd_std_dict_meters,
'noisy_val_logpz_mean_dict_meters': self.noisy_val_logpz_mean_dict_meters,
'noisy_val_logpz_std_dict_meters': self.noisy_val_logpz_std_dict_meters,
'noisy_val_deltalogp_mean_dict_meters': self.noisy_val_deltalogp_mean_dict_meters,
'noisy_val_deltalogp_std_dict_meters': self.noisy_val_deltalogp_std_dict_meters,
'isc_mean_meter': self.isc_mean_meter,
'isc_std_meter': self.isc_std_meter,
'fid_meter': self.fid_meter,
},
f, protocol=pickle.HIGHEST_PROTOCOL)
def load_meters(self):
meters_pkl = os.path.join(self.args.save_path, 'meters.pkl')
if not os.path.exists(meters_pkl):
print(f"{meters_pkl} does not exist! Returning.")
return False
with open(meters_pkl, "rb") as f:
a = pickle.load(f)
# Load
self.lr_meter = a['lr_meter']
self.elapsed_meter = a['elapsed_meter']
self.itr_time_meter = a['itr_time_meter']
self.train_time_meter = a['train_time_meter']
self.loss_meter = a['loss_meter']
self.nll_loss_meter = a['nll_loss_meter']
self.bpd_meter = a['bpd_meter']
self.reg_loss_meter = a['reg_loss_meter']
self.nfe_meter = a['nfe_meter']
self.grad_meter = a['grad_meter']
self.bpd_mean_dict_meters = a['bpd_mean_dict_meters']
self.bpd_std_dict_meters = a['bpd_std_dict_meters']
self.logpz_mean_dict_meters = a['logpz_mean_dict_meters']
self.logpz_std_dict_meters = a['logpz_std_dict_meters']
self.deltalogp_mean_dict_meters = a['deltalogp_mean_dict_meters']
self.deltalogp_std_dict_meters = a['deltalogp_std_dict_meters']
self.val_time_meter = a['val_time_meter']
self.val_loss_meter = a['val_loss_meter']
self.val_bpd_meter = a['val_bpd_meter']
self.val_nfe_meter = a['val_nfe_meter']
self.val_bpd_mean_dict_meters = a['val_bpd_mean_dict_meters']
self.val_bpd_std_dict_meters = a['val_bpd_std_dict_meters']
self.val_logpz_mean_dict_meters = a['val_logpz_mean_dict_meters']
self.val_logpz_std_dict_meters = a['val_logpz_std_dict_meters']
self.val_deltalogp_mean_dict_meters = a['val_deltalogp_mean_dict_meters']
self.val_deltalogp_std_dict_meters = a['val_deltalogp_std_dict_meters']
self.noisy_val_loss_meter = a['noisy_val_loss_meter']
self.noisy_val_bpd_meter = a['noisy_val_bpd_meter']
self.noisy_val_nfe_meter = a['noisy_val_nfe_meter']
self.noisy_val_bpd_mean_dict_meters = a['noisy_val_bpd_mean_dict_meters']
self.noisy_val_bpd_std_dict_meters = a['noisy_val_bpd_std_dict_meters']
self.noisy_val_logpz_mean_dict_meters = a['noisy_val_logpz_mean_dict_meters']
self.noisy_val_logpz_std_dict_meters = a['noisy_val_logpz_std_dict_meters']
self.noisy_val_deltalogp_mean_dict_meters = a['noisy_val_deltalogp_mean_dict_meters']
self.noisy_val_deltalogp_std_dict_meters = a['noisy_val_deltalogp_std_dict_meters']
self.isc_mean_meter = a['isc_mean_meter']
self.isc_std_meter = a['isc_std_meter']
self.fid_meter = a['fid_meter']
return True
# https://discuss.pytorch.org/t/how-to-load-part-of-pre-trained-model/1113
def load_my_state_dict(self, state_dict):
own_state = self.model.state_dict()
for name, param in state_dict.items():
print(name)
if name not in own_state:
print("continue")
continue
if isinstance(param, torch.nn.Parameter):
# backwards compatibility for serialized parameters
param = param.data
own_state[name].copy_(param)
def define_optimizer(self):
# Optimizer
lr = self.args.lr if self.args.joint else self.args.lr_per_scale[self.model.module.scale if self.args.distributed else self.model.scale]
if self.args.optimizer == 'adam':
self.optimizer = optim.Adam(filter(lambda p: p.requires_grad, self.model.parameters()), lr=lr, weight_decay=self.args.weight_decay)
elif self.args.optimizer == 'sgd':
self.optimizer = optim.SGD(filter(lambda p: p.requires_grad, self.model.parameters()), lr=lr, weight_decay=self.args.weight_decay, momentum=0.9, nesterov=False)
# Scheduler
if self.args.lr_scheduler == "plateau":
self.scheduler = optim.lr_scheduler.ReduceLROnPlateau(self.optimizer, factor=self.args.plateau_factor, patience=self.args.plateau_patience//self.args.val_freq, verbose=True, threshold=self.args.plateau_threshold, threshold_mode=self.args.plateau_threshold_mode)
elif self.args.lr_scheduler == "step":
self.scheduler = optim.lr_scheduler.StepLR(self.optimizer, self.args.lr_step, self.args.lr_gamma, verbose=True)
elif self.args.lr_scheduler == "multiplicative":
self.scheduler = optim.lr_scheduler.LambdaLR(self.optimizer, lambda epoch: self.args.lr_gamma, verbose=True)
def lr_warmup_factor(self):
return min(float(self.itr + 1) / max(self.args.lr_warmup_iters, 1), 1.0)
def update_lr(self, opt=None, final_lr=None, gamma=True):
if opt is None:
opt = self.optimizer
if self.itr < self.args.lr_warmup_iters:
if final_lr is None:
final_lr = self.args.lr if self.args.joint else self.args.lr_per_scale[self.scale]
lr = final_lr * self.lr_warmup_factor()
for param_group in opt.param_groups:
param_group["lr"] = lr
elif gamma:
if self.itr % len(self.train_loader) == 0:
for param_group in opt.param_groups:
param_group["lr"] = param_group["lr"] * self.args.lr_gamma
def update_scale(self, new_scale):
self.save_model(os.path.join(args.save_path, "checkpoints", f"ckpt_scale{self.scale}.pth"))
self.scale = new_scale
if self.write_log:
curr_time_str, elapsed = self.get_time()
self.logger.info(f'\n{curr_time_str} | {elapsed} | SCALE UP: Setting to Scale {new_scale} : {self.image_shapes[new_scale]}\n')
self.elapsed_meter.reset()
self.itr_time_meter.reset()
self.lr_meter.reset()
# Train
self.loss_meter.reset()
self.nll_loss_meter.reset()
self.bpd_meter.reset()
self.reg_loss_meter.reset()
self.nfe_meter.reset()
self.grad_meter.reset()
for sc in range(self.args.max_scales):
# bpd
self.bpd_mean_dict_meters[sc].reset()
self.bpd_std_dict_meters[sc].reset()
# logpz
self.logpz_mean_dict_meters[sc].reset()
self.logpz_std_dict_meters[sc].reset()
# deltalogp
self.deltalogp_mean_dict_meters[sc].reset()
self.deltalogp_std_dict_meters[sc].reset()
# Val
self.val_time_meter.reset()
self.val_loss_meter.reset()
self.val_bpd_meter.reset()
self.val_nfe_meter.reset()
for sc in range(self.args.max_scales):
# bpd
self.val_bpd_mean_dict_meters[sc].reset()
self.val_bpd_std_dict_meters[sc].reset()
# logpz
self.val_logpz_mean_dict_meters[sc].reset()
self.val_logpz_std_dict_meters[sc].reset()
# deltalogp
self.val_deltalogp_mean_dict_meters[sc].reset()
self.val_deltalogp_std_dict_meters[sc].reset()
# Noisy Val
self.noisy_val_loss_meter.reset()
self.noisy_val_bpd_meter.reset()
self.noisy_val_nfe_meter.reset()
# bpd
for sc in range(self.args.max_scales):
self.noisy_val_bpd_mean_dict_meters[sc].reset()
self.noisy_val_bpd_std_dict_meters[sc].reset()
# logpz
for sc in range(self.args.max_scales):
self.noisy_val_logpz_mean_dict_meters[sc].reset()
self.noisy_val_logpz_std_dict_meters[sc].reset()
# deltalogp
for sc in range(self.args.max_scales):
self.noisy_val_deltalogp_mean_dict_meters[sc].reset()
self.noisy_val_deltalogp_std_dict_meters[sc].reset()
# IS, FID
self.isc_mean_meter.reset()
self.isc_std_meter.reset()
self.fid_meter.reset()
# Turn off updates for parameters in other scale models
if self.args.distributed:
self.model.module.scale = new_scale
else:
self.model.scale = new_scale
# Loaders
self.train_loader = self.train_loaders[new_scale]
self.test_loader = self.test_loaders[new_scale]
self.batches_in_epoch = len(self.train_loader)
# Reset optimizer
self.define_optimizer()
# Fixed images for noise
self.fixed_images_for_noise()
# Reset itr
self.itr = 0
self.min_lr_counter = 0
self.scale_change_epochs.append(self.epoch - 1)
def save_model(self, save_path):
if self.args.local_rank == 0:
if self.write_log:
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | Saving model {save_path}")
torch.save({
"epoch": self.epoch,
"batch": self.batch,
"itr": self.itr,
"scale": self.scale,
"state_dict": self.model.module.state_dict() if hasattr(self.model, "module") else self.model.state_dict(),
"optim_state_dict": self.optimizer.state_dict(),
"lr_meter_val": self.lr_meter.val,
"fixed_z": self.fixed_z,
"fixed_strict_z": self.fixed_strict_z,
"train_time": self.train_time_total
}, save_path)
def compute_loss(self, imgs, noisy=True):
logpx, reg_states, bpd_dict, z_dict, logpz_dict, deltalogp_dict = self.model(imgs, noisy=noisy) # run model forward
if self.args.joint:
dim = imgs.nelement()/len(imgs)
else:
dim = np.prod(self.image_shapes[self.model.module.scale if self.args.distributed else self.model.scale])
# bpd = -(logpx/dim - np.log(2**self.args.nbits)) / np.log(2)
bpd = logpx_to_bpd(logpx, dim, self.args.nbits)
loss = bpd.mean()
if torch.isnan(loss):
if self.write_log: self.logger.info('ValueError: model returned nan during training')
raise ValueError('model returned nan during training')
elif torch.isinf(loss):
if self.write_log: self.logger.info('ValueError: model returned inf during training')
raise ValueError('model returned inf during training')
reg_coeffs = self.model.module.regularization_coeffs if self.args.distributed else self.model.regularization_coeffs
if reg_coeffs and len(reg_states):
reg_loss = torch.stack([reg_state * coeff for reg_state, coeff in zip(reg_states, reg_coeffs)]).sum()
loss = loss + reg_loss
else:
reg_loss = torch.tensor(0., device=self.device)
return loss, bpd, reg_loss, reg_states, bpd_dict, logpz_dict, deltalogp_dict
def fixed_images_for_noise(self):
# Fixed x for z
for (self.fixed_train_imgs, _) in self.train_loader:
break
for (self.fixed_val_imgs, _) in self.test_loader:
break
# Save train images
nb = int(np.ceil(np.sqrt(float(self.fixed_train_imgs.size(0)))))
fixed_train_imgs_resized = resize(self.fixed_train_imgs.float()/255, self.image_shapes[-1][-2:], interp)
vutils.save_image(fixed_train_imgs_resized, os.path.join(self.args.save_path, "samples", f"noise_train_fixed_scale{self.scale}.png"), nrow=nb)
# Save val images
nb = int(np.ceil(np.sqrt(float(self.fixed_val_imgs.size(0)))))
fixed_val_imgs_resized = resize(self.fixed_val_imgs.float()/255, self.image_shapes[-1][-2:], interp)
vutils.save_image(fixed_val_imgs_resized, os.path.join(self.args.save_path, "samples", f"noise_val_fixed_scale{self.scale}.png"), nrow=nb)
def _set_req_grad(self, module, value):
for p in module.parameters():
p.requires_grad = value
def train(self, train_loaders, test_loaders, train_im_dataset=None):
self.train_loaders = train_loaders
self.test_loaders = test_loaders
if self.args.joint:
self.train_loader = self.train_loaders[0]
self.test_loader = self.test_loaders[0]
else:
self.train_loader = self.train_loaders[self.args.scale]
self.test_loader = self.test_loaders[self.args.scale]
self.batches_in_epoch = len(self.train_loader)
# Fixed images for noise
self.fixed_images_for_noise()
# Sync machines before training
if self.args.distributed:
if self.write_log: self.logger.info("Syncing machines before training")
dist_utils.sum_tensor(torch.tensor([1.0]).float().cuda())
if self.write_log:
mem = torch.cuda.memory_allocated() / 10**9 if self.device != torch.device('cpu') else 0.0
if self.write_log: self.logger.info(f"GPU Mem before train start: {mem:.3g} GB")
self.start_time = time.time()
self.min_lr_counter = 0
self.lr_change_epochs = []
self.scale_change_epochs = []
self.lrs = []
self.skip_epochs = 0
if self.write_log:
curr_time_str, elapsed = self.get_time()
self.logger.info(f"EXPERIMENT {self.args.save_path}")
self.logger.info(f'\n{curr_time_str} | {elapsed} | Starting at scale {self.scale if not self.args.joint else -1} : {self.image_shapes[self.scale if not self.args.joint else -1]}')
for self.epoch in range(self.begin_epoch, self.args.num_epochs + 1):
if self.epoch + self.skip_epochs > self.args.num_epochs:
break
# Check for new scale
if not self.args.joint:
new_scale = int(np.sum(self.epoch + self.skip_epochs > np.cumsum(self.args.epochs_per_scale)))
if new_scale >= self.num_scales:
break
if new_scale > self.scale:
self.update_scale(new_scale)
self.model.train()
for self.batch, (imgs, _) in enumerate(self.train_loader):
if self.batch < self.begin_batch:
continue
if self.write_log:
start = time.time()
self.optimizer.zero_grad()
self.update_lr()
self.lr_meter.update(self.optimizer.param_groups[0]['lr'], self.epoch - 1 + (self.batch)/len(self.train_loader))
# FFJORD Loss
self.imgs = imgs.clone()
loss, bpd, reg_loss, reg_states, bpd_dict, logpz_dict, deltalogp_dict = self.compute_loss(self.imgs, noisy=args.add_noise)
loss.backward()
mem = torch.cuda.memory_allocated() / 10**9 if self.device != torch.device('cpu') else 0.0
# Optimize
grad_norm = torch.nn.utils.clip_grad_norm_(self.model.parameters(), self.args.max_grad_norm)
# Only optimize if the grad_norm is less than 5*max_grad_norm
if grad_norm < 5*self.args.max_grad_norm:
self.optimizer.step()
self.high_grad_norm = 0
else:
self.high_grad_norm += 1
# Accumulate from distributed training
batch_size = self.imgs.size(0)
nfe_opt = count_nfe(self.model)
metrics = torch.tensor([1., mem, batch_size, loss.item() + loss_recon.item(), bpd.mean().item(), reg_loss.item(), nfe_opt, grad_norm, *reg_states]).float().to(self.device)
# if not self.args.joint:
self.rv = reg_states
if self.args.distributed:
total_gpus, self.r_mem, batch_total, r_loss, r_bpd, r_reg_loss, r_nfe, r_grad_norm, *self.rv = dist_utils.sum_tensor(metrics).cpu().numpy()
else:
total_gpus, self.r_mem, batch_total, r_loss, r_bpd, r_reg_loss, r_nfe, r_grad_norm, *self.rv = metrics.cpu().numpy()
# Log
if self.write_log:
itr_time = time.time() - start
self.train_time_total += itr_time
self.itr_time_meter.update(itr_time)
self.loss_meter.update(r_loss/total_gpus, self.epoch - 1 + (self.batch + 1)/len(self.train_loader))
self.bpd_meter.update(r_bpd/total_gpus)
self.reg_loss_meter.update(r_reg_loss/total_gpus)
self.nfe_meter.update(r_nfe/total_gpus)
self.grad_meter.update(r_grad_norm/total_gpus)
for sc in bpd_dict.keys():
self.bpd_mean_dict_meters[sc].update(bpd_dict[sc].mean().item(), self.epoch - 1 + (self.batch + 1)/len(self.train_loader))
self.bpd_std_dict_meters[sc].update(bpd_dict[sc].std().item())
for sc in logpz_dict.keys():
self.logpz_mean_dict_meters[sc].update(logpz_dict[sc].mean().item(), self.epoch - 1 + (self.batch + 1)/len(self.train_loader))
self.logpz_std_dict_meters[sc].update(logpz_dict[sc].std().item())
for sc in deltalogp_dict.keys():
self.deltalogp_mean_dict_meters[sc].update(deltalogp_dict[sc].mean().item(), self.epoch - 1 + (self.batch + 1)/len(self.train_loader))
self.deltalogp_std_dict_meters[sc].update(deltalogp_dict[sc].std().item())
self.logg(mode='train', total_gpus=total_gpus)
del loss, bpd, reg_loss, reg_states, self.imgs
self.itr += 1
# Min lr counter
if self.lr_meter.val <= self.args.min_lr:
self.min_lr_counter += 1
# If min lr was for min_lr_max_iters epochs, break
if self.min_lr_counter >= self.args.min_lr_max_iters:
if self.write_log:
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | min_lr <= {self.args.min_lr} lasted for {self.min_lr_counter} iterations, breaking!\n")
break
# Save model within an epoch
if self.args.save_freq_within_epoch > 0:
if self.itr % self.args.save_freq_within_epoch == 0:
# Time
if self.write_log:
self.train_time_meter.update(convert_time_stamp_to_hrs(str(datetime.timedelta(seconds=self.train_time_total))), self.epoch - 1 + (self.batch + 1)/len(self.train_loader))
curr_time = time.time()
elapsed = str(datetime.timedelta(seconds=(curr_time - self.start_time)))
self.elapsed_meter.update(convert_time_stamp_to_hrs(elapsed))
# Save model
if grad_norm < 5*self.args.max_grad_norm:
if self.write_log:
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | WITHIN EPOCH: Saving model ckpt.pth")
self.save_model(os.path.join(self.args.save_path, "checkpoints", "ckpt.pth"))
# Save best
loss = self.loss_meter.val
if loss < self.best_train_loss and self.args.local_rank==0:
self.best_train_loss = loss
dest = os.path.join(self.args.save_path, "checkpoints", f"best_train_scale{self.scale}.pth")
if self.write_log:
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | Saving best model: {dest}")
shutil.copyfile(os.path.join(self.args.save_path, "checkpoints", "ckpt.pth"), dest)
# Visualize samples
if self.write_log and not self.args.disable_viz:
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | Scale {self.scale if not self.args.joint else -1} | Itr {self.itr:06d} | Epoch {self.epoch:04d} | Batch {self.batch}/{self.batches_in_epoch} | Visualizing samples...")
# Generate images
gen_imgs_scales, _, _ = self.model(self.fixed_z, reverse=True)
# Save gen images
nb = int(np.ceil(np.sqrt(float(self.fixed_z[0].size(0)))))
if not self.args.joint:
gen_imgs = gen_imgs_scales[self.scale].detach().cpu()
# gen_imgs = gen_imgs.reshape(-1, *self.image_shapes[self.scale])
gen_imgs = resize(gen_imgs, self.image_shapes[-1][-2:], interp)
vutils.save_image(gen_imgs, os.path.join(self.args.save_path, "samples",
f"gen_scale{self.scale}_epoch{self.epoch - 1 + (self.batch + 1)/len(self.train_loader):09.04f}.png"), nrow=nb)
else:
for sc in sorted(gen_imgs_scales.keys()):
gen_imgs = gen_imgs_scales[sc].detach().cpu()
gen_imgs = resize(gen_imgs, self.image_shapes[-1][-2:], interp)
vutils.save_image(gen_imgs, os.path.join(self.args.save_path, "samples",
f"gen_scale{sc}_epoch{self.epoch - 1 + (self.batch + 1)/len(self.train_loader):09.04f}.png"), nrow=nb)
del gen_imgs_scales
# Plot graphs
if self.write_log:
self.save_meters()
curr_time_str, elapsed = self.get_time()
try:
plot_graphs_process.join()
except:
pass
self.logger.info(f"{curr_time_str} | {elapsed} | Scale {self.scale if not self.args.joint else -1} | Itr {self.itr:06d} | Epoch {self.epoch:04d} | Batch {self.batch}/{self.batches_in_epoch} | Plotting graphs...")
plot_graphs_process = Process(target=self.plot_graphs)
plot_graphs_process.start()
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | Plotting graphs DONE!\n")
if self.high_grad_norm > self.args.grad_norm_patience:
break
if self.high_grad_norm > self.args.grad_norm_patience:
if self.args.joint:
if self.write_log:
self.logger.info(f"HIGH GRAD NORM for > patience {self.args.grad_norm_patience}!! ENDING!!\n")
break
else:
if self.write_log:
self.logger.info(f"HIGH GRAD NORM for > patience {self.args.grad_norm_patience}!! SKIPPING SCALE!!\n")
self.skip_epochs += abs(self.epoch + self.skip_epochs - np.cumsum(self.args.epochs_per_scale)[self.scale])
self.begin_batch = 0
# Time
if self.write_log:
self.train_time_meter.update(convert_time_stamp_to_hrs(str(datetime.timedelta(seconds=self.train_time_total))), self.epoch)
curr_time = time.time()
elapsed = str(datetime.timedelta(seconds=(curr_time - self.start_time)))
self.elapsed_meter.update(convert_time_stamp_to_hrs(elapsed))
# Save
if self.write_log:
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | AFTER EPOCH: Saving model ckpt.pth")
self.save_model(os.path.join(self.args.save_path, "checkpoints", "ckpt.pth"))
# Validate
if self.epoch % self.args.val_freq == 0:
if self.write_log:
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | Scale {self.scale if not self.args.joint else -1} | Epoch {self.epoch:04d} | Validating...")
start = time.time()
val_metrics, val_bpd_mean_dict, val_bpd_std_dict, \
val_logpz_mean_dict, val_logpz_std_dict, \
val_deltalogp_mean_dict, val_deltalogp_std_dict, \
noisy_val_metrics, noisy_val_bpd_mean_dict, noisy_val_bpd_std_dict, \
noisy_val_logpz_mean_dict, noisy_val_logpz_std_dict, \
noisy_val_deltalogp_mean_dict, noisy_val_deltalogp_std_dict = self.validate(self.test_loader)
# Accumulate from distributed training
if self.args.distributed:
total_gpus, r_loss, r_bpd, r_nfe = dist_utils.sum_tensor(val_metrics).cpu().numpy()
noisy_total_gpus, noisy_r_loss, noisy_r_bpd, noisy_r_nfe = dist_utils.sum_tensor(noisy_val_metrics).cpu().numpy()
else:
total_gpus, r_loss, r_bpd, r_nfe = val_metrics.cpu().numpy()
noisy_total_gpus, noisy_r_loss, noisy_r_bpd, noisy_r_nfe = noisy_val_metrics.cpu().numpy()
# Log
if self.write_log:
val_time = time.time() - start
self.val_time_meter.update(val_time/2)
self.val_loss_meter.update(r_loss/total_gpus, self.epoch)
self.val_bpd_meter.update(r_bpd/total_gpus)
self.val_nfe_meter.update(r_nfe/total_gpus)
# bpd
for sc in val_bpd_mean_dict.keys():
self.val_bpd_mean_dict_meters[sc].update(val_bpd_mean_dict[sc], self.epoch)
self.val_bpd_std_dict_meters[sc].update(val_bpd_std_dict[sc])
# logpz
for sc in val_logpz_mean_dict.keys():
self.val_logpz_mean_dict_meters[sc].update(val_logpz_mean_dict[sc], self.epoch)
self.val_logpz_std_dict_meters[sc].update(val_logpz_std_dict[sc])
# deltalogp
for sc in val_deltalogp_mean_dict.keys():
self.val_deltalogp_mean_dict_meters[sc].update(val_deltalogp_mean_dict[sc], self.epoch)
self.val_deltalogp_std_dict_meters[sc].update(val_deltalogp_std_dict[sc])
self.logg(mode='val', total_gpus=total_gpus)
# Noisy
self.noisy_val_loss_meter.update(noisy_r_loss/noisy_total_gpus)
self.noisy_val_bpd_meter.update(noisy_r_bpd/noisy_total_gpus)
self.noisy_val_nfe_meter.update(noisy_r_nfe/noisy_total_gpus)
# bpd
for sc in noisy_val_bpd_mean_dict.keys():
self.noisy_val_bpd_mean_dict_meters[sc].update(noisy_val_bpd_mean_dict[sc], self.epoch)
self.noisy_val_bpd_std_dict_meters[sc].update(noisy_val_bpd_std_dict[sc])
# logpz
for sc in noisy_val_logpz_mean_dict.keys():
self.noisy_val_logpz_mean_dict_meters[sc].update(noisy_val_logpz_mean_dict[sc], self.epoch)
self.noisy_val_logpz_std_dict_meters[sc].update(noisy_val_logpz_std_dict[sc])
# deltalogp
for sc in noisy_val_deltalogp_mean_dict.keys():
self.noisy_val_deltalogp_mean_dict_meters[sc].update(noisy_val_deltalogp_mean_dict[sc], self.epoch)
self.noisy_val_deltalogp_std_dict_meters[sc].update(noisy_val_deltalogp_std_dict[sc])
self.logg(mode='noisy_val', total_gpus=noisy_total_gpus)
del val_metrics, noisy_val_metrics
# Save best
loss = self.val_loss_meter.val
if loss < self.best_val_loss and self.args.local_rank==0:
self.best_val_loss = loss
dest = os.path.join(self.args.save_path, "checkpoints", f"best_scale{self.scale}.pth")
shutil.copyfile(os.path.join(self.args.save_path, "checkpoints", "ckpt.pth"), dest)
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | Saving best val model: {dest}")
# Schedule
if self.itr > self.args.lr_warmup_iters:
if self.args.lr_scheduler == 'plateau':
self.scheduler.step(self.val_loss_meter.val)
else:
self.scheduler.step()
# Record change in LR
if self.optimizer.param_groups[0]["lr"] == self.args.plateau_factor * self.lr_meter.val:
self.lr_change_epochs.append(self.epoch)
if self.write_log: self.logger.info(f"Reduced LR: Epoch {self.epoch}, LR {self.optimizer.param_groups[0]['lr']}")
# Visualize samples
if self.write_log and self.epoch % self.args.plot_freq == 0 and not self.args.disable_viz:
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | Scale {self.scale if not self.args.joint else -1} | Epoch {self.epoch:04d} | Visualizing samples...")
# Generate images
with torch.no_grad():
gen_imgs_scales, _, _ = self.model(self.fixed_z, reverse=True)
# Save gen images
nb = int(np.ceil(np.sqrt(float(self.fixed_z[0].size(0)))))
if not self.args.joint:
gen_imgs = gen_imgs_scales[self.scale].detach().cpu()
# gen_imgs = gen_imgs.reshape(-1, *self.image_shapes[self.scale])
gen_imgs = resize(gen_imgs, self.image_shapes[-1][-2:], interp)
vutils.save_image(gen_imgs, os.path.join(self.args.save_path, "samples",
f"gen_scale{self.scale}_epoch{self.epoch:09.04f}.png" if self.args.save_freq_within_epoch > 0 else f"gen_scale{self.scale}_epoch{self.epoch:04d}.png"), nrow=nb)
else:
for sc in sorted(gen_imgs_scales.keys()):
gen_imgs = resize(gen_imgs_scales[sc], self.image_shapes[-1][-2:], interp)
vutils.save_image(gen_imgs, os.path.join(self.args.save_path, "samples",
f"gen_scale{self.scale}_epoch{self.epoch:09.04f}.png" if self.args.save_freq_within_epoch > 0 else f"gen_scale{sc}_epoch{self.epoch:04d}.png"), nrow=nb)
del gen_imgs_scales
# Generate images
with torch.no_grad():
# TODO: visualize figures at multiple scales
gen_imgs_scales, _, _ = self.model(self.fixed_strict_z, reverse=True)
gen_imgs = gen_imgs_scales[self.scale].detach().cpu() if not self.args.joint else gen_imgs_scales[sorted(list(gen_imgs_scales.keys()))[-1]].detach().cpu()
del gen_imgs_scales
# Save gen images
# gen_imgs = gen_imgs.reshape(-1, *self.image_shapes[self.scale])
gen_imgs = resize(gen_imgs, self.image_shapes[-1][-2:], interp)
vutils.save_image(gen_imgs, os.path.join(self.args.save_path, "samples", f"gen_STRICT_scale{self.scale}.png"), nrow=8)
# Plot graphs
if self.write_log and self.epoch % self.args.plot_freq == 0:
self.save_meters()
curr_time_str, elapsed = self.get_time()
try:
plot_graphs_process.join()
except:
pass
self.logger.info(f"{curr_time_str} | {elapsed} | Scale {self.scale if not self.args.joint else -1} | Epoch {self.epoch:04d} | Plotting graphs...")
plot_graphs_process = Process(target=self.plot_graphs)
plot_graphs_process.start()
curr_time_str, elapsed = self.get_time()
self.logger.info(f"{curr_time_str} | {elapsed} | Plotting graphs DONE!\n")
# If min lr was for min_lr_max_iters epochs, skip to the next scale
if self.min_lr_counter >= self.args.min_lr_max_iters:
if self.args.joint:
break
else:
self.skip_epochs += abs(self.epoch + self.skip_epochs - np.cumsum(self.args.epochs_per_scale)[self.scale])
def validate(self, val_loader):
self.model.eval()
loss_means, bpd_means, nfes = [], [], []
noisy_loss_means, noisy_bpd_means, noisy_nfes = [], [], []
bpd_mean_dict, bpd_std_dict = {}, {}
logpz_mean_dict, logpz_std_dict = {}, {}
deltalogp_mean_dict, deltalogp_std_dict = {}, {}
noisy_bpd_mean_dict, noisy_bpd_std_dict = {}, {}
noisy_logpz_mean_dict, noisy_logpz_std_dict = {}, {}
noisy_deltalogp_mean_dict, noisy_deltalogp_std_dict = {}, {}
def add_to_dict(my_dict, key, val):
if key in my_dict.keys():
my_dict[key].append(val)
else:
my_dict[key] = [val]
# with torch.no_grad():
for batch, (imgs, _) in tqdm(enumerate(val_loader), total=len(val_loader), leave=False, desc='Validating'):
self.imgs = imgs.clone()
# Not noisy
loss, bpd, _, _, bpd_dict, logpz_dict, deltalogp_dict = self.compute_loss(self.imgs, noisy=False)
del self.imgs
loss_means.append(loss.item())
bpd_means.append(bpd.mean().item())
nfes.append(count_nfe(self.model))
# bpd
for sc in bpd_dict.keys():
add_to_dict(bpd_mean_dict, sc, bpd_dict[sc].mean().item())
add_to_dict(bpd_std_dict, sc, bpd_dict[sc].std().item())
# logpz
for sc in logpz_dict.keys():
add_to_dict(logpz_mean_dict, sc, logpz_dict[sc].mean().item())
add_to_dict(logpz_std_dict, sc, logpz_dict[sc].std().item())
# deltalogp
for sc in deltalogp_dict.keys():
add_to_dict(deltalogp_mean_dict, sc, deltalogp_dict[sc].mean().item())
add_to_dict(deltalogp_std_dict, sc, deltalogp_dict[sc].std().item())
# del
del loss, bpd, bpd_dict, logpz_dict, deltalogp_dict
# Noisy
self.imgs = imgs.clone()
noisy_loss, noisy_bpd, _, _, noisy_bpd_dict, noisy_logpz_dict, noisy_deltalogp_dict = self.compute_loss(self.imgs, noisy=True)
del self.imgs
noisy_loss_means.append(noisy_loss.item())
noisy_bpd_means.append(noisy_bpd.mean().item())
noisy_nfes.append(count_nfe(self.model))
# bpd
for sc in noisy_bpd_dict.keys():
add_to_dict(noisy_bpd_mean_dict, sc, noisy_bpd_dict[sc].mean().item())
add_to_dict(noisy_bpd_std_dict, sc, noisy_bpd_dict[sc].std().item())
# logpz
for sc in noisy_logpz_dict.keys():
add_to_dict(noisy_logpz_mean_dict, sc, noisy_logpz_dict[sc].mean().item())
add_to_dict(noisy_logpz_std_dict, sc, noisy_logpz_dict[sc].std().item())
# deltalogp
for sc in noisy_deltalogp_dict.keys():
add_to_dict(noisy_deltalogp_mean_dict, sc, noisy_deltalogp_dict[sc].mean().item())
add_to_dict(noisy_deltalogp_std_dict, sc, noisy_deltalogp_dict[sc].std().item())
# del
del noisy_loss, noisy_bpd, noisy_bpd_dict, noisy_logpz_dict, noisy_deltalogp_dict
loss_mean = np.mean(loss_means)
bpd_mean = np.mean(bpd_means)
nfe = np.mean(nfes)
# bpd
for sc in bpd_mean_dict.keys():
bpd_mean_dict[sc] = np.mean(bpd_mean_dict[sc])
bpd_std_dict[sc] = np.mean(bpd_std_dict[sc])
# logpz
for sc in logpz_mean_dict.keys():
logpz_mean_dict[sc] = np.mean(logpz_mean_dict[sc])
logpz_std_dict[sc] = np.mean(logpz_std_dict[sc])
# deltalogp
for sc in deltalogp_mean_dict.keys():
deltalogp_mean_dict[sc] = np.mean(deltalogp_mean_dict[sc])
deltalogp_std_dict[sc] = np.mean(deltalogp_std_dict[sc])
noisy_loss_mean = np.mean(noisy_loss_means)
noisy_bpd_mean = np.mean(noisy_bpd_means)
noisy_nfe = np.mean(noisy_nfes)
# bpd
for sc in noisy_bpd_mean_dict.keys():
noisy_bpd_mean_dict[sc] = np.mean(noisy_bpd_mean_dict[sc])
noisy_bpd_std_dict[sc] = np.mean(noisy_bpd_std_dict[sc])
# logpz
for sc in noisy_logpz_mean_dict.keys():
noisy_logpz_mean_dict[sc] = np.mean(noisy_logpz_mean_dict[sc])
noisy_logpz_std_dict[sc] = np.mean(noisy_logpz_std_dict[sc])
# deltalogp
for sc in noisy_deltalogp_mean_dict.keys():
noisy_deltalogp_mean_dict[sc] = np.mean(noisy_deltalogp_mean_dict[sc])
noisy_deltalogp_std_dict[sc] = np.mean(noisy_deltalogp_std_dict[sc])
metrics = torch.tensor([1., loss_mean, bpd_mean, nfe]).float().to(self.device)
noisy_metrics = torch.tensor([1., noisy_loss_mean, noisy_bpd_mean, noisy_nfe]).float().to(self.device)
return metrics, bpd_mean_dict, bpd_std_dict, \
logpz_mean_dict, logpz_std_dict, \
deltalogp_mean_dict, deltalogp_std_dict, \
noisy_metrics, noisy_bpd_mean_dict, noisy_bpd_std_dict, \
noisy_logpz_mean_dict, noisy_logpz_std_dict, \
noisy_deltalogp_mean_dict, noisy_deltalogp_std_dict
def savefig(self, path, bbox_inches='tight', pad_inches=0.1):
try:
plt.savefig(path, bbox_inches=bbox_inches, pad_inches=pad_inches)
except KeyboardInterrupt:
raise KeyboardInterrupt
except:
print(sys.exc_info()[0])
def plot_graphs(self):
# Time
plt.plot(self.train_time_meter.epochs, self.train_time_meter.vals, label='Train time')
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.xlabel("Epochs")
plt.ylabel("Hrs")
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'time_train.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# Elapsed
plt.plot(self.train_time_meter.epochs, self.elapsed_meter.vals, label='Elapsed')
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.xlabel("Epochs")
plt.ylabel("Hrs")
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'time_elapsed.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# LR
plt.plot(self.lr_meter.epochs, self.lr_meter.vals, color='red', label='lr')
for e in self.lr_change_epochs:
plt.axvline(e, linestyle='--', color='0.8')
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.xlabel("Epochs")
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'lr.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# Train loss
plt.plot(self.loss_meter.epochs, self.loss_meter.vals, color='C0', label="train loss")
plt.plot(self.loss_meter.epochs, self.bpd_meter.vals, '--', color='C0', label="nll_loss (bpd)")
plt.plot(self.loss_meter.epochs, self.reg_loss_meter.vals, '--', color='C4', label="reg loss")
for e in self.lr_change_epochs:
plt.axvline(e, linestyle='--', color='0.8')
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.xlabel("Epochs")
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'train_loss.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# Train + Val losses
plt.plot(self.loss_meter.epochs, self.loss_meter.vals, color='C0', alpha=0.4, label="train loss")
plt.plot(self.val_loss_meter.epochs, self.val_loss_meter.vals, color='C1', alpha=0.7, label="val loss")
plt.xlabel("Epochs")
for e in self.lr_change_epochs:
plt.axvline(e, linestyle='--', color='0.8')
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'losses.png'), bbox_inches='tight', pad_inches=0.1)
plt.plot(self.val_loss_meter.epochs, self.noisy_val_loss_meter.vals, color='C2', alpha=0.7, label="noisy val loss")
plt.legend()
# plt.yscale("linear")
self.savefig(os.path.join(self.args.save_path, 'plots', 'losses_wnoisy.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# Val BPD
# VAL
x, y = self.val_loss_meter.epochs, self.val_bpd_meter.vals
plt.plot(x, y, color='C1', alpha=0.7, label="val bpd")
try:
plt.scatter(x[-1], y[-1], color='C1'); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
min_index = y.index(min(y))
if min_index != len(y) - 1:
plt.scatter(x[min_index], y[min_index], color='C1'); plt.text(x[min_index], y[min_index], f"{y[min_index]:.02f}")
except:
pass
plt.xlabel("Epochs")
for e in self.lr_change_epochs:
plt.axvline(e, linestyle='--', color='0.8')
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'bpd.png'), bbox_inches='tight', pad_inches=0.1)
if (np.array(y) < 1e-6).sum() > 0:
plt.yscale("symlog")
else:
plt.yscale("log")
self.savefig(os.path.join(self.args.save_path, 'plots', 'bpd_logy.png'), bbox_inches='tight', pad_inches=0.1)
# NOISY VAL
x, y = self.val_loss_meter.epochs, self.noisy_val_bpd_meter.vals
plt.plot(x, y, color='C2', alpha=0.7, label="noisy val bpd")
try:
plt.scatter(x[-1], y[-1], color='C2'); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
min_index = y.index(min(y))
if min_index != len(y) - 1:
plt.scatter(x[min_index], y[min_index], color='C2'); plt.text(x[min_index], y[min_index], f"{y[min_index]:.02f}")
except:
pass
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'bpd_wnoisy_logy.png'), bbox_inches='tight', pad_inches=0.1)
plt.yscale("linear")
self.savefig(os.path.join(self.args.save_path, 'plots', 'bpd_wnoisy.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# Train + Val BPD
# TRAIN
x, y = self.loss_meter.epochs, self.bpd_meter.vals
plt.plot(x, y, color='C0', alpha=0.4, label="train bpd")
try:
plt.scatter(x[-1], y[-1], color='C0'); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
min_index = y.index(min(y))
if min_index != len(y) - 1:
plt.scatter(x[min_index], y[min_index], color='b'); plt.text(x[min_index], y[min_index], f"{y[min_index]:.02f}")
except:
pass
# VAL
x, y = self.val_loss_meter.epochs, self.val_bpd_meter.vals
plt.plot(x, y, color='C1', alpha=0.7, label="val bpd")
try:
plt.scatter(x[-1], y[-1], color='C1'); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
min_index = y.index(min(y))
if min_index != len(y) - 1:
plt.scatter(x[min_index], y[min_index], color='C1'); plt.text(x[min_index], y[min_index], f"{y[min_index]:.02f}")
except:
pass
plt.xlabel("Epochs")
for e in self.lr_change_epochs:
plt.axvline(e, linestyle='--', color='0.8')
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'bpd_all.png'), bbox_inches='tight', pad_inches=0.1)
if (np.array(y) < 1e-6).sum() > 0:
plt.yscale("symlog")
else:
plt.yscale("log")
self.savefig(os.path.join(self.args.save_path, 'plots', 'bpd_all_logy.png'), bbox_inches='tight', pad_inches=0.1)
# NOISY VAL
x, y = self.val_loss_meter.epochs, self.noisy_val_bpd_meter.vals
plt.plot(x, y, color='C2', alpha=0.7, label="noisy val bpd")
try:
plt.scatter(x[-1], y[-1], color='C2'); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
min_index = y.index(min(y))
if min_index != len(y) - 1:
plt.scatter(x[min_index], y[min_index], color='C2'); plt.text(x[min_index], y[min_index], f"{y[min_index]:.02f}")
except:
pass
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'bpd_all_wnoisy_logy.png'), bbox_inches='tight', pad_inches=0.1)
plt.yscale("linear")
self.savefig(os.path.join(self.args.save_path, 'plots', 'bpd_all_wnoisy.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# Train + Val NFE
plt.plot(self.loss_meter.epochs, self.nfe_meter.vals, color='C0', alpha=0.7, label="train NFE")
plt.plot(self.val_loss_meter.epochs, self.val_nfe_meter.vals, color='C1', alpha=0.7, label="val NFE")
plt.plot(self.val_loss_meter.epochs, self.noisy_val_nfe_meter.vals, color='C2', alpha=0.7, label="noisy val NFE")
plt.xlabel("Epochs")
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'nfe.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# Train grad
plt.plot(self.loss_meter.epochs, self.grad_meter.vals, color='C0', alpha=0.7, label="train Grad Norm")
plt.xlabel("Epochs")
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'grad.png'), bbox_inches='tight', pad_inches=0.1)
plt.yscale("log")
self.savefig(os.path.join(self.args.save_path, 'plots', 'grad_logy.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# bpd_dict
# sym = False
# VAL
for sc in self.val_bpd_mean_dict_meters.keys():
# plt.errorbar(self.val_bpd_mean_dict_meters[sc].epochs, self.val_bpd_mean_dict_meters[sc].vals, yerr=self.val_bpd_std_dict_meters[sc].vals, alpha=0.5, label=f"val sc{sc}")
x, y, err = self.val_bpd_mean_dict_meters[sc].epochs, np.array(self.val_bpd_mean_dict_meters[sc].vals), np.array(self.val_bpd_std_dict_meters[sc].vals)
if len(x) > 0:
if (y < 1e-6).sum() > 0:
sym = True
plt.plot(x, y, alpha=0.5, label=f"val bpd sc{sc}", c=f"C{sc+1}")
plt.fill_between(x, y-err, y+err, alpha=0.2, linewidth=0, color=f"C{sc+1}")
plt.scatter(x[-1], y[-1], color=plt.gca().lines[-1].get_color()); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
plt.xlabel("Epochs")
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'scales_bpd.png'), bbox_inches='tight', pad_inches=0.1)
# Noisy VAL
for sc in self.noisy_val_bpd_mean_dict_meters.keys():
# plt.errorbar(self.noisy_val_bpd_mean_dict_meters[sc].epochs, self.noisy_val_bpd_mean_dict_meters[sc].vals, yerr=self.noisy_val_bpd_std_dict_meters[sc].vals, alpha=0.5, label=f"noisy val sc{sc}")
x, y, err = self.noisy_val_bpd_mean_dict_meters[sc].epochs, np.array(self.noisy_val_bpd_mean_dict_meters[sc].vals), np.array(self.noisy_val_bpd_std_dict_meters[sc].vals)
if len(x) > 0:
plt.plot(x, y, alpha=0.5, label=f"noisy val bpd sc{sc}", c=f"C{sc+1}", linestyle="--")
if (y < 1e-6).sum() > 0:
sym = True
plt.fill_between(x, y-err, y+err, alpha=0.2, linewidth=0, color=f"C{sc+1}")
plt.scatter(x[-1], y[-1], color=plt.gca().lines[-1].get_color()); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
# plt.yscale("linear")
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'scales_bpd_wnoisy.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# bpd_dict
# sym = False
# Train
x, y, err = [], [], []
for sc in self.bpd_mean_dict_meters.keys():
# plt.errorbar(self.bpd_mean_dict_meters[sc].epochs, self.bpd_mean_dict_meters[sc].vals, yerr=self.bpd_std_dict_meters[sc].vals, alpha=0.5, label=f"train sc{sc}")
x += self.bpd_mean_dict_meters[sc].epochs
y += self.bpd_mean_dict_meters[sc].vals
err += self.bpd_std_dict_meters[sc].vals
y, err = np.array(y), np.array(err)
# if (y < 1e-6).sum() > 0:
# sym = True
plt.plot(x, y, alpha=0.5, label=f"train bpd")
plt.fill_between(x, y-err, y+err, alpha=0.2, linewidth=0)
if len(x) > 0:
plt.scatter(x[-1], y[-1], color=plt.gca().lines[-1].get_color()); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
# VAL
for sc in self.val_bpd_mean_dict_meters.keys():
# plt.errorbar(self.val_bpd_mean_dict_meters[sc].epochs, self.val_bpd_mean_dict_meters[sc].vals, yerr=self.val_bpd_std_dict_meters[sc].vals, alpha=0.5, label=f"val sc{sc}")
x, y, err = self.val_bpd_mean_dict_meters[sc].epochs, np.array(self.val_bpd_mean_dict_meters[sc].vals), np.array(self.val_bpd_std_dict_meters[sc].vals)
if len(x) > 0:
if (y < 1e-6).sum() > 0:
sym = True
plt.plot(x, y, alpha=0.5, label=f"val bpd sc{sc}")
plt.fill_between(x, y-err, y+err, alpha=0.2, linewidth=0)
plt.scatter(x[-1], y[-1], color=plt.gca().lines[-1].get_color()); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.xlabel("Epochs")
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'scales_bpd_all.png'), bbox_inches='tight', pad_inches=0.1)
# Noisy VAL
for sc in self.noisy_val_bpd_mean_dict_meters.keys():
# plt.errorbar(self.noisy_val_bpd_mean_dict_meters[sc].epochs, self.noisy_val_bpd_mean_dict_meters[sc].vals, yerr=self.noisy_val_bpd_std_dict_meters[sc].vals, alpha=0.5, label=f"noisy val sc{sc}")
x, y, err = self.noisy_val_bpd_mean_dict_meters[sc].epochs, np.array(self.noisy_val_bpd_mean_dict_meters[sc].vals), np.array(self.noisy_val_bpd_std_dict_meters[sc].vals)
if len(x) > 0:
plt.plot(x, y, alpha=0.5, label=f"noisy val bpd sc{sc}")
if (y < 1e-6).sum() > 0:
sym = True
plt.fill_between(x, y-err, y+err, alpha=0.2, linewidth=0)
plt.scatter(x[-1], y[-1], color=plt.gca().lines[-1].get_color()); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
# plt.yscale("linear")
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'scales_bpd_all_wnoisy.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# VAL
for sc in self.val_bpd_mean_dict_meters.keys():
# plt.errorbar(self.val_bpd_mean_dict_meters[sc].epochs, self.val_bpd_mean_dict_meters[sc].vals, yerr=self.val_bpd_std_dict_meters[sc].vals, alpha=0.5, label=f"val sc{sc}")
x, y, err = self.val_bpd_mean_dict_meters[sc].epochs, np.array(self.val_bpd_mean_dict_meters[sc].vals), np.array(self.val_bpd_std_dict_meters[sc].vals)
if len(x) > 0:
if (y < 1e-6).sum() > 0:
sym = True
plt.plot(x, y, alpha=0.5, label=f"val bpd sc{sc}", c=f"C{sc+1}")
# plt.fill_between(x, y-err, y+err, alpha=0.2, linewidth=0, color='C1')
plt.scatter(x[-1], y[-1], color=plt.gca().lines[-1].get_color()); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
plt.xlabel("Epochs")
for e in self.scale_change_epochs:
plt.axvline(e, color='k')
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'scales_bpd_wofill.png'), bbox_inches='tight', pad_inches=0.1)
# Noisy VAL
for sc in self.noisy_val_bpd_mean_dict_meters.keys():
# plt.errorbar(self.noisy_val_bpd_mean_dict_meters[sc].epochs, self.noisy_val_bpd_mean_dict_meters[sc].vals, yerr=self.noisy_val_bpd_std_dict_meters[sc].vals, alpha=0.5, label=f"noisy val sc{sc}")
x, y, err = self.noisy_val_bpd_mean_dict_meters[sc].epochs, np.array(self.noisy_val_bpd_mean_dict_meters[sc].vals), np.array(self.noisy_val_bpd_std_dict_meters[sc].vals)
if len(x) > 0:
plt.plot(x, y, alpha=0.5, label=f"noisy bpd val sc{sc}", c=f"C{sc+1}", linestyle='--')
# plt.fill_between(x, y-err, y+err, alpha=0.2, linewidth=0, color='C2')
plt.scatter(x[-1], y[-1], color=plt.gca().lines[-1].get_color()); plt.text(x[-1], y[-1], f"{y[-1]:.02f}")
# plt.yscale("linear")
plt.legend()
self.savefig(os.path.join(self.args.save_path, 'plots', 'scales_bpd_wofill_wnoisy.png'), bbox_inches='tight', pad_inches=0.1)
plt.clf()
plt.close()
# bpd_dict w/o fill_between
# sym = False
# Train
x, y, err = [], [], []
for sc in self.bpd_mean_dict_meters.keys():
# plt.errorbar(self.bpd_mean_dict_meters[sc].epochs, self.bpd_mean_dict_meters[sc].vals, yerr=self.bpd_std_dict_meters[sc].vals, alpha=0.5, label=f"train sc{sc}")
x += self.bpd_mean_dict_meters[sc].epochs
y += self.bpd_mean_dict_meters[sc].vals
err += self.bpd_std_dict_meters[sc].vals
y, err = | np.array(y) | numpy.array |
import matplotlib.pyplot as plt
import numpy as np
import matplotlibex as plx
import matplotlibex.mlplot as plx
import dmp.equations as deq
class LocalFunc(object):
def __init__(self):
pass
def __call__(self, x):
raise NotImplementedError()
def plot(self, t, x):
plt.plot(range(len(t)), self(x))
class RBFLocalFunc(LocalFunc):
def __init__(self, center, sigmasqr):
super(RBFLocalFunc, self).__init__()
self.center = center
self.sigmasqr = sigmasqr
def __call__(self, x):
return deq.RBF(self.center, self.sigmasqr, x)
class MisesBFLocalFunc(LocalFunc):
def __init__(self, center, sigmasqr):
super(MisesBFLocalFunc, self).__init__()
self.center = center
self.sigmasqr = sigmasqr
def __call__(self, x):
return deq.MisesBF(self.center, self.sigmasqr, x)
class LWR_1D(object):
def __init__(self, x, y, npsi=20, regressor_func=None, local_funcs=None):
self.x = x.copy()
self.y = y.copy()
if regressor_func is None:
regressor_func = lambda x: np.ones_like(x)
self.regressor_func = regressor_func
if local_funcs is None:
xmin = np.min(self.x)
xmax = np.max(self.x)
psi_cs = np.linspace(xmin, xmax, npsi) # basis functions centres
psi_ls = np.zeros([npsi]) + 0.5 * ((xmax - xmin) / npsi)**2
local_funcs = [RBFLocalFunc(center=psi_cs[i], sigmasqr=psi_ls[i]) for i in range(npsi)]
self.local_funcs = local_funcs
self.npsi = len(self.local_funcs)
ksi = self.regressor_func(x)
self.ws = | np.zeros([self.npsi]) | numpy.zeros |
#!/usr/bin/env python3
"""Soil masking Transformer
"""
import argparse
import logging
import os
import numpy as np
from agpypeline import entrypoint, algorithm, geoimage
from agpypeline.environment import Environment
from agpypeline.checkmd import CheckMD
from cv2 import cv2
from osgeo import gdal
# from PIL import Image Used by code that's getting deprecated
from skimage import morphology
from configuration import ConfigurationSoilmask
SATURATE_THRESHOLD = 245
MAX_PIXEL_VAL = 255
SMALL_AREA_THRESHOLD = 200
class __internal__:
"""Class for functions intended for internal use only for this file
"""
def __init__(self):
"""Performs initialization of class instance
"""
@staticmethod
def prepare_metadata_for_geotiff(transformer_info: dict = None) -> dict:
"""Create geotiff-embedable metadata from extractor_info and other metadata pieces.
Arguments:
transformer_info: details about the transformer
Return:
A dict containing information to save with an image
"""
extra_metadata = {}
if transformer_info:
extra_metadata["transformer_name"] = str(transformer_info.get("name", ""))
extra_metadata["transformer_version"] = str(transformer_info.get("version", ""))
extra_metadata["transformer_author"] = str(transformer_info.get("author", ""))
extra_metadata["transformer_description"] = str(transformer_info.get("description", ""))
if "repository" in transformer_info and transformer_info["repository"] and \
"repUrl" in transformer_info["repository"]:
extra_metadata["transformer_repo"] = str(transformer_info["repository"]["repUrl"])
else:
extra_metadata["transformer_repo"] = ""
return extra_metadata
@staticmethod
def gen_plant_mask(color_img: np.ndarray, kernel_size: int = 3) -> np.ndarray:
"""Generates an image with plants masked in.
Arguments:
color_img: RGB image to mask
kernel_size: masking kernel size
Return:
An RGB image with plants masked in
"""
r_channel = color_img[:, :, 2]
g_channel = color_img[:, :, 1]
b_channel = color_img[:, :, 0]
sub_img = (g_channel.astype('int') - r_channel.astype('int')) > 1
mask = np.zeros_like(b_channel)
mask[sub_img] = MAX_PIXEL_VAL
blur = cv2.blur(mask, (kernel_size, kernel_size))
pix = np.array(blur)
sub_mask = pix > 128
mask_1 = np.zeros_like(b_channel)
mask_1[sub_mask] = MAX_PIXEL_VAL
return mask_1
@staticmethod
def remove_small_area_mask(mask_img: np.ndarray, min_area_size: int) -> np.ndarray:
"""Removes small anomalies in the mask
Arguments:
mask_img: the mask image to remove anomalies from
min_area_size: the size of anomalies to look for
Return:
A new mask image with the anomalies removed
"""
mask_array = mask_img > 0
rel_array = morphology.remove_small_objects(mask_array, min_area_size)
rel_img = np.zeros_like(mask_img)
rel_img[rel_array] = MAX_PIXEL_VAL
return rel_img
@staticmethod
def remove_small_holes_mask(mask_image: np.ndarray, max_hole_size: int) -> np.ndarray:
"""Removes small holes from the mask image
Arguments:
mask_image: the mask image to remove holes from
max_hole_size: the maximum size of holes to remove
Return:
A new mask image with the holes removed
"""
mask_array = mask_image > 0
rel_array = morphology.remove_small_holes(mask_array, max_hole_size)
rel_img = np.zeros_like(mask_image)
rel_img[rel_array] = MAX_PIXEL_VAL
return rel_img
@staticmethod
def saturated_pixel_classification(gray_img: np.ndarray, base_mask: np.ndarray, saturated_mask: np.ndarray,
dilate_size: int = 0) -> np.ndarray:
"""Returns an image with pixes classified for masking
Arguments:
Returns:
A mask image with the pixels classified
"""
# add saturated area into basic mask
saturated_mask = morphology.binary_dilation(saturated_mask, morphology.diamond(dilate_size))
rel_img = | np.zeros_like(gray_img) | numpy.zeros_like |
# -*- coding: utf-8 -*-
"""
Created on Mon Mar 18 08:55:30 2019
@author: messinjf
"""
import numpy as np
import matplotlib.pyplot as plt
n = 10
bounds = [np.array([0,0]), np.array([n,0]), np.array([n,2*n]), np.array([0.5 * n, 2 * n]), np.array([0, n])]
#bounds = [np.array([0,0]), np.array([n,0]), np.array([n,n]), np.array([0,n])]
for i in range(4):
subdivide_bounds = []
for i in range(-1,len(bounds)-1):
bound_center = (bounds[i] + bounds[i+1]) / 2
subdivide_bounds.append(bounds[i])
subdivide_bounds.append(bound_center)
subdivide_bounds.append(bounds[i+1])
bounds = subdivide_bounds
def control(X,Y):
R = X * 0 + Y * 0
U, V = R * np.cos(T), R * np.sin(T)
return U, V
def centroid(bounds):
C_x = 0
C_y = 0
A = 0
for i in range(-1,len(bounds)-1):
x_0 = bounds[i][0]
x_1 = bounds[i+1][0]
y_0 = bounds[i][1]
y_1 = bounds[i+1][1]
C_x += (x_0 + x_1) * (x_0*y_1-x_1*y_0)
C_y += (y_0 + y_1) * (x_0*y_1-x_1*y_0)
A += 0.5 * (x_0*y_1-x_1*y_0)
C_x /= 6 * A
C_y /= 6 * A
return np.array([C_x, C_y])
def STC(X,Y):
U = np.zeros(X.shape)
V = np.zeros(Y.shape)
center = centroid(bounds)
for x_i in range(len(X)):
for y_i in range(len(X[0])):
p = np.array([X[x_i][y_i],Y[x_i][y_i]])
force = (center - p) / np.linalg.norm(center - p)
U[x_i, y_i] = force[0]
V[x_i, y_i] = force[1]
return U, V
def APFForceOnPoint(p, C=0.00897, lambda_const=2.656):
force = np.zeros(p.shape)
#print("p = {}".format(p))
#print("force = {}".format(force))
for i in range(-1,len(bounds)-1):
bound_center = (bounds[i] + bounds[i+1]) / 2
#print(bound_center)
wall_length = np.linalg.norm(bounds[i] - bounds[i+1])
d = p - bound_center
force += d * C * wall_length / ( | np.linalg.norm(d) | numpy.linalg.norm |
""" test autofile.system
"""
import os
import numbers
import tempfile
import numpy
import pytest
import automol
import autofile.info
import autofile.system
PREFIX = tempfile.mkdtemp()
print(PREFIX)
# create a dummy root DataSeries for testing
ROOT_SPEC_DFILE = autofile.system.file_.locator(
file_prefix='dir',
map_dct_={
'loc1': lambda locs: locs[0],
'loc2': lambda locs: locs[1],
'other': lambda locs: 'something else',
},
loc_keys=['loc1', 'loc2'],
)
def root_data_series_directory(prefix):
""" root DataSeries
"""
return autofile.system.model.DataSeries(
prefix,
map_=lambda x: os.path.join(*map(str, x)),
nlocs=2,
depth=2,
loc_dfile=ROOT_SPEC_DFILE,)
def test__file__input_file():
""" test autofile.system.file_.input_file
"""
ref_inp_str = '<input file contents>'
inp_dfile = autofile.system.file_.input_file('test')
assert not inp_dfile.exists(PREFIX)
inp_dfile.write(ref_inp_str, PREFIX)
assert inp_dfile.exists(PREFIX)
inp_str = inp_dfile.read(PREFIX)
assert inp_str == ref_inp_str
print(inp_str)
def test__file__output_file():
""" test autofile.system.file_.output_file
"""
ref_out_str = '<output file contents>'
out_dfile = autofile.system.file_.output_file('test')
assert not out_dfile.exists(PREFIX)
out_dfile.write(ref_out_str, PREFIX)
assert out_dfile.exists(PREFIX)
out_str = out_dfile.read(PREFIX)
assert out_str == ref_out_str
print(out_str)
def test__file__information():
""" test autofile.system.file_.information
"""
def information(nsamp, tors_ranges):
""" base information object
"""
tors_ranges = autofile.info.Info(**dict(tors_ranges))
assert isinstance(nsamp, numbers.Integral)
inf_obj = autofile.info.Info(nsamp=nsamp, tors_ranges=tors_ranges)
assert autofile.info.matches_function_signature(inf_obj, information)
return inf_obj
ref_inf_obj = information(
nsamp=4, tors_ranges={'d1': (0., 1.), 'd2': (0., 3.)})
inf_dfile = autofile.system.file_.information('test', function=information)
assert not inf_dfile.exists(PREFIX)
inf_dfile.write(ref_inf_obj, PREFIX)
assert inf_dfile.exists(PREFIX)
inf_obj = inf_dfile.read(PREFIX)
assert inf_obj == ref_inf_obj
print(inf_obj)
def test__file__energy():
""" test autofile.system.file_.energy
"""
ref_ene = -187.38518070487598
ene_dfile = autofile.system.file_.energy('test')
assert not ene_dfile.exists(PREFIX)
ene_dfile.write(ref_ene, PREFIX)
assert ene_dfile.exists(PREFIX)
ene = ene_dfile.read(PREFIX)
assert numpy.isclose(ene, ref_ene)
print(ene)
def test__file__geometry():
""" test autofile.system.file_.geometry
"""
ref_geo = (('C', (0.066541036329, -0.86543409422, -0.56994517889)),
('O', (0.066541036329, -0.86543409422, 2.13152981129)),
('O', (0.066541036329, 1.6165813318, -1.63686376233)),
('H', (-1.52331011945, -1.99731957213, -1.31521725797)),
('H', (1.84099386813, -1.76479255185, -1.16213243427)),
('H', (-1.61114836922, -0.17751142359, 2.6046492029)),
('H', (-1.61092727126, 2.32295906780, -1.19178601663)))
geo_dfile = autofile.system.file_.geometry('test')
assert not geo_dfile.exists(PREFIX)
geo_dfile.write(ref_geo, PREFIX)
assert geo_dfile.exists(PREFIX)
geo = geo_dfile.read(PREFIX)
assert automol.geom.almost_equal(geo, ref_geo)
print(geo)
def test__file__gradient():
""" test autofile.system.file_.gradient
"""
ref_grad = ((0.00004103632, 0.00003409422, 0.00004517889),
(0.00004103632, 0.00003409422, 0.00002981129),
(0.00004103632, 0.00008133180, 0.00006376233),
(0.00001011945, 0.00001957213, 0.00001725797),
(0.00009386813, 0.00009255185, 0.00003243427),
(0.00004836922, 0.00001142359, 0.00004920290),
(0.00002727126, 0.00005906780, 0.00008601663))
grad_dfile = autofile.system.file_.gradient('test')
assert not grad_dfile.exists(PREFIX)
grad_dfile.write(ref_grad, PREFIX)
assert grad_dfile.exists(PREFIX)
grad = grad_dfile.read(PREFIX)
assert numpy.allclose(grad, ref_grad)
print(grad)
def test__file__hessian():
""" test autofile.system.file_.hessian
"""
ref_hess = (
(-0.21406, 0., 0., -0.06169, 0., 0., 0.27574, 0., 0.),
(0., 2.05336, 0.12105, 0., -0.09598, 0.08316, 0., -1.95737, -0.20421),
(0., 0.12105, 0.19177, 0., -0.05579, -0.38831, 0., -0.06525, 0.19654),
(-0.06169, 0., 0., 0.0316, 0., 0., 0.03009, 0., 0.),
(0., -0.09598, -0.05579, 0., 0.12501, -0.06487, 0., -0.02902,
0.12066),
(0., 0.08316, -0.38831, 0., -0.06487, 0.44623, 0., -0.01829,
-0.05792),
(0.27574, 0., 0., 0.03009, 0., 0., -0.30583, 0., 0.),
(0., -1.95737, -0.06525, 0., -0.02902, -0.01829, 0., 1.9864,
0.08354),
(0., -0.20421, 0.19654, 0., 0.12066, -0.05792, 0., 0.08354,
-0.13862))
hess_dfile = autofile.system.file_.hessian('test')
assert not hess_dfile.exists(PREFIX)
hess_dfile.write(ref_hess, PREFIX)
assert hess_dfile.exists(PREFIX)
hess = hess_dfile.read(PREFIX)
assert numpy.allclose(hess, ref_hess)
print(hess)
def test__file__zmatrix():
""" test autofile.system.file_.zmatrix
"""
ref_zma = (
(('C', (None, None, None), (None, None, None)),
('O', (0, None, None), ('r1', None, None)),
('O', (0, 1, None), ('r2', 'a1', None)),
('H', (0, 1, 2), ('r3', 'a2', 'd1')),
('H', (0, 1, 2), ('r4', 'a3', 'd2')),
('H', (1, 0, 2), ('r5', 'a4', 'd3')),
('H', (2, 0, 1), ('r6', 'a5', 'd4'))),
{'r1': 2.65933,
'r2': 2.65933, 'a1': 1.90743,
'r3': 2.06844, 'a2': 1.93366, 'd1': 4.1477,
'r4': 2.06548, 'a3': 1.89469, 'd2': 2.06369,
'r5': 1.83126, 'a4': 1.86751, 'd3': 1.44253,
'r6': 1.83126, 'a5': 1.86751, 'd4': 4.84065})
zma_dfile = autofile.system.file_.zmatrix('test')
assert not zma_dfile.exists(PREFIX)
zma_dfile.write(ref_zma, PREFIX)
assert zma_dfile.exists(PREFIX)
zma = zma_dfile.read(PREFIX)
assert automol.zmatrix.almost_equal(zma, ref_zma)
print(zma)
def test__file__vmatrix():
""" test autofile.system.file_.vmatrix
"""
ref_vma = (('C', (None, None, None), (None, None, None)),
('O', (0, None, None), ('r1', None, None)),
('O', (0, 1, None), ('r2', 'a1', None)),
('H', (0, 1, 2), ('r3', 'a2', 'd1')),
('H', (0, 1, 2), ('r4', 'a3', 'd2')),
('H', (1, 0, 2), ('r5', 'a4', 'd3')),
('H', (2, 0, 1), ('r6', 'a5', 'd4')))
vma_dfile = autofile.system.file_.vmatrix('test')
assert not vma_dfile.exists(PREFIX)
vma_dfile.write(ref_vma, PREFIX)
assert vma_dfile.exists(PREFIX)
vma = vma_dfile.read(PREFIX)
assert vma == ref_vma
print(vma)
def test__file__trajectory():
""" test autofile.system.file_.trajectory
"""
ref_geos = [
(('C', (0.0, 0.0, 0.0)),
('O', (0.0, 0.0, 2.699694868173)),
('O', (0.0, 2.503038629201, -1.011409768236)),
('H', (-1.683942509299, -1.076047850358, -0.583313101501)),
('H', (1.684063451772, -0.943916309940, -0.779079279468)),
('H', (1.56980872050, 0.913848877557, 3.152002706027)),
('H', (-1.57051358834, 3.264399836517, -0.334901043405))),
(('C', (0.0, 0.0, 0.0)),
('O', (0.0, 0.0, 2.70915105770)),
('O', (0.0, 2.55808068205, -0.83913477573)),
('H', (-1.660164085463, -1.04177010816, -0.73213470306)),
('H', (1.711679909369, -0.895873802652, -0.779058492481)),
('H', (0.0238181080852, -1.813377410537, 3.16912929390)),
('H', (-1.36240560905, 3.348313125118, 0.1732746576216)))]
ref_comments = ['energy: -187.3894105487809',
'energy: -187.3850624381528']
ref_traj = list(zip(ref_comments, ref_geos))
traj_dfile = autofile.system.file_.trajectory('test')
assert not traj_dfile.exists(PREFIX)
traj_dfile.write(ref_traj, PREFIX)
assert traj_dfile.exists(PREFIX)
# I'm not going to bother implementing a reader, since the trajectory files
# are for human use only -- we aren't going to use this for data storage
def test__file__lennard_jones_epsilon():
""" test autofile.system.file_.lennard_jones_epsilon
"""
ref_eps = 247.880866746988
eps_dfile = autofile.system.file_.lennard_jones_epsilon('test')
assert not eps_dfile.exists(PREFIX)
eps_dfile.write(ref_eps, PREFIX)
assert eps_dfile.exists(PREFIX)
eps = eps_dfile.read(PREFIX)
assert numpy.isclose(eps, ref_eps)
print(eps)
def test__file__lennard_jones_sigma():
""" test autofile.system.file_.lennard_jones_sigma
"""
ref_sig = 3.55018590361446
sig_dfile = autofile.system.file_.lennard_jones_sigma('test')
assert not sig_dfile.exists(PREFIX)
sig_dfile.write(ref_sig, PREFIX)
assert sig_dfile.exists(PREFIX)
sig = sig_dfile.read(PREFIX)
assert | numpy.isclose(sig, ref_sig) | numpy.isclose |
import numpy as np
import pytest
from scipy.stats import (bootstrap, BootstrapDegenerateDistributionWarning,
monte_carlo_test, permutation_test)
from numpy.testing import assert_allclose, assert_equal, suppress_warnings
from scipy import stats
from scipy import special
from .. import _resampling as _resampling
from scipy._lib._util import rng_integers
from scipy.optimize import root
def test_bootstrap_iv():
message = "`data` must be a sequence of samples."
with pytest.raises(ValueError, match=message):
bootstrap(1, np.mean)
message = "`data` must contain at least one sample."
with pytest.raises(ValueError, match=message):
bootstrap(tuple(), np.mean)
message = "each sample in `data` must contain two or more observations..."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3], [1]), np.mean)
message = ("When `paired is True`, all samples must have the same length ")
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3], [1, 2, 3, 4]), np.mean, paired=True)
message = "`vectorized` must be `True` or `False`."
with pytest.raises(ValueError, match=message):
bootstrap(1, np.mean, vectorized='ekki')
message = "`axis` must be an integer."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, axis=1.5)
message = "could not convert string to float"
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, confidence_level='ni')
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, n_resamples=-1000)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, n_resamples=1000.5)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, batch=-1000)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, batch=1000.5)
message = "`method` must be in"
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, method='ekki')
message = "`method = 'BCa' is only available for one-sample statistics"
def statistic(x, y, axis):
mean1 = np.mean(x, axis)
mean2 = np.mean(y, axis)
return mean1 - mean2
with pytest.raises(ValueError, match=message):
bootstrap(([.1, .2, .3], [.1, .2, .3]), statistic, method='BCa')
message = "'herring' cannot be used to seed a"
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, random_state='herring')
@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
@pytest.mark.parametrize("axis", [0, 1, 2])
def test_bootstrap_batch(method, axis):
# for one-sample statistics, batch size shouldn't affect the result
np.random.seed(0)
x = np.random.rand(10, 11, 12)
res1 = bootstrap((x,), np.mean, batch=None, method=method,
random_state=0, axis=axis, n_resamples=100)
res2 = bootstrap((x,), np.mean, batch=10, method=method,
random_state=0, axis=axis, n_resamples=100)
assert_equal(res2.confidence_interval.low, res1.confidence_interval.low)
assert_equal(res2.confidence_interval.high, res1.confidence_interval.high)
assert_equal(res2.standard_error, res1.standard_error)
@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
def test_bootstrap_paired(method):
# test that `paired` works as expected
np.random.seed(0)
n = 100
x = np.random.rand(n)
y = np.random.rand(n)
def my_statistic(x, y, axis=-1):
return ((x-y)**2).mean(axis=axis)
def my_paired_statistic(i, axis=-1):
a = x[i]
b = y[i]
res = my_statistic(a, b)
return res
i = np.arange(len(x))
res1 = bootstrap((i,), my_paired_statistic, random_state=0)
res2 = bootstrap((x, y), my_statistic, paired=True, random_state=0)
assert_allclose(res1.confidence_interval, res2.confidence_interval)
assert_allclose(res1.standard_error, res2.standard_error)
@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
@pytest.mark.parametrize("axis", [0, 1, 2])
@pytest.mark.parametrize("paired", [True, False])
def test_bootstrap_vectorized(method, axis, paired):
# test that paired is vectorized as expected: when samples are tiled,
# CI and standard_error of each axis-slice is the same as those of the
# original 1d sample
if not paired and method == 'BCa':
# should re-assess when BCa is extended
pytest.xfail(reason="BCa currently for 1-sample statistics only")
np.random.seed(0)
def my_statistic(x, y, z, axis=-1):
return x.mean(axis=axis) + y.mean(axis=axis) + z.mean(axis=axis)
shape = 10, 11, 12
n_samples = shape[axis]
x = np.random.rand(n_samples)
y = np.random.rand(n_samples)
z = np.random.rand(n_samples)
res1 = bootstrap((x, y, z), my_statistic, paired=paired, method=method,
random_state=0, axis=0, n_resamples=100)
reshape = [1, 1, 1]
reshape[axis] = n_samples
x = np.broadcast_to(x.reshape(reshape), shape)
y = np.broadcast_to(y.reshape(reshape), shape)
z = np.broadcast_to(z.reshape(reshape), shape)
res2 = bootstrap((x, y, z), my_statistic, paired=paired, method=method,
random_state=0, axis=axis, n_resamples=100)
assert_allclose(res2.confidence_interval.low,
res1.confidence_interval.low)
assert_allclose(res2.confidence_interval.high,
res1.confidence_interval.high)
assert_allclose(res2.standard_error, res1.standard_error)
result_shape = list(shape)
result_shape.pop(axis)
assert_equal(res2.confidence_interval.low.shape, result_shape)
assert_equal(res2.confidence_interval.high.shape, result_shape)
assert_equal(res2.standard_error.shape, result_shape)
@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
def test_bootstrap_against_theory(method):
# based on https://www.statology.org/confidence-intervals-python/
data = stats.norm.rvs(loc=5, scale=2, size=5000, random_state=0)
alpha = 0.95
dist = stats.t(df=len(data)-1, loc=np.mean(data), scale=stats.sem(data))
expected_interval = dist.interval(confidence=alpha)
expected_se = dist.std()
res = bootstrap((data,), np.mean, n_resamples=5000,
confidence_level=alpha, method=method,
random_state=0)
assert_allclose(res.confidence_interval, expected_interval, rtol=5e-4)
assert_allclose(res.standard_error, expected_se, atol=3e-4)
tests_R = {"basic": (23.77, 79.12),
"percentile": (28.86, 84.21),
"BCa": (32.31, 91.43)}
@pytest.mark.parametrize("method, expected", tests_R.items())
def test_bootstrap_against_R(method, expected):
# Compare against R's "boot" library
# library(boot)
# stat <- function (x, a) {
# mean(x[a])
# }
# x <- c(10, 12, 12.5, 12.5, 13.9, 15, 21, 22,
# 23, 34, 50, 81, 89, 121, 134, 213)
# # Use a large value so we get a few significant digits for the CI.
# n = 1000000
# bootresult = boot(x, stat, n)
# result <- boot.ci(bootresult)
# print(result)
x = np.array([10, 12, 12.5, 12.5, 13.9, 15, 21, 22,
23, 34, 50, 81, 89, 121, 134, 213])
res = bootstrap((x,), np.mean, n_resamples=1000000, method=method,
random_state=0)
assert_allclose(res.confidence_interval, expected, rtol=0.005)
tests_against_itself_1samp = {"basic": 1780,
"percentile": 1784,
"BCa": 1784}
@pytest.mark.parametrize("method, expected",
tests_against_itself_1samp.items())
def test_bootstrap_against_itself_1samp(method, expected):
# The expected values in this test were generated using bootstrap
# to check for unintended changes in behavior. The test also makes sure
# that bootstrap works with multi-sample statistics and that the
# `axis` argument works as expected / function is vectorized.
np.random.seed(0)
n = 100 # size of sample
n_resamples = 999 # number of bootstrap resamples used to form each CI
confidence_level = 0.9
# The true mean is 5
dist = stats.norm(loc=5, scale=1)
stat_true = dist.mean()
# Do the same thing 2000 times. (The code is fully vectorized.)
n_replications = 2000
data = dist.rvs(size=(n_replications, n))
res = bootstrap((data,),
statistic=np.mean,
confidence_level=confidence_level,
n_resamples=n_resamples,
batch=50,
method=method,
axis=-1)
ci = res.confidence_interval
# ci contains vectors of lower and upper confidence interval bounds
ci_contains_true = np.sum((ci[0] < stat_true) & (stat_true < ci[1]))
assert ci_contains_true == expected
# ci_contains_true is not inconsistent with confidence_level
pvalue = stats.binomtest(ci_contains_true, n_replications,
confidence_level).pvalue
assert pvalue > 0.1
tests_against_itself_2samp = {"basic": 892,
"percentile": 890}
@pytest.mark.parametrize("method, expected",
tests_against_itself_2samp.items())
def test_bootstrap_against_itself_2samp(method, expected):
# The expected values in this test were generated using bootstrap
# to check for unintended changes in behavior. The test also makes sure
# that bootstrap works with multi-sample statistics and that the
# `axis` argument works as expected / function is vectorized.
np.random.seed(0)
n1 = 100 # size of sample 1
n2 = 120 # size of sample 2
n_resamples = 999 # number of bootstrap resamples used to form each CI
confidence_level = 0.9
# The statistic we're interested in is the difference in means
def my_stat(data1, data2, axis=-1):
mean1 = np.mean(data1, axis=axis)
mean2 = np.mean(data2, axis=axis)
return mean1 - mean2
# The true difference in the means is -0.1
dist1 = stats.norm(loc=0, scale=1)
dist2 = stats.norm(loc=0.1, scale=1)
stat_true = dist1.mean() - dist2.mean()
# Do the same thing 1000 times. (The code is fully vectorized.)
n_replications = 1000
data1 = dist1.rvs(size=(n_replications, n1))
data2 = dist2.rvs(size=(n_replications, n2))
res = bootstrap((data1, data2),
statistic=my_stat,
confidence_level=confidence_level,
n_resamples=n_resamples,
batch=50,
method=method,
axis=-1)
ci = res.confidence_interval
# ci contains vectors of lower and upper confidence interval bounds
ci_contains_true = np.sum((ci[0] < stat_true) & (stat_true < ci[1]))
assert ci_contains_true == expected
# ci_contains_true is not inconsistent with confidence_level
pvalue = stats.binomtest(ci_contains_true, n_replications,
confidence_level).pvalue
assert pvalue > 0.1
@pytest.mark.parametrize("method", ["basic", "percentile"])
@pytest.mark.parametrize("axis", [0, 1])
def test_bootstrap_vectorized_3samp(method, axis):
def statistic(*data, axis=0):
# an arbitrary, vectorized statistic
return sum((sample.mean(axis) for sample in data))
def statistic_1d(*data):
# the same statistic, not vectorized
for sample in data:
assert sample.ndim == 1
return statistic(*data, axis=0)
np.random.seed(0)
x = np.random.rand(4, 5)
y = np.random.rand(4, 5)
z = np.random.rand(4, 5)
res1 = bootstrap((x, y, z), statistic, vectorized=True,
axis=axis, n_resamples=100, method=method, random_state=0)
res2 = bootstrap((x, y, z), statistic_1d, vectorized=False,
axis=axis, n_resamples=100, method=method, random_state=0)
assert_allclose(res1.confidence_interval, res2.confidence_interval)
assert_allclose(res1.standard_error, res2.standard_error)
@pytest.mark.xfail_on_32bit("Failure is not concerning; see gh-14107")
@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
@pytest.mark.parametrize("axis", [0, 1])
def test_bootstrap_vectorized_1samp(method, axis):
def statistic(x, axis=0):
# an arbitrary, vectorized statistic
return x.mean(axis=axis)
def statistic_1d(x):
# the same statistic, not vectorized
assert x.ndim == 1
return statistic(x, axis=0)
np.random.seed(0)
x = np.random.rand(4, 5)
res1 = bootstrap((x,), statistic, vectorized=True, axis=axis,
n_resamples=100, batch=None, method=method,
random_state=0)
res2 = bootstrap((x,), statistic_1d, vectorized=False, axis=axis,
n_resamples=100, batch=10, method=method,
random_state=0)
assert_allclose(res1.confidence_interval, res2.confidence_interval)
assert_allclose(res1.standard_error, res2.standard_error)
@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
def test_bootstrap_degenerate(method):
data = 35 * [10000.]
if method == "BCa":
with np.errstate(invalid='ignore'):
with pytest.warns(BootstrapDegenerateDistributionWarning):
res = bootstrap([data, ], np.mean, method=method)
assert_equal(res.confidence_interval, (np.nan, np.nan))
else:
res = bootstrap([data, ], np.mean, method=method)
assert_equal(res.confidence_interval, (10000., 10000.))
assert_equal(res.standard_error, 0)
@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
def test_bootstrap_gh15678(method):
# Check that gh-15678 is fixed: when statistic function returned a Python
# float, method="BCa" failed when trying to add a dimension to the float
rng = np.random.default_rng(354645618886684)
dist = stats.norm(loc=2, scale=4)
data = dist.rvs(size=100, random_state=rng)
data = (data,)
res = bootstrap(data, stats.skew, method=method, n_resamples=100,
random_state=np.random.default_rng(9563))
# this always worked because np.apply_along_axis returns NumPy data type
ref = bootstrap(data, stats.skew, method=method, n_resamples=100,
random_state=np.random.default_rng(9563), vectorized=False)
assert_allclose(res.confidence_interval, ref.confidence_interval)
assert_allclose(res.standard_error, ref.standard_error)
assert isinstance(res.standard_error, np.float64)
def test_jackknife_resample():
shape = 3, 4, 5, 6
np.random.seed(0)
x = np.random.rand(*shape)
y = next(_resampling._jackknife_resample(x))
for i in range(shape[-1]):
# each resample is indexed along second to last axis
# (last axis is the one the statistic will be taken over / consumed)
slc = y[..., i, :]
expected = np.delete(x, i, axis=-1)
assert np.array_equal(slc, expected)
y2 = np.concatenate(list(_resampling._jackknife_resample(x, batch=2)),
axis=-2)
assert np.array_equal(y2, y)
@pytest.mark.parametrize("rng_name", ["RandomState", "default_rng"])
def test_bootstrap_resample(rng_name):
rng = getattr(np.random, rng_name, None)
if rng is None:
pytest.skip(f"{rng_name} not available.")
rng1 = rng(0)
rng2 = rng(0)
n_resamples = 10
shape = 3, 4, 5, 6
np.random.seed(0)
x = np.random.rand(*shape)
y = _resampling._bootstrap_resample(x, n_resamples, random_state=rng1)
for i in range(n_resamples):
# each resample is indexed along second to last axis
# (last axis is the one the statistic will be taken over / consumed)
slc = y[..., i, :]
js = rng_integers(rng2, 0, shape[-1], shape[-1])
expected = x[..., js]
assert np.array_equal(slc, expected)
@pytest.mark.parametrize("score", [0, 0.5, 1])
@pytest.mark.parametrize("axis", [0, 1, 2])
def test_percentile_of_score(score, axis):
shape = 10, 20, 30
np.random.seed(0)
x = np.random.rand(*shape)
p = _resampling._percentile_of_score(x, score, axis=-1)
def vectorized_pos(a, score, axis):
return np.apply_along_axis(stats.percentileofscore, axis, a, score)
p2 = vectorized_pos(x, score, axis=-1)/100
assert_allclose(p, p2, 1e-15)
def test_percentile_along_axis():
# the difference between _percentile_along_axis and np.percentile is that
# np.percentile gets _all_ the qs for each axis slice, whereas
# _percentile_along_axis gets the q corresponding with each axis slice
shape = 10, 20
np.random.seed(0)
x = np.random.rand(*shape)
q = np.random.rand(*shape[:-1]) * 100
y = _resampling._percentile_along_axis(x, q)
for i in range(shape[0]):
res = y[i]
expected = np.percentile(x[i], q[i], axis=-1)
assert_allclose(res, expected, 1e-15)
@pytest.mark.parametrize("axis", [0, 1, 2])
def test_vectorize_statistic(axis):
# test that _vectorize_statistic vectorizes a statistic along `axis`
def statistic(*data, axis):
# an arbitrary, vectorized statistic
return sum((sample.mean(axis) for sample in data))
def statistic_1d(*data):
# the same statistic, not vectorized
for sample in data:
assert sample.ndim == 1
return statistic(*data, axis=0)
# vectorize the non-vectorized statistic
statistic2 = _resampling._vectorize_statistic(statistic_1d)
np.random.seed(0)
x = np.random.rand(4, 5, 6)
y = np.random.rand(4, 1, 6)
z = np.random.rand(1, 5, 6)
res1 = statistic(x, y, z, axis=axis)
res2 = statistic2(x, y, z, axis=axis)
assert_allclose(res1, res2)
@pytest.mark.xslow()
@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
def test_vector_valued_statistic(method):
# Generate 95% confidence interval around MLE of normal distribution
# parameters. Repeat 100 times, each time on sample of size 100.
# Check that confidence interval contains true parameters ~95 times.
# Confidence intervals are estimated and stochastic; a test failure
# does not necessarily indicate that something is wrong. More important
# than values of `counts` below is that the shapes of the outputs are
# correct.
rng = np.random.default_rng(2196847219)
params = 1, 0.5
sample = stats.norm.rvs(*params, size=(100, 100), random_state=rng)
def statistic(data):
return stats.norm.fit(data)
res = bootstrap((sample,), statistic, method=method, axis=-1,
vectorized=False)
counts = np.sum((res.confidence_interval.low.T < params)
& (res.confidence_interval.high.T > params),
axis=0)
assert np.all(counts >= 90)
assert np.all(counts <= 100)
assert res.confidence_interval.low.shape == (2, 100)
assert res.confidence_interval.high.shape == (2, 100)
assert res.standard_error.shape == (2, 100)
# --- Test Monte Carlo Hypothesis Test --- #
class TestMonteCarloHypothesisTest:
atol = 2.5e-2 # for comparing p-value
def rvs(self, rvs_in, rs):
return lambda *args, **kwds: rvs_in(*args, random_state=rs, **kwds)
def test_input_validation(self):
# test that the appropriate error messages are raised for invalid input
def stat(x):
return stats.skewnorm(x).statistic
message = "`axis` must be an integer."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat, axis=1.5)
message = "`vectorized` must be `True` or `False`."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat, vectorized=1.5)
message = "`rvs` must be callable."
with pytest.raises(TypeError, match=message):
monte_carlo_test([1, 2, 3], None, stat)
message = "`statistic` must be callable."
with pytest.raises(TypeError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, None)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat,
n_resamples=-1000)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat,
n_resamples=1000.5)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat, batch=-1000)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat, batch=1000.5)
message = "`alternative` must be in..."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat,
alternative='ekki')
def test_batch(self):
# make sure that the `batch` parameter is respected by checking the
# maximum batch size provided in calls to `statistic`
rng = np.random.default_rng(23492340193)
x = rng.random(10)
def statistic(x, axis):
batch_size = 1 if x.ndim == 1 else len(x)
statistic.batch_size = max(batch_size, statistic.batch_size)
statistic.counter += 1
return stats.skewtest(x, axis=axis).statistic
statistic.counter = 0
statistic.batch_size = 0
kwds = {'sample': x, 'statistic': statistic,
'n_resamples': 1000, 'vectorized': True}
kwds['rvs'] = self.rvs(stats.norm.rvs, np.random.default_rng(32842398))
res1 = monte_carlo_test(batch=1, **kwds)
assert_equal(statistic.counter, 1001)
assert_equal(statistic.batch_size, 1)
kwds['rvs'] = self.rvs(stats.norm.rvs, np.random.default_rng(32842398))
statistic.counter = 0
res2 = monte_carlo_test(batch=50, **kwds)
assert_equal(statistic.counter, 21)
assert_equal(statistic.batch_size, 50)
kwds['rvs'] = self.rvs(stats.norm.rvs, np.random.default_rng(32842398))
statistic.counter = 0
res3 = monte_carlo_test(**kwds)
assert_equal(statistic.counter, 2)
assert_equal(statistic.batch_size, 1000)
assert_equal(res1.pvalue, res3.pvalue)
assert_equal(res2.pvalue, res3.pvalue)
@pytest.mark.parametrize('axis', range(-3, 3))
def test_axis(self, axis):
# test that Nd-array samples are handled correctly for valid values
# of the `axis` parameter
rng = np.random.default_rng(2389234)
norm_rvs = self.rvs(stats.norm.rvs, rng)
size = [2, 3, 4]
size[axis] = 100
x = norm_rvs(size=size)
expected = stats.skewtest(x, axis=axis)
def statistic(x, axis):
return stats.skewtest(x, axis=axis).statistic
res = monte_carlo_test(x, norm_rvs, statistic, vectorized=True,
n_resamples=20000, axis=axis)
assert_allclose(res.statistic, expected.statistic)
assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
@pytest.mark.parametrize('alternative', ("less", "greater"))
@pytest.mark.parametrize('a', np.linspace(-0.5, 0.5, 5)) # skewness
def test_against_ks_1samp(self, alternative, a):
# test that monte_carlo_test can reproduce pvalue of ks_1samp
rng = np.random.default_rng(65723433)
x = stats.skewnorm.rvs(a=a, size=30, random_state=rng)
expected = stats.ks_1samp(x, stats.norm.cdf, alternative=alternative)
def statistic1d(x):
return stats.ks_1samp(x, stats.norm.cdf, mode='asymp',
alternative=alternative).statistic
norm_rvs = self.rvs(stats.norm.rvs, rng)
res = monte_carlo_test(x, norm_rvs, statistic1d,
n_resamples=1000, vectorized=False,
alternative=alternative)
assert_allclose(res.statistic, expected.statistic)
if alternative == 'greater':
assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
elif alternative == 'less':
assert_allclose(1-res.pvalue, expected.pvalue, atol=self.atol)
@pytest.mark.parametrize('hypotest', (stats.skewtest, stats.kurtosistest))
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
@pytest.mark.parametrize('a', np.linspace(-2, 2, 5)) # skewness
def test_against_normality_tests(self, hypotest, alternative, a):
# test that monte_carlo_test can reproduce pvalue of normality tests
rng = np.random.default_rng(85723405)
x = stats.skewnorm.rvs(a=a, size=150, random_state=rng)
expected = hypotest(x, alternative=alternative)
def statistic(x, axis):
return hypotest(x, axis=axis).statistic
norm_rvs = self.rvs(stats.norm.rvs, rng)
res = monte_carlo_test(x, norm_rvs, statistic, vectorized=True,
alternative=alternative)
assert_allclose(res.statistic, expected.statistic)
assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
@pytest.mark.parametrize('a', np.arange(-2, 3)) # skewness parameter
def test_against_normaltest(self, a):
# test that monte_carlo_test can reproduce pvalue of normaltest
rng = np.random.default_rng(12340513)
x = stats.skewnorm.rvs(a=a, size=150, random_state=rng)
expected = stats.normaltest(x)
def statistic(x, axis):
return stats.normaltest(x, axis=axis).statistic
norm_rvs = self.rvs(stats.norm.rvs, rng)
res = monte_carlo_test(x, norm_rvs, statistic, vectorized=True,
alternative='greater')
assert_allclose(res.statistic, expected.statistic)
assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
@pytest.mark.parametrize('a', np.linspace(-0.5, 0.5, 5)) # skewness
def test_against_cramervonmises(self, a):
# test that monte_carlo_test can reproduce pvalue of cramervonmises
rng = np.random.default_rng(234874135)
x = stats.skewnorm.rvs(a=a, size=30, random_state=rng)
expected = stats.cramervonmises(x, stats.norm.cdf)
def statistic1d(x):
return stats.cramervonmises(x, stats.norm.cdf).statistic
norm_rvs = self.rvs(stats.norm.rvs, rng)
res = monte_carlo_test(x, norm_rvs, statistic1d,
n_resamples=1000, vectorized=False,
alternative='greater')
assert_allclose(res.statistic, expected.statistic)
assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
@pytest.mark.parametrize('dist_name', ('norm', 'logistic'))
@pytest.mark.parametrize('i', range(5))
def test_against_anderson(self, dist_name, i):
# test that monte_carlo_test can reproduce results of `anderson`. Note:
# `anderson` does not provide a p-value; it provides a list of
# significance levels and the associated critical value of the test
# statistic. `i` used to index this list.
# find the skewness for which the sample statistic matches one of the
# critical values provided by `stats.anderson`
def fun(a):
rng = np.random.default_rng(394295467)
x = stats.tukeylambda.rvs(a, size=100, random_state=rng)
expected = stats.anderson(x, dist_name)
return expected.statistic - expected.critical_values[i]
with suppress_warnings() as sup:
sup.filter(RuntimeWarning)
sol = root(fun, x0=0)
assert(sol.success)
# get the significance level (p-value) associated with that critical
# value
a = sol.x[0]
rng = np.random.default_rng(394295467)
x = stats.tukeylambda.rvs(a, size=100, random_state=rng)
expected = stats.anderson(x, dist_name)
expected_stat = expected.statistic
expected_p = expected.significance_level[i]/100
# perform equivalent Monte Carlo test and compare results
def statistic1d(x):
return stats.anderson(x, dist_name).statistic
dist_rvs = self.rvs(getattr(stats, dist_name).rvs, rng)
with suppress_warnings() as sup:
sup.filter(RuntimeWarning)
res = monte_carlo_test(x, dist_rvs,
statistic1d, n_resamples=1000,
vectorized=False, alternative='greater')
assert_allclose(res.statistic, expected_stat)
assert_allclose(res.pvalue, expected_p, atol=2*self.atol)
class TestPermutationTest:
rtol = 1e-14
# -- Input validation -- #
def test_permutation_test_iv(self):
def stat(x, y, axis):
return stats.ttest_ind((x, y), axis).statistic
message = "each sample in `data` must contain two or more ..."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1]), stat)
message = "`data` must be a tuple containing at least two samples"
with pytest.raises(ValueError, match=message):
permutation_test((1,), stat)
with pytest.raises(TypeError, match=message):
permutation_test(1, stat)
message = "`axis` must be an integer."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, axis=1.5)
message = "`permutation_type` must be in..."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat,
permutation_type="ekki")
message = "`vectorized` must be `True` or `False`."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, vectorized=1.5)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, n_resamples=-1000)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, n_resamples=1000.5)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, batch=-1000)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, batch=1000.5)
message = "`alternative` must be in..."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, alternative='ekki')
message = "'herring' cannot be used to seed a"
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat,
random_state='herring')
# -- Test Parameters -- #
@pytest.mark.parametrize('permutation_type',
['pairings', 'samples', 'independent'])
def test_batch(self, permutation_type):
# make sure that the `batch` parameter is respected by checking the
# maximum batch size provided in calls to `statistic`
np.random.seed(0)
x = np.random.rand(10)
y = | np.random.rand(10) | numpy.random.rand |
#!/usr/bin/env python
# Copyright 2014-2019 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import time
from functools import reduce
import numpy
import scipy.linalg
from pyscf import lib
from pyscf import gto
from pyscf.lib import logger
from pyscf.scf import hf
from pyscf.scf import chkfile
from pyscf import __config__
WITH_META_LOWDIN = getattr(__config__, 'scf_analyze_with_meta_lowdin', True)
PRE_ORTH_METHOD = getattr(__config__, 'scf_analyze_pre_orth_method', 'ANO')
BREAKSYM = getattr(__config__, 'scf_uhf_init_guess_breaksym', True)
MO_BASE = getattr(__config__, 'MO_BASE', 1)
def init_guess_by_minao(mol, breaksym=BREAKSYM):
'''Generate initial guess density matrix based on ANO basis, then project
the density matrix to the basis set defined by ``mol``
Returns:
Density matrices, a list of 2D ndarrays for alpha and beta spins
'''
dm = hf.init_guess_by_minao(mol)
dma = dmb = dm*.5
if breaksym:
#remove off-diagonal part of beta DM
dmb = numpy.zeros_like(dma)
for b0, b1, p0, p1 in mol.aoslice_by_atom():
dmb[p0:p1,p0:p1] = dma[p0:p1,p0:p1]
return numpy.array((dma,dmb))
def init_guess_by_1e(mol, breaksym=BREAKSYM):
return UHF(mol).init_guess_by_1e(mol, breaksym)
def init_guess_by_atom(mol, breaksym=BREAKSYM):
dm = hf.init_guess_by_atom(mol)
dma = dmb = dm*.5
if breaksym:
#Add off-diagonal part for alpha DM
dma = mol.intor('int1e_ovlp') * 1e-2
for b0, b1, p0, p1 in mol.aoslice_by_atom():
dma[p0:p1,p0:p1] = dmb[p0:p1,p0:p1]
return numpy.array((dma,dmb))
def init_guess_by_chkfile(mol, chkfile_name, project=None):
'''Read SCF chkfile and make the density matrix for UHF initial guess.
Kwargs:
project : None or bool
Whether to project chkfile's orbitals to the new basis. Note when
the geometry of the chkfile and the given molecule are very
different, this projection can produce very poor initial guess.
In PES scanning, it is recommended to swith off project.
If project is set to None, the projection is only applied when the
basis sets of the chkfile's molecule are different to the basis
sets of the given molecule (regardless whether the geometry of
the two molecules are different). Note the basis sets are
considered to be different if the two molecules are derived from
the same molecule with different ordering of atoms.
'''
from pyscf.scf import addons
chk_mol, scf_rec = chkfile.load_scf(chkfile_name)
if project is None:
project = not gto.same_basis_set(chk_mol, mol)
# Check whether the two molecules are similar
im1 = scipy.linalg.eigvalsh(mol.inertia_moment())
im2 = scipy.linalg.eigvalsh(chk_mol.inertia_moment())
# im1+1e-7 to avoid 'divide by zero' error
if abs((im1-im2)/(im1+1e-7)).max() > 0.01:
logger.warn(mol, "Large deviations found between the input "
"molecule and the molecule from chkfile\n"
"Initial guess density matrix may have large error.")
if project:
s = hf.get_ovlp(mol)
def fproj(mo):
if project:
mo = addons.project_mo_nr2nr(chk_mol, mo, mol)
norm = numpy.einsum('pi,pi->i', mo.conj(), s.dot(mo))
mo /= numpy.sqrt(norm)
return mo
mo = scf_rec['mo_coeff']
mo_occ = scf_rec['mo_occ']
if getattr(mo[0], 'ndim', None) == 1: # RHF
if numpy.iscomplexobj(mo):
raise NotImplementedError('TODO: project DHF orbital to UHF orbital')
mo_coeff = fproj(mo)
mo_occa = (mo_occ>1e-8).astype(numpy.double)
mo_occb = mo_occ - mo_occa
dm = make_rdm1([mo_coeff,mo_coeff], [mo_occa,mo_occb])
else: #UHF
if getattr(mo[0][0], 'ndim', None) == 2: # KUHF
logger.warn(mol, 'k-point UHF results are found. Density matrix '
'at Gamma point is used for the molecular SCF initial guess')
mo = mo[0]
dm = make_rdm1([fproj(mo[0]),fproj(mo[1])], mo_occ)
return dm
def get_init_guess(mol, key='minao'):
return UHF(mol).get_init_guess(mol, key)
def make_rdm1(mo_coeff, mo_occ, **kwargs):
'''One-particle density matrix
Returns:
A list of 2D ndarrays for alpha and beta spins
'''
mo_a = mo_coeff[0]
mo_b = mo_coeff[1]
dm_a = numpy.dot(mo_a*mo_occ[0], mo_a.conj().T)
dm_b = numpy.dot(mo_b*mo_occ[1], mo_b.conj().T)
# DO NOT make tag_array for DM here because the DM arrays may be modified and
# passed to functions like get_jk, get_vxc. These functions may take the tags
# (mo_coeff, mo_occ) to compute the potential if tags were found in the DM
# arrays and modifications to DM arrays may be ignored.
return numpy.array((dm_a,dm_b))
def get_veff(mol, dm, dm_last=0, vhf_last=0, hermi=1, vhfopt=None):
r'''Unrestricted Hartree-Fock potential matrix of alpha and beta spins,
for the given density matrix
.. math::
V_{ij}^\alpha &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta)
- \sum_{kl} (il|kj)\gamma_{lk}^\alpha \\
V_{ij}^\beta &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta)
- \sum_{kl} (il|kj)\gamma_{lk}^\beta
Args:
mol : an instance of :class:`Mole`
dm : a list of ndarrays
A list of density matrices, stored as (alpha,alpha,...,beta,beta,...)
Kwargs:
dm_last : ndarray or a list of ndarrays or 0
The density matrix baseline. When it is not 0, this function computes
the increment of HF potential w.r.t. the reference HF potential matrix.
vhf_last : ndarray or a list of ndarrays or 0
The reference HF potential matrix.
hermi : int
Whether J, K matrix is hermitian
| 0 : no hermitian or symmetric
| 1 : hermitian
| 2 : anti-hermitian
vhfopt :
A class which holds precomputed quantities to optimize the
computation of J, K matrices
Returns:
:math:`V_{hf} = (V^\alpha, V^\beta)`. :math:`V^\alpha` (and :math:`V^\beta`)
can be a list matrices, corresponding to the input density matrices.
Examples:
>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dmsa = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dmsb = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dms = numpy.vstack((dmsa,dmsb))
>>> dms.shape
(6, 2, 2)
>>> vhfa, vhfb = scf.uhf.get_veff(mol, dms, hermi=0)
>>> vhfa.shape
(3, 2, 2)
>>> vhfb.shape
(3, 2, 2)
'''
dm = numpy.asarray(dm)
nao = dm.shape[-1]
ddm = dm - numpy.asarray(dm_last)
# dm.reshape(-1,nao,nao) to remove first dim, compress (dma,dmb)
vj, vk = hf.get_jk(mol, ddm.reshape(-1,nao,nao), hermi=hermi, vhfopt=vhfopt)
vj = vj.reshape(dm.shape)
vk = vk.reshape(dm.shape)
assert(vj.ndim >= 3 and vj.shape[0] == 2)
vhf = vj[0] + vj[1] - vk
vhf += numpy.asarray(vhf_last)
return vhf
def get_fock(mf, h1e=None, s1e=None, vhf=None, dm=None, cycle=-1, diis=None,
diis_start_cycle=None, level_shift_factor=None, damp_factor=None):
if h1e is None: h1e = mf.get_hcore()
if vhf is None: vhf = mf.get_veff(mf.mol, dm)
f = h1e + vhf
if f.ndim == 2:
f = (f, f)
if cycle < 0 and diis is None: # Not inside the SCF iteration
return f
if diis_start_cycle is None:
diis_start_cycle = mf.diis_start_cycle
if level_shift_factor is None:
level_shift_factor = mf.level_shift
if damp_factor is None:
damp_factor = mf.damp
if s1e is None: s1e = mf.get_ovlp()
if dm is None: dm = self.make_rdm1()
if isinstance(level_shift_factor, (tuple, list, numpy.ndarray)):
shifta, shiftb = level_shift_factor
else:
shifta = shiftb = level_shift_factor
if isinstance(damp_factor, (tuple, list, numpy.ndarray)):
dampa, dampb = damp_factor
else:
dampa = dampb = damp_factor
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = [dm*.5] * 2
if 0 <= cycle < diis_start_cycle-1 and abs(dampa)+abs(dampb) > 1e-4:
f = (hf.damping(s1e, dm[0], f[0], dampa),
hf.damping(s1e, dm[1], f[1], dampb))
if diis and cycle >= diis_start_cycle:
f = diis.update(s1e, dm, f, mf, h1e, vhf)
if abs(shifta)+abs(shiftb) > 1e-4:
f = (hf.level_shift(s1e, dm[0], f[0], shifta),
hf.level_shift(s1e, dm[1], f[1], shiftb))
return numpy.array(f)
def get_occ(mf, mo_energy=None, mo_coeff=None):
if mo_energy is None: mo_energy = mf.mo_energy
e_idx_a = numpy.argsort(mo_energy[0])
e_idx_b = numpy.argsort(mo_energy[1])
e_sort_a = mo_energy[0][e_idx_a]
e_sort_b = mo_energy[1][e_idx_b]
nmo = mo_energy[0].size
n_a, n_b = mf.nelec
mo_occ = numpy.zeros_like(mo_energy)
mo_occ[0,e_idx_a[:n_a]] = 1
mo_occ[1,e_idx_b[:n_b]] = 1
if mf.verbose >= logger.INFO and n_a < nmo and n_b > 0 and n_b < nmo:
if e_sort_a[n_a-1]+1e-3 > e_sort_a[n_a]:
logger.warn(mf, 'alpha nocc = %d HOMO %.15g >= LUMO %.15g',
n_a, e_sort_a[n_a-1], e_sort_a[n_a])
else:
logger.info(mf, ' alpha nocc = %d HOMO = %.15g LUMO = %.15g',
n_a, e_sort_a[n_a-1], e_sort_a[n_a])
if e_sort_b[n_b-1]+1e-3 > e_sort_b[n_b]:
logger.warn(mf, 'beta nocc = %d HOMO %.15g >= LUMO %.15g',
n_b, e_sort_b[n_b-1], e_sort_b[n_b])
else:
logger.info(mf, ' beta nocc = %d HOMO = %.15g LUMO = %.15g',
n_b, e_sort_b[n_b-1], e_sort_b[n_b])
if e_sort_a[n_a-1]+1e-3 > e_sort_b[n_b]:
logger.warn(mf, 'system HOMO %.15g >= system LUMO %.15g',
e_sort_b[n_a-1], e_sort_b[n_b])
numpy.set_printoptions(threshold=nmo)
logger.debug(mf, ' alpha mo_energy =\n%s', mo_energy[0])
logger.debug(mf, ' beta mo_energy =\n%s', mo_energy[1])
numpy.set_printoptions(threshold=1000)
if mo_coeff is not None and mf.verbose >= logger.DEBUG:
ss, s = mf.spin_square((mo_coeff[0][:,mo_occ[0]>0],
mo_coeff[1][:,mo_occ[1]>0]), mf.get_ovlp())
logger.debug(mf, 'multiplicity <S^2> = %.8g 2S+1 = %.8g', ss, s)
return mo_occ
def get_grad(mo_coeff, mo_occ, fock_ao):
'''UHF Gradients'''
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
viridxa = ~occidxa
viridxb = ~occidxb
ga = reduce(numpy.dot, (mo_coeff[0][:,viridxa].T, fock_ao[0].T,
mo_coeff[0][:,occidxa].conj()))
gb = reduce(numpy.dot, (mo_coeff[1][:,viridxb].T, fock_ao[1].T,
mo_coeff[1][:,occidxb].conj()))
return numpy.hstack((ga.ravel(), gb.ravel()))
def energy_elec(mf, dm=None, h1e=None, vhf=None):
'''Electronic energy of Unrestricted Hartree-Fock
Returns:
Hartree-Fock electronic energy and the 2-electron part contribution
'''
if dm is None: dm = mf.make_rdm1()
if h1e is None:
h1e = mf.get_hcore()
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = numpy.array((dm*.5, dm*.5))
if vhf is None:
vhf = mf.get_veff(mf.mol, dm)
e1 = numpy.einsum('ij,ji', h1e, dm[0])
e1+= numpy.einsum('ij,ji', h1e, dm[1])
e_coul =(numpy.einsum('ij,ji', vhf[0], dm[0]) +
numpy.einsum('ij,ji', vhf[1], dm[1])) * .5
logger.debug(mf, 'E1 = %s Ecoul = %s', e1, e_coul.real)
return (e1+e_coul).real, e_coul
# mo_a and mo_b are occupied orbitals
def spin_square(mo, s=1):
r'''Spin square and multiplicity of UHF determinant
.. math::
S^2 = \frac{1}{2}(S_+ S_- + S_- S_+) + S_z^2
where :math:`S_+ = \sum_i S_{i+}` is effective for all beta occupied
orbitals; :math:`S_- = \sum_i S_{i-}` is effective for all alpha occupied
orbitals.
1. There are two possibilities for :math:`S_+ S_-`
1) same electron :math:`S_+ S_- = \sum_i s_{i+} s_{i-}`,
.. math::
\sum_i \langle UHF|s_{i+} s_{i-}|UHF\rangle
= \sum_{pq}\langle p|s_+s_-|q\rangle \gamma_{qp} = n_\alpha
2) different electrons :math:`S_+ S_- = \sum s_{i+} s_{j-}, (i\neq j)`.
There are in total :math:`n(n-1)` terms. As a two-particle operator,
.. math::
\langle S_+ S_- \rangle = \langle ij|s_+ s_-|ij\rangle
- \langle ij|s_+ s_-|ji\rangle
= -\langle i^\alpha|j^\beta\rangle
\langle j^\beta|i^\alpha\rangle
2. Similarly, for :math:`S_- S_+`
1) same electron
.. math::
\sum_i \langle s_{i-} s_{i+}\rangle = n_\beta
2) different electrons
.. math::
\langle S_- S_+ \rangle = -\langle i^\beta|j^\alpha\rangle
\langle j^\alpha|i^\beta\rangle
3. For :math:`S_z^2`
1) same electron
.. math::
\langle s_z^2\rangle = \frac{1}{4}(n_\alpha + n_\beta)
2) different electrons
.. math::
&\frac{1}{2}\sum_{ij}(\langle ij|2s_{z1}s_{z2}|ij\rangle
-\langle ij|2s_{z1}s_{z2}|ji\rangle) \\
&=\frac{1}{4}(\langle i^\alpha|i^\alpha\rangle \langle j^\alpha|j^\alpha\rangle
- \langle i^\alpha|i^\alpha\rangle \langle j^\beta|j^\beta\rangle
- \langle i^\beta|i^\beta\rangle \langle j^\alpha|j^\alpha\rangle
+ \langle i^\beta|i^\beta\rangle \langle j^\beta|j^\beta\rangle) \\
&-\frac{1}{4}(\langle i^\alpha|j^\alpha\rangle \langle j^\alpha|i^\alpha\rangle
+ \langle i^\beta|j^\beta\rangle\langle j^\beta|i^\beta\rangle) \\
&=\frac{1}{4}(n_\alpha^2 - n_\alpha n_\beta - n_\beta n_\alpha + n_\beta^2)
-\frac{1}{4}(n_\alpha + n_\beta) \\
&=\frac{1}{4}((n_\alpha-n_\beta)^2 - (n_\alpha+n_\beta))
In total
.. math::
\langle S^2\rangle &= \frac{1}{2}
(n_\alpha-\sum_{ij}\langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle
+n_\beta -\sum_{ij}\langle i^\beta|j^\alpha\rangle\langle j^\alpha|i^\beta\rangle)
+ \frac{1}{4}(n_\alpha-n_\beta)^2 \\
Args:
mo : a list of 2 ndarrays
Occupied alpha and occupied beta orbitals
Kwargs:
s : ndarray
AO overlap
Returns:
A list of two floats. The first is the expectation value of S^2.
The second is the corresponding 2S+1
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> mo = (mf.mo_coeff[0][:,mf.mo_occ[0]>0], mf.mo_coeff[1][:,mf.mo_occ[1]>0])
>>> print('S^2 = %.7f, 2S+1 = %.7f' % spin_square(mo, mol.intor('int1e_ovlp_sph')))
S^2 = 0.7570150, 2S+1 = 2.0070027
'''
mo_a, mo_b = mo
nocc_a = mo_a.shape[1]
nocc_b = mo_b.shape[1]
s = reduce(numpy.dot, (mo_a.T.conj(), s, mo_b))
ssxy = (nocc_a+nocc_b) * .5 - numpy.einsum('ij,ij->', s.conj(), s)
ssz = (nocc_b-nocc_a)**2 * .25
ss = (ssxy + ssz).real
s = numpy.sqrt(ss+.25) - .5
return ss, s*2+1
def analyze(mf, verbose=logger.DEBUG, with_meta_lowdin=WITH_META_LOWDIN,
**kwargs):
'''Analyze the given SCF object: print orbital energies, occupancies;
print orbital coefficients; Mulliken population analysis; Dipole moment
'''
from pyscf.lo import orth
from pyscf.tools import dump_mat
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
mo_coeff = mf.mo_coeff
nmo = len(mo_occ[0])
log = logger.new_logger(mf, verbose)
if log.verbose >= logger.NOTE:
log.note('**** MO energy ****')
log.note(' alpha | beta alpha | beta')
for i in range(nmo):
log.note('MO #%-3d energy= %-18.15g | %-18.15g occ= %g | %g',
i+MO_BASE, mo_energy[0][i], mo_energy[1][i],
mo_occ[0][i], mo_occ[1][i])
ovlp_ao = mf.get_ovlp()
if log.verbose >= logger.DEBUG:
label = mf.mol.ao_labels()
if with_meta_lowdin:
log.debug(' ** MO coefficients (expansion on meta-Lowdin AOs) for alpha spin **')
orth_coeff = orth.orth_ao(mf.mol, 'meta_lowdin', s=ovlp_ao)
c_inv = numpy.dot(orth_coeff.T, ovlp_ao)
dump_mat.dump_rec(mf.stdout, c_inv.dot(mo_coeff[0]), label,
start=MO_BASE, **kwargs)
log.debug(' ** MO coefficients (expansion on meta-Lowdin AOs) for beta spin **')
dump_mat.dump_rec(mf.stdout, c_inv.dot(mo_coeff[1]), label,
start=MO_BASE, **kwargs)
else:
log.debug(' ** MO coefficients (expansion on AOs) for alpha spin **')
dump_mat.dump_rec(mf.stdout, mo_coeff[0], label,
start=MO_BASE, **kwargs)
log.debug(' ** MO coefficients (expansion on AOs) for beta spin **')
dump_mat.dump_rec(mf.stdout, mo_coeff[1], label,
start=MO_BASE, **kwargs)
dm = mf.make_rdm1(mo_coeff, mo_occ)
if with_meta_lowdin:
return (mf.mulliken_meta(mf.mol, dm, s=ovlp_ao, verbose=log),
mf.dip_moment(mf.mol, dm, verbose=log))
else:
return (mf.mulliken_pop(mf.mol, dm, s=ovlp_ao, verbose=log),
mf.dip_moment(mf.mol, dm, verbose=log))
def mulliken_pop(mol, dm, s=None, verbose=logger.DEBUG):
'''Mulliken population analysis
'''
if s is None: s = hf.get_ovlp(mol)
log = logger.new_logger(mol, verbose)
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = numpy.array((dm*.5, dm*.5))
pop_a = numpy.einsum('ij,ji->i', dm[0], s).real
pop_b = numpy.einsum('ij,ji->i', dm[1], s).real
log.info(' ** Mulliken pop alpha | beta **')
for i, s in enumerate(mol.ao_labels()):
log.info('pop of %s %10.5f | %-10.5f',
s, pop_a[i], pop_b[i])
log.info('In total %10.5f | %-10.5f', sum(pop_a), sum(pop_b))
log.note(' ** Mulliken atomic charges ( Nelec_alpha | Nelec_beta ) **')
nelec_a = numpy.zeros(mol.natm)
nelec_b = numpy.zeros(mol.natm)
for i, s in enumerate(mol.ao_labels(fmt=None)):
nelec_a[s[0]] += pop_a[i]
nelec_b[s[0]] += pop_b[i]
chg = mol.atom_charges() - (nelec_a + nelec_b)
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
log.note('charge of %d%s = %10.5f ( %10.5f %10.5f )',
ia, symb, chg[ia], nelec_a[ia], nelec_b[ia])
return (pop_a,pop_b), chg
def mulliken_meta(mol, dm_ao, verbose=logger.DEBUG,
pre_orth_method=PRE_ORTH_METHOD, s=None):
'''Mulliken population analysis, based on meta-Lowdin AOs.
'''
from pyscf.lo import orth
if s is None: s = hf.get_ovlp(mol)
log = logger.new_logger(mol, verbose)
if isinstance(dm_ao, numpy.ndarray) and dm_ao.ndim == 2:
dm_ao = numpy.array((dm_ao*.5, dm_ao*.5))
c = orth.restore_ao_character(mol, pre_orth_method)
orth_coeff = orth.orth_ao(mol, 'meta_lowdin', pre_orth_ao=c, s=s)
c_inv = numpy.dot(orth_coeff.T, s)
dm_a = reduce(numpy.dot, (c_inv, dm_ao[0], c_inv.T.conj()))
dm_b = reduce(numpy.dot, (c_inv, dm_ao[1], c_inv.T.conj()))
log.note(' ** Mulliken pop alpha/beta on meta-lowdin orthogonal AOs **')
return mulliken_pop(mol, (dm_a,dm_b), numpy.eye(orth_coeff.shape[0]), log)
mulliken_pop_meta_lowdin_ao = mulliken_meta
def canonicalize(mf, mo_coeff, mo_occ, fock=None):
'''Canonicalization diagonalizes the UHF Fock matrix within occupied,
virtual subspaces separatedly (without change occupancy).
'''
mo_occ = numpy.asarray(mo_occ)
assert(mo_occ.ndim == 2)
if fock is None:
dm = mf.make_rdm1(mo_coeff, mo_occ)
fock = mf.get_hcore() + mf.get_veff(mf.mol, dm)
occidxa = mo_occ[0] == 1
occidxb = mo_occ[1] == 1
viridxa = mo_occ[0] == 0
viridxb = mo_occ[1] == 0
def eig_(fock, mo_coeff, idx, es, cs):
if numpy.count_nonzero(idx) > 0:
orb = mo_coeff[:,idx]
f1 = reduce(numpy.dot, (orb.T.conj(), fock, orb))
e, c = scipy.linalg.eigh(f1)
es[idx] = e
cs[:,idx] = numpy.dot(orb, c)
mo = numpy.empty_like(mo_coeff)
mo_e = numpy.empty(mo_occ.shape)
eig_(fock[0], mo_coeff[0], occidxa, mo_e[0], mo[0])
eig_(fock[0], mo_coeff[0], viridxa, mo_e[0], mo[0])
eig_(fock[1], mo_coeff[1], occidxb, mo_e[1], mo[1])
eig_(fock[1], mo_coeff[1], viridxb, mo_e[1], mo[1])
return mo_e, mo
def det_ovlp(mo1, mo2, occ1, occ2, ovlp):
r''' Calculate the overlap between two different determinants. It is the product
of single values of molecular orbital overlap matrix.
.. math::
S_{12} = \langle \Psi_A | \Psi_B \rangle
= (\mathrm{det}\mathbf{U}) (\mathrm{det}\mathbf{V^\dagger})\prod\limits_{i=1}\limits^{2N} \lambda_{ii}
where :math:`\mathbf{U}, \mathbf{V}, \lambda` are unitary matrices and single
values generated by single value decomposition(SVD) of the overlap matrix
:math:`\mathbf{O}` which is the overlap matrix of two sets of molecular orbitals:
.. math::
\mathbf{U}^\dagger \mathbf{O} \mathbf{V} = \mathbf{\Lambda}
Args:
mo1, mo2 : 2D ndarrays
Molecualr orbital coefficients
occ1, occ2: 2D ndarrays
occupation numbers
Return:
A list: the product of single values: float
x_a, x_b: 1D ndarrays
:math:`\mathbf{U} \mathbf{\Lambda}^{-1} \mathbf{V}^\dagger`
They are used to calculate asymmetric density matrix
'''
if not numpy.array_equal(occ1, occ2):
raise RuntimeError('Electron numbers are not equal. Electronic coupling does not exist.')
c1_a = mo1[0][:, occ1[0]>0]
c1_b = mo1[1][:, occ1[1]>0]
c2_a = mo2[0][:, occ2[0]>0]
c2_b = mo2[1][:, occ2[1]>0]
o_a = reduce(numpy.dot, (c1_a.conj().T, ovlp, c2_a))
o_b = reduce(numpy.dot, (c1_b.conj().T, ovlp, c2_b))
u_a, s_a, vt_a = numpy.linalg.svd(o_a)
u_b, s_b, vt_b = numpy.linalg.svd(o_b)
x_a = reduce(numpy.dot, (u_a*numpy.reciprocal(s_a), vt_a))
x_b = reduce(numpy.dot, (u_b*numpy.reciprocal(s_b), vt_b))
return numpy.prod(s_a)*numpy.prod(s_b), numpy.array((x_a, x_b))
def make_asym_dm(mo1, mo2, occ1, occ2, x):
r'''One-particle asymmetric density matrix
Args:
mo1, mo2 : 2D ndarrays
Molecualr orbital coefficients
occ1, occ2: 2D ndarrays
Occupation numbers
x: 2D ndarrays
:math:`\mathbf{U} \mathbf{\Lambda}^{-1} \mathbf{V}^\dagger`.
See also :func:`det_ovlp`
Return:
A list of 2D ndarrays for alpha and beta spin
Examples:
>>> mf1 = scf.UHF(gto.M(atom='H 0 0 0; F 0 0 1.3', basis='ccpvdz')).run()
>>> mf2 = scf.UHF(gto.M(atom='H 0 0 0; F 0 0 1.4', basis='ccpvdz')).run()
>>> s = gto.intor_cross('int1e_ovlp_sph', mf1.mol, mf2.mol)
>>> det, x = det_ovlp(mf1.mo_coeff, mf1.mo_occ, mf2.mo_coeff, mf2.mo_occ, s)
>>> adm = make_asym_dm(mf1.mo_coeff, mf1.mo_occ, mf2.mo_coeff, mf2.mo_occ, x)
>>> adm.shape
(2, 19, 19)
'''
mo1_a = mo1[0][:, occ1[0]>0]
mo1_b = mo1[1][:, occ1[1]>0]
mo2_a = mo2[0][:, occ2[0]>0]
mo2_b = mo2[1][:, occ2[1]>0]
dm_a = reduce(numpy.dot, (mo1_a, x[0], mo2_a.T.conj()))
dm_b = reduce(numpy.dot, (mo1_b, x[1], mo2_b.T.conj()))
return numpy.array((dm_a, dm_b))
dip_moment = hf.dip_moment
class UHF(hf.SCF):
__doc__ = hf.SCF.__doc__ + '''
Attributes for UHF:
nelec : (int, int)
If given, freeze the number of (alpha,beta) electrons to the given value.
level_shift : number or two-element list
level shift (in Eh) for alpha and beta Fock if two-element list is given.
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> print('S^2 = %.7f, 2S+1 = %.7f' % mf.spin_square())
S^2 = 0.7570150, 2S+1 = 2.0070027
'''
def __init__(self, mol):
hf.SCF.__init__(self, mol)
# self.mo_coeff => [mo_a, mo_b]
# self.mo_occ => [mo_occ_a, mo_occ_b]
# self.mo_energy => [mo_energy_a, mo_energy_b]
self.nelec = None
@property
def nelec(self):
if self._nelec is not None:
return self._nelec
else:
return self.mol.nelec
@nelec.setter
def nelec(self, x):
self._nelec = x
@property
def nelectron_alpha(self):
return self.nelec[0]
@nelectron_alpha.setter
def nelectron_alpha(self, x):
logger.warn(self, 'WARN: Attribute .nelectron_alpha is deprecated. '
'Set .nelec instead')
#raise RuntimeError('API updates')
self.nelec = (x, self.mol.nelectron-x)
def dump_flags(self, verbose=None):
hf.SCF.dump_flags(self, verbose)
logger.info(self, 'number electrons alpha = %d beta = %d', *self.nelec)
def eig(self, fock, s):
e_a, c_a = self._eigh(fock[0], s)
e_b, c_b = self._eigh(fock[1], s)
return numpy.array((e_a,e_b)), numpy.array((c_a,c_b))
get_fock = get_fock
get_occ = get_occ
def get_grad(self, mo_coeff, mo_occ, fock=None):
if fock is None:
dm1 = self.make_rdm1(mo_coeff, mo_occ)
fock = self.get_hcore(self.mol) + self.get_veff(self.mol, dm1)
return get_grad(mo_coeff, mo_occ, fock)
@lib.with_doc(make_rdm1.__doc__)
def make_rdm1(self, mo_coeff=None, mo_occ=None, **kwargs):
if mo_coeff is None:
mo_coeff = self.mo_coeff
if mo_occ is None:
mo_occ = self.mo_occ
return make_rdm1(mo_coeff, mo_occ, **kwargs)
energy_elec = energy_elec
def init_guess_by_minao(self, mol=None, breaksym=BREAKSYM):
'''Initial guess in terms of the overlap to minimal basis.'''
if mol is None: mol = self.mol
if mol.spin != 0:
# For spin polarized system, there is no need to manually break spin symmetry
breaksym = False
return init_guess_by_minao(mol, breaksym)
def init_guess_by_atom(self, mol=None, breaksym=BREAKSYM):
if mol is None: mol = self.mol
if mol.spin != 0:
# For spin polarized system, there is no need to manually break spin symmetry
breaksym = False
return init_guess_by_atom(mol, breaksym)
def init_guess_by_1e(self, mol=None, breaksym=BREAKSYM):
if mol is None: mol = self.mol
logger.info(self, 'Initial guess from hcore.')
h1e = self.get_hcore(mol)
s1e = self.get_ovlp(mol)
mo_energy, mo_coeff = self.eig((h1e,h1e), s1e)
mo_occ = self.get_occ(mo_energy, mo_coeff)
dma, dmb = self.make_rdm1(mo_coeff, mo_occ)
if mol.spin == 0 and breaksym:
#remove off-diagonal part of beta DM
dmb = numpy.zeros_like(dma)
for b0, b1, p0, p1 in mol.aoslice_by_atom():
dmb[p0:p1,p0:p1] = dma[p0:p1,p0:p1]
return numpy.array((dma,dmb))
def init_guess_by_chkfile(self, chkfile=None, project=None):
if chkfile is None: chkfile = self.chkfile
return init_guess_by_chkfile(self.mol, chkfile, project=project)
def get_jk(self, mol=None, dm=None, hermi=1):
'''Coulomb (J) and exchange (K)
Args:
dm : a list of 2D arrays or a list of 3D arrays
(alpha_dm, beta_dm) or (alpha_dms, beta_dms)
'''
if mol is None: mol = self.mol
if dm is None: dm = self.make_rdm1()
if self._eri is not None or mol.incore_anyway or self._is_mem_enough():
if self._eri is None:
self._eri = mol.intor('int2e', aosym='s8')
vj, vk = hf.dot_eri_dm(self._eri, dm, hermi)
else:
vj, vk = hf.SCF.get_jk(self, mol, dm, hermi)
return numpy.asarray(vj), numpy.asarray(vk)
@lib.with_doc(get_veff.__doc__)
def get_veff(self, mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1):
if mol is None: mol = self.mol
if dm is None: dm = self.make_rdm1()
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = numpy.asarray((dm*.5,dm*.5))
if self._eri is not None or not self.direct_scf:
vj, vk = self.get_jk(mol, dm, hermi)
vhf = vj[0] + vj[1] - vk
else:
ddm = | numpy.asarray(dm) | numpy.asarray |
#!/usr/bin/env python
# Copyright (c) 2016, wradlib developers.
# Distributed under the MIT License. See LICENSE.txt for more info.
"""
Composition
^^^^^^^^^^^
Combine data from different radar locations on one common set of locations
.. autosummary::
:nosignatures:
:toctree: generated/
extract_circle
togrid
compose_ko
compose_weighted
"""
import numpy as np
# from scipy.spatial import KDTree
# def extract_circle(center, radius, coords):
# """
# Extract the indices of coords which fall within a circle
# defined by center and radius
#
# Parameters
# ----------
# center : float
# radius : float
# coords : array of float with shape (numpoints,2)
#
# Returns
# -------
# output : 1-darray of integers
# index array referring to the coords array
#
# """
# print 'Building tree takes:'
# t0 = dt.datetime.now()
# tree = KDTree(coords)
# print dt.datetime.now() - t0
# print 'Query tree takes:'
# t0 = dt.datetime.now()
# ix = tree.query(center, k=len(coords), distance_upper_bound=radius)[1]
# print dt.datetime.now() - t0
# ix = ix[np.where(ix<len(coords))[0]]
# return ix
def extract_circle(center, radius, coords):
"""
Extract the indices of coords which fall within a circle
defined by center and radius
Parameters
----------
center : float
radius : float
coords : array of float with shape (numpoints,2)
Returns
-------
output : 1-darray of integers
index array referring to the coords array
"""
return np.where(((coords - center) ** 2).sum(axis=-1) < radius ** 2)[0]
def togrid(src, trg, radius, center, data, interpol, *args, **kwargs):
"""
Interpolate data from a radar location to the composite grid or set of
locations
Parameters
----------
src : ndarray of float of shape (numpoints, ndim)
cartesian x / y coordinates of the radar bins
trg : ndarray of float of shape (numpoints, ndim)
cartesian x / y coordinates of the composite
radius : float
the radius of the radar circle (same units as src and trg)
center : array of float
the location coordinates of the radar
data : ndarray of float
the data that should be transferred to composite
interpol : an interpolation class name from :meth:`wradlib.ipol`
e.g. :class:`~wradlib.ipol.Nearest` or :class:`~wradlib.ipol.Idw`
Other Parameters
----------------
*args : arguments of Interpolator (see class documentation)
Keyword Arguments
-----------------
**kwargs : keyword arguments of Interpolator (see class documentation)
Returns
-------
output : ndarray of float
data of the radar circle which is interpolated on the composite grid
Examples
--------
See :ref:`notebooks/basics/wradlib_workflow.ipynb#Gridding`.
"""
# get indices to select the subgrid from the composite grid
ix = extract_circle(center, radius, trg)
# interpolate on subgrid
ip = interpol(src, trg[ix], *args, **kwargs)
data_on_subgrid = ip(data).reshape((len(ix)))
# create container for entire grid
composegridshape = [len(trg)]
composegridshape.extend(data.shape[1:])
compose_grid = np.repeat(np.nan, len(trg) *
np.prod(data.shape[1:])).reshape(composegridshape)
# push subgrid results into the large grid
compose_grid[ix] = data_on_subgrid
return compose_grid
def compose_ko(radargrids, qualitygrids):
"""Composes grids according to quality information using quality \
information as a knockout criterion.
The value of the composed pixel is taken from the radargrid whose
quality grid has the highest value.
Parameters
----------
radargrids : list of arrays
radar data to be composited. Each item in the list corresponds to the
data of one radar location. All items must have the same shape.
qualitygrids : list of arrays
quality data to decide upon which radar site will contribute its pixel
to the composite. Then length of this list must be the same as that
of `radargrids`. All items must have the same shape and be aligned with
the items in `radargrids`.
Returns
-------
composite : array
"""
# first add a fallback array for all pixels having missing values in all
# radargrids
radarfallback = (np.repeat(np.nan, np.prod(radargrids[0].shape))
.reshape(radargrids[0].shape))
radargrids.append(radarfallback)
radarinfo = np.array(radargrids)
# then do the same for the quality grids
qualityfallback = (np.repeat(-np.inf, np.prod(radargrids[0].shape))
.reshape(radargrids[0].shape))
qualitygrids.append(qualityfallback)
qualityinfo = np.array(qualitygrids)
select = np.nanargmax(qualityinfo, axis=0)
composite = (radarinfo.reshape((radarinfo.shape[0], -1))
[select.ravel(), np.arange( | np.prod(radarinfo.shape[1:]) | numpy.prod |
import datetime
import os
import subprocess
import numpy
from scipy.stats import norm
from . import romannumerals
# ToDo: Bring back scale bar
# ToDo: Add option for solid fill of vectors
def roundto(num, nearest):
"""
Rounds :param:`num` to the nearest increment of :param:`nearest`
"""
return int((num + (nearest / 2)) // nearest * nearest)
def convert_chromosome_name(chrom_string, dialect='ucsc'):
"""
Try to auto-detect chromosome number and convert it to the specified "dialect".
Valid dialects are "ucsc", "ensembl" and "yeast".
:param chrom_string:
:param source:
:param dest:
:return:
"""
try:
chrom_string = str(romannumerals.roman_to_int(chrom_string))
except ValueError:
pass
if dialect == 'ensembl':
if chrom_string == 'chrM':
return 'dmel_mitochonrdion_genome'
elif chrom_string[:3].lower() == 'chr':
return chrom_string[3:]
else:
return chrom_string
elif dialect == 'ucsc':
if chrom_string == 'dmel_mitochondrion_genome':
return 'chrM'
elif chrom_string[:3].lower() == 'chr':
return chrom_string
else:
return 'chr{}'.format(chrom_string)
elif dialect == 'yeast':
if chrom_string[:3].lower() == 'chr':
chrom_string = chrom_string[3:]
try:
return romannumerals.int_to_roman(int(chrom_string))
except ValueError:
return chrom_string
else:
raise ValueError('Unknown dialect {}'.format(dialect))
def binary_search_tag_file(tag_filename, search_target):
"""
Find the offset (in bytes) in :param:`tag_filename` that corresponds
to the start of the first tag that is equal to or greater than :param:`search_target`.
If none of the reads have a start position greater than :param:`search_target`,
return None.
Note that positions in tag files have a 1-based index.
"""
def get_read_start(file_offset):
tag_file.seek(file_offset)
if file_offset > 0:
_ = tag_file.readline() # read forward to get to a line start
this_line = tag_file.readline().strip()
if tag_file.tell() >= filesize:
# We've reached the end of the file and the reads are still upstream of the target
return None
else:
return int(this_line.split('\t')[1])
filesize = os.path.getsize(tag_filename)
search_window_start = 0
search_window_end = filesize - 1
guess_genomic_start = -1
guess = int((search_window_start + search_window_end) / 2)
with open(tag_filename, 'rt') as tag_file:
first_genomic_start = get_read_start(search_window_start)
# last_genomic_start = get_read_position(search_window_end)
if search_target < first_genomic_start:
return search_window_start
while search_window_end - search_window_start > 1:
guess = int((search_window_start + search_window_end) / 2)
guess_genomic_start = get_read_start(guess)
if guess_genomic_start == None:
return None
# print(search_window_start, guess, search_window_end, guess_genomic_start)
if guess_genomic_start < search_target:
# print('\ttoo low!')
search_window_start = guess
elif guess_genomic_start > search_target:
search_window_end = guess
# print('\ttoo high!')
else:
# print('\tjust right!')
break
if guess_genomic_start == -1:
return None
if guess_genomic_start < search_target:
guess += 1
tag_file.seek(guess)
_ = tag_file.readline()
guess = tag_file.tell()
return guess
def bgzip_gff(gff3_fname, bgzipped_fname):
"""
Compress a GFF3 file in block-gzip format (requires that bgzip be accessible on the current path).
If :param gff3_fname: ends with '.gz' assumes that the file is gzipped, otherwise assumes it is uncompressed.
:param gzipped_fname:
:param bgzipped_fname:
:return:
"""
if bgzipped_fname == gff3_fname:
log_print('Destination and source file cannot have the same name!')
cmd_line = '{} {} | sort -k1,1 -k4,4n | bgzip > {}'.format(('cat', 'zcat')[gff3_fname.endswith('.gz')], gff3_fname,
bgzipped_fname)
try:
assert os.path.isfile(gff3_fname) # needed since no error occurs otherwise
subprocess.check_call(cmd_line, shell=True)
except subprocess.CalledProcessError as cpe:
log_print('Unsuccessful. Got return code {}'.format(cpe.returncode))
except AssertionError:
log_print('{} not found!'.format(gff3_fname))
else:
log_print('Successfully generated block-gzipped file {} from {}'.format(bgzipped_fname, gff3_fname))
def generate_tabix_index(target_fname):
"""
Index :param target_fname: with tabix. Requires that the directory in which :param:target_fname: resides is
writeable.
:param target_fname:
:return:
"""
cmd_line = 'tabix -f -p gff {}'.format(target_fname)
try:
return_code = subprocess.check_call(cmd_line, shell=True)
except subprocess.CalledProcessError as cpe:
log_print('Unsuccessful. Got return code {}'.format(cpe.returncode))
else:
log_print('Successfully indexed block-gzipped file {}'.format(target_fname))
def pretty_now():
"""
Returns the current date/time in a nicely formatted string (without decimal seconds)
"""
return datetime.datetime.strftime(datetime.datetime.now(), '%Y-%b-%d %H:%M:%S')
def log_print(message, tabs=1):
"""
Print a chunk of text preceded by a timestamp and an optional number of tabs (default 1).
:param message:
:param tabs:
:return:
"""
print('{}{}{}'.format(pretty_now(), '\t' * tabs, message))
def gaussian_kernel(sd, sd_cutoff=3, normalize=False):
"""
Generate and return a numpy.Array whose elements are proportional to the PDF of a normal distribution
having standard deviation :param:`sd`.
:param sd:
:param sd_cutoff:
:param normalize:
:return:
"""
bw = sd_cutoff * sd * 2 + 1
midpoint = sd_cutoff * sd
kern = | numpy.zeros(bw) | numpy.zeros |
from physDBD import ImportHelper, DataDesc, ParamsTraj, RxnSpec, RxnInputsLayer, ParamsTETraj, RxnModel
import numpy as np
import tensorflow as tf
import sys
import os
data_desc = DataDesc(
no_seeds=50,
time_start=0,
time_end=20,
time_interval=0.5,
species=["ca2i","ip3"]
)
data_dir = "playground_data"
vol_exp = 12
no_ip3r = 100
ip3_dir = "ip3_0p100"
vol_dir = "vol_exp_%02d" % vol_exp
no_ip3r_dir = "ip3r_%05d" % no_ip3r
data_dir = os.path.join(data_dir, vol_dir, no_ip3r_dir, ip3_dir)
data = ImportHelper.import_gillespie_ssa_from_data_desc(
data_desc=data_desc,
data_dir=data_dir
)
if False:
# Create params traj and export
muh = np.zeros(1)
varh_diag = np.ones(1)
params_traj = ParamsTraj.fromPCA(data, data_desc.times, muh, varh_diag)
# Export
params_traj.export("cache_params.txt")
else:
# Import params traj
params_traj = ParamsTraj.fromFile("cache_params.txt", nv=2, nh=1)
if False:
# Differentiate
alphas = {
"wt00": 1.0,
"wt01": 1.0,
"b0": 1.0,
"b1": 1.0,
"sig2": 1.0
}
non_zero_vals = list(alphas.keys())
paramsTE_traj = params_traj.differentiate_with_TVR(
alphas=alphas,
no_opt_steps=10,
non_zero_vals=non_zero_vals
)
# Export
paramsTE_traj.export("cache_derivs.txt")
else:
# Import paramsTE_traj
paramsTE_traj = ParamsTETraj.fromFile("cache_derivs.txt", nv=2, nh=1)
# Integrate derivatives
params_traj_filtered = ParamsTraj.fromIntegrating(
paramsTE_traj=paramsTE_traj,
params_init=params_traj.params_traj[0],
tpt_start=0,
no_steps=len(params_traj.params_traj)-1
)
# Write
params_traj_filtered.export("cache_filtered.txt")
train_inputs = params_traj.get_tf_inputs_assuming_params0()
train_outputs, \
train_outputs_mean, \
train_outputs_std = paramsTE_traj.get_tf_outputs_normalized_assuming_params0(
percent=0.2,
non_zero_outputs=["wt00_TE","b0_TE"]
)
# Freqs, coffs for fourier
nv = 2
nh = 1
freqs = np.random.rand(3)
muh_sin_coeffs_init = np.random.rand(3)
muh_cos_coeffs_init = np.random.rand(3)
varh_sin_coeffs_init = | np.random.rand(3) | numpy.random.rand |
"""
PTM_BTRACE
Magnetic field tracing and analysis for magnetic field data on scattered grids. This module is intended
to supercede the PTM_FIELDS_TRACING module.
This module defines a "GRIDDED_MAGNETIC_FIELD" object that reads in gridded magnetic field data
and allows for the fields to be arbitrarily evaluated, allows for field lines to be traced, and
allows for the determination of the magnetic equator.
GRIDDED_MAGNETIC_FIELD
Public Methods (see individual methods for documentation)
configure_reader
get_bhat
get_bvec
get_bmag
find_min_B
find_field_line
trace_field_line
trace_magnetic_equator
EXAMPLE USAGE
import ptm_btrace as bt
bfield=bt.gridded_magnetic_field(istep=360,searchdir='/Users/jwoodroffe/Workspace/Projects/PTM/Events/7-18-2013/gridded/')
mageq=bfield.trace_magnetic_equator(6.6)
<NAME>
6/28/2016
"""
import numpy as np
from numpy import linalg
from scipy import optimize
from scipy import integrate
from scipy import interpolate
class gridded_magnetic_field(object):
"""
Base object for SWMF field line tracing
"""
__dtor = np.pi/180.0
__rtod = 180.0/np.pi
def __init__(self,istep=None,searchdir=None):
if(istep==None):
self.__istep=0
else:
self.__istep=istep
if(any([searchdir==None,searchdir=='',searchdir=='.'])):
self.__searchdir=''
else:
if(searchdir[-1]!='/'):
self.__searchdir=searchdir+'/'
else:
self.__searchdir=searchdir
self.__xgrid=np.fromfile(self.__searchdir+'xgrid.bin')
self.__ygrid=np.fromfile(self.__searchdir+'ygrid.bin')
self.__zgrid=np.fromfile(self.__searchdir+'zgrid.bin')
self.__nx=self.__xgrid.size
self.__ny=self.__ygrid.size
self.__nz=self.__zgrid.size
bdims=(self.__nx,self.__ny,self.__nz)
self.__bx=np.fromfile(self.__searchdir+'bx3d_%4.4i.bin' % self.__istep).reshape(bdims)
self.__by=np.fromfile(self.__searchdir+'by3d_%4.4i.bin' % self.__istep).reshape(bdims)
self.__bz=np.fromfile(self.__searchdir+'bz3d_%4.4i.bin' % self.__istep).reshape(bdims)
bxi=interpolate.RegularGridInterpolator((self.__xgrid,self.__ygrid,self.__zgrid),self.__bx)
byi=interpolate.RegularGridInterpolator((self.__xgrid,self.__ygrid,self.__zgrid),self.__by)
bzi=interpolate.RegularGridInterpolator((self.__xgrid,self.__ygrid,self.__zgrid),self.__bz)
def bhat_ode(s,xv):
bhat=np.r_[bxi(xv),byi(xv),bzi(xv)]
bhat/=linalg.norm(bhat)
return bhat
def bhat_odeint(xv,s):
bhat=np.r_[bxi(xv),byi(xv),bzi(xv)]
bhat/=linalg.norm(bhat)
return bhat
def get_bhat(xv):
bhat=np.r_[bxi(xv),byi(xv),bzi(xv)]
bhat/=linalg.norm(bvec)
return bhat
def get_bvec(xv):
bvec=np.r_[bxi(xv),byi(xv),bzi(xv)]
return bvec
def get_bmag(xv):
res=linalg.norm(np.r_[bxi(xv),byi(xv),bzi(xv)])
return res
# Create persistent methods
self.get_bhat = get_bhat
self.get_bvec = get_bvec
self.get_bmag = get_bmag
self.__bhat_ode = bhat_ode
self.__bhat_odeint = bhat_odeint
def __mlt_to_phi(self,myMlt):
# Convert from magnetic local time in hours to azimuthal angle in degrees
if(myMlt < 12.0):
mlt=myMlt+24
else:
mlt=myMlt
res = 15*(mlt-12.0)
return res
def __phi_to_mlt(self,myPhi):
# Convert from azimuthal angle in degrees to magnetic local time in hours
mlt = myPhi/15.0+12
if(mlt >= 24.0): mlt-=24
return mlt
def configure_reader(self,istep=None,searchdir=None):
"""
Change data source
"""
self.__init__(istep,searchdir)
def trace_field_line_section(self,mlt,rad,lat,ds=0.05,smax=2.0):
"""
Given a point in MLT, radial distance, latitude space, trace a section of the
corresponding field line to a distance +-smax.
<NAME>
7/27/2016
"""
phi=self.__mlt_to_phi(mlt)
x0=rad*np.cos(self.__dtor*phi)*cos(self.__dtor*lat)
y0=rad*np.sin(self.__dtor*phi)*cos(self.__dtor*lat)
z0=rad*np.sin(self.__dtor*lat)
swant=np.arange(0.0,smax,ds)
ics=r_[x0,y0,z0]
yplus=integrate.odeint(self.__bhat_odeint,ics,swant)
yminus=integrate.odeint(self.__bhat_odeint,ics,-swant)
y=np.vstack([yminus[::-1,:],yplus[1:,:]])
bt = np.array([self.get_bmag(y[i,:]) for i in enumerate(y[:,0])])
return y[:,0], y[:,1], y[:,2], bt
def trace_field_line(self,mlt,rad,lat,ds=0.05,istep_max=100000):
"""
Given a point in MLT, radial distance, latitude space, trace the corresponding
magnetic field line to both ionospheres. Also determines the total length of the
field line which may be useful e.g. in determining resonant frequencies.
<NAME>
5/18/16
"""
phi=self.__mlt_to_phi(mlt)
x0=rad*np.cos(self.__dtor*phi)*np.cos(self.__dtor*lat)
y0=rad*np.sin(self.__dtor*phi)*np.cos(self.__dtor*lat)
z0=rad*np.sin(self.__dtor*lat)
xp=np.zeros([istep_max])
yp=np.zeros_like(xp)
zp=np.zeros_like(xp)
bp=np.zeros_like(xp)
xm=np.zeros_like(xp)
ym=np.zeros_like(xp)
zm=np.zeros_like(xp)
bm=np.zeros_like(xp)
r=integrate.ode(self.__bhat_ode).set_integrator('vode',method='adams')
stot = 0.0
# Trace north
ics=np.r_[x0,y0,z0]
s0=0.0
xp[0]=x0
yp[0]=y0
zp[0]=z0
bp[0]=self.get_bmag(ics)
r.set_initial_value(ics,s0)
doIntegrate = True
istep=0
while r.successful() and doIntegrate:
r.integrate(r.t+ds)
istep+=1
xp[istep]=r.y[0]
yp[istep]=r.y[1]
zp[istep]=r.y[2]
bp[istep]=self.get_bmag(r.y)
if(linalg.norm(r.y)<=1.0):
doIntegrate=False
if(r.y[0]<self.__xgrid.min()+1.0 or r.y[0]>self.__xgrid.max()-1.0):
doIntegrate=False
if(r.y[1]<self.__ygrid.min()+1.0 or r.y[1]>self.__ygrid.max()-1.0):
doIntegrate=False
if(r.y[2]<self.__zgrid.min()+1.0 or r.y[2]>self.__zgrid.max()-1.0):
doIntegrate=False
xk=xp[:istep]
yk=yp[:istep]
zk=zp[:istep]
bk=bp[:istep]
stot+=np.abs(r.t)
# Trace south
ics=np.r_[x0,y0,z0]
s0=0.0
xm[0]=x0
ym[0]=y0
zm[0]=z0
bm[0]=self.get_bmag(ics)
r.set_initial_value(ics,s0)
doIntegrate = True
istep=0
while r.successful() and doIntegrate:
r.integrate(r.t-ds)
istep+=1
xm[istep]=r.y[0]
ym[istep]=r.y[1]
zm[istep]=r.y[2]
bm[istep]=self.get_bmag(r.y)
if(linalg.norm(r.y)<=1.0):
doIntegrate=False
if(r.y[0]<self.__xgrid.min()+1.0 or r.y[0]>self.__xgrid.max()-1.0):
doIntegrate=False
if(r.y[1]<self.__ygrid.min()+1.0 or r.y[1]>self.__ygrid.max()-1.0):
doIntegrate=False
if(r.y[2]<self.__zgrid.min()+1.0 or r.y[2]>self.__zgrid.max()-1.0):
doIntegrate=False
stot+=np.abs(r.t)
xl = xm[:istep]
yl = ym[:istep]
zl = zm[:istep]
bl = bm[:istep]
xr=np.r_[xl[::-1][:-1],xk]
yr=np.r_[yl[::-1][:-1],yk]
zr=np.r_[zl[::-1][:-1],zk]
br=np.r_[bl[::-1][:-1],bk]
return xr,yr,zr,br,stot
def find_min_B(self,mlt,rad,lat,ds=0.05):
"""
Locate the position of minimum magnetic field along a given
magnetic field line.
<NAME>
6/28/2016
"""
xt,yt,zt,bt,stot=self.trace_field_line(mlt,rad,lat,ds=ds)
imin=np.argmin(bt)
pos=np.r_[xt[imin],yt[imin],zt[imin]]
return pos
def __find_min_B_root(self,mlt,rad,lat,ds=0.05,smax=1.0):
xt,yt,zt,bt=self.trace_field_line_section(mlt,rad,lat,ds=ds)
imin=np.argmin(bt)
pos=np.r_[xt[imin],yt[imin],zt[imin]]
return pos
def __find_field_line_root(self,mlt,r0,lat,ds=0.05,smax=1.0):
"""
Find the magnetic field line that has minimum B at a given radial distance and
magnetic local time.
<NAME>
6/28/2016
"""
def rtfun(x):
pos=self.__find_min_B_root(mlt,r0,x,ds=ds,smax=smax)
rval=linalg.norm(pos)
sol=rval-r0
return sol
minlat=optimize.newton(rtfun,lat,tol=1e-3)
phi = self.__mlt_to_phi(mlt)
x = r0*np.cos(self.__dtor*minlat)*np.cos(self.__dtor*phi)
y = r0*np.cos(self.__dtor*minlat)*np.sin(self.__dtor*phi)
z = r0*np.sin(self.__dtor*minlat)
pos = np.r_[x,y,z]
return pos
def __find_field_line_arc(self,r0,mlt,arcSize=15.0,numpts=100,rlev=2,smplane=False):
"""
Find the location of minimum B along an arc at a given radial distance and magnetic local time.
For simple magnetic geometries, this locates the minimum-B field line. For more complicated sitatuions,
this provides a good guess for the more exhaustive __find_field_line_root. The combination of these
two functionalities is provided by the general find_field_line routine below.
<NAME>
7/27/2016
"""
# Get initial guess from dipole approximation
lat0,phi=self.__dipole_eq(mlt,r0)
if not smplane: # Improve by searching along arc
# Intial bounds for arc search
lmin=lat0-arcSize
lmax=lat0+arcSize
for ilev in xrange(rlev):
# Parameterize the arc
latv=self.__dtor*np.linspace(lmin,lmax,numpts)
xv=r0*np.cos(latv)*np.cos(self.__dtor*phi)
yv=r0*np.cos(latv)*np.sin(self.__dtor*phi)
zv=r0*np.sin(latv)
bmat=np.zeros([latv.size,4])
# Calculate magnetic field magnitudes along the arc
for i in xrange(latv.size):
bmat[i,:3]=self.get_bvec(r_[xv[i],yv[i],zv[i]])
bmat[i, 3]=linalg.norm(bmat[i,:3])
# Refine bracketing
imin=np.argmin(bmat[:,-1])
isub=imin-2 if imin>2 else 0
iadd=imin+2 if imin<numpts-3 else numpts-1
lmin=self.__rtod*latv[isub]
lmax=self.__rtod*latv[iadd]
xr,yr,zr = xv[imin], yv[imin], zv[imin]
else:
xr=r0*np.cos(self.__dtor*lat0)*np.cos(self.__dtor*phi)
yr=r0*np.cos(self.__dtor*lat0)*np.sin(self.__dtor*phi)
zr=r0*np.sin(self.__dtor*lat0)
return xr, yr, zr
def __dipole_eq(self,mlt,r):
"""
Determine the location of the specified point on the dipole magnetic equator.
<NAME>
7/28/2016
"""
# Calculate the magnetic moment vector
bvec=self.get_bvec(np.r_[3.0,0.0,0.0])
rhat=np.r_[1.0,0.0,0.0]
mvec=1.5*dot(rhat,bvec)*rhat-bvec
# Determine the planar coefficients for the magnetic equator
mhat=mvec/linalg.norm(mvec)
a=mhat[0]
b=mhat[1]
c=mhat[2]
# Determine the location by enforcing planar and fixed distance constraints
phi = self.__mlt_to_phi(mlt)*self.__dtor
rho=r*np.abs(c)/np.sqrt((a*np.cos(phi)+b*np.sin(phi))**2+c**2)
x=rho*np.cos(phi)
y=rho*np.sin(phi)
z=r*(a*np.cos(phi)+b* | np.sin(phi) | numpy.sin |
from math import exp, sqrt
import numpy as np
import scipy.optimize as sciopt
import cgn
from do_test import do_test
from problem import TestProblem
def F(x, y):
out = np.array([x[0] + exp(-x[1] + sqrt(y[0])),
x[0] ** 2 + 2 * x[1] + 1 - sqrt(y[0])])
return out
def DF(x, y):
jac = np.array([[1., -exp(-x[1]), 0.5 / sqrt(y[0])],
[2 * x[0], 2., - 0.5 / sqrt(y[0])]])
return jac
def g(x):
out = x[0] + x[0] ** 3 + x[1] + x[1] ** 2
return np.array([out])
def Dg(x):
jac = np.array([1 + 3 * x[0] ** 2, 1. + 2 * x[1]]).reshape((1, 2))
return jac
class MultiParameterProblem(TestProblem):
def __init__(self):
TestProblem.__init__(self)
self._tol = 1e-6
x = cgn.Parameter(start=np.zeros(2), name="x")
x.regop = np.array([[1., 2.], [3., 4.]])
x.mean = | np.array([1., 1.]) | numpy.array |
import numpy as np
import cv2
from time import time
import sys
from cameras import cam2mat as cameraMatrix0
from cameras import cam2dcoef as distCoeffs0
from cameras import cam3mat as cameraMatrix1
from cameras import cam3dcoef as distCoeffs1
cameraMatrix0 = np.array(cameraMatrix0)
distCoeffs0 = np.array(distCoeffs0)
cameraMatrix1 = np.array(cameraMatrix1)
distCoeffs1 = np.array(distCoeffs1)
print(cameraMatrix0)
print(cameraMatrix1)
print(distCoeffs0)
print(distCoeffs1)
#these are the measurements of the paper
objectPoints = np.array([(0, 0, 0), (10, 0, 0), (10, -7.5, 0), (0, -7.5,
0)])*2.54/1.39
def getHomoMat(rot0,t0):
'''takes in rotation and translation vectors and returns homography matrix to
go from one camera to another'''
a0, _ = cv2.Rodrigues(rot0)
h0 = np.zeros((4,4))
h0[3,3] = 1
h0[:3,:3] = a0
h0[:3,3] = t0.T[0]
return h0
def solveperp(imagePoints, method):
if method == 1:
# print('image points:',imagePoints)
# obj points (size of led array), image points(pixel values of said
# points, camera mat(intrinsic camera matrix, distCoef(distortion
# coefficients of the camera from the intrinsic calibration)
return cv2.solvePnP(objectPoints, imagePoints, cameraMatrix0,
distCoeffs0)
elif method == 2:
return cv2.solvePnPRansac(
objectPoints, imagePoints, cameraMatrix0, distCoeffs0
)
else:
return cv2.solveP3P(objectPoints, imagePoints, cameraMatrix0,
distCoeffs0)
def solveperp1(imagePoints, method):
if method == 1:
# print(imagePoints)
# print(type(imagePoints))
return cv2.solvePnP(objectPoints, imagePoints, cameraMatrix1,
distCoeffs1)
elif method == 2:
return cv2.solvePnPRansac(
objectPoints, imagePoints, cameraMatrix1, distCoeffs1
)
else:
return cv2.solveP3P(objectPoints, imagePoints, cameraMatrix1,
distCoeffs1)
# def cameraPoseFromHomography(H):
# pose = np.eye(4, 4)
# norm0 = np.linalg.norm(H[:3,0])
# norm1 = np.linalg.norm(H[:3,1])
# tnorm = (norm0 + norm1) / 2
# # p1 = H[:,0]
# # p2 = pose[:,0]
# temp = np.array(pose[:3,0])
# cv2.normalize(H[:3,0], temp)
# pose[:3,0] = temp
# # p1 = H.col(1); // Pointer to second column of H
# # p2 = pose.col(1); // Pointer to second column of pose (empty)
# temp2 = np.array(pose[:3,1])
# cv2.normalize(H[:3,1], temp2)
# pose[:3,1] = temp2
# # p1 = pose.col(0);
# # p2 = pose.col(1);
# # Mat p3 = p1.cross(p2); // Computes the cross-product of p1 and p2
# # Mat c2 = pose.col(2); // Pointer to third column of pose
# # p3.copyTo(c2); // Third column is the crossproduct of columns one and two
# pose[:3,2] = np.cross(pose[:3,0],pose[:3,1])
# pose[:3,3] = H[:3,2]/tnorm #; //vector t [R|t] is the last column of pose
# return pose
def cameraPoseFromHomography(H):
norm1 = np.linalg.norm(H[:, 0])
norm2 = np.linalg.norm(H[:, 1])
tnorm = (norm1 + norm2) / 2.0;
H1 = H[:, 0] / norm1
H2 = H[:, 1] / norm2
H3 = np.cross(H1, H2)
T = H[:, 2] / tnorm
ret = np.zeros((4,4))
ret[:3,:] = np.array([H1, H2, H3, T]).transpose()
ret[3,3] = 1
return ret
def order_points(pts, img):
# initialzie a list of coordinates that will be ordered
# such that the first entry in the list is the top-left,
# the second entry is the top-right, the third is the
# bottom-right, and the fourth is the bottom-left
rect = [[0,0],[0,0],[0,0],[0,0]]
if len(pts) != 4:
return np.array(rect)
# the top-left point will have the smallest sum, whereas
# the bottom-right point will have the largest sum
s = [sum(pt.pt) for pt in pts]
# print(type(np.argmin(s)))
# print(type( pts[int(np.argmin(s) )].pt ))
rect[0] = pts[int(np.argmin(s))]
rect[2] = pts[int(np.argmax(s))]
# now, compute the difference between the points, the
# top-right point will have the smallest difference,
# whereas the bottom-left will have the largest difference
diff = [pt.pt[0] - pt.pt[1] for pt in pts]
rect[1] = pts[np.argmin(diff)]
rect[3] = pts[np.argmax(diff)]
# return the ordered coordinates
rect = np.array([(pt.pt[0], pt.pt[1]) for pt in rect])
shift = 0
for p in rect:
# print( img[int(p[1]), int(p[0]) ])
if img[int(p[1]), int(p[0]) ] == 0:
break
# shift += 1
shift = p
# print(shift)
# rect = rect[shift:] + rect[:shift]
return rect
def four_point_transform(image, pts):
# obtain a consistent order of the points and unpack them
# individually
rect = order_points(pts)
(tl, tr, br, bl) = rect
# compute the width of the new image, which will be the
# maximum distance between bottom-right and bottom-left
# x-coordiates or the top-right and top-left x-coordinates
widthA = np.sqrt(((br[0] - bl[0])**2) + ((br[1] - bl[1])**2))
widthB = np.sqrt(((tr[0] - tl[0])**2) + ((tr[1] - tl[1])**2))
maxWidth = max(int(widthA), int(widthB))
# compute the height of the new image, which will be the
# maximum distance between the top-right and bottom-right
# y-coordinates or the top-left and bottom-left y-coordinates
heightA = np.sqrt(((tr[0] - br[0])**2) + ((tr[1] - br[1])**2))
heightB = np.sqrt(((tl[0] - bl[0])**2) + ((tl[1] - bl[1])**2))
maxHeight = max(int(heightA), int(heightB))
# now that we have the dimensions of the new image, construct
# the set of destination points to obtain a "birds eye view",
# (i.e. top-down view) of the image, again specifying points
# in the top-left, top-right, bottom-right, and bottom-left
# order
dst = np.array(
[
[0, 0], [maxWidth - 1, 0], [maxWidth - 1, maxHeight - 1],
[0, maxHeight - 1]
],
dtype="float32"
)
# compute the perspective transform matrix and then apply it
M = cv2.getPerspectiveTransform(rect, dst)
warped = cv2.warpPerspective(image, M, (maxWidth, maxHeight))
# return the warped image
return warped
vc0 = cv2.VideoCapture(0)
ret, frame0 = vc0.read()
if not ret :
raise Exception
vc1 = cv2.VideoCapture(2)
ret, frame1 = vc1.read()
if not ret :
raise Exception
cv2.namedWindow("cam0")
cv2.namedWindow("cam1")
for i in range(2):
vc0.read()
vc1.read()
print("done with loop")
# vout = None
# if (int(sys.argv[5])):
# fourcc = cv2.VideoWriter_fourcc(*'x264')
# vout = cv2.VideoWriter('pupiltest.mp4', fourcc, 24.0,
# (int(vc.get(3)),int(vc.get(4))))
if vc0.isOpened(): # try to get the first frame
rval, frame0 = vc0.read()
else:
rval = False
print("failed reading the frame cam 0")
exit()
if vc1.isOpened(): # try to get the first frame
rval, frame1 = vc1.read()
else:
print("failed reading the frame cam 1")
rval = False
exit()
params = cv2.SimpleBlobDetector_Params()
# Change thresholds
params.minThreshold = 0
params.maxThreshold = 255
# Filter by Area.
params.filterByArea = True
params.minArea = 10
# Filter by Circularity
params.filterByCircularity = True
params.minCircularity = 0.7
# Filter by Convexity
params.filterByConvexity = True
params.minConvexity = 0.4
# Filter by Inertia
params.filterByInertia = True
params.minInertiaRatio = 0.3
# Create a detector with the parameters
detector = cv2.SimpleBlobDetector_create(params)
ptime = time()
nf = 0
retval0, rvec0, tvec0 = 0,0,0
retval1, rvec1, tvec1 = 0,0,0
while rval:
# frame = cv2.rotate(frame, cv2.ROTATE_180)
roi_gray0 = cv2.cvtColor(frame0, cv2.COLOR_BGR2GRAY)
roi_gray1 = cv2.cvtColor(frame1, cv2.COLOR_BGR2GRAY)
keypoints0 = detector.detect(roi_gray0)
keypoints1 = detector.detect(roi_gray1)
ii=0
for point in keypoints0:
if ii==0:
frame0 = cv2.drawMarker(frame0, (int(point.pt[0]),int(point.pt[1])), (0, 0, 255))
else:
frame0 = cv2.drawMarker(frame0, (int(point.pt[0]),int(point.pt[1])),(0, 255, 255))
ii+=1
ii=0
for point in keypoints1:
if ii==0:
frame1 = cv2.drawMarker(frame1, (int(point.pt[0]),int(point.pt[1])), (0, 0, 255))
else:
frame1 = cv2.drawMarker(frame1, (int(point.pt[0]),int(point.pt[1])),(0, 255, 255))
ii+=1
imagePoints0 = order_points(keypoints0, roi_gray0)
imagePoints1 = order_points(keypoints1, roi_gray1)
try:
retval0, rvec0, tvec0 = solveperp(imagePoints0, 1)
except:
# print('didnt solve pnp0',len(keypoints0))
pass
try:
retval1, rvec1, tvec1 = solveperp1(imagePoints1, 1)
except:
# print('didnt solve pnp1',len(keypoints1))
pass
# print(rvec0)
# print(rvec1)
cv2.imshow("cam0", frame0)
cv2.imshow("cam1", frame1)
# if vout:
# vout.write(frame)
nf = nf + 1
if time() - ptime > 5:
PointArray0 = []
PointArray1 = []
for pointt in keypoints0:
p = [int(pointt.pt[0]), int(pointt.pt[1])]
PointArray0.append(p)
for pointt in keypoints1:
p = [int(pointt.pt[0]), int(pointt.pt[1])]
PointArray1.append(p)
PointArray0 = np.array(PointArray0)
PointArray1 = np.array(PointArray1)
print('\n R-Vec0\n', rvec0 ,'\n' )
print('\n T-Vec0\n', tvec0 ,'\n' )
#print(str(nf / (time() - ptime))) # framerate
try:
a,_ = cv2.Rodrigues(rvec0)
print(a)
b,_ = cv2.Rodrigues(rvec1)
print(b)
homo0 = getHomoMat(rvec0,tvec0)
homo1 = getHomoMat(rvec1,tvec1)
print('homo 0',homo0)
print('homo 1',homo1)
h1inv = np.linalg.inv(homo1)
print('h1inv',h1inv)
pt0 = keypoints0[0].pt
pt1 = keypoints1[0].pt
p0 = np.zeros((4,1))
p0[:2] = np.array([pt0]).T
p0[3]= 1
r0 = np.matmul(homo0,p0)
p1 = np.zeros((4,1))
p1[:2] = np.array([pt1]).T
p1[3]= 1
r1 = | np.matmul(homo1,p1) | numpy.matmul |
# 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]) | numpy.array |
# Copyright 2018 <NAME> All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
import tensorflow as tf
import numpy as np
import os
def _dream_cropping(image, label, specs, cropped_size):
image = tf.expand_dims(image, -1) # (HWC)
if cropped_size < specs['image_size']:
image = tf.image.resize_image_with_crop_or_pad(
image, cropped_size, cropped_size)
# convert from 0 ~ 255 to 0. ~ 1.
image = tf.cast(image, tf.float32) * (1. / 255.)
# transpose image into (CHW)
image = tf.transpose(image, [2, 0, 1]) # (HWC)
feature = {
'image':image,
'label': tf.one_hot(label, 10)
}
return feature
def _dream_process(feature):
batched_features = {
'images': feature['image'],
'labels': feature['label']
}
return batched_features
def _dream_sample_pairs(split, data_dir, max_epochs, n_repeats,
total_batch_size=1):
"""
We do the following steps to produce the dataset:
1. sample one (image, label) pair in one class;
2. repeat pair in 1. {n_repeats} times;
3. go back to do 1. unless we finish one iteration
(after a {num_classes} time loop). And we consider
this as one epoch.
4. go back to do 1. again to finish {max_epochs} loop.
So there will be {max_epochs} number of unique pairs selected for
each class.
Args:
split: 'train' or 'test', which split of dataset to read from.
data_dir: path to the mnist data directory.
max_epochs: maximum epochs to go through the model.
n_repeats: number of computed gradients
batch_size: total number of images per batch.
Returns:
processed images, labels and specs
"""
"""Dataset specs"""
specs = {
'split': split,
'max_epochs': max_epochs,
'steps_per_epoch': n_repeats,
'batch_size': total_batch_size,
'image_size': 28,
'depth': 1,
'num_classes': 10
}
"""Load data from numpy array file"""
with np.load(os.path.join(data_dir, 'mnist.npz')) as f:
images, labels = f['x_%s' % split], f['y_%s' % split]
# image: 0 ~ 255 uint8
# labels 0 ~ 9 uint8
assert images.shape[0] == labels.shape[0]
specs['total_size'] = int(images.shape[0])
"""Process np arrary"""
# sort by labels to get the index permutation
# classes: 0 1 2 3 4 5 6 7 8 9
if split == 'train':
indices = [0, 5923, 12665, 18623, 24754, 30596, 36017, 41935, 48200, 54051, 60000]
elif split == 'test':
indices = [0, 980, 2115, 3147, 4157, 5139, 6031, 6989, 8017, 8991, 10000]
perm = labels.argsort()
images = images[perm]
labels = labels[perm]
sampled_idc_lists = [] # [list of indices for 0, ... for 1, ...]
for start in indices[:-1]:
sampled_idc_lists.append(
np.arange(start, start + max_epochs).tolist())
sampled_idc_mat = np.array(sampled_idc_lists)
sampled_idc_mat = np.transpose(sampled_idc_mat, [1, 0])
sampled_idc_lists = sampled_idc_mat.flatten().tolist()
assert len(sampled_idc_lists) == max_epochs * specs['num_classes']
# we let n_repeats = steps_per_epoch = number of computed gradients
list_of_images = []
list_of_labels = []
for idx in sampled_idc_lists:
for _ in range(n_repeats):
list_of_images.append(images[idx])
list_of_labels.append(labels[idx])
res_images = np.stack(list_of_images, axis=0)
res_labels = | np.array(list_of_labels) | numpy.array |
import torch
import numpy as np
import scipy.optimize as opt
from tqdm import tqdm
from clean_data import dist
from functools import partial
from neural_network import ffn
from method import ls, phi_meta, grad_phi_meta
if __name__ == '__main__':
''' read data '''
fname = 'task3'
mat, anchors= list(), list()
with open(f"{fname}.txt", 'r', encoding='utf-8') as fin:
fdata = fin.read().strip().split('\n')
anchors, data = fdata[:4], fdata[4:]
anchors = [list(map(int, line.strip().split(','))) for line in anchors]
for i in range(int(round(len(data) / 4))):
get_data = lambda x: int(x.strip().split(':')[5])
mat.append(list(map(get_data, (data[4*i], data[4*i+1], data[4*i+2], data[4*i+3]))))
mat = np.array(mat)
''' generate feature '''
states = [0b0000, 0b0001, 0b0010, 0b0100, 0b1000]
features = list()
for t in tqdm(range(len(mat))):
b_init = ls(anchors, mat[t])
feat = list()
for s in states:
signal = [0, 0, 0, 0]
for j in range(4):
if (s >> j) & 1 == 1:
signal[j] = mat[t][j] - 400
else:
signal[j] = mat[t][j] + 45
sols = list()
''' compute reference node '''
phi = partial(phi_meta, ref=anchors, data=signal)
grad_phi = partial(grad_phi_meta, ref=anchors, data=signal)
ref_node = opt.root(grad_phi, b_init, method='lm').x
feat.append(phi(ref_node)) # ref node error
''' compute three test nodes '''
test_node_err, node_dist = list(), list()
for j in range(4):
p_anchors = [anchors[k] for k in range(4) if k != j]
p_data = [signal[k] for k in range(4) if k != j]
phi = partial(phi_meta, ref=p_anchors, data=p_data)
grad_phi = partial(grad_phi_meta, ref=p_anchors, data=p_data)
sol = opt.root(grad_phi, b_init, method='lm').x
sols.append(sol)
test_node_err.append(phi(sol)) # test node error
node_dist.append(dist(sol, ref_node)) # node distence
node_var = (np.array(sols).std(axis=0) ** 2).tolist()
feat = feat + test_node_err + node_dist + node_var
features.append(np.array(feat))
features = | np.array(features) | numpy.array |
#!/usr/bin/env python
# coding: utf-8
# In[5]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from libsvm.svmutil import *
from sklearn import svm
from sklearn.model_selection import GridSearchCV
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline
from timeit import default_timer as timer
#Reading files
data_points_train = pd.read_csv('2019MT60763.csv', header = None, nrows = 3000)
data = np.array((data_points_train.sort_values(data_points_train.columns[25])).values)
dp = np.array(data)
class_label = dp[:,25]
# counting no of occurence of labels of each class
unique, counts = np.unique(class_label, return_counts=True)
dict(zip(unique, counts))
#print(counts)
# for 25 features
# FOR CLASSES {0,1}
text_x = dp[:631,:25]
text_t = dp[:631,25]
# for cross_validation
tp_x_1 = np.append(dp[:100,:25],dp[306:406,:25],axis=0)
tp_t_1 = np.append(dp[:100,25],dp[306:406,25],axis=0)
tp_x_2 = np.append(dp[101:201,:25],dp[407:507,:25],axis=0)
tp_t_2 = np.append(dp[101:201,25],dp[407:507,25],axis=0)
tp_x_3 = np.append(dp[202:305,:25],dp[508:631,:25],axis=0)
tp_t_3 = np.append(dp[202:305,25],dp[508:631,25],axis=0)
PIPE = Pipeline([('scaler', StandardScaler()), ('SVM', svm.SVC(kernel='linear'))])
parameters = {'SVM__C':np.logspace(0, 1, 10)}
G = GridSearchCV(PIPE, param_grid=parameters, cv=5)
G.fit(text_x, text_t)
print ('Training score',G.score(text_x, text_t))
print (G.best_params_)
G.fit(tp_x_1,tp_t_1)
x = G.score(tp_x_2, tp_t_2)
x+=G.score(tp_x_3, tp_t_3)
G.fit(tp_x_2,tp_t_2)
x+=G.score(tp_x_3, tp_t_3)
x+=G.score(tp_x_1, tp_t_1)
G.fit(tp_x_3,tp_t_3)
x+=G.score(tp_x_2, tp_t_2)
x+=G.score(tp_x_1, tp_t_1)
print('Cross_validation score',x/6)
print(((svm.SVC(kernel = 'linear', C = 1)).fit(text_x,text_t)).support_)
fig = plt.figure(1)
c = np.logspace(0, 1, 10)
matrix = np.zeros((10,3))
for i in range (10):
svc = svm.SVC(kernel='linear',C = c[i])
svc.fit(text_x, text_t)
matrix[i][0] = i
matrix[i][1] = svc.score(text_x, text_t)
svc.fit(tp_x_1,tp_t_1)
x1 = svc.score(tp_x_2, tp_t_2)
x1+=svc.score(tp_x_3, tp_t_3)
svc.fit(tp_x_2,tp_t_2)
x1+=svc.score(tp_x_3, tp_t_3)
x1+=svc.score(tp_x_1, tp_t_1)
svc.fit(tp_x_3,tp_t_3)
x1+=svc.score(tp_x_2, tp_t_2)
x1+=svc.score(tp_x_1, tp_t_1)
matrix[i][2] = x1/6
plt.plot(matrix[:,0:1],matrix[:,1:2],label = 'cross_validation score')
plt.plot(matrix[:,0:1],matrix[:,2:3],label = 'Training score')
plt.title('C vs Accuracy')
plt.xlabel('C')
plt.ylabel('Accuracy')
plt.xscale('log')
plt.legend()
plt.show()
PIPE = Pipeline([('scaler', StandardScaler()), ('SVM', svm.SVC(kernel='rbf'))])
parameters = {'SVM__C':np.logspace(0, 1, 10), 'SVM__gamma':np.logspace(0, 1, 10)}
G = GridSearchCV(PIPE, param_grid=parameters, cv=5)
G.fit(text_x, text_t)
print ('Training score',G.score(text_x, text_t))
print (G.best_params_)
G.fit(tp_x_1,tp_t_1)
y = G.score(tp_x_2, tp_t_2)
y+=G.score(tp_x_3, tp_t_3)
G.fit(tp_x_2,tp_t_2)
y+=G.score(tp_x_3, tp_t_3)
y+=G.score(tp_x_1, tp_t_1)
G.fit(tp_x_3,tp_t_3)
y+=G.score(tp_x_2, tp_t_2)
y+=G.score(tp_x_1, tp_t_1)
print('Cross_validation score',y/6)
print(((svm.SVC(kernel = 'rbf', C = 1.29,gamma = 1)).fit(text_x,text_t)).support_)
puto = np.zeros((100,1))
luto = np.zeros((100,1))
c = np.logspace(0, 1, 10)
g = np.logspace(0, 1, 10)
for i in range (10):
for j in range(10):
svc = svm.SVC(kernel='rbf',C = c[i],gamma = g[j])
svc.fit(text_x, text_t)
puto[10*i+j][0] = svc.score(text_x, text_t)
svc.fit(tp_x_1,tp_t_1)
y1 = svc.score(tp_x_2, tp_t_2)
y1+=svc.score(tp_x_3, tp_t_3)
svc.fit(tp_x_2,tp_t_2)
y1+=svc.score(tp_x_3, tp_t_3)
y1+=svc.score(tp_x_1, tp_t_1)
svc.fit(tp_x_3,tp_t_3)
y1+=svc.score(tp_x_2, tp_t_2)
y1+=svc.score(tp_x_1, tp_t_1)
luto[10*i+j][0] = y1/6
g, c = np.meshgrid(g, c)
graph = np.ravel(puto)
patrix = np.ravel(luto)
patrix = patrix.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, patrix)
cbar = fig.colorbar(k)
plt.title('Accuracy v/s C and gamma (cross-validation)')
plt.xlabel('C')
plt.ylabel('gamma')
plt.xscale('log')
plt.yscale('log')
plt.show()
graph = graph.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, graph)
cbar = fig.colorbar(k)
plt.title('Accuracy v/s C and gamma (training)')
plt.xlabel('C')
plt.ylabel('gamma')
plt.xscale('log')
plt.yscale('log')
plt.show()
start = timer()
PIPE = Pipeline([('scaler', StandardScaler()), ('SVM', svm.SVC(kernel='poly'))])
parameters = {'SVM__C':np.logspace(0, 1, 10), 'SVM__gamma':np.logspace(0, 1, 10),'SVM__degree':[1,5]}
G = GridSearchCV(PIPE, param_grid=parameters, cv=5)
G.fit(text_x, text_t)
print ('Training score',G.score(text_x, text_t))
print (G.best_params_)
G.fit(tp_x_1,tp_t_1)
z = G.score(tp_x_2, tp_t_2)
z+=G.score(tp_x_3, tp_t_3)
G.fit(tp_x_2,tp_t_2)
z+=G.score(tp_x_3, tp_t_3)
z+=G.score(tp_x_1, tp_t_1)
G.fit(tp_x_3,tp_t_3)
z+=G.score(tp_x_2, tp_t_2)
z+=G.score(tp_x_1, tp_t_1)
print('Cross_validation score',z/6)
end = timer()
print('TIME',end - start)
print(((svm.SVC(kernel = 'poly', C = 1,gamma = 1,degree = 1)).fit(text_x,text_t)).support_)
suto = np.zeros((100,1))
nuto = np.zeros((100,1))
c = np.logspace(0, 1, 10)
g = np.logspace(0, 1, 10)
for i in range (10):
for j in range(10):
svc = svm.SVC(kernel='poly',C = c[i],gamma = g[j],degree = 1)
svc.fit(text_x, text_t)
suto[10*i+j][0] = svc.score(text_x, text_t)
svc.fit(tp_x_1,tp_t_1)
z1 = svc.score(tp_x_2, tp_t_2)
z1+=svc.score(tp_x_3, tp_t_3)
svc.fit(tp_x_2,tp_t_2)
z1+=svc.score(tp_x_3, tp_t_3)
z1+=svc.score(tp_x_1, tp_t_1)
svc.fit(tp_x_3,tp_t_3)
z1+=svc.score(tp_x_2, tp_t_2)
z1+=svc.score(tp_x_1, tp_t_1)
nuto[10*i+j][0] = z1/6
g, c = np.meshgrid(g, c)
trix = np.ravel(suto)
prix = np.ravel(nuto)
prix = prix.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, prix)
cbar = fig.colorbar(k)
plt.xlabel('C')
plt.ylabel('gamma')
plt.title('Contour plot for Accuracy v/s C and gamma (cross-validation)')
plt.xscale('log')
plt.yscale('log')
plt.show()
# training
trix = trix.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, trix)
cbar = fig.colorbar(k)
plt.xlabel('C')
plt.ylabel('gamma')
plt.title('Contour plot for Accuracy v/s C and gamma (training)')
plt.xscale('log')
plt.yscale('log')
plt.show()
PIPE = Pipeline([('scaler', StandardScaler()), ('SVM', svm.SVC(kernel='sigmoid'))])
parameters = {'SVM__C':np.logspace(0, 1, 10), 'SVM__gamma':np.logspace(0, 1, 10)}
G = GridSearchCV(PIPE, param_grid=parameters, cv=5)
G.fit(text_x, text_t)
print ('Training score',G.score(text_x, text_t))
print (G.best_params_)
G.fit(tp_x_1,tp_t_1)
f = G.score(tp_x_2, tp_t_2)
f+=G.score(tp_x_3, tp_t_3)
G.fit(tp_x_2,tp_t_2)
f+=G.score(tp_x_3, tp_t_3)
f+=G.score(tp_x_1, tp_t_1)
G.fit(tp_x_3,tp_t_3)
f+=G.score(tp_x_2, tp_t_2)
f+=G.score(tp_x_1, tp_t_1)
print('Cross_validation score',f/6)
print(((svm.SVC(kernel = 'sigmoid', C = 10,gamma = 1)).fit(text_x,text_t)).support_)
jito = np.zeros((100,1))
kito = np.zeros((100,1))
c = np.logspace(0, 1, 10)
g = np.logspace(0, 1, 10)
for i in range (10):
for j in range(10):
svc = svm.SVC(kernel='sigmoid',C = c[i],gamma = g[j])
svc.fit(text_x, text_t)
jito[10*i+j][0] = svc.score(text_x, text_t)
svc.fit(tp_x_1,tp_t_1)
f1 = svc.score(tp_x_2, tp_t_2)
f1+=svc.score(tp_x_3, tp_t_3)
svc.fit(tp_x_2,tp_t_2)
f1+=svc.score(tp_x_3, tp_t_3)
f1+=svc.score(tp_x_1, tp_t_1)
svc.fit(tp_x_3,tp_t_3)
f1+=svc.score(tp_x_2, tp_t_2)
f1+=svc.score(tp_x_1, tp_t_1)
kito[10*i+j][0] = f1/6
g, c = np.meshgrid(g, c)
tatrix = np.ravel(jito)
katrix = np.ravel(kito)
katrix = katrix.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, katrix)
cbar = fig.colorbar(k)
plt.title('Accuracy v/s C and gamma (cross-validation)')
plt.xlabel('C')
plt.ylabel('gamma')
plt.xscale('log')
plt.yscale('log')
plt.show()
tatrix = tatrix.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, tatrix)
cbar = fig.colorbar(k)
plt.title('Accuracy v/s C and gamma (training)')
plt.xlabel('C')
plt.ylabel('gamma')
plt.xscale('log')
plt.yscale('log')
plt.show()
# In[5]:
# FOR CLASSES {2,3}
text_x_2 = (dp[632:1230,:25])
text_t_2 = (dp[632:1230,25])
# for cross_validation
tp_x_1 = np.append(dp[632:732,:25],dp[943:1043,:25],axis=0)
tp_t_1 = np.append(dp[632:732,25],dp[943:1043,25],axis=0)
tp_x_2 = np.append(dp[732:832,:25],dp[1043:1143,:25],axis=0)
tp_t_2 = np.append(dp[732:832,25],dp[1043:1143,25],axis=0)
tp_x_3 = np.append(dp[832:942,:25],dp[1143:1230,:25],axis=0)
tp_t_3 = np.append(dp[832:942,25],dp[1143:1230,25],axis=0)
PIPE = Pipeline([('scaler', StandardScaler()), ('SVM', svm.SVC(kernel='linear'))])
parameters = {'SVM__C':np.logspace(0, 1, 10)}
G = GridSearchCV(PIPE, param_grid=parameters, cv=5)
G.fit(text_x_2, text_t_2)
print ('Training score',G.score(text_x_2, text_t_2))
print (G.best_params_)
G.fit(tp_x_1,tp_t_1)
l1 = G.score(tp_x_2, tp_t_2)
l1+=G.score(tp_x_3, tp_t_3)
G.fit(tp_x_2,tp_t_2)
l1+=G.score(tp_x_3, tp_t_3)
l1+=G.score(tp_x_1, tp_t_1)
G.fit(tp_x_3,tp_t_3)
l1+=G.score(tp_x_2, tp_t_2)
l1+=G.score(tp_x_1, tp_t_1)
print('Cross_validation score',l1/6)
print(((svm.SVC(kernel = 'linear', C = 7.74)).fit(text_x_2,text_t_2)).support_)
fig = plt.figure(2)
c = np.logspace(0, 1, 10)
matrix = np.zeros((10,3))
for i in range (10):
svc = svm.SVC(kernel='linear',C = c[i])
svc.fit(text_x_2, text_t_2)
matrix[i][0] = i
matrix[i][1] = svc.score(text_x_2, text_t_2)
svc.fit(tp_x_1,tp_t_1)
l2 = svc.score(tp_x_2, tp_t_2)
l2+=svc.score(tp_x_3, tp_t_3)
svc.fit(tp_x_2,tp_t_2)
l2+=svc.score(tp_x_3, tp_t_3)
l2+=svc.score(tp_x_1, tp_t_1)
svc.fit(tp_x_3,tp_t_3)
l2+=svc.score(tp_x_2, tp_t_2)
l2+=svc.score(tp_x_1, tp_t_1)
matrix[i][2] = l2/6
plt.plot(matrix[:,0:1],matrix[:,1:2],label = 'cross_validation score')
plt.plot(matrix[:,0:1],matrix[:,2:3],label = 'Training score')
plt.title('C vs Accuracy')
plt.xlabel('C')
plt.ylabel('Accuracy')
plt.xscale('log')
plt.legend()
plt.show()
PIPE = Pipeline([('scaler', StandardScaler()), ('SVM', svm.SVC(kernel='rbf'))])
parameters = {'SVM__C':np.logspace(0, 1, 10), 'SVM__gamma':np.logspace(0, 1, 10)}
G = GridSearchCV(PIPE, param_grid=parameters, cv=5)
G.fit(text_x_2, text_t_2)
print ('Training score',G.score(text_x_2, text_t_2))
print (G.best_params_)
G.fit(tp_x_1,tp_t_1)
l3 = G.score(tp_x_2, tp_t_2)
l3+=G.score(tp_x_3, tp_t_3)
G.fit(tp_x_2,tp_t_2)
l3+=G.score(tp_x_3, tp_t_3)
l3+=G.score(tp_x_1, tp_t_1)
G.fit(tp_x_3,tp_t_3)
l3+=G.score(tp_x_2, tp_t_2)
l3+=G.score(tp_x_1, tp_t_1)
print('Cross_validation score',l3/6)
print(((svm.SVC(kernel = 'rbf', C = 1.29,gamma =1)).fit(text_x_2,text_t_2)).support_)
puto = np.zeros((100,1))
luto = np.zeros((100,1))
c = np.logspace(0, 1, 10)
g = np.logspace(0, 1, 10)
for i in range (10):
for j in range(10):
svc = svm.SVC(kernel='rbf',C = c[i],gamma = g[j])
svc.fit(text_x_2, text_t_2)
puto[10*i+j][0] = svc.score(text_x_2, text_t_2)
svc.fit(tp_x_1,tp_t_1)
l4 = svc.score(tp_x_2, tp_t_2)
l4+=svc.score(tp_x_3, tp_t_3)
svc.fit(tp_x_2,tp_t_2)
l4+=svc.score(tp_x_3, tp_t_3)
l4+=svc.score(tp_x_1, tp_t_1)
svc.fit(tp_x_3,tp_t_3)
l4+=svc.score(tp_x_2, tp_t_2)
l4+=svc.score(tp_x_1, tp_t_1)
luto[10*i+j][0] = l4/6
g, c = np.meshgrid(g, c)
graph = np.ravel(puto)
patrix = np.ravel(luto)
patrix = patrix.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, patrix)
cbar = fig.colorbar(k)
plt.title('Accuracy v/s C and gamma (cross-validation)')
plt.xlabel('C')
plt.ylabel('gamma')
plt.xscale('log')
plt.yscale('log')
plt.show()
graph = graph.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, graph)
cbar = fig.colorbar(k)
plt.title('Accuracy v/s C and gamma (training)')
plt.xlabel('C')
plt.ylabel('gamma')
plt.xscale('log')
plt.yscale('log')
plt.show()
start1 = timer()
PIPE = Pipeline([('scaler', StandardScaler()), ('SVM', svm.SVC(kernel='poly'))])
parameters = {'SVM__C':np.logspace(0, 1, 10), 'SVM__gamma':np.logspace(0, 1, 10),'SVM__degree':[1,5]}
G = GridSearchCV(PIPE, param_grid=parameters, cv=5)
G.fit(text_x_2, text_t_2)
print ('Training score',G.score(text_x_2, text_t_2))
print (G.best_params_)
G.fit(tp_x_1,tp_t_1)
l5 = G.score(tp_x_2, tp_t_2)
l5+=G.score(tp_x_3, tp_t_3)
G.fit(tp_x_2,tp_t_2)
l5+=G.score(tp_x_3, tp_t_3)
l5+=G.score(tp_x_1, tp_t_1)
G.fit(tp_x_3,tp_t_3)
l5+=G.score(tp_x_2, tp_t_2)
l5+=G.score(tp_x_1, tp_t_1)
print('Cross_validation score',l5/6)
end1 = timer()
print('TIME',end1 - start1)
print(((svm.SVC(kernel = 'poly', C = 1,gamma =1 ,degree=5)).fit(text_x_2,text_t_2)).support_)
suto = np.zeros((100,1))
nuto = np.zeros((100,1))
c = np.logspace(0, 1, 10)
g = np.logspace(0, 1, 10)
for i in range (10):
for j in range(10):
svc = svm.SVC(kernel='poly',C = c[i],gamma = g[j],degree = 5)
svc.fit(text_x_2, text_t_2)
suto[10*i+j][0] = svc.score(text_x_2, text_t_2)
svc.fit(tp_x_1,tp_t_1)
l6 = svc.score(tp_x_2, tp_t_2)
l6+=svc.score(tp_x_3, tp_t_3)
svc.fit(tp_x_2,tp_t_2)
l6+=svc.score(tp_x_3, tp_t_3)
l6+=svc.score(tp_x_1, tp_t_1)
svc.fit(tp_x_3,tp_t_3)
l6+=svc.score(tp_x_2, tp_t_2)
l6+=svc.score(tp_x_1, tp_t_1)
nuto[10*i+j][0] = l6/6
g, c = np.meshgrid(g, c)
trix = np.ravel(suto)
prix = np.ravel(nuto)
prix = prix.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, prix)
cbar = fig.colorbar(k)
plt.title('Accuracy v/s C and gamma (cross-validation)')
plt.xlabel('C')
plt.ylabel('gamma')
plt.xscale('log')
plt.yscale('log')
plt.show()
trix = trix.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, trix)
cbar = fig.colorbar(k)
plt.title('Accuracy v/s C and gamma (training)')
plt.xlabel('C')
plt.ylabel('gamma')
plt.xscale('log')
plt.yscale('log')
plt.show()
PIPE = Pipeline([('scaler', StandardScaler()), ('SVM', svm.SVC(kernel='sigmoid'))])
parameters = {'SVM__C':np.logspace(0, 1, 10), 'SVM__gamma':np.logspace(0, 1, 10)}
G = GridSearchCV(PIPE, param_grid=parameters, cv=5)
G.fit(text_x_2, text_t_2)
print ('Training score',G.score(text_x_2, text_t_2))
print (G.best_params_)
G.fit(tp_x_1,tp_t_1)
l7 = G.score(tp_x_2, tp_t_2)
l7+=G.score(tp_x_3, tp_t_3)
G.fit(tp_x_2,tp_t_2)
l7+=G.score(tp_x_3, tp_t_3)
l7+=G.score(tp_x_1, tp_t_1)
G.fit(tp_x_3,tp_t_3)
l7+=G.score(tp_x_2, tp_t_2)
l7+=G.score(tp_x_1, tp_t_1)
print('Cross_validation score',l7/6)
print(((svm.SVC(kernel = 'sigmoid', C = 1.66,gamma = 3.59 )).fit(text_x_2,text_t_2)).support_)
jito = np.zeros((100,1))
kito = np.zeros((100,1))
c = np.logspace(0, 1, 10)
g = np.logspace(0, 1, 10)
for i in range (10):
for j in range(10):
svc = svm.SVC(kernel='sigmoid',C = c[i],gamma = g[j])
svc.fit(text_x_2, text_t_2)
jito[10*i+j][0] = svc.score(text_x_2, text_t_2)
svc.fit(tp_x_1,tp_t_1)
l8 = svc.score(tp_x_2, tp_t_2)
l8+=svc.score(tp_x_3, tp_t_3)
svc.fit(tp_x_2,tp_t_2)
l8+=svc.score(tp_x_3, tp_t_3)
l8+=svc.score(tp_x_1, tp_t_1)
svc.fit(tp_x_3,tp_t_3)
l8+=svc.score(tp_x_2, tp_t_2)
l8+=svc.score(tp_x_1, tp_t_1)
kito[10*i+j][0] = l8/6
g, c = np.meshgrid(g, c)
tatrix = np.ravel(jito)
katrix = np.ravel(kito)
katrix = katrix.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, katrix)
cbar = fig.colorbar(k)
plt.title('Accuracy v/s C and gamma (cross-validation)')
plt.xlabel('C')
plt.ylabel('gamma')
plt.xscale('log')
plt.yscale('log')
plt.show()
tatrix = tatrix.reshape(c.shape)
fig, p = plt.subplots()
k = p.contourf(c, g, tatrix)
cbar = fig.colorbar(k)
plt.title('Accuracy v/s C and gamma (training)')
plt.xlabel('C')
plt.ylabel('gamma')
plt.xscale('log')
plt.yscale('log')
plt.show()
# In[6]:
# FOR CLASSES {4,5}
text_x_3 = dp[1232:1800,:25]
text_t_3 = dp[1232:1800,25]
# for cross_validation
tp_x_1 = np.append(dp[1232:1332,:25],dp[1533:1610,:25],axis=0)
tp_t_1 = np.append(dp[1232:1332,25],dp[1533:1610,25],axis=0)
tp_x_2 = np.append(dp[1333:1433,:25],dp[1610:1699,:25],axis=0)
tp_t_2 = np.append(dp[1333:1433,25],dp[1610:1699,25],axis=0)
tp_x_3 = np.append(dp[1433:1532,:25],dp[1700:1800,:25],axis=0)
tp_t_3 = np.append(dp[1433:1532,25],dp[1700:1800,25],axis=0)
PIPE = Pipeline([('scaler', StandardScaler()), ('SVM', svm.SVC(kernel='linear'))])
parameters = {'SVM__C':np.logspace(0, 1, 10)}
G = GridSearchCV(PIPE, param_grid=parameters, cv=5)
G.fit(text_x_3, text_t_3)
print ('Training score',G.score(text_x_3, text_t_3))
print (G.best_params_)
G.fit(tp_x_1,tp_t_1)
p1 = G.score(tp_x_2, tp_t_2)
p1+=G.score(tp_x_3, tp_t_3)
G.fit(tp_x_2,tp_t_2)
p1+=G.score(tp_x_3, tp_t_3)
p1+=G.score(tp_x_1, tp_t_1)
G.fit(tp_x_3,tp_t_3)
p1+=G.score(tp_x_2, tp_t_2)
p1+=G.score(tp_x_1, tp_t_1)
print('Cross_validation score',p1/6)
print(((svm.SVC(kernel = 'linear', C = 1.29)).fit(text_x_3,text_t_3)).support_)
fig = plt.figure(3)
c = np.logspace(0, 1, 10)
matrix = np.zeros((10,3))
for i in range (10):
svc = svm.SVC(kernel='linear',C = c[i])
svc.fit(text_x_3, text_t_3)
matrix[i][0] = i
matrix[i][1] = svc.score(text_x_3, text_t_3)
svc.fit(tp_x_1,tp_t_1)
p2 = svc.score(tp_x_2, tp_t_2)
p2+=svc.score(tp_x_3, tp_t_3)
svc.fit(tp_x_2,tp_t_2)
p2+=svc.score(tp_x_3, tp_t_3)
p2+=svc.score(tp_x_1, tp_t_1)
svc.fit(tp_x_3,tp_t_3)
p2+=svc.score(tp_x_1, tp_t_1)
p2+=svc.score(tp_x_2, tp_t_2)
matrix[i][2] = p2/6
plt.plot(matrix[:,0:1],matrix[:,1:2],label = 'cross_validation score')
plt.plot(matrix[:,0:1],matrix[:,2:3],label = 'Training score')
plt.title('C vs Accuracy')
plt.xlabel('C')
plt.ylabel('Accuracy')
plt.xscale('log')
plt.legend()
plt.show()
PIPE = Pipeline([('scaler', StandardScaler()), ('SVM', svm.SVC(kernel='rbf'))])
parameters = {'SVM__C':np.logspace(0, 1, 10), 'SVM__gamma':np.logspace(0, 1, 10)}
G = GridSearchCV(PIPE, param_grid=parameters, cv=5)
G.fit(text_x_3, text_t_3)
print ('Training score',G.score(text_x_3, text_t_3))
print (G.best_params_)
G.fit(tp_x_1,tp_t_1)
p3 = G.score(tp_x_2, tp_t_2)
p3+=G.score(tp_x_3, tp_t_3)
G.fit(tp_x_2,tp_t_2)
p3+=G.score(tp_x_3, tp_t_3)
p3+=G.score(tp_x_1, tp_t_1)
G.fit(tp_x_3,tp_t_3)
p3+=G.score(tp_x_2, tp_t_2)
p3+=G.score(tp_x_1, tp_t_1)
print('Cross_validation score',p3/6)
print(((svm.SVC(kernel = 'rbf', C = 1.29,gamma =1)).fit(text_x_3,text_t_3)).support_)
puto = np.zeros((100,1))
luto = np.zeros((100,1))
c = np.logspace(0, 1, 10)
g = np.logspace(0, 1, 10)
for i in range (10):
for j in range(10):
svc = svm.SVC(kernel='rbf',C = c[i],gamma = g[j])
svc.fit(text_x_3, text_t_3)
puto[10*i+j][0] = svc.score(text_x_3, text_t_3)
svc.fit(tp_x_1,tp_t_1)
p4 = svc.score(tp_x_2, tp_t_2)
p4+=svc.score(tp_x_3, tp_t_3)
svc.fit(tp_x_2,tp_t_2)
p4+=svc.score(tp_x_3, tp_t_3)
p4+=svc.score(tp_x_1, tp_t_1)
svc.fit(tp_x_3,tp_t_3)
p4+=svc.score(tp_x_2, tp_t_2)
p4+=svc.score(tp_x_1, tp_t_1)
luto[10*i+j][0] = p4/6
g, c = np.meshgrid(g, c)
graph = | np.ravel(puto) | numpy.ravel |
import numpy as np
import math
import os
import sys
import multiprocessing
import pyfftw
#Author: <NAME>, EMBL Heidelberg, Sachse Group (2019)
#-------------------------------------------------------------------------------------
def estimateNoiseFromMap(map, windowSize, boxCoord):
#**************************************************
#****** function to estimate var an mean from *****
#**** nonoverlapping boxes outside the particle ***
#**************************************************
if boxCoord == 0:
#extract a sample of pure noise from the map
sizeMap = map.shape;
sizePatch = np.array([windowSize, windowSize, windowSize]);
center = np.array([0.5*sizeMap[0], 0.5*sizeMap[1], 0.5*sizeMap[2]]);
sampleMap1 = map[int(center[0]-0.5*sizePatch[0]):(int(center[0]-0.5*sizePatch[0]) + sizePatch[0]),
int(0.02*sizeMap[1]):(int(0.02*sizeMap[1]) + sizePatch[1]),
(int(center[2]-0.5*sizePatch[2])):(int((center[2]-0.5*sizePatch[2]) + sizePatch[2]))];
sampleMap2 = map[int(center[0]-0.5*sizePatch[0]):(int(center[0]-0.5*sizePatch[0]) + sizePatch[0]),
int(0.98*sizeMap[1] - sizePatch[1]):(int(0.98*sizeMap[1])),
(int(center[2]-0.5*sizePatch[2])):(int((center[2]-0.5*sizePatch[2]) + sizePatch[2]))];
sampleMap3 = map[int(center[0]-0.5*sizePatch[0]):(int(center[0]-0.5*sizePatch[0]) + sizePatch[0]),
(int(center[1]-0.5*sizePatch[1])):(int((center[1]-0.5*sizePatch[1]) + sizePatch[1])),
int(0.02*sizeMap[2]):(int(0.02*sizeMap[2]) + sizePatch[2])];
sampleMap4 = map[int(center[0]-0.5*sizePatch[0]):(int(center[0]-0.5*sizePatch[0]) + sizePatch[0]),
(int(center[1]-0.5*sizePatch[1])):(int((center[1]-0.5*sizePatch[1]) + sizePatch[1])),
int(0.98*sizeMap[2]) - sizePatch[2]:(int(0.98*sizeMap[2]))];
#concatenate the two samples
sampleMap = np.concatenate((sampleMap1, sampleMap2, sampleMap3, sampleMap4), axis=0);
else:
sizePatch = np.array([windowSize, windowSize, windowSize]);
center = np.array(boxCoord);
sampleMap = map[int(center[0]-0.5*sizePatch[0]):(int(center[0]-0.5*sizePatch[0]) + sizePatch[0]),
int(center[1]-0.5*sizePatch[1]):(int(center[1]-0.5*sizePatch[1]) + sizePatch[1]),
(int(center[2]-0.5*sizePatch[2])):(int((center[2]-0.5*sizePatch[2]) + sizePatch[2]))];
#estimate variance and mean from the sample
mean = np.mean(sampleMap);
var = np.var(sampleMap);
if var == 0.0:
print("Variance is estimated to be 0. You are probably estimating noise in a masked region. Exit ...")
sys.exit();
return mean, var, sampleMap;
#---------------------------------------------------------------------------------
def makeHannWindow(map):
#***********************************************************
#*** generate Hann window with the size of the given map ***
#***********************************************************
#some initialization
mapSize = map.shape;
if map.ndim == 3:
x = np.linspace(-math.floor(mapSize[0]/2.0), -math.floor(mapSize[0]/2.0) + mapSize[0], mapSize[0]);
y = np.linspace(-math.floor(mapSize[1]/2.0), -math.floor(mapSize[1]/2.0) + mapSize[1], mapSize[1]);
z = np.linspace(-math.floor(mapSize[2]/2.0), -math.floor(mapSize[2]/2.0) + mapSize[2], mapSize[2]);
xx, yy, zz = np.meshgrid(x, y, z, indexing='ij');
radiusMap = np.sqrt(xx**2 + yy**2 + zz**2);
windowMap = 0.5*(1.0 - np.cos((2.0*np.pi*radiusMap/map.shape[0]) + np.pi));
elif map.ndim == 2:
x = np.linspace(-math.floor(mapSize[0]/2.0), -math.floor(mapSize[0]/2.0) + mapSize[0], mapSize[0]);
y = np.linspace(-math.floor(mapSize[1]/2.0), -math.floor(mapSize[1]/2.0) + mapSize[1], mapSize[1]);
xx, yy = np.meshgrid(x, y, indexing='ij');
radiusMap = np.sqrt(xx**2 + yy**2);
windowMap = 0.5*(1.0 - np.cos((2.0*np.pi*radiusMap/map.shape[0]) + np.pi));
windowMap[radiusMap>(mapSize[0]/2.0)] = 0.0;
return windowMap;
#-------------------------------------------------------------------------------------
def estimateNoiseFromMapInsideMask(map, mask):
#**************************************************
#****** function to estimate var an mean from *****
#******* map outside the user provided mask *******
#**************************************************
mask[mask<=0.5] = 0.0;
mask[mask>0.0] = 1000.0;
mask[mask<1000.0] = 1.0;
mask[mask==1000.0] = 0.0;
sampleMap = np.copy(map)*mask;
sampleMap = sampleMap[sampleMap != 0.0];
#estimate variance and mean from the sample
mean = np.mean(sampleMap);
var = np.var(sampleMap);
return mean, var, sampleMap;
#-------------------------------------------------------------------------------------
def estimateNoiseFromHalfMaps(halfmap1, halfmap2, circularMask):
halfmapDiff = halfmap1 - halfmap2;
varianceBackground = np.var(halfmapDiff[circularMask>0.5]);
return varianceBackground;
#-------------------------------------------------------------------------------------
def estimateECDFFromMap(map, windowSize, boxCoord):
#**************************************************
#****** function to estimate empirical cumul. *****
#**** distribution function from solvent area *****
#**************************************************
if boxCoord == 0:
#extract a sample of pure noise from the map
sizeMap = map.shape;
sizePatch = np.array([windowSize, windowSize, windowSize]);
center = np.array([0.5*sizeMap[0], 0.5*sizeMap[1], 0.5*sizeMap[2]]);
sampleMap1 = map[int(center[0]-0.5*sizePatch[0]):(int(center[0]-0.5*sizePatch[0]) + sizePatch[0]),
int(0.02*sizeMap[1]):(int(0.02*sizeMap[1]) + sizePatch[1]),
(int(center[2]-0.5*sizePatch[2])):(int((center[2]-0.5*sizePatch[2]) + sizePatch[2]))];
sampleMap2 = map[int(center[0]-0.5*sizePatch[0]):(int(center[0]-0.5*sizePatch[0]) + sizePatch[0]),
int(0.98*sizeMap[1] - sizePatch[1]):(int(0.98*sizeMap[1])),
(int(center[2]-0.5*sizePatch[2])):(int((center[2]-0.5*sizePatch[2]) + sizePatch[2]))];
sampleMap3 = map[int(center[0]-0.5*sizePatch[0]):(int(center[0]-0.5*sizePatch[0]) + sizePatch[0]),
(int(center[1]-0.5*sizePatch[1])):(int((center[1]-0.5*sizePatch[1]) + sizePatch[1])),
int(0.02*sizeMap[2]):(int(0.02*sizeMap[2]) + sizePatch[2])];
sampleMap4 = map[int(center[0]-0.5*sizePatch[0]):(int(center[0]-0.5*sizePatch[0]) + sizePatch[0]),
(int(center[1]-0.5*sizePatch[1])):(int((center[1]-0.5*sizePatch[1]) + sizePatch[1])),
int(0.98*sizeMap[2]) - sizePatch[2]:(int(0.98*sizeMap[2]))];
#conatenate the two samples
sampleMap = np.concatenate((sampleMap1, sampleMap2, sampleMap3, sampleMap4), axis=0);
elif boxCoord == -1:
sampleMap = map;
else:
sizePatch = np.array([windowSize, windowSize, windowSize]);
center = np.array(boxCoord);
sampleMap = map[int(center[0]-0.5*sizePatch[0]):(int(center[0]-0.5*sizePatch[0]) + sizePatch[0]),
int(center[1]-0.5*sizePatch[1]):(int(center[1]-0.5*sizePatch[1]) + sizePatch[1]),
(int(center[2]-0.5*sizePatch[2])):(int((center[2]-0.5*sizePatch[2]) + sizePatch[2]))];
#estimate ECDF from map
sampleMap = sampleMap.flatten();
#downsize the sample
finalSampleSize = min(100000, sampleMap.size);
sampleMap = np.random.choice(sampleMap, finalSampleSize, replace = False);
numSamples = sampleMap.size;
sampleMapSort = np.sort(sampleMap);
minX = sampleMapSort[0];
maxX = sampleMapSort[numSamples-1];
numInterval = numSamples;
spacingX = (maxX - minX)/(float(numInterval));
ECDF = np.zeros(numInterval);
for index in range(numInterval):
val = sampleMapSort[index];
ECDF[index] = ((sampleMapSort[sampleMapSort<= val]).size)/float(numSamples);
return ECDF, sampleMapSort;
#------------------------------------------------------------------------------------
def getCDF(x, ECDF, sampleMapSort):
#****************************************************
#********* get the value of the CDF at point x ******
#******* CDF : Cumulative distribution function *****
#****************************************************
numSamples = sampleMapSort.size;
minX = sampleMapSort[0];
maxX = sampleMapSort[numSamples-1];
if x >= maxX:
CDFval = 1.0;
elif x <= minX:
CDFval = 0.0;
else:
#get the index in the ECDF array
index = np.searchsorted(sampleMapSort, x) - 1;
CDFval = ECDF[index];
return CDFval;
#------------------------------------------------------------------------------------
def AndersonDarling(sample):
#********************************************
#*** Anderson-Darling test for normality ****
#********************************************
sample = np.random.choice(sample, min(10000,sample.size), replace=False);
sampleMapSort = np.sort(sample);
numSamples = sampleMapSort.size;
Ad = -1.0*numSamples;
for i in range(numSamples):
CDF_Yi = 0.5 * (1.0 + math.erf(sampleMapSort[i]/math.sqrt(2.0)));
CDF_Yn = 0.5 * (1.0 + math.erf(sampleMapSort[numSamples-i-1]/math.sqrt(2.0)));
if CDF_Yi == 0:
CDF_Yi = 0.000001;
if CDF_Yi == 1:
CDF_Yi = 0.999999;
if CDF_Yn == 0:
CDF_Yn = 0.000001;
if CDF_Yn == 1:
CDF_Yn = 0.999999;
#calculate the Anderson-Darling test statistic
Ad = Ad - (1.0/float(numSamples)) * (2*(i+1)-1)*(math.log(CDF_Yi) + (math.log(1.0-CDF_Yn)));
#do adjustment for estimation of mean and variance, as unknown before
Ad = Ad*(1 + 0.75/float(numSamples) + 2.25/float(numSamples*numSamples));
#calculate p-values
# <NAME> and <NAME>, Eds., 1986, Goodness-of-Fit Techniques, <NAME>
try:
if Ad >= 0.6:
pVal = math.exp(1.2937 - 5.709*(Ad) + 0.0186*Ad*Ad);
elif 0.34<Ad<0.6:
pVal = math.exp(0.9177 - 4.279*Ad - 1.38 * Ad*Ad);
elif 0.2 < Ad <= 0.34:
pVal = 1 - math.exp(-8.318 + 42.796*Ad - 59.938*Ad*Ad);
else:
pVal = 1 - math.exp(-13.436 + 101.14 * Ad - 223.73 * Ad*Ad);
except:
pVal = -1.0;
return Ad, pVal, numSamples;
#------------------------------------------------------------------------------------
def KolmogorowSmirnow(ECDF, sampleMapSort):
#***********************************************
#***** KS test by supremum of distance *********
#*********** between CDF and ECDF **************
#***********************************************
#some initialization
numSamples = sampleMapSort.size;
X = np.linspace(-5, 5, 200000);
vectorizedErf = np.vectorize(math.erf);
#maximum distances between CDF and ECDF over the whole defintion region
Y_stdNorm = 0.5 * (1.0 + vectorizedErf(X/math.sqrt(2.0)));
Y_ecdf = np.interp(X, sampleMapSort, ECDF, left=0.0, right=1.0);
Dn = np.amax(np.absolute(np.subtract(Y_stdNorm,Y_ecdf)));
#get Kolmogorow-Smirnow test statistic
KS_testStat = math.sqrt(numSamples)*Dn;
#maximum distances between CDF and ECDF for tail regions
X_tail_right = X[X>2.0];
X_tail_left = X[X<-2.0];
X_tail = np.concatenate((X_tail_right, X_tail_left));
Y_stdNorm = 0.5 * (1.0 + vectorizedErf(X_tail/math.sqrt(2.0)));
Y_ecdf = np.interp(X_tail, sampleMapSort, ECDF, left=0.0, right=1.0);
Dn_tail = np.amax(np.absolute(np.subtract(Y_stdNorm,Y_ecdf)));
return KS_testStat, Dn, Dn_tail, numSamples;
#-----------------------------------------------------------------------------------
def checkNormality(map, windowSize, boxCoord):
#***************************************
#** check normal distribution ass. *****
#***************************************
print('Checking the normal distribution assumption ...');
mean, var, _ = estimateNoiseFromMap(map, windowSize, boxCoord);
map = np.subtract(map, mean);
tMap = np.multiply(map, (1.0/(math.sqrt(var))));
map = np.copy(tMap);
#get maximum distances between ECDF and CDF
ECDFvals, sampleSort = estimateECDFFromMap(map, windowSize, boxCoord);
KSstat, Dn, Dn_tail, n = KolmogorowSmirnow(ECDFvals, sampleSort);
output = "Maximum Distance Dn between ECDF and CDF: Dn=" + " %.4f" %Dn + ", in Tail:" + " %.4f" %Dn_tail + ". Sample size used: " + repr(n);
print(output);
#do Anderson-Darling test for normality
AnDarl, pVal, n = AndersonDarling(sampleSort);
output = "Anderson-Darling test summary: " + repr(AnDarl) + ". p-Value: " + "%.4f" %pVal + ". Sample size used: " + repr(n);
if pVal != -1.0:
print(output);
else:
pVal = -1.0;
if (Dn_tail > 0.01):
output = "WARNING: Deviation in the tail areas between the normal distribution and the empircal CDF is higher than 1%. If boxes for background noise estimation are set properly, please consider using the flag -ecdf to use the empirical CDF instead of the normal distribution."
print(output);
#------------------------------------------------------------------------------------
def studentizeMap(map, mean, var):
#****************************************
#********* normalize map ****************
#****************************************
if | np.isscalar(var) | numpy.isscalar |
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright 1999-2018 Alibaba Group Holding Ltd.
#
# 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 sys
import unittest
import numpy as np
from mars.deploy.local.core import new_cluster
from mars.session import new_session, LocalSession
from mars.tests.core import mock
@unittest.skipIf(sys.platform == 'win32', 'does not run in windows')
class Test(unittest.TestCase):
@mock.patch('webbrowser.open_new_tab', new=lambda *_, **__: True)
def testMutableTensorCreateAndGet(self):
def testWithGivenSession(session):
mut1 = session.create_mutable_tensor("test", (4, 5), dtype=np.double, chunk_size=3)
mut2 = session.get_mutable_tensor("test")
self.assertEqual(tuple(mut1.shape), (4, 5))
self.assertEqual(mut1.dtype, np.double)
self.assertEqual(mut1.nsplits, ((3, 1), (3, 2)))
# mut1 and mut2 are not the same object, but has the same properties.
self.assertTrue(mut1 is not mut2)
self.assertEqual(mut1.shape, mut2.shape)
self.assertEqual(mut1.dtype, mut2.dtype)
self.assertEqual(mut1.nsplits, mut2.nsplits)
for chunk1, chunk2 in zip(mut2.chunks, mut2.chunks):
self.assertEqual(chunk1.key, chunk2.key)
self.assertEqual(chunk1.index, chunk2.index)
self.assertEqual(chunk1.shape, chunk2.shape)
self.assertEqual(chunk1.dtype, chunk2.dtype)
with new_cluster(scheduler_n_process=2, worker_n_process=2,
shared_memory='20M', web=True) as cluster:
with new_session(cluster.endpoint).as_default() as session:
testWithGivenSession(session)
with new_session('http://' + cluster._web_endpoint).as_default() as web_session:
testWithGivenSession(web_session)
def testMutableTensorWrite(self):
with new_cluster(scheduler_n_process=2, worker_n_process=2,
shared_memory='20M') as cluster:
with new_session(cluster.endpoint) as session:
mut = session.create_mutable_tensor("test", (4, 5), dtype=np.double, chunk_size=3)
# write [1:4, 2], and buffer is not full.
chunk_records = mut._do_write((slice(1, 4, None), 2), 8)
self.assertEqual(chunk_records, [])
chunk_records = mut._do_flush()
chunk_records_map = dict((k, v) for k, _, v in chunk_records)
result = chunk_records_map[mut.cix[(0, 0)].key]
expected = np.array([[5, 8.], [8, 8.]])
self.assertRecordsEqual(result, expected)
result = chunk_records_map[mut.cix[(1, 0)].key]
expected = np.array([[2, 8.]])
self.assertRecordsEqual(result, expected)
# write [2:4], and buffer is not full.
chunk_records = mut._do_write(slice(2, 4, None), np.arange(10).reshape((2, 5)))
self.assertEqual(chunk_records, [])
chunk_records = mut._do_flush()
chunk_records_map = dict((k, v) for k, _, v in chunk_records)
result = chunk_records_map[mut.cix[(0, 0)].key]
expected = np.array([[6, 0.], [7, 1.], [8, 2.]])
self.assertRecordsEqual(result, expected)
result = chunk_records_map[mut.cix[(0, 1)].key]
expected = np.array([[4, 3.], [5, 4.]])
self.assertRecordsEqual(result, expected)
result = chunk_records_map[mut.cix[(1, 0)].key]
expected = np.array([[0, 5.], [1, 6.], [2, 7.]])
self.assertRecordsEqual(result, expected)
result = chunk_records_map[mut.cix[(1, 1)].key]
expected = np.array([[0, 8.], [1, 9.]])
self.assertRecordsEqual(result, expected)
# write [1], and buffer is not full.
chunk_records = mut._do_write(1, np.arange(5))
self.assertEqual(chunk_records, [])
chunk_records = mut._do_flush()
chunk_records_map = dict((k, v) for k, _, v in chunk_records)
result = chunk_records_map[mut.cix[(0, 0)].key]
expected = np.array([[3, 0.], [4, 1.], [5, 2.]])
self.assertRecordsEqual(result, expected)
result = chunk_records_map[mut.cix[(0, 1)].key]
expected = np.array([[2, 3.], [3, 4.]])
self.assertRecordsEqual(result, expected)
# write [2, [0, 2, 4]] (fancy index), and buffer is not full.
chunk_records = mut._do_write((2, [0, 2, 4]), np.array([11, 22, 33]))
self.assertEqual(chunk_records, [])
chunk_records = mut._do_flush()
chunk_records_map = dict((k, v) for k, _, v in chunk_records)
result = chunk_records_map[mut.cix[(0, 0)].key]
expected = np.array([[6, 11.], [8, 22.]])
self.assertRecordsEqual(result, expected)
result = chunk_records_map[mut.cix[(0, 1)].key]
expected = np.array([[5, 33.]])
self.assertRecordsEqual(result, expected)
# write [:], and the first buffer is full.
chunk_records = mut._do_write(slice(None, None, None), 999)
chunk_records_map = dict((k, v) for k, _, v in chunk_records)
result = chunk_records_map[mut.cix[(0, 0)].key]
expected = np.array([[0, 999.], [1, 999.], [2, 999.], [3, 999.], [4, 999.],
[5, 999.], [6, 999.], [7, 999.], [8, 999.]])
self.assertRecordsEqual(result, expected)
# check other chunks
chunk_records = mut._do_flush()
chunk_records_map = dict((k, v) for k, _, v in chunk_records)
result = chunk_records_map[mut.cix[(0, 1)].key]
expected = np.array([[0, 999.], [1, 999.], [2, 999.], [3, 999.], [4, 999.],
[5, 999.]])
self.assertRecordsEqual(result, expected)
result = chunk_records_map[mut.cix[(1, 0)].key]
expected = np.array([[0, 999.], [1, 999.], [2, 999.]])
self.assertRecordsEqual(result, expected)
result = chunk_records_map[mut.cix[(1, 1)].key]
expected = np.array([[0, 999.], [1, 999.]])
self.assertRecordsEqual(result, expected)
@mock.patch('webbrowser.open_new_tab', new=lambda *_, **__: True)
def testMutableTensorSeal(self):
def testWithGivenSession(session):
mut = session.create_mutable_tensor("test", (4, 5), dtype='int32', chunk_size=3)
mut[1:4, 2] = 8
mut[2:4] = np.arange(10).reshape(2, 5)
mut[1] = np.arange(5)
arr = mut.seal()
expected = np.zeros((4, 5), dtype='int32')
expected[1:4, 2] = 8
expected[2:4] = np.arange(10).reshape(2, 5)
expected[1] = np.arange(5)
# check chunk properties
for chunk1, chunk2 in zip(mut.chunks, arr.chunks):
self.assertEqual(chunk1.key, chunk2.key)
self.assertEqual(chunk1.index, chunk2.index)
self.assertEqual(chunk1.shape, chunk2.shape)
self.assertEqual(chunk1.dtype, chunk2.dtype)
# check value
np.testing.assert_array_equal(session.fetch(arr), expected)
# check operations on the sealed tensor
np.testing.assert_array_equal(session.run(arr + 1), expected + 1)
np.testing.assert_array_equal(session.run(arr + arr), expected + expected)
np.testing.assert_array_equal(session.run(arr.sum()), expected.sum())
with new_cluster(scheduler_n_process=2, worker_n_process=2,
shared_memory='20M', web=True) as cluster:
session = cluster.session.as_default()
testWithGivenSession(session)
with new_session('http://' + cluster._web_endpoint).as_default() as web_session:
testWithGivenSession(web_session)
@mock.patch('webbrowser.open_new_tab', new=lambda *_, **__: True)
def testMutableTensorDuplicateName(self):
def testWithGivenSession(session):
session.create_mutable_tensor("test", (4, 5), dtype='int32')
# The two unsealed mutable tensors cannot have the same name.
with self.assertRaises(ValueError) as cm:
session.create_mutable_tensor("test", (4, 5), dtype='int32')
expected_msg = "The mutable tensor named 'test' already exists."
self.assertEqual(cm.exception.args[0], expected_msg)
with new_session().as_default() as session:
testWithGivenSession(session)
with new_cluster(scheduler_n_process=2, worker_n_process=2, shared_memory='20M', web=True) as cluster:
session = cluster.session.as_default()
testWithGivenSession(session)
with new_session('http://' + cluster._web_endpoint).as_default() as web_session:
testWithGivenSession(web_session)
@mock.patch('webbrowser.open_new_tab', new=lambda *_, **__: True)
def testMutableTensorRaiseAfterSeal(self):
def testWithGivenSession(session):
mut = session.create_mutable_tensor("test", (4, 5), dtype='int32', chunk_size=3)
mut.seal()
expected_msg = "The mutable tensor named 'test' doesn't exist, or has already been sealed."
# Cannot get after seal
with self.assertRaises(ValueError) as cm:
session.get_mutable_tensor("test")
self.assertEqual(cm.exception.args[0], expected_msg)
# Cannot write after seal
with self.assertRaises(ValueError) as cm:
mut[:] = 111
self.assertEqual(cm.exception.args[0], expected_msg)
# Cannot seal after seal
with self.assertRaises(ValueError) as cm:
session.seal(mut)
self.assertEqual(cm.exception.args[0], expected_msg)
with new_session().as_default() as session:
testWithGivenSession(session)
with new_cluster(scheduler_n_process=2, worker_n_process=2,
shared_memory='20M', web=True) as cluster:
session = cluster.session.as_default()
testWithGivenSession(session)
with new_session('http://' + cluster._web_endpoint).as_default() as web_session:
testWithGivenSession(web_session)
@mock.patch('webbrowser.open_new_tab', new=lambda *_, **__: True)
def testMutableTensorStructured(self):
def testWithGivenSession(session):
rec_type = np.dtype([('a', np.int32), ('b', np.double), ('c', np.dtype([('a', np.int16), ('b', np.int64)]))])
mut = session.create_mutable_tensor("test", (4, 5), dtype=rec_type, chunk_size=3)
mut[1:4, 1] = (3, 4., (5, 6))
mut[1:4, 2] = 8
mut[2:4] = np.arange(10).reshape(2, 5)
mut[1] = np.arange(5)
arr = mut.seal()
expected = np.zeros((4, 5), dtype=rec_type)
expected[1:4, 1] = (3, 4., (5, 6))
expected[1:4, 2] = 8
expected[2:4] = np.arange(10).reshape(2, 5)
expected[1] = np.arange(5)
# check dtype and value
self.assertEqual(np.dtype(arr.dtype), expected.dtype)
np.testing.assert_array_equal(session.fetch(arr), expected)
with new_session().as_default() as session:
testWithGivenSession(session)
with new_cluster(scheduler_n_process=2, worker_n_process=2,
shared_memory='20M', web=True) as cluster:
session = cluster.session.as_default()
testWithGivenSession(session)
with new_session('http://' + cluster._web_endpoint).as_default() as web_session:
testWithGivenSession(web_session)
def testMutableTensorLocal(self):
with new_session().as_default() as session:
mut = session.create_mutable_tensor("test", (4, 5), dtype='int32', chunk_size=3)
mut2 = session.get_mutable_tensor("test")
# In local session, mut1 and mut2 should be the same object
self.assertEqual(id(mut), id(mut2))
# Check the property
self.assertEqual(mut.shape, (4, 5))
self.assertEqual(np.dtype(mut.dtype), np.int32)
# Mutable tensor doesn't have chunks in local session
self.assertEqual(mut.chunks, None)
# Check write and seal
mut[1:4, 2] = 8
mut[2:4] = np.arange(10).reshape(2, 5)
mut[1] = np.arange(5)
arr = mut.seal()
# The arr should be executed after seal
self.assertIn(arr.key, session._sess.executed_tileables)
# The arr should has chunks
self.assertNotEqual(arr.chunks, None)
expected = np.zeros((4, 5), dtype='int32')
expected[1:4, 2] = 8
expected[2:4] = np.arange(10).reshape(2, 5)
expected[1] = np.arange(5)
# Check the value
np.testing.assert_array_equal(session.fetch(arr), expected)
# check operations on the sealed tensor
np.testing.assert_array_equal(session.run(arr + 1), expected + 1)
np.testing.assert_array_equal(session.run(arr + arr), expected + expected)
np.testing.assert_array_equal(session.run(arr.sum()), expected.sum())
@mock.patch('webbrowser.open_new_tab', new=lambda *_, **__: True)
def testMutableTensorCtor(self):
def testWithGivenSession(session):
from mars.tensor.core import mutable_tensor
# cannot get non-existing mutable tensor
with self.assertRaises(ValueError):
mutable_tensor("test")
# should be create
mut1 = mutable_tensor("test", (4, 5), dtype='int32', chunk_size=3)
# should be get
mut2 = mutable_tensor("test")
# mut1 should equal to mut2, but are not the same object
self.assertEqual(mut1.shape, mut2.shape)
self.assertEqual(mut1.dtype, mut2.dtype)
# LocalSession return the same MutableTensor instance when `get_mutable_tensor`.
if isinstance(session._sess, LocalSession):
self.assertTrue(mut1 is mut2)
else:
self.assertTrue(mut1 is not mut2)
mut2[1:4, 2] = 8
mut2[2:4] = np.arange(10).reshape(2, 5)
expected = np.zeros((4, 5), dtype='int32')
expected[1:4, 2] = 8
expected[2:4] = np.arange(10).reshape(2, 5)
# cannot be sealed twice
#
# Note that we operate on `mut2`, if we seal `mut1`, the result may not be correct.
#
# When we operate both on `mut1` and `mut2`, the result may not correct since the
# two MutableTensor instances both main their own local buffers, but they cannot
# be both sealed.
arr = mut2.seal()
with self.assertRaises(ValueError):
mut1.seal()
# check value
np.testing.assert_array_equal(session.fetch(arr), expected)
with new_session().as_default() as session:
testWithGivenSession(session)
with new_cluster(scheduler_n_process=2, worker_n_process=2,
shared_memory='20M', web=True) as cluster:
session = cluster.session.as_default()
testWithGivenSession(session)
with new_session('http://' + cluster._web_endpoint).as_default() as web_session:
testWithGivenSession(web_session)
@mock.patch('webbrowser.open_new_tab', new=lambda *_, **__: True)
def testMutableTensorFillValue(self):
def testWithGivenSession(session):
from mars.tensor.core import mutable_tensor
# simple dtype.
mut1 = mutable_tensor("test", (4, 5), dtype='double', fill_value=123.456, chunk_size=3)
mut1[1:4, 2] = 8
mut1[2:4] = | np.arange(10) | numpy.arange |
import six
import numbers
from collections import defaultdict, Counter
import numpy as np
import scipy.sparse as sp
from sklearn.feature_extraction.text import TfidfVectorizer, TfidfTransformer, \
_make_int_array, _document_frequency
class DeltaTfidfTransformer(TfidfTransformer):
def fit(self, X_pos, X_neg, y):
if not sp.issparse(X_pos):
X_pos = sp.csc_matrix(X_pos)
if not sp.issparse(X_neg):
X_neg = sp.csc_matrix(X_neg)
if self.use_idf:
n_samples, n_features = X_pos.shape
counter = Counter(y)
n_pos_samples = counter[1]
n_neg_samples = counter[-1]
df_pos = _document_frequency(X_pos)
df_neg = _document_frequency(X_neg)
# perform idf smoothing if required
df_pos += int(self.smooth_idf)
df_neg += int(self.smooth_idf)
n_samples += int(self.smooth_idf)
n_pos_samples += int(self.smooth_idf)
n_neg_samples += int(self.smooth_idf)
# log+1 instead of log makes sure terms with zero idf don't get
# suppressed entirely.
idf = np.log(float(n_pos_samples) / df_pos) - np.log(float(n_neg_samples) / df_neg) + 1.0
self._idf_diag = sp.spdiags(idf, diags=0, m=n_features,
n=n_features, format='csr')
return self
class DeltaTfidfVectorizer(TfidfVectorizer):
def __init__(self, input='content', encoding='utf-8',
decode_error='strict', strip_accents=None, lowercase=True,
preprocessor=None, tokenizer=None, analyzer='word',
stop_words=None, token_pattern=r"(?u)\b\w\w+\b",
ngram_range=(1, 1), max_df=1.0, min_df=1,
max_features=None, vocabulary=None, binary=False,
dtype=np.int64, norm='l2', use_idf=True, smooth_idf=True,
sublinear_tf=False):
super(TfidfVectorizer, self).__init__(
input=input, encoding=encoding, decode_error=decode_error,
strip_accents=strip_accents, lowercase=lowercase,
preprocessor=preprocessor, tokenizer=tokenizer, analyzer=analyzer,
stop_words=stop_words, token_pattern=token_pattern,
ngram_range=ngram_range, max_df=max_df, min_df=min_df,
max_features=max_features, vocabulary=vocabulary, binary=binary,
dtype=dtype)
self._tfidf = DeltaTfidfTransformer(norm=norm, use_idf=use_idf,
smooth_idf=smooth_idf,
sublinear_tf=sublinear_tf)
def _count_vocab(self, raw_documents, fixed_vocab, y=None):
if not y:
return super(DeltaTfidfVectorizer, self)._count_vocab(raw_documents, fixed_vocab)
if fixed_vocab:
vocabulary = self.vocabulary_
else:
# Add a new value when a new vocabulary item is seen
vocabulary = defaultdict()
vocabulary.default_factory = vocabulary.__len__
analyze = self.build_analyzer()
j_indices = []
indptr = _make_int_array()
values = _make_int_array()
pos_values = _make_int_array()
neg_values = _make_int_array()
indptr.append(0)
for i, doc in enumerate(raw_documents):
feature_counter = defaultdict(int)
pos_feature_counter = defaultdict(int)
neg_feature_counter = defaultdict(int)
for feature in analyze(doc):
try:
feature_idx = vocabulary[feature]
feature_counter[feature_idx] += 1
pos_feature_counter[feature_idx] += int(y[i] == 1)
neg_feature_counter[feature_idx] += int(y[i] == -1)
except KeyError:
# Ignore out-of-vocabulary items for fixed_vocab=True
continue
j_indices.extend(feature_counter.keys())
values.extend(feature_counter.values())
pos_values.extend(pos_feature_counter.values())
neg_values.extend(neg_feature_counter.values())
indptr.append(len(j_indices))
if not fixed_vocab:
# disable defaultdict behaviour
vocabulary = dict(vocabulary)
if not vocabulary:
raise ValueError("empty vocabulary; perhaps the documents only"
" contain stop words")
j_indices = np.asarray(j_indices, dtype=np.intc)
indptr = np.frombuffer(indptr, dtype=np.intc)
values = np.frombuffer(values, dtype=np.intc)
pos_values = | np.frombuffer(pos_values, dtype=np.intc) | numpy.frombuffer |
# Author: <NAME> (sylla801)
# File: TSKS11-Lab5
from print_graph import print_graph
import numpy as np
import scipy.sparse
file1 = 'karate-network.csv'
file2 = 'mini-example.csv'
file3 = 'neural-example.csv'
network = file1
# num_lines = sum(1 for line in open(file1))
f_list = []
t_list = []
data = []
np_matrix = | np.zeros(shape=(34, 34)) | numpy.zeros |
"""
created on Jan 29, 2014
@author: <NAME>, jajcay(at)cs.cas.cz
based on class by <NAME> -- https://github.com/vejmelkam/ndw-climate --
last update on Sep 26, 2017
"""
import csv
from datetime import date, timedelta, datetime
import numpy as np
from dateutil.relativedelta import relativedelta
from pyclits.functions import detrend_with_return
class DataField:
"""
Class holds the time series of a geophysical field. The fields for reanalysis data are
3-dimensional - two spatial and one temporal dimension. The fields for station data contains
temporal dimension and location specification.
"""
def __init__(self, data_folder='', data=None, lons=None, lats=None, time=None, verbose=False):
"""
Initializes either an empty data set or with given values.
"""
self.data_folder = data_folder
self.data = data
self.lons = lons
self.lats = lats
self.time = time
self.location = None # for station data
self.missing = None # for station data where could be some missing values
self.station_id = None # for station data
self.station_elev = None # in metres, for station data
self.var_name = None
self.nans = False
self.cos_weights = None
self.data_mask = None
self.verbose = verbose
def __str__(self):
"""
String representation.
"""
if self.data is not None:
return ("Geo data of shape %s as time x lat x lon." % str(self.data.shape))
else:
return("Empty DataField instance.")
def shape(self):
"""
Prints shape of data field.
"""
if self.data is not None:
return self.data.shape
else:
raise Exception("DataField is empty.")
def __getitem__(self, key):
"""
getitem representation.
"""
if self.data is not None:
return self.data[key]
else:
raise Exception("DataField is empty.")
def load(self, filename=None, variable_name=None, dataset='ECA-reanalysis', print_prog=True):
"""
Loads geophysical data from netCDF file for reanalysis or from text file for station data.
Now supports following datasets: (dataset - keyword passed to function)
ECA&D E-OBS gridded dataset reanalysis - 'ECA-reanalysis'
ECMWF gridded reanalysis - 'ERA'
NCEP/NCAR Reanalysis 1 - 'NCEP'
"""
from netCDF4 import Dataset
if dataset == 'ECA-reanalysis':
d = Dataset(self.data_folder + filename, 'r')
v = d.variables[variable_name]
data = v[:] # masked array - only land data, not ocean/sea
self.data = data.data.copy() # get only data, not mask
self.data[data.mask] = np.nan # filled masked values with NaNs
self.lons = d.variables['longitude'][:]
self.lats = d.variables['latitude'][:]
self.time = d.variables['time'][:] # days since 1950-01-01 00:00
self.time += date.toordinal(date(1950, 1, 1))
self.var_name = variable_name
if np.any(np.isnan(self.data)):
self.nans = True
if print_prog:
print("Data saved to structure. Shape of the data is %s" % (str(self.data.shape)))
print("Lats x lons saved to structure. Shape is %s x %s" % (str(self.lats.shape[0]), str(self.lons.shape[0])))
print("Time stamp saved to structure as ordinal values where Jan 1 of year 1 is 1")
print("The first data value is from %s and the last is from %s" % (str(self.get_date_from_ndx(0)), str(self.get_date_from_ndx(-1))))
print("Default temporal sampling in the data is %.2f day(s)" % (np.nanmean(np.diff(self.time))))
if np.any(np.isnan(self.data)):
print("The data contains NaNs! All methods are compatible with NaNs, just to let you know!")
d.close()
elif dataset == 'ERA':
d = Dataset(self.data_folder + filename, 'r')
v = d.variables[variable_name]
data = v[:]
if isinstance(data, np.ma.masked_array):
self.data = data.data.copy() # get only data, not mask
self.data[data.mask] = np.nan # filled masked values with NaNs
else:
self.data = data
self.lons = d.variables['longitude'][:]
self.lats = d.variables['latitude'][:]
if 'level' in d.variables.keys():
self.level = d.variables['level'][:]
self.time = d.variables['time'][:] # hours since 1900-01-01 00:00
self.time = self.time / 24.0 + date.toordinal(date(1900, 1, 1))
self.var_name = variable_name
if np.any(np.isnan(self.data)):
self.nans = True
if print_prog:
print("Data saved to structure. Shape of the data is %s" % (str(self.data.shape)))
print("Lats x lons saved to structure. Shape is %s x %s" % (str(self.lats.shape[0]), str(self.lons.shape[0])))
print("Time stamp saved to structure as ordinal values where Jan 1 of year 1 is 1")
print("The first data value is from %s and the last is from %s" % (str(self.get_date_from_ndx(0)), str(self.get_date_from_ndx(-1))))
print("Default temporal sampling in the data is %.2f day(s)" % (np.nanmean(np.diff(self.time))))
if np.any(np.isnan(self.data)):
print("The data contains NaNs! All methods are compatible with NaNs, just to let you know!")
d.close()
elif dataset == 'NCEP':
d = Dataset(self.data_folder + filename, 'r')
v = d.variables[variable_name]
data = v[:] # masked array - only land data, not ocean/sea
if isinstance(data, np.ma.masked_array):
self.data = data.data.copy() # get only data, not mask
self.data[data.mask] = np.nan # filled masked values with NaNs
else:
self.data = data
self.lons = d.variables['lon'][:]
if np.any(self.lons < 0):
self._shift_lons_to_360()
self.lats = d.variables['lat'][:]
if 'level' in d.variables.keys():
self.level = d.variables['level'][:]
self.time = d.variables['time'][:] # hours or days since some date
date_since = self._parse_time_units(d.variables['time'].units)
if "hours" in d.variables['time'].units:
self.time = self.time / 24.0 + date.toordinal(date_since)
elif "days" in d.variables['time'].units:
self.time += date.toordinal(date_since)
elif "months" in d.variables['time'].units:
from dateutil.relativedelta import relativedelta
for t in range(self.time.shape[0]):
self.time[t] = date.toordinal(date_since + relativedelta(months=+int(self.time[t])))
self.var_name = variable_name
if np.any(np.isnan(self.data)):
self.nans = True
if print_prog:
print("Data saved to structure. Shape of the data is %s" % (str(self.data.shape)))
print("Lats x lons saved to structure. Shape is %s x %s" % (str(self.lats.shape[0]), str(self.lons.shape[0])))
print("Time stamp saved to structure as ordinal values where Jan 1 of year 1 is 1")
print("The first data value is from %s and the last is from %s" % (str(self.get_date_from_ndx(0)), str(self.get_date_from_ndx(-1))))
print("Default temporal sampling in the data is %.2f day(s)" % (np.nanmean(np.diff(self.time))))
if np.any(np.isnan(self.data)):
print("The data contains NaNs! All methods are compatible with NaNs, just to let you know!")
d.close()
elif dataset == 'arbitrary':
d = Dataset(self.data_folder + filename, 'r')
v = d.variables[variable_name]
data = v[:] # masked array - only land data, not ocean/sea
if isinstance(data, np.ma.masked_array):
self.data = data.data.copy() # get only data, not mask
self.data[data.mask] = np.nan # filled masked values with NaNs
self.data_mask = data.mask.copy()
else:
self.data = data.copy()
self.data = np.squeeze(self.data)
for key in d.variables.keys():
if key == variable_name:
continue
if 'lat' in str(d.variables[key].name):
self.lats = d.variables[key][:]
if 'lon' in str(d.variables[key].name):
self.lons = d.variables[key][:]
if np.any(self.lons < 0):
self._shift_lons_to_360()
try: # handling when some netCDF variable hasn't assigned units
if 'since' in d.variables[key].units:
self.time = d.variables[key][:]
date_since = self._parse_time_units(d.variables[key].units)
if "hours" in d.variables[key].units:
self.time = self.time / 24.0 + date.toordinal(date_since)
elif "seconds" in d.variables[key].units:
self.time = self.time / 86400. + date.toordinal(date_since)
elif "days" in d.variables[key].units:
self.time += date.toordinal(date_since)
elif "months" in d.variables[key].units:
from dateutil.relativedelta import relativedelta
for t in range(self.time.shape[0]):
self.time[t] = date.toordinal(date_since + relativedelta(months = +int(self.time[t])))
except AttributeError:
pass
self.var_name = variable_name
if np.any(np.isnan(self.data)):
self.nans = True
if print_prog:
print("Data saved to structure. Shape of the data is %s" % (str(self.data.shape)))
print("Lats x lons saved to structure. Shape is %s x %s" % (str(self.lats.shape[0]), str(self.lons.shape[0])))
print("Time stamp saved to structure as ordinal values where Jan 1 of year 1 is 1")
print("The first data value is from %s and the last is from %s" % (str(self.get_date_from_ndx(0)), str(self.get_date_from_ndx(-1))))
print("Default temporal sampling in the data is %.2f day(s)" % (np.nanmean(np.diff(self.time))))
if np.any(np.isnan(self.data)):
print("The data contains NaNs! All methods are compatible with NaNs, just to let you know!")
d.close()
else:
raise Exception("Unknown or unsupported dataset!")
def _shift_lons_to_360(self):
"""
Shifts lons to 0-360 degree east.
"""
self.lons[self.lons < 0] += 360
ndx = np.argsort(self.lons)
self.lons = self.lons[ndx]
self.data = self.data[..., ndx]
@staticmethod
def _parse_time_units(time_string):
"""
Parses time units from netCDF file, returns date since the record.
"""
date_split = time_string.split('-')
y = ("%04d" % int(date_split[0][-4:]))
m = ("%02d" % int(date_split[1]))
d = ("%02d" % int(date_split[2][:2]))
return datetime.strptime("%s-%s-%s" % (y, m, d), '%Y-%m-%d')
def load_station_data(self, filename, dataset='ECA-station', print_prog=True, offset_in_file=0):
"""
Loads station data, usually from text file. Uses numpy.loadtxt reader.
"""
if dataset == 'Klem_day':
raw_data = np.loadtxt(self.data_folder + filename) # first column is continous year and second is actual data
self.data = np.array(raw_data[:, 1])
time = []
# use time iterator to go through the dates
y = int(np.modf(raw_data[0, 0])[1])
if np.modf(raw_data[0, 0])[0] == 0:
start_date = date(y, 1, 1)
delta = timedelta(days = 1)
d = start_date
while len(time) < raw_data.shape[0]:
time.append(d.toordinal())
d += delta
self.time = np.array(time)
self.location = 'Praha-Klementinum, Czech Republic'
print("Station data from %s saved to structure. Shape of the data is %s" % (self.location, str(self.data.shape)))
print("Time stamp saved to structure as ordinal values where Jan 1 of year 1 is 1")
if dataset == 'ECA-station':
with open(self.data_folder + filename, 'rb') as f:
time = []
data = []
missing = []
i = 0 # line-counter
reader = csv.reader(f)
for row in reader:
i += 1
if i == 16 + offset_in_file: # line with location
c_list = filter(None, row[1].split(" "))
del c_list[-2:]
country = ' '.join(c_list).lower()
station = ' '.join(row[0].split(" ")[7:]).lower()
self.location = station.title() + ', ' + country.title()
if i > 20 + offset_in_file: # actual data - len(row) = 5 as STAID, SOUID, DATE, TG, Q_TG
staid = int(row[0])
value = float(row[3])
year = int(row[2][:4])
month = int(row[2][4:6])
day = int(row[2][6:])
time.append(date(year, month, day).toordinal())
if value == -9999.:
missing.append(date(year, month, day).toordinal())
data.append(np.nan)
else:
data.append(value/10.)
self.station_id = staid
self.data = np.array(data)
self.time = np.array(time)
self.missing = np.array(missing)
if print_prog:
print("Station data from %s saved to structure. Shape of the data is %s" % (self.location, str(self.data.shape)))
print("Time stamp saved to structure as ordinal values where Jan 1 of year 1 is 1")
if self.missing.shape[0] != 0 and self.verbose:
print("** WARNING: There were some missing values! To be precise, %d missing values were found!" % (self.missing.shape[0]))
def copy_data(self):
"""
Returns the copy of data.
"""
return self.data.copy()
def copy(self, temporal_ndx=None):
"""
Returns a copy of DataField with data, lats, lons and time fields.
If temporal_ndx is not None, copies only selected temporal part of data.
"""
copied = DataField()
copied.data = self.data.copy()
copied.time = self.time.copy()
if temporal_ndx is not None:
copied.data = copied.data[temporal_ndx]
copied.time = copied.time[temporal_ndx]
if self.lats is not None:
copied.lats = self.lats.copy()
if self.lons is not None:
copied.lons = self.lons.copy()
if self.location is not None:
copied.location = self.location
if self.missing is not None:
copied.missing = self.missing.copy()
if self.station_id is not None:
copied.station_id = self.station_id
if self.station_elev is not None:
copied.station_elev = self.station_elev
if self.var_name is not None:
copied.var_name = self.var_name
if self.cos_weights is not None:
copied.cos_weights = self.cos_weights
if self.data_mask is not None:
copied.data_mask = self.data_mask
copied.nans = self.nans
return copied
def select_date(self, date_from, date_to, apply_to_data=True, exclusive=True):
"""
Selects the date range - date_from is inclusive, date_to is exclusive. Input is date(year, month, day).
"""
d_start = date_from.toordinal()
d_to = date_to.toordinal()
if exclusive:
ndx = np.logical_and(self.time >= d_start, self.time < d_to)
else:
ndx = np.logical_and(self.time >= d_start, self.time <= d_to)
if apply_to_data:
self.time = self.time[ndx] # slice time stamp
self.data = self.data[ndx, ...] # slice data
if self.data_mask is not None and self.data_mask.ndim > 2:
self.data_mask = self.data_mask[ndx, ...] # slice missing if exists
if self.missing is not None:
missing_ndx = np.logical_and(self.missing >= d_start, self.missing < d_to)
self.missing = self.missing[missing_ndx] # slice missing if exists
return ndx
def get_sliding_window_indexes(self, window_length, window_shift, unit='m', return_half_dates=False):
"""
Returns list of indices for sliding window analysis.
If return_half_dates is True, also returns dates in the middle of the interval for reference.
"""
from dateutil.relativedelta import relativedelta
if unit == 'm':
length = relativedelta(months = +window_length)
shift = relativedelta(months = +window_shift)
elif unit == 'd':
length = relativedelta(days = +window_length)
shift = relativedelta(days = +window_shift)
elif unit == 'y':
length = relativedelta(years = +window_length)
shift = relativedelta(years = +window_shift)
else:
raise Exception("Unknown time unit! Please, use one of the 'd', 'm', 'y'!")
ndxs = []
if return_half_dates:
half_dates = []
window_start = self.get_date_from_ndx(0)
window_end = window_start + length
while window_end <= self.get_date_from_ndx(-1):
ndx = self.select_date(window_start, window_end, apply_to_data=False)
ndxs.append(ndx)
if return_half_dates:
half_dates.append(window_start + (window_end - window_start) / 2)
window_start += shift
window_end = window_start + length
# add last
ndxs.append(self.select_date(window_start, window_end, apply_to_data=False))
if return_half_dates:
half_dates.append(window_start + (self.get_date_from_ndx(-1) - window_start) / 2)
if np.sum(ndxs[-1]) != np.sum(ndxs[-2]) and self.verbose:
print("**WARNING: last sliding window is shorter than others! (%d vs. %d in others)"
% (np.sum(ndxs[-1]), np.sum(ndxs[-2])))
if return_half_dates:
return ndxs, half_dates
else:
return ndxs
def create_time_array(self, date_from, sampling='m'):
"""
Creates time array for already saved data in 'self.data'.
From date_from to date_from + data length. date_from is inclusive.
Sampling:
'm' for monthly, could be just 'm' or '3m' as three-monthly
'd' for daily
'xh' where x = {1, 6, 12} for sub-daily.
"""
if 'm' in sampling:
if 'm' != sampling:
n_months = int(sampling[:-1])
timedelta = relativedelta(months=+n_months)
elif 'm' == sampling:
timedelta = relativedelta(months=+1)
elif sampling == 'd':
timedelta = relativedelta(days=+1)
elif sampling in ['1h', '6h', '12h']:
hourly_data = int(sampling[:-1])
timedelta = relativedelta(hours=+hourly_data)
elif sampling == 'y':
timedelta = relativedelta(years=+1)
else:
raise Exception("Unknown sampling.")
d_now = date_from
self.time = np.zeros((self.data.shape[0],))
for t in range(self.data.shape[0]):
self.time[t] = d_now.toordinal()
d_now += timedelta
def get_date_from_ndx(self, ndx):
"""
Returns the date of the variable from given index.
"""
return date.fromordinal(np.int(self.time[ndx]))
def get_spatial_dims(self):
"""
Returns the spatial dimensions of the data as list.
"""
return list(self.data.shape[-2:])
def find_date_ndx(self, date):
"""
Returns index which corresponds to the date. Returns None if the date is not contained in the data.
"""
d = date.toordinal()
pos = np.nonzero(self.time == d)
if not np.all(np.isnan(pos)):
return int(pos[0])
else:
return None
def get_closest_lat_lon(self, lat, lon):
"""
Returns closest lat, lon index in the data.
"""
return [np.abs(self.lats - lat).argmin(), np.abs(self.lons - lon).argmin()]
def select_months(self, months, apply_to_data=True):
"""
Subselects only certain months. Input as a list of months number.
"""
ndx = filter(lambda i: date.fromordinal(int(self.time[i])).month in months, range(len(self.time)))
if apply_to_data:
self.time = self.time[ndx]
self.data = self.data[ndx, ...]
return ndx
def select_lat_lon(self, lats, lons, apply_to_data = True):
"""
Selects region in lat/lon. Input is for both [from, to], both are inclusive. If None, the dimension is not modified.
"""
if self.lats is not None and self.lons is not None:
if lats is not None:
lat_ndx = np.nonzero(np.logical_and(self.lats >= lats[0], self.lats <= lats[1]))[0]
else:
lat_ndx = np.arange(len(self.lats))
if lons is not None:
if lons[0] < lons[1]:
lon_ndx = np.nonzero(np.logical_and(self.lons >= lons[0], self.lons <= lons[1]))[0]
elif lons[0] > lons[1]:
l1 = list(np.nonzero(np.logical_and(self.lons >= lons[0], self.lons <= 360))[0])
l2 = list(np.nonzero(np.logical_and(self.lons >= 0, self.lons <= lons[1]))[0])
lon_ndx = np.array(l1 + l2)
else:
lon_ndx = np.arange(len(self.lons))
if apply_to_data:
if self.data.ndim >= 3:
d = self.data.copy()
d = d[..., lat_ndx, :]
self.data = d[..., lon_ndx].copy()
self.lats = self.lats[lat_ndx]
self.lons = self.lons[lon_ndx]
if self.data_mask is not None:
d = self.data_mask
d = d[..., lat_ndx, :]
self.data_mask = d[..., lon_ndx]
elif self.data.ndim == 2: # multiple stations data
d = self.data.copy()
d = d[:, lat_ndx]
self.lons = self.lons[lat_ndx]
self.lats = self.lats[lat_ndx]
if lons is not None:
if lons[0] < lons[1]:
lon_ndx = np.nonzero(np.logical_and(self.lons >= lons[0], self.lons <= lons[1]))[0]
elif lons[0] > lons[1]:
l1 = list(np.nonzero(np.logical_and(self.lons >= lons[0], self.lons <= 360))[0])
l2 = list(np.nonzero(np.logical_and(self.lons >= 0, self.lons <= lons[1]))[0])
lon_ndx = np.array(l1 + l2)
else:
lon_ndx = np.arange(len(self.lons))
self.data = d[:, lon_ndx].copy()
self.lons = self.lons[lon_ndx]
self.lats = self.lats[lon_ndx]
if np.any(np.isnan(self.data)):
self.nans = True
else:
self.nans = False
return lat_ndx, lon_ndx
else:
raise Exception('Slicing data with no spatial dimensions, probably station data.')
def cut_lat_lon(self, lats_to_cut, lons_to_cut):
"""
Cuts region in lats/lons (puts NaNs in the selected regions).
Input is for both [from, to], both are inclusive. If None, the dimension is not modified.
"""
if self.lats is not None and self.lons is not None:
if lats_to_cut is not None:
lat_ndx = np.nonzero(np.logical_and(self.lats >= lats_to_cut[0], self.lats <= lats_to_cut[1]))[0]
if lons_to_cut is None:
self.data[..., lat_ndx, :] = np.nan
if lons_to_cut is not None:
if lons_to_cut[0] < lons_to_cut[1]:
lon_ndx = np.nonzero(np.logical_and(self.lons >= lons_to_cut[0], self.lons <= lons_to_cut[1]))[0]
elif lons_to_cut[0] > lons_to_cut[1]:
l1 = list(np.nonzero(np.logical_and(self.lons >= lons_to_cut[0], self.lons <= 360))[0])
l2 = list(np.nonzero(np.logical_and(self.lons >= 0, self.lons <= lons_to_cut[1]))[0])
lon_ndx = np.array(l1 + l2)
if lats_to_cut is None:
self.data[..., lon_ndx] = np.nan
if lats_to_cut is not None and lons_to_cut is not None:
for lat in lat_ndx:
for lon in lon_ndx:
self.data[..., lat, lon] = np.nan
else:
raise Exception('Slicing data with no spatial dimensions, probably station data.')
def select_level(self, level):
"""
Selects the proper level from the data. Input should be integer >= 0.
"""
if self.data.ndim > 3:
self.data = self.data[:, level, ...]
self.level = self.level[level]
else:
raise Exception('Slicing level in single-level data.')
def extract_day_month_year(self):
"""
Extracts the self.time field into three fields containg days, months and years.
"""
n_days = len(self.time)
days = np.zeros((n_days,), dtype = np.int)
months = np.zeros((n_days,), dtype = np.int)
years = np.zeros((n_days,), dtype = np.int)
for i,d in zip(range(n_days), self.time):
dt = date.fromordinal(int(d))
days[i] = dt.day
months[i] = dt.month
years[i] = dt.year
return days, months, years
def latitude_cos_weights(self):
"""
Returns a grid with scaling weights based on cosine of latitude.
"""
if (np.all(self.cos_weights) is not None) and (self.cos_weights.shape == self.get_spatial_dims()):
return self.cos_weights
cos_weights = np.zeros(self.get_spatial_dims())
for ndx in range(self.lats.shape[0]):
cos_weights[ndx, :] = np.cos(self.lats[ndx] * np.pi/180.) ** 0.5
self.cos_weights = cos_weights
return cos_weights
def missing_day_month_year(self):
"""
Extracts the self.missing field (if exists and is non-empty) into three fields containing days, months and years.
"""
if (self.missing is not None) and (self.missing.shape[0] != 0):
n_days = len(self.missing)
days = np.zeros((n_days,), dtype = np.int)
months = np.zeros((n_days,), dtype = np.int)
years = np.zeros((n_days,), dtype = np.int)
for i,d in zip(range(n_days), self.missing):
dt = date.fromordinal(int(d))
days[i] = dt.day
months[i] = dt.month
years[i] = dt.year
return days, months, years
else:
raise Exception('Luckily for you, there is no missing values!')
def flatten_field(self, f = None):
"""
Reshape the field to 2dimensions such that axis 0 is temporal and axis 1 is spatial.
If f is None, reshape the self.data field, else reshape the f field.
Should only be used with single-level data.
"""
if f is None:
if self.data.ndim == 3:
self.data = np.reshape(self.data, (self.data.shape[0], np.prod(self.data.shape[1:])))
else:
raise Exception('Data field is already flattened, multi-level or only temporal (e.g. station)!')
elif f is not None:
if f.ndim == 3:
f = np.reshape(f, (f.shape[0], np.prod(f.shape[1:])))
return f
else:
raise Exception('The field f is already flattened, multi-level or only temporal (e.g. station)!')
def reshape_flat_field(self, f = None):
"""
Reshape flattened field to original time x lat x lon shape.
If f is None, reshape the self.data field, else reshape the f field.
Supposes single-level data.
"""
if f is None:
if self.data.ndim == 2:
new_shape = [self.data.shape[0]] + list((self.lats.shape[0], self.lons.shape[0]))
self.data = np.reshape(self.data, new_shape)
else:
raise Exception('Data field is not flattened, is multi-level or is only temporal (e.g. station)!')
elif f is not None:
if f.ndim == 2:
new_shape = [f.shape[0]] + list((self.lats.shape[0], self.lons.shape[0]))
f = np.reshape(f, new_shape)
return f
else:
raise Exception('The field f is not flattened, is multi-level or is only temporal (e.g. station)!')
def get_data_of_precise_length(self, length = '16k', start_date = None, end_date = None, apply_to_data = False):
"""
Selects the data such that the length of the time series is exactly length.
If apply_to_data is True, it will replace the data and time, if False it will return them.
If end_date is defined, it is exclusive.
"""
if isinstance(length, int):
ln = length
elif 'k' in length:
order = int(length[:-1])
pow2list = np.array([np.power(2,n) for n in range(10,22)])
ln = pow2list[np.where(order == pow2list/1000)[0][0]]
else:
raise Exception('Could not understand the length! Please type length as integer or as string like "16k".')
if start_date is not None and self.find_date_ndx(start_date) is None:
start_date = self.get_date_from_ndx(0)
if end_date is not None and self.find_date_ndx(end_date) is None:
end_date = self.get_date_from_ndx(-1)
if end_date is None and start_date is not None:
# from start date until length
idx = self.find_date_ndx(start_date)
data_temp = self.data[idx : idx + ln, ...].copy()
time_temp = self.time[idx : idx + ln, ...].copy()
idx_tuple = (idx, idx+ln)
elif start_date is None and end_date is not None:
idx = self.find_date_ndx(end_date)
data_temp = self.data[idx - ln + 1 : idx + 1, ...].copy()
time_temp = self.time[idx - ln + 1 : idx + 1, ...].copy()
idx_tuple = (idx - ln, idx)
else:
raise Exception('You messed start / end date selection! Pick only one!')
if apply_to_data:
self.data = data_temp.copy()
self.time = time_temp.copy()
return idx_tuple
else:
return data_temp, time_temp, idx_tuple
def _shift_index_by_month(self, current_idx):
"""
Returns the index in data shifted by month.
"""
dt = date.fromordinal(np.int(self.time[current_idx]))
if dt.month < 12:
mi = dt.month + 1
y = dt.year
else:
mi = 1
y = dt.year + 1
return self.find_date_ndx(date(y, mi, dt.day))
def get_annual_data(self, means = True, ts = None):
"""
Converts the data to annual means or sums.
If ts is None, uses self.data.
if means is True, computes annual means, otherwise computes sums.
"""
yearly_data = []
yearly_time = []
_, _, year = self.extract_day_month_year()
for y in range(year[0], year[-1]+1, 1):
year_ndx = np.where(year == y)[0]
if ts is None:
if means:
yearly_data.append(np.squeeze(np.nanmean(self.data[year_ndx, ...], axis = 0)))
else:
yearly_data.append(np.squeeze(np.nansum(self.data[year_ndx, ...], axis = 0)))
else:
if means:
yearly_data.append(np.squeeze(np.nanmean(ts[year_ndx, ...], axis = 0)))
else:
yearly_data.append(np.squeeze(np.nansum(ts[year_ndx, ...], axis = 0)))
yearly_time.append(date(y, 1, 1).toordinal())
if ts is None:
self.data = np.array(yearly_data)
self.time = np.array(yearly_time)
else:
return np.array(yearly_data)
def get_monthly_data(self, means = True):
"""
Converts the daily data to monthly means or sums.
"""
delta = self.time[1] - self.time[0]
if delta == 1:
# daily data
day, mon, year = self.extract_day_month_year()
monthly_data = []
monthly_time = []
# if first day of the data is not the first day of month - shift month
# by one to start with the full month
if day[0] != 1:
mi = mon[0]+1 if mon[0] < 12 else 1
y = year[0] if mon[0] < 12 else year[0] + 1
else:
mi = mon[0]
y = year[0]
start_idx = self.find_date_ndx(date(y, mi, 1))
end_idx = self._shift_index_by_month(start_idx)
while end_idx <= self.data.shape[0] and end_idx is not None:
if means:
monthly_data.append(np.nanmean(self.data[start_idx : end_idx, ...], axis = 0))
else:
monthly_data.append(np.nansum(self.data[start_idx : end_idx, ...], axis = 0))
monthly_time.append(self.time[start_idx])
start_idx = end_idx
end_idx = self._shift_index_by_month(start_idx)
if end_idx is None: # last piece, then exit the loop
if means:
monthly_data.append(np.nanmean(self.data[start_idx : , ...], axis = 0))
else:
monthly_data.append(np.nansum(self.data[start_idx : , ...], axis = 0))
monthly_time.append(self.time[start_idx])
self.data = np.array(monthly_data)
self.time = np.array(monthly_time)
elif abs(delta - 30) < 3.0:
# monhtly data
print('The data are already monthly values. Nothing happend.')
else:
raise Exception('Unknown temporal sampling in the field.')
def average_to_daily(self):
"""
Averages the sub-daily values (e.g. ERA-40 basic sampling is 6 hours) into daily.
"""
delta = self.time[1] - self.time[0]
if delta < 1:
n_times = int(1 / delta)
d = np.zeros_like(self.data)
d = np.delete(d, slice(0, (n_times-1) * d.shape[0]/n_times), axis = 0)
t = np.zeros(self.time.shape[0] / n_times)
for i in range(d.shape[0]):
d[i, ...] = np.nanmean(self.data[n_times*i : n_times*i+(n_times-1), ...], axis = 0)
t[i] = self.time[n_times*i]
self.data = d
self.time = t.astype(np.int)
else:
raise Exception('No sub-daily values, you can average to daily only values with finer time sampling.')
@staticmethod
def _interp_temporal(a):
"""
Helper function for temporal interpolation
"""
import scipy.interpolate as si
i, j, old_time, data, new_time, kind = a
f = si.interp1d(old_time, data, kind = kind)
new_data = f(new_time)
return i, j, new_data
def interpolate_to_finer_temporal_resolution(self, to_resolution = 'm', kind = 'linear', use_to_data = False,
pool = None):
"""
Interpolates data to finer temporal resolution, e.g. yearly to monthly.
Uses scipy's interp1d, for 'kind' keyword see the scipy's documentation.
If use_to_data is True, rewrites data in the class, else returns data.
"""
if self.data.ndim > 2:
num_lats = self.lats.shape[0]
num_lons = self.lons.shape[0]
elif self.data.ndim == 2: # lot of station data
num_lats = self.lats.shape[0]
num_lons = 1
self.data = self.data[:, :, np.newaxis]
else:
num_lats = 1
num_lons = 1
self.data = self.data[:, np.newaxis, np.newaxis]
if 'm' in to_resolution:
if 'm' != to_resolution:
n_months = int(to_resolution[:-1])
timedelta = relativedelta(months = +n_months)
elif 'm' == to_resolution:
timedelta = relativedelta(months = +1)
elif to_resolution == 'd':
timedelta = relativedelta(days = +1)
elif to_resolution in ['1h', '6h', '12h']:
hourly_data = int(to_resolution[:-1])
timedelta = relativedelta(hours = +hourly_data)
elif to_resolution == 'y':
timedelta = relativedelta(years = +1)
else:
raise Exception("Unknown to_resolution.")
new_time = []
first_date = self.get_date_from_ndx(0)
last_day = self.get_date_from_ndx(-1)
current_date = first_date
while current_date <= last_day:
new_time.append(current_date.toordinal())
current_date += timedelta
new_time = np.array(new_time)
job_args = [ (i, j, self.time, self.data[:, i, j], new_time, kind) for i in range(num_lats) for j in range(num_lons) ]
interp_data = np.zeros([new_time.shape[0]] + list(self.get_spatial_dims()))
if pool is None:
job_result = map(self._interp_temporal, job_args)
elif pool is not None:
job_result = pool.map(self._interp_temporal, job_args)
del job_args
for i, j, res in job_result:
interp_data[:, i, j] = res
interp_data = np.squeeze(interp_data)
self.data = np.squeeze(self.data)
if use_to_data:
self.time = new_time.copy()
self.data = interp_data.copy()
else:
return interp_data, new_time
def _ascending_descending_lat_lons(self, lats = True, lons = False, direction = 'asc'):
"""
Transforms the data (and lats and lons) so that they have strictly ascending (direction = 'asc')
or descending (direction = 'des') order. (Needed for interpolation).
Returns True if manipulation took place.
"""
lat_flg, lon_flg = False, False
if np.all(np.diff(self.lats) < 0) and lats and direction == 'asc':
self.lats = self.lats[::-1]
self.data = self.data[..., ::-1, :]
lat_flg = True
elif np.all(np.diff(self.lats) > 0) and lats and direction == 'des':
self.lats = self.lats[::-1]
self.data = self.data[..., ::-1, :]
lat_flg = True
if np.all(np.diff(self.lons) < 0) and lons and direction == 'asc':
self.lons = self.lons[::-1]
self.data = self.data[..., ::-1]
lon_flg = True
elif np.all(np.diff(self.lons) > 0) and lons and direction == 'des':
self.lons = self.lons[::-1]
self.data = self.data[..., ::-1]
lon_flg = True
return lat_flg, lon_flg
def subsample_spatial(self, lat_to, lon_to, start, average = False):
"""
Subsamples the data in the spatial sense to grid "lat_to" x "lon_to" in degress.
Start is starting point for subsampling in degrees as [lat, lon]
If average is True, the subsampling is due to averaging the data -- using SciPy's spline
interpolation on the rectangle. The interpolation is done for each time step and level
independently.
If average is False, the subsampling is just subsampling certain values.
"""
if self.lats is not None and self.lons is not None:
delta_lats = np.abs(self.lats[1] - self.lats[0])
delta_lons = np.abs(self.lons[1] - self.lons[0])
if lat_to % delta_lats == 0 and lon_to % delta_lons == 0:
lat_ndx = int(lat_to // delta_lats)
lon_ndx = int(lon_to // delta_lons)
lat_flg, lon_flg = self._ascending_descending_lat_lons(lats = True, lons = True, direction = 'asc')
start_lat_ndx = np.where(self.lats == start[0])[0]
start_lon_ndx = np.where(self.lons == start[1])[0]
if start_lon_ndx.size == 1 and start_lat_ndx.size == 1:
start_lat_ndx = start_lat_ndx[0]
start_lon_ndx = start_lon_ndx[0]
if not average:
self.lats = self.lats[start_lat_ndx::lat_ndx]
self.lons = self.lons[start_lon_ndx::lon_ndx]
d = self.data
d = d[..., start_lat_ndx::lat_ndx, :]
self.data = d[..., start_lon_ndx::lon_ndx]
else:
nan_flag = False
if self.nans:
if self.check_NaNs_only_spatial():
# for interpolation purposes, fill NaNs with 0.
msk = np.isnan(self.data)
self.data[msk] = 0.
msk = msk[0, ...]
nan_flag = True
else:
raise Exception("NaNs in the data are not only spatial, cannot interpolate!")
from scipy.interpolate import RectBivariateSpline
# if data is single-level - create additional dummy dimension
if self.data.ndim == 3:
self.data = self.data[:, np.newaxis, :, :]
# fields for new lats / lons
new_lats = np.arange(start[0], self.lats[-1]+lat_to, lat_to)
new_lons = np.arange(start[1], self.lons[-1], lon_to)
d = np.zeros((list(self.data.shape[:2]) + [new_lats.shape[0], new_lons.shape[0]]))
# interpolate using Bivariate spline
for t in range(self.time.shape[0]):
for lvl in range(self.data.shape[1]):
int_scheme = RectBivariateSpline(self.lats, self.lons, self.data[t, lvl, ...])
d[t, lvl, ...] = int_scheme(new_lats, new_lons)
if nan_flag:
# subsample mask to new grid
msk_temp = msk[start_lat_ndx::lat_ndx, :]
msk = msk_temp[..., start_lon_ndx::lon_ndx]
# return back NaNs
for t in range(self.time.shape[0]):
for lvl in range(self.data.shape[1]):
d[t, lvl, msk] = np.nan
self.lats = new_lats
self.lons = new_lons
self.data = np.squeeze(d)
if np.any(np.isnan(self.data)):
self.nans = True
else:
self.nans = False
else:
raise Exception("Start lat and / or lon for subsampling does not exist in the data!")
self._ascending_descending_lat_lons(lats = lat_flg, lons = lon_flg, direction = 'des')
else:
raise Exception("Subsampling lats only to multiples of %.2f and lons of %.2f" % (delta_lats, delta_lons))
else:
raise Exception("Cannot subsample station data, or data from one grid point!")
def smoothing_running_avg(self, points, cut_edges = False, use_to_data = False, ts = None):
"""
Smoothing of time series using running average over points.
If use_to_data is False, returns the data, otherwise rewrites the data in class.
"""
if ts is None:
ts = self.data.copy()
if cut_edges:
d = np.zeros(([ts.shape[0] - points + 1] + list(ts.shape[1:])))
else:
d = np.zeros_like(ts)
window = points//2
for i in range(d.shape[0]):
if cut_edges:
d[i, ...] = np.nanmean(ts[i : i+points, ...], axis = 0)
else:
d[i, ...] = np.nanmean(ts[max(i-window,1) : min(i+window,d.shape[0]), ...], axis = 0)
if use_to_data and ts is None:
self.data = d.copy()
if cut_edges:
if points % 2 == 1:
# time slicing when points is odd -- cut points//2 from the beginning and from the end
self.time = self.time[points//2 : -points//2 + 1]
else:
# time slicing when points is even -- not sure where to cut
pass
else:
return d
def plot_FFT_spectrum(self, ts = None, log = True, vlines = np.arange(1,11), fname = None):
"""
Estimates power spectrum using Welch method.
if ts is None, plots spectrum of the data.
ts should have same sampling frequency as data!
y axis is log by default, if log is True, also x axis is log.
"""
import matplotlib.pyplot as plt
delta = self.time[1] - self.time[0]
if delta == 1:
# daily time series
fs = 1./86400 # Hz
elif abs(delta - 30) < 3.0:
# monthly time series
fs = 1./2.628e+6
elif abs(delta - 365) < 2.0:
# yearly time series
fs = 1./3.154e+7
plt.figure(figsize = (15,7))
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.gca().spines['left'].set_visible(False)
ts = ts if ts is not None else self.data.copy()
if isinstance(ts, list):
ts = np.array(ts).T
if ts.ndim > 2:
ts = ts.reshape([ts.shape[0], np.prod(ts.shape[1:])])
fft = np.abs(np.fft.rfft(ts, axis = 0))
freqs = np.fft.rfftfreq(ts.shape[0], d = 1./fs)
freqs *= 3.154e+7
if log:
plt.semilogx(freqs, 20*np.log10(fft), linewidth = 0.8) # in dB hopefully...
plt.xlabel('FREQUENCY [log 1/year]', size = 25)
else:
plt.plot(freqs, 20*np.log10(fft), linewidth = 0.8)
plt.xlabel('FREQUENCY [1/year]', size = 25)
for vline in vlines:
plt.axvline(1./vline, 0, 1, linestyle = ':',linewidth = 0.6, color = "#333333")
plt.xlim([freqs[0], freqs[-1]])
plt.ylabel('FFT SPECTRUM [dB]', size = 25)
if fname is None:
plt.show()
else:
plt.savefig(fname, bbox_inches = 'tight')
def temporal_filter(self, cutoff, btype, ftype = 'butter', order = 2, cut = 1, pool = None, cut_time = False,
rp = None, rs = None, cut_data = False):
"""
Filters data in temporal sense.
Uses Butterworth filter of order order.
btype:
lowpass
highpass
bandpass
bandstop
cutoff:
for low/high pass one frequency in months
for band* list of frequencies in months
ftype:
butter - for Butterworth filter
cheby1 - for Chebyshev type I filter
cheby2 - for Chebyshev type II filter
ellip - for Cauer/elliptic filter
bessel - for Bessel/Thomson filter
cut in years
"""
from scipy.signal import iirfilter
delta = self.time[1] - self.time[0]
if delta == 1:
# daily time series
fs = 1./86400 # Hz
y = 365.25
elif abs(delta - 30) < 3.0:
# monthly time series
fs = 1./2.628e+6 # Hz
y = 12
nyq = 0.5 * fs # Nyquist frequency
if 'cheby' in ftype or 'ellip' == ftype:
rp = rp if rp is not None else 60
if type(cutoff) == list and btype in ['bandpass', 'bandstop']:
low = cutoff[0] if cutoff[0] > cutoff[1] else cutoff[1]
high = cutoff[1] if cutoff[0] > cutoff[1] else cutoff[0]
low = 1./(low*2.628e+6) # in months
high = 1./(high*2.628e+6)
# get coefficients
b, a = iirfilter(order, [low/nyq, high/nyq], rp = rp, rs = rs, btype = btype, analog = False, ftype = ftype)
elif btype in ['lowpass', 'highpass']:
cutoff = 1./(cutoff*2.628e+6)
b, a = iirfilter(order, cutoff/nyq, rp = rp, rs = rs, btype = btype, analog = False, ftype = ftype)
else:
raise Exception("For band filter cutoff must be a list of [low,high] for low/high-pass cutoff must be a integer!")
if pool is None:
map_func = map
elif pool is not None:
map_func = pool.map
if self.data.ndim > 1:
num_lats = self.lats.shape[0]
num_lons = self.lons.shape[0]
else:
num_lats = 1
num_lons = 1
self.data = self.data[:, np.newaxis, np.newaxis]
self.filtered_data = np.zeros_like(self.data)
job_args = [ (i, j, self.data[:, i, j], b, a) for i in range(num_lats) for j in range(num_lons) ]
job_result = map_func(self._get_filtered_data, job_args)
del job_args
for i, j, res in job_result:
self.filtered_data[:, i, j] = res
del job_result
if cut is not None:
to_cut = int(y*cut)
if cut_time:
self.time = self.time[to_cut:-to_cut]
if cut_data:
self.data = self.data[to_cut:-to_cut]
self.data = np.squeeze(self.data)
self.filtered_data = np.squeeze(self.filtered_data) if cut is None else np.squeeze(self.filtered_data[to_cut:-to_cut, ...])
def spatial_filter(self, filter_weights = [1, 2, 1], use_to_data = False):
"""
Filters the data in spatial sense with weights filter_weights.
If use_to_data is False, returns the data, otherwise rewrites the data in class.
"""
if self.data.ndim == 3:
self.data = self.data[:, np.newaxis, :, :]
mask = np.zeros(self.data.shape[-2:])
filt = np.outer(filter_weights, filter_weights)
mask[:filt.shape[0], :filt.shape[1]] = filt
d = np.zeros((list(self.data.shape[:-2]) + [self.lats.shape[0] - len(filter_weights) + 1, self.lons.shape[0] - len(filter_weights) + 1]))
for i in range(d.shape[-2]):
for j in range(d.shape[-1]):
avg_mask = np.array([[mask for _ in range(d.shape[1])] for _ in range(d.shape[0])])
d[:, :, i, j] = np.average(self.data, axis = (2, 3), weights = avg_mask)
mask = np.roll(mask, 1, axis = 1)
# return mask to correct y position
mask = np.roll(mask, len(filter_weights)-1, axis = 1)
mask = np.roll(mask, 1, axis = 0)
if use_to_data:
self.data = np.squeeze(d).copy()
# space slicing when length of filter is odd -- cut length//2 from the beginning and from the end
if len(filter_weights) % 2 == 1:
self.lats = self.lats[len(filter_weights)//2 : -len(filter_weights)//2 + 1]
self.lons = self.lons[len(filter_weights)//2 : -len(filter_weights)//2 + 1]
else:
# space slicing when length of filter is even -- not sure where to cut
pass
else:
return np.squeeze(d)
@staticmethod
def _interp_spatial(a):
"""
Helper function for spatial interpolation.
"""
import scipy.interpolate as si
t, d, points, msk, grid_lat, grid_lon, method = a
new_data = si.griddata(points, d[~msk], (grid_lat, grid_lon), method = method)
return t, new_data
def interpolate_spatial_nans(self, method = 'cubic', apply_to_data = True, pool = None):
"""
Interpolates data with spatial NaNs in them.
Method is one of the following:
nearest, linear, cubic
If apply to data, interpolation is done in-place, if False, data field is returned.
Uses scipy's griddata.
"""
if self.nans:
if self.check_NaNs_only_spatial():
import scipy.interpolate as si
if self.data.ndim < 4:
self.data = self.data[:, np.newaxis, ...]
new_data = np.zeros_like(self.data)
for lvl in range(self.data.shape[1]):
msk = np.isnan(self.data[0, lvl, ...]) # nan mask
grid_lat, grid_lon = np.meshgrid(self.lats, self.lons, indexing = 'ij') # final grids
points = np.zeros((grid_lat[~msk].shape[0], 2))
points[:, 0] = grid_lat[~msk]
points[:, 1] = grid_lon[~msk]
args = [(t, self.data[t, lvl, ...], points, msk, grid_lat, grid_lon, method) for t in range(self.time.shape[0])]
if pool is None:
job_res = map(self._interp_spatial, args)
else:
job_res = pool.map(self._interp_spatial, args)
for t, i_data in job_res:
new_data[t, lvl, ...] = i_data
new_data = np.squeeze(new_data)
if apply_to_data:
self.data = new_data.copy()
else:
self.data = np.squeeze(self.data)
return new_data
else:
raise Exception("NaNs are also temporal, no way to filter them out!")
else:
print("No NaNs in the data, nothing happened!")
def check_NaNs_only_spatial(self, field = None):
"""
Returns True if the NaNs contained in the data are of spatial nature, e.g.
masked land from sea dataset and so on.
returns False if also there are some NaNs in the temporal sense.
E.g. with spatial NaNs, the PCA could be still done, when filtering out the NaNs.
"""
if self.nans or field is not None:
field = self.data.copy() if field is None else field
cnt = 0
nangrid0 = np.isnan(field[0, ...])
for t in range(1, field.shape[0]):
if np.all(nangrid0 == np.isnan(field[t, ...])):
cnt += 1
if field.shape[0] - cnt == 1:
return True
else:
return False
else:
pass
# print("No NaNs in the data, nothing happened!")
def filter_out_NaNs(self, field = None):
"""
Returns flattened version of 3D data field without NaNs (e.g. for computational purposes).
The data is just returned, self.data is still full 3D version. Returned data has first axis
temporal and second combined spatial.
Mask is saved for internal purposes (e.g. PCA) but also returned.
"""
if (field is None and self.nans) or (field is not None and np.any(np.isnan(field))):
if self.check_NaNs_only_spatial(field = field):
d = self.data.copy() if field is None else field
d = self.flatten_field(f = d)
mask = np.isnan(d)
spatial_mask = mask[0, :]
d_out_shape = (d.shape[0], d.shape[1] - np.sum(spatial_mask))
d_out = d[~mask].reshape(d_out_shape)
self.spatial_mask = spatial_mask
return d_out, spatial_mask
else:
raise Exception("NaNs are also temporal, no way to filter them out!")
else:
print("No NaNs in the data, nothing happened!")
def return_NaNs_to_data(self, field, mask = None):
"""
Returns NaNs to the data and reshapes it to the original shape.
Field has first axis temporal and second combined spatial.
"""
if self.nans:
if mask is not None or self.spatial_mask is not None:
mask = mask if mask is not None else self.spatial_mask
d_out = np.zeros((field.shape[0], mask.shape[0]))
ndx = np.where(mask == False)[0]
d_out[:, ndx] = field
d_out[:, mask] = np.nan
return self.reshape_flat_field(f = d_out)
else:
raise Exception("No mask given!")
else:
print("No NaNs in the data, nothing happened!")
@staticmethod
def _rotate_varimax(U, rtol=np.finfo(np.float32).eps ** 0.5, gamma=1.0, maxiter=500):
"""
Helper function for rotating the matrix U according to VARIMAX scheme.
The implementation is based on MATLAB docs & code, algorithm is due to DN Lawley and AE Maxwell.
Written by <NAME> -- https://github.com/vejmelkam/ndw-climate/blob/master/src/component_analysis.py
"""
from scipy.linalg import svd
n,m = U.shape
Ur = U.copy(order='C')
ColNorms = np.zeros((1, m))
dsum = 0.0
for indx in range(maxiter):
old_dsum = dsum
np.sum(Ur**2, axis=0, out=ColNorms[0,:])
C = n * Ur**3
if gamma > 0.0:
C -= gamma * Ur * ColNorms # numpy will broadcast on rows
L, d, Mt = svd(np.dot(Ur.T, C), False, True, True)
R = np.dot(L, Mt)
dsum = np.sum(d)
np.dot(U, R, out=Ur)
if abs(dsum - old_dsum) / dsum < rtol:
break
# flip signs of components, where max-abs in col is negative
for i in range(m):
if np.amax(Ur[:,i]) < -np.amin(Ur[:,i]):
Ur[:,i] *= -1.0
R[i,:] *= -1.0
return Ur, R, indx
@staticmethod
def _residual_var(d, pc):
"""
Helper function for computing residual variance in orthomax PCA.
"""
import scipy.stats as sts
rvar = 0.0
for i in range(d.shape[1]):
sl, inter, _, _, _ = sts.linregress(pc, d[:, i])
rvar += np.var(d[:, i] - (sl * pc + inter))
return rvar
def pca_components(self, n_comps, field=None, rotate_varimax=False):
"""
Estimate the PCA (EOF) components of geo-data.
Shoud be used on single-level data.
Returns eofs as (n_comps x lats x lons), pcs as (n_comps x time) and var as (n_comps)
"""
if self.data.ndim == 3:
from scipy.linalg import svd
# reshape field so the first axis is temporal and second is combined spatial
# if nans, filter-out
if (self.nans and field is None) or (field is not None and np.any(np.isnan(field))):
d = self.filter_out_NaNs(field)[0]
else:
if field is None:
d = self.data.copy()
else:
d = field.copy()
d = self.flatten_field(f = d)
# remove mean of each time series
pca_mean = np.mean(d, axis = 0)
if field is None:
self.pca_mean = pca_mean
d -= pca_mean
U, s, V = svd(d, False, True, True)
exp_var = (s ** 2) / (self.time.shape[0] - 1)
exp_var /= np.sum(exp_var)
eofs = V[:n_comps]
var = exp_var[:n_comps]
pcs = U[:, :n_comps]
if rotate_varimax:
eofs, T, _ = self._rotate_varimax(eofs.T)
rot = np.matrix(T)
S2 = np.dot(np.dot(np.transpose(rot), np.matrix(np.diag(var))), rot)
expvar = np.diag(S2)
pcs = np.array(np.dot(np.transpose(rot), np.diag(s[:n_comps])) * pcs.T)
# var
total_var = np.sum(np.var(d, axis=0))
reg_expvar = np.zeros(expvar.shape)
for i in range(n_comps):
reg_expvar[i] = total_var - self._residual_var(d, pcs[i, :])
# reorder according to expvar
nord = np.argsort(expvar)[::-1]
eofs = eofs[:, nord].T
expvar = expvar[nord]
reg_expvar = reg_expvar[nord]
pcs = pcs[nord, :].T
var = reg_expvar / total_var
if self.nans:
eofs = self.return_NaNs_to_data(field = eofs)
else:
eofs = self.reshape_flat_field(f = eofs)
if field is not None:
return eofs, pcs.T, var, pca_mean
elif field is None:
return eofs, pcs.T, var
else:
raise Exception("PCA analysis cannot be used on multi-level data or only temporal (e.g. station) data!")
def invert_pca(self, eofs, pcs, pca_mean = None):
"""
Inverts the PCA and returns the original data.
Suitable for modelling, pcs could be different than obtained from PCA.
"""
if self.nans:
e = self.filter_out_NaNs(field = eofs)[0]
else:
e = eofs.copy()
e = self.flatten_field(f = e)
e = e.transpose()
pca_mean = pca_mean if pca_mean is not None else self.pca_mean
recons = np.dot(e, pcs).T
recons += pca_mean.T
if self.nans:
recons = self.return_NaNs_to_data(field = recons)
else:
recons = self.reshape_flat_field(f = recons)
return recons
def anomalise(self, base_period = None, ts = None):
"""
Removes the seasonal/yearly cycle from the data.
If base_period is None, the seasonal cycle is relative to whole period,
else base_period = (date, date) for climatology within period. Both dates are inclusive.
"""
delta = self.time[1] - self.time[0]
seasonal_mean = np.zeros_like(self.data) if ts is None else np.zeros_like(ts)
if base_period is None:
ndx = np.arange(self.time.shape[0])
else:
ndx = np.logical_and(self.time >= base_period[0].toordinal(), self.time <= base_period[1].toordinal())
d = self.data.copy() if ts is None else ts
t = self.time.copy()
self.time = self.time[ndx]
if delta == 1:
# daily data
day_avg, mon_avg, _ = self.extract_day_month_year()
self.time = t.copy()
day_data, mon_data, _ = self.extract_day_month_year()
d = d[ndx, ...]
for mi in range(1,13):
mon_mask_avg = (mon_avg == mi)
mon_mask_data = (mon_data == mi)
for di in range(1,32):
sel_avg = np.logical_and(mon_mask_avg, day_avg == di)
sel_data = np.logical_and(mon_mask_data, day_data == di)
if np.sum(sel_avg) == 0:
continue
seasonal_mean[sel_data, ...] = np.nanmean(d[sel_avg, ...], axis = 0)
if ts is None:
self.data[sel_data, ...] -= seasonal_mean[sel_data, ...]
else:
ts[sel_data, ...] -= seasonal_mean[sel_data, ...]
elif abs(delta - 30) < 3.0:
# monthly data
_, mon_avg, _ = self.extract_day_month_year()
self.time = t.copy()
_, mon_data, _ = self.extract_day_month_year()
d = d[ndx, ...]
for mi in range(1,13):
sel_avg = (mon_avg == mi)
sel_data = (mon_data == mi)
if np.sum(sel_avg) == 0:
continue
seasonal_mean[sel_data, ...] = np.nanmean(d[sel_avg, ...], axis = 0)
if ts is None:
self.data[sel_data, ...] -= seasonal_mean[sel_data, ...]
else:
ts[sel_data, ...] -= seasonal_mean[sel_data, ...]
else:
raise Exception('Unknown temporal sampling in the field.')
return seasonal_mean
def get_seasonality(self, detrend = False, base_period = None):
"""
Removes the seasonality in both mean and std (detrending is optional) and
returns the seasonal mean and std arrays.
If base_period is None, the seasonal cycle is relative to whole period,
else base_period = (date, date) for climatology within period. Both dates are inclusive.
"""
delta = self.time[1] - self.time[0]
seasonal_mean = np.zeros_like(self.data)
seasonal_var = np.zeros_like(self.data)
if base_period is None:
ndx = np.arange(self.time.shape[0])
else:
ndx = np.logical_and(self.time >= base_period[0].toordinal(), self.time <= base_period[1].toordinal())
d = self.data.copy()
t = self.time.copy()
self.time = self.time[ndx]
if detrend:
data_copy = self.data.copy()
self.data, _, _ = detrend_with_return(self.data, axis = 0)
trend = data_copy - self.data
if delta == 1:
# daily data
day_avg, mon_avg, _ = self.extract_day_month_year()
self.time = t.copy()
day_data, mon_data, _ = self.extract_day_month_year()
d = d[ndx, ...]
for mi in range(1,13):
mon_mask_avg = (mon_avg == mi)
mon_mask_data = (mon_data == mi)
for di in range(1,32):
sel_avg = np.logical_and(mon_mask_avg, day_avg == di)
sel_data = np.logical_and(mon_mask_data, day_data == di)
if np.sum(sel_avg) == 0:
continue
seasonal_mean[sel_data, ...] = np.nanmean(d[sel_avg, ...], axis = 0)
self.data[sel_data, ...] -= seasonal_mean[sel_data, ...]
seasonal_var[sel_data, ...] = np.nanstd(d[sel_avg, ...], axis = 0, ddof = 1)
if np.any(seasonal_var[sel_data, ...] == 0.0) and self.verbose:
print('**WARNING: some zero standard deviations found for date %d.%d' % (di, mi))
seasonal_var[seasonal_var == 0.0] = 1.0
self.data[sel_data, ...] /= seasonal_var[sel_data, ...]
else:
trend = None
elif abs(delta - 30) < 3.0:
# monthly data
_, mon_avg, _ = self.extract_day_month_year()
self.time = t.copy()
_, mon_data, _ = self.extract_day_month_year()
d = d[ndx, ...]
for mi in range(1,13):
sel_avg = (mon_avg == mi)
sel_data = (mon_data == mi)
if np.sum(sel_avg) == 0:
continue
seasonal_mean[sel_data, ...] = np.nanmean(d[sel_avg, ...], axis = 0)
self.data[sel_data, ...] -= seasonal_mean[sel_data, ...]
seasonal_var[sel_data, ...] = np.nanstd(d[sel_avg, ...], axis = 0, ddof = 1)
self.data[sel_data, ...] /= seasonal_var[sel_data, ...]
else:
trend = None
else:
raise Exception('Unknown temporal sampling in the field.')
return seasonal_mean, seasonal_var, trend
def return_seasonality(self, mean, var, trend):
"""
Return the seasonality to the data.
"""
self.data *= var
self.data += mean
if trend is not None:
self.data += trend
def center_data(self, var = False, return_fields = False):
"""
Centers data time series to zero mean and unit variance (without respect for the seasons or temporal sampling).
"""
mean = np.nanmean(self.data, axis = 0)
self.data -= mean
if var:
var = np.nanstd(self.data, axis = 0, ddof = 1)
self.data /= var
if return_fields:
return mean if var is False else (mean, var)
def save_field(self, fname):
"""
Saves entire Data Field to cPickle format.
"""
import cPickle
with open(fname, "wb") as f:
cPickle.dump(self.__dict__, f, protocol = cPickle.HIGHEST_PROTOCOL)
def load_field(self, fname):
"""
Loads entire Data Field from pickled file.
"""
import cPickle
with open(fname, "rb") as f:
data = cPickle.load(f)
self.__dict__ = data
@staticmethod
def _get_oscillatory_modes(a):
"""
Helper function for wavelet.
"""
import wavelet_analysis as wvlt
i, j, s0, data, flag, amp_to_data, k0, cont_ph, cut = a
if not np.any(np.isnan(data)):
wave, _, _, _ = wvlt.continous_wavelet(data, 1, True, wvlt.morlet, dj = 0, s0 = s0, j1 = 0, k0 = k0)
phase = np.arctan2(np.imag(wave), np.real(wave))[0, :]
amplitude = np.sqrt(np.power(np.real(wave),2) + np.power(np.imag(wave),2))[0, :]
if amp_to_data:
reconstruction = amplitude * np.cos(phase)
fit_x = np.vstack([reconstruction, np.ones(reconstruction.shape[0])]).T
m, c = np.linalg.lstsq(fit_x, data)[0]
amplitude = m * amplitude + c
if cut is not None:
phase = phase[cut:-cut]
amplitude = amplitude[cut:-cut]
wave = wave[0, cut:-cut]
if cont_ph:
for t in range(phase.shape[0] - 1):
if np.abs(phase[t+1] - phase[t]) > 1:
phase[t+1: ] += 2 * np.pi
ret = [phase, amplitude]
if flag:
ret.append(wave)
return i, j, ret
else:
if flag:
return i, j, [np.nan, np.nan, np.nan]
else:
return i, j, [np.nan, np.nan]
@staticmethod
def _get_parametric_phase(a):
"""
Helper function for parametric phase.
"""
i, j, freq, data, window, flag, save_wave, cont_ph, cut = a
if not np.any(np.isnan(data)):
half_length = int(np.floor(data.shape[0]/2))
upper_bound = half_length + 1 if data.shape[0] & 0x1 else half_length
# center data to zero mean (NOT climatologically)
data -= np.mean(data, axis = 0)
# compute smoothing wave from signal
c = np.cos(np.arange(-half_length, upper_bound, 1) * freq)
s = np.sin(np.arange(-half_length, upper_bound, 1) * freq)
cx = np.dot(c, data) / data.shape[0]
sx = np.dot(s, data) / data.shape[0]
mx = np.sqrt(cx**2 + sx**2)
phi = np.angle(cx - 1j*sx)
z = mx * np.cos(np.arange(-half_length, upper_bound, 1) * freq + phi)
# iterate with window
iphase = np.zeros_like(data)
half_window = int(np.floor(window/2))
upper_bound_window = half_window + 1 if window & 0x1 else half_window
co = np.cos(np.arange(-half_window, upper_bound_window, 1) *freq)
so = np.sin(np.arange(-half_window, upper_bound_window, 1) *freq)
for shift in range(0, data.shape[0] - window + 1):
y = data[shift:shift + window].copy()
y -= | np.mean(y) | numpy.mean |
import io
import os
import os.path as osp
import shutil
import warnings
import mmcv
import numpy as np
from mmcv.fileio import FileClient
from torch.nn.modules.utils import _pair
from ...utils import get_random_string, get_shm_dir, get_thread_id
from ..registry import PIPELINES
@PIPELINES.register_module()
class SampleFrames(object):
"""Sample frames from the video.
Required keys are "filename", "total_frames", "start_index" , added or
modified keys are "frame_inds", "frame_interval" and "num_clips".
Args:
clip_len (int): Frames of each sampled output clip.
frame_interval (int): Temporal interval of adjacent sampled frames.
Default: 1.
num_clips (int): Number of clips to be sampled. Default: 1.
temporal_jitter (bool): Whether to apply temporal jittering.
Default: False.
twice_sample (bool): Whether to use twice sample when testing.
If set to True, it will sample frames with and without fixed shift,
which is commonly used for testing in TSM model. Default: False.
out_of_bound_opt (str): The way to deal with out of bounds frame
indexes. Available options are 'loop', 'repeat_last'.
Default: 'loop'.
test_mode (bool): Store True when building test or validation dataset.
Default: False.
start_index (None): This argument is deprecated and moved to dataset
class (``BaseDataset``, ``VideoDatset``, ``RawframeDataset``, etc),
see this: https://github.com/open-mmlab/mmaction2/pull/89.
"""
def __init__(self,
clip_len,
frame_interval=1,
num_clips=1,
temporal_jitter=False,
twice_sample=False,
out_of_bound_opt='loop',
test_mode=False,
start_index=None):
self.clip_len = clip_len
self.frame_interval = frame_interval
self.num_clips = num_clips
self.temporal_jitter = temporal_jitter
self.twice_sample = twice_sample
self.out_of_bound_opt = out_of_bound_opt
self.test_mode = test_mode
assert self.out_of_bound_opt in ['loop', 'repeat_last']
if start_index is not None:
warnings.warn('No longer support "start_index" in "SampleFrames", '
'it should be set in dataset class, see this pr: '
'https://github.com/open-mmlab/mmaction2/pull/89')
def _get_train_clips(self, num_frames):
"""Get clip offsets in train mode.
It will calculate the average interval for selected frames,
and randomly shift them within offsets between [0, avg_interval].
If the total number of frames is smaller than clips num or origin
frames length, it will return all zero indices.
Args:
num_frames (int): Total number of frame in the video.
Returns:
np.ndarray: Sampled frame indices in train mode.
"""
ori_clip_len = self.clip_len * self.frame_interval
avg_interval = (num_frames - ori_clip_len + 1) // self.num_clips
if avg_interval > 0:
base_offsets = np.arange(self.num_clips) * avg_interval
clip_offsets = base_offsets + np.random.randint(
avg_interval, size=self.num_clips)
elif num_frames > max(self.num_clips, ori_clip_len):
clip_offsets = np.sort(
np.random.randint(
num_frames - ori_clip_len + 1, size=self.num_clips))
elif avg_interval == 0:
ratio = (num_frames - ori_clip_len + 1.0) / self.num_clips
clip_offsets = np.around(np.arange(self.num_clips) * ratio)
else:
clip_offsets = np.zeros((self.num_clips, ), dtype=np.int)
return clip_offsets
def _get_test_clips(self, num_frames):
"""Get clip offsets in test mode.
Calculate the average interval for selected frames, and shift them
fixedly by avg_interval/2. If set twice_sample True, it will sample
frames together without fixed shift. If the total number of frames is
not enough, it will return all zero indices.
Args:
num_frames (int): Total number of frame in the video.
Returns:
np.ndarray: Sampled frame indices in test mode.
"""
ori_clip_len = self.clip_len * self.frame_interval
avg_interval = (num_frames - ori_clip_len + 1) / float(self.num_clips)
if num_frames > ori_clip_len - 1:
base_offsets = np.arange(self.num_clips) * avg_interval
clip_offsets = (base_offsets + avg_interval / 2.0).astype(np.int)
if self.twice_sample:
clip_offsets = np.concatenate([clip_offsets, base_offsets])
else:
clip_offsets = np.zeros((self.num_clips, ), dtype=np.int)
return clip_offsets
def _sample_clips(self, num_frames):
"""Choose clip offsets for the video in a given mode.
Args:
num_frames (int): Total number of frame in the video.
Returns:
np.ndarray: Sampled frame indices.
"""
if self.test_mode:
clip_offsets = self._get_test_clips(num_frames)
else:
clip_offsets = self._get_train_clips(num_frames)
return clip_offsets
def __call__(self, results):
"""Perform the SampleFrames loading.
Args:
results (dict): The resulting dict to be modified and passed
to the next transform in pipeline.
"""
total_frames = results['total_frames']
clip_offsets = self._sample_clips(total_frames)
frame_inds = clip_offsets[:, None] + np.arange(
self.clip_len)[None, :] * self.frame_interval
frame_inds = np.concatenate(frame_inds)
if self.temporal_jitter:
perframe_offsets = np.random.randint(
self.frame_interval, size=len(frame_inds))
frame_inds += perframe_offsets
frame_inds = frame_inds.reshape((-1, self.clip_len))
if self.out_of_bound_opt == 'loop':
frame_inds = np.mod(frame_inds, total_frames)
elif self.out_of_bound_opt == 'repeat_last':
safe_inds = frame_inds < total_frames
unsafe_inds = 1 - safe_inds
last_ind = np.max(safe_inds * frame_inds, axis=1)
new_inds = (safe_inds * frame_inds + (unsafe_inds.T * last_ind).T)
frame_inds = new_inds
else:
raise ValueError('Illegal out_of_bound option.')
start_index = results['start_index']
frame_inds = np.concatenate(frame_inds) + start_index
results['frame_inds'] = frame_inds.astype(np.int)
results['clip_len'] = self.clip_len
results['frame_interval'] = self.frame_interval
results['num_clips'] = self.num_clips
return results
@PIPELINES.register_module()
class UntrimmedSampleFrames(object):
"""Sample frames from the untrimmed video.
Required keys are "filename", "total_frames", added or modified keys are
"frame_inds", "frame_interval" and "num_clips".
Args:
clip_len (int): The length of sampled clips. Default: 1.
frame_interval (int): Temporal interval of adjacent sampled frames.
Default: 16.
start_index (int): Specify a start index for frames in consideration of
different filename format. However, when taking videos as input,
it should be set to 0, since frames loaded from videos count
from 0. Default: 1.
"""
def __init__(self, clip_len=1, frame_interval=16, start_index=1):
self.clip_len = clip_len
self.frame_interval = frame_interval
self.start_index = start_index
def __call__(self, results):
"""Perform the SampleFrames loading.
Args:
results (dict): The resulting dict to be modified and passed
to the next transform in pipeline.
"""
total_frames = results['total_frames']
clip_centers = np.arange(self.frame_interval // 2, total_frames,
self.frame_interval)
num_clips = clip_centers.shape[0]
frame_inds = clip_centers[:, None] + np.arange(
-(self.clip_len // 2), self.clip_len -
(self.clip_len // 2))[None, :]
# clip frame_inds to legal range
frame_inds = np.clip(frame_inds, 0, total_frames - 1)
frame_inds = np.concatenate(frame_inds) + self.start_index
results['frame_inds'] = frame_inds.astype(np.int)
results['clip_len'] = self.clip_len
results['frame_interval'] = self.frame_interval
results['num_clips'] = num_clips
return results
@PIPELINES.register_module()
class DenseSampleFrames(SampleFrames):
"""Select frames from the video by dense sample strategy.
Required keys are "filename", added or modified keys are "total_frames",
"frame_inds", "frame_interval" and "num_clips".
Args:
clip_len (int): Frames of each sampled output clip.
frame_interval (int): Temporal interval of adjacent sampled frames.
Default: 1.
num_clips (int): Number of clips to be sampled. Default: 1.
sample_range (int): Total sample range for dense sample.
Default: 64.
num_sample_positions (int): Number of sample start positions, Which is
only used in test mode. Default: 10.
temporal_jitter (bool): Whether to apply temporal jittering.
Default: False.
test_mode (bool): Store True when building test or validation dataset.
Default: False.
"""
def __init__(self,
clip_len,
frame_interval=1,
num_clips=1,
sample_range=64,
num_sample_positions=10,
temporal_jitter=False,
out_of_bound_opt='loop',
test_mode=False):
super().__init__(
clip_len,
frame_interval,
num_clips,
temporal_jitter,
out_of_bound_opt=out_of_bound_opt,
test_mode=test_mode)
self.sample_range = sample_range
self.num_sample_positions = num_sample_positions
def _get_train_clips(self, num_frames):
"""Get clip offsets by dense sample strategy in train mode.
It will calculate a sample position and sample interval and set
start index 0 when sample_pos == 1 or randomly choose from
[0, sample_pos - 1]. Then it will shift the start index by each
base offset.
Args:
num_frames (int): Total number of frame in the video.
Returns:
np.ndarray: Sampled frame indices in train mode.
"""
sample_position = max(1, 1 + num_frames - self.sample_range)
interval = self.sample_range // self.num_clips
start_idx = 0 if sample_position == 1 else np.random.randint(
0, sample_position - 1)
base_offsets = np.arange(self.num_clips) * interval
clip_offsets = (base_offsets + start_idx) % num_frames
return clip_offsets
def _get_test_clips(self, num_frames):
"""Get clip offsets by dense sample strategy in test mode.
It will calculate a sample position and sample interval and evenly
sample several start indexes as start positions between
[0, sample_position-1]. Then it will shift each start index by the
base offsets.
Args:
num_frames (int): Total number of frame in the video.
Returns:
np.ndarray: Sampled frame indices in train mode.
"""
sample_position = max(1, 1 + num_frames - self.sample_range)
interval = self.sample_range // self.num_clips
start_list = np.linspace(
0, sample_position - 1, num=self.num_sample_positions, dtype=int)
base_offsets = np.arange(self.num_clips) * interval
clip_offsets = list()
for start_idx in start_list:
clip_offsets.extend((base_offsets + start_idx) % num_frames)
clip_offsets = | np.array(clip_offsets) | numpy.array |
#!/usr/bin/python2
# Copyright (C) 2016 <NAME>
# License WTFPL
#
# This program is free software. It comes without any warranty, to the extent
# permitted by applicable law.
# You can redistribute it and/or modify it under the terms of the Do What The
# Fuck You Want To Public License, Version 2, as published by Sam Hocevar. See
# http://www.wtfpl.net/ for more details.
#
import numpy as np
from math import pi, sqrt
__all__ = [
'ACV_A1',
'ACV_A2',
'ACV_A3',
'ACV_A4',
'ACV_A5',
'ACV_A6',
'ACV_A7',
'ACV_A8'
]
#Heavyside step function
H_num = lambda t: 1 if t > 0 else 0
H = lambda T: np.asarray([1 if t > 0 else 0 for t in T])
# pure sine
def ACV_A1(T, Hz=50):
"""
Generate a pure sine wave at a specified frequency
keyword arguments:
T -- time points to generate the waveform given in seconds
Hz -- The desired frequency of the signal (default:50)
"""
ampl = 1000
T = np.asarray(T, dtype=np.float64)
return ampl * sqrt(2) * np.sin(2*pi*Hz * T)
def ACV_A2(T, Hz=50):
"""
Generate a pure sine wave with a DC offset at a specified frequency
keyword arguments:
T -- time points to generate the waveform given in seconds
Hz -- The desired frequency of the signal (default:50)
"""
ampl = 1000
offset = 500
T = np.asarray(T, dtype=np.float64)
return ampl * sqrt(2) * np.sin(2*pi*Hz * T) + offset
def ACV_A3(T, Hz=50):
"""
Generate a fundamental with a 3rd overtone
keyword arguments:
T -- time points to generate the waveform given in seconds
Hz -- The desired frequency of the signal (default:50)
"""
ampl = 1000
T = np.asarray(T, dtype=np.float64)
main_wave = np.sin(2*pi*Hz * T)
harmonic_wave = 0.05 * np.sin(2*pi*Hz * T * 4 + pi * 2 / 3)
return ampl * sqrt(2) * (main_wave + harmonic_wave)
def ACV_A4(T, Hz=50):
"""
Generate a fundamental with a 4th overtone
keyword arguments:
T -- time points to generate the waveform given in seconds
Hz -- The desired frequency of the signal (default:50)
"""
ampl = 1000
T = np.asarray(T, dtype=np.float64)
main_wave = np.sin(2*pi*Hz * T)
harmonic_wave = 0.07 * np.sin(2*pi*Hz * T * 5 + pi * 22 / 18)
return ampl * sqrt(2) * (main_wave + harmonic_wave)
def ACV_A5(T, Hz=50):
"""
Generate a realistic triangle wave
keyword arguments:
T -- time points to generate the waveform given in seconds
Hz -- The desired frequency of the signal (default:50)
"""
ampl = 1000
T = np.asarray(T, dtype=np.float64)
wave_1 = np.sin(2*pi*Hz * T)
wave_2 = 0.05 * np.sin(2*pi*Hz * T * 3 - pi)
wave_3 = 0.05 * np.sin(2*pi*Hz * T * 5)
wave_4 = 0.02 * np.sin(2*pi*Hz * T * 7 - pi)
wave_5 = 0.01 * np.sin(2*pi*Hz * T * 9)
return ampl * sqrt(2) * (wave_1 + wave_2 + wave_3 + wave_4 + wave_5)
def ACV_A6(T, Hz=50):
"""
Generate a realistic triangle wave
keyword arguments:
T -- time points to generate the waveform given in seconds
Hz -- The desired frequency of the signal (default:50)
"""
ampl = 1000
T = np.asarray(T, dtype=np.float64)
wave_1 = | np.sin(2*pi*Hz * T) | numpy.sin |
import batoid
import numpy as np
from test_helpers import timer, init_gpu, rays_allclose, checkAngle, do_pickle
@timer
def test_properties():
rng = np.random.default_rng(5)
size = 10
for i in range(100):
x = rng.normal(size=size)
y = rng.normal(size=size)
z = rng.normal(size=size)
vx = rng.normal(size=size)
vy = rng.normal(size=size)
vz = rng.normal(size=size)
t = rng.normal(size=size)
w = rng.normal(size=size)
fx = rng.normal(size=size)
vig = rng.choice([True, False], size=size)
fa = rng.choice([True, False], size=size)
cs = batoid.CoordSys(
origin=rng.normal(size=3),
rot=batoid.RotX(rng.normal())@batoid.RotY(rng.normal())
)
rv = batoid.RayVector(x, y, z, vx, vy, vz, t, w, fx, vig, fa, cs)
np.testing.assert_array_equal(rv.x, x)
np.testing.assert_array_equal(rv.y, y)
np.testing.assert_array_equal(rv.z, z)
np.testing.assert_array_equal(rv.r[:, 0], x)
np.testing.assert_array_equal(rv.r[:, 1], y)
np.testing.assert_array_equal(rv.r[:, 2], z)
np.testing.assert_array_equal(rv.vx, vx)
np.testing.assert_array_equal(rv.vy, vy)
np.testing.assert_array_equal(rv.vz, vz)
np.testing.assert_array_equal(rv.v[:, 0], vx)
np.testing.assert_array_equal(rv.v[:, 1], vy)
np.testing.assert_array_equal(rv.v[:, 2], vz)
np.testing.assert_array_equal(rv.k[:, 0], rv.kx)
np.testing.assert_array_equal(rv.k[:, 1], rv.ky)
np.testing.assert_array_equal(rv.k[:, 2], rv.kz)
np.testing.assert_array_equal(rv.t, t)
np.testing.assert_array_equal(rv.wavelength, w)
np.testing.assert_array_equal(rv.flux, fx)
np.testing.assert_array_equal(rv.vignetted, vig)
np.testing.assert_array_equal(rv.failed, fa)
assert rv.coordSys == cs
rv._syncToDevice()
do_pickle(rv)
@timer
def test_positionAtTime():
rng = np.random.default_rng(57)
size = 10_000
x = rng.uniform(-1, 1, size=size)
y = rng.uniform(-1, 1, size=size)
z = rng.uniform(-0.1, 0.1, size=size)
vx = rng.uniform(-0.05, 0.05, size=size)
vy = rng.uniform(-0.05, 0.05, size=size)
vz = np.sqrt(1.0 - vx*vx - vy*vy)
# Try with default t=0 first
rv = batoid.RayVector(x, y, z, vx, vy, vz)
np.testing.assert_equal(rv.x, x)
np.testing.assert_equal(rv.y, y)
np.testing.assert_equal(rv.z, z)
np.testing.assert_equal(rv.vx, vx)
np.testing.assert_equal(rv.vy, vy)
np.testing.assert_equal(rv.vz, vz)
np.testing.assert_equal(rv.t, 0.0)
np.testing.assert_equal(rv.wavelength, 0.0)
for t1 in [0.0, 1.0, -1.1, 2.5]:
np.testing.assert_equal(
rv.positionAtTime(t1),
rv.r + t1 * rv.v
)
# Now add some random t's
t = rng.uniform(-1.0, 1.0, size=size)
rv = batoid.RayVector(x, y, z, vx, vy, vz, t)
np.testing.assert_equal(rv.x, x)
np.testing.assert_equal(rv.y, y)
np.testing.assert_equal(rv.z, z)
np.testing.assert_equal(rv.vx, vx)
np.testing.assert_equal(rv.vy, vy)
np.testing.assert_equal(rv.vz, vz)
np.testing.assert_equal(rv.t, t)
np.testing.assert_equal(rv.wavelength, 0.0)
for t1 in [0.0, 1.4, -1.3, 2.1]:
np.testing.assert_equal(
rv.positionAtTime(t1),
rv.r + rv.v*(t1-rv.t)[:,None]
)
@timer
def test_propagate():
rng = np.random.default_rng(577)
size = 10_000
x = rng.uniform(-1, 1, size=size)
y = rng.uniform(-1, 1, size=size)
z = rng.uniform(-0.1, 0.1, size=size)
vx = rng.uniform(-0.05, 0.05, size=size)
vy = rng.uniform(-0.05, 0.05, size=size)
vz = np.sqrt(1.0 - vx*vx - vy*vy)
# Try with default t=0 first
rv = batoid.RayVector(x, y, z, vx, vy, vz)
for t1 in [0.0, 1.0, -1.1, 2.5]:
rvcopy = rv.copy()
r1 = rv.positionAtTime(t1)
rvcopy.propagate(t1)
np.testing.assert_equal(
rvcopy.r,
r1
)
np.testing.assert_equal(
rvcopy.v,
rv.v
)
np.testing.assert_equal(
rvcopy.t,
t1
)
# Now add some random t's
t = rng.uniform(-1.0, 1.0, size=size)
rv = batoid.RayVector(x, y, z, vx, vy, vz, t)
for t1 in [0.0, 1.0, -1.1, 2.5]:
rvcopy = rv.copy()
r1 = rv.positionAtTime(t1)
rvcopy.propagate(t1)
np.testing.assert_equal(
rvcopy.r,
r1
)
np.testing.assert_equal(
rvcopy.v,
rv.v
)
np.testing.assert_equal(
rvcopy.t,
t1
)
@timer
def test_phase():
rng = np.random.default_rng(5772)
size = 10_000
for n in [1.0, 1.3]:
x = rng.uniform(-1, 1, size=size)
y = rng.uniform(-1, 1, size=size)
z = rng.uniform(-0.1, 0.1, size=size)
vx = rng.uniform(-0.05, 0.05, size=size)
vy = rng.uniform(-0.05, 0.05, size=size)
vz = np.sqrt(1.0/(n*n) - vx*vx - vy*vy)
t = rng.uniform(-1.0, 1.0, size=size)
wavelength = rng.uniform(300e-9, 1100e-9, size=size)
rv = batoid.RayVector(x, y, z, vx, vy, vz, t, wavelength)
# First explicitly check that phase is 0 at position and time of individual
# rays
for i in rng.choice(size, size=10):
np.testing.assert_equal(
rv.phase(rv.r[i], rv.t[i])[i],
0.0
)
# Now use actual formula
# phi = k.(r-r0) - (t-t0)omega
# k = 2 pi v / lambda |v|^2
# omega = 2 pi / lambda
# |v| = 1 / n
for r1, t1 in [
((0, 0, 0), 0),
((0, 1, 2), 3),
((-1, 2, 4), -1),
((0, 1, -4), -2)
]:
phi = np.einsum("ij,ij->i", rv.v, r1-rv.r)
phi *= n*n
phi -= (t1-rv.t)
phi *= 2*np.pi/wavelength
np.testing.assert_allclose(
rv.phase(r1, t1),
phi,
rtol=0,
atol=1e-7
)
for i in rng.choice(size, size=10):
s = slice(i, i+1)
rvi = batoid.RayVector(
x[s], y[s], z[s],
vx[s], vy[s], vz[s],
t[s].copy(), wavelength[s].copy()
)
# Move integer number of wavelengths ahead
ti = rvi.t[0]
wi = rvi.wavelength[0]
r1 = rvi.positionAtTime(ti + 5123456789*wi)[0]
a = rvi.amplitude(r1, ti)
np.testing.assert_allclose(a.real, 1.0, rtol=0, atol=2e-5)
np.testing.assert_allclose(a.imag, 0.0, rtol=0, atol=2e-5)
# Half wavelength
r1 = rvi.positionAtTime(ti + 6987654321.5*wi)[0]
a = rvi.amplitude(r1, ti)
np.testing.assert_allclose(a.real, -1.0, rtol=0, atol=2e-5)
np.testing.assert_allclose(a.imag, 0.0, rtol=0, atol=2e-5)
# Quarter wavelength
r1 = rvi.positionAtTime(ti + 0.25*wi)[0]
a = rvi.amplitude(r1, ti)
np.testing.assert_allclose(a.real, 0.0, rtol=0, atol=2e-5)
np.testing.assert_allclose(a.imag, 1.0, rtol=0, atol=2e-5)
# Three-quarters wavelength
r1 = rvi.positionAtTime(ti + 7182738495.75*wi)[0]
a = rvi.amplitude(r1, ti)
np.testing.assert_allclose(a.real, 0.0, rtol=0, atol=2e-5)
np.testing.assert_allclose(a.imag, -1.0, rtol=0, atol=2e-5)
# We can also keep the position the same and change the time in
# half/quarter integer multiples of the period.
a = rvi.amplitude(rvi.r[0], rvi.t[0]+5e9*wi)
np.testing.assert_allclose(a.real, 1.0, rtol=0, atol=1e-5)
np.testing.assert_allclose(a.imag, 0.0, rtol=0, atol=1e-5)
a = rvi.amplitude(rvi.r[0], rvi.t[0]+(5e9+5.5)*wi)
np.testing.assert_allclose(a.real, -1.0, rtol=0, atol=1e-5)
np.testing.assert_allclose(a.imag, 0.0, rtol=0, atol=1e-5)
a = rvi.amplitude(rvi.r[0], rvi.t[0]+(5e9+2.25)*wi)
np.testing.assert_allclose(a.real, 0.0, rtol=0, atol=1e-5)
np.testing.assert_allclose(a.imag, -1.0, rtol=0, atol=1e-5)
a = rvi.amplitude(rvi.r[0], rvi.t[0]+(5e9+1.75)*wi)
np.testing.assert_allclose(a.real, 0.0, rtol=0, atol=1e-5)
np.testing.assert_allclose(a.imag, 1.0, rtol=0, atol=1e-5)
# If we pick a point anywhere along a vector originating at the ray
# position, but orthogonal to its direction of propagation, then we
# should get phase = 0 (mod 2pi).
v1 = np.array([1.0, 0.0, 0.0])
v1 = np.cross(rvi.v[0], v1)
p1 = rvi.r[0] + v1
a = rvi.amplitude(p1, rvi.t[0])
np.testing.assert_allclose(a.real, 1.0, rtol=0, atol=1e-5)
np.testing.assert_allclose(a.imag, 0.0, rtol=0, atol=1e-5)
@timer
def test_sumAmplitude():
import time
rng = np.random.default_rng(57721)
size = 10_000
for n in [1.0, 1.3]:
x = rng.uniform(-1, 1, size=size)
y = rng.uniform(-1, 1, size=size)
z = rng.uniform(-0.1, 0.1, size=size)
vx = rng.uniform(-0.05, 0.05, size=size)
vy = rng.uniform(-0.05, 0.05, size=size)
vz = np.sqrt(1.0/(n*n) - vx*vx - vy*vy)
t = rng.uniform(-1.0, 1.0, size=size)
wavelength = rng.uniform(300e-9, 1100e-9, size=size)
rv = batoid.RayVector(x, y, z, vx, vy, vz, t, wavelength)
satime = 0
atime = 0
for r1, t1 in [
((0, 0, 0), 0),
((0, 1, 2), 3),
((-1, 2, 4), -1),
((0, 1, -4), -2)
]:
at0 = time.time()
s1 = rv.sumAmplitude(r1, t1)
at1 = time.time()
s2 = np.sum(rv.amplitude(r1, t1))
at2 = time.time()
np.testing.assert_allclose(s1, s2, rtol=0, atol=1e-11)
satime += at1-at0
atime += at2-at1
# print(f"sumAplitude() time: {satime}")
# print(f"np.sum(amplitude()) time: {atime}")
@timer
def test_equals():
import time
rng = np.random.default_rng(577215)
size = 10_000
x = rng.uniform(-1, 1, size=size)
y = rng.uniform(-1, 1, size=size)
z = rng.uniform(-0.1, 0.1, size=size)
vx = rng.uniform(-0.05, 0.05, size=size)
vy = rng.uniform(-0.05, 0.05, size=size)
vz = np.sqrt(1.0 - vx*vx - vy*vy)
t = rng.uniform(-1.0, 1.0, size=size)
wavelength = rng.uniform(300e-9, 1100e-9, size=size)
flux = rng.uniform(0.9, 1.1, size=size)
vignetted = rng.choice([True, False], size=size)
failed = rng.choice([True, False], size=size)
args = x, y, z, vx, vy, vz, t, wavelength, flux, vignetted, failed
rv = batoid.RayVector(*args)
rv2 = rv.copy()
assert rv == rv2
for i in range(len(args)):
newargs = [args[i].copy() for i in range(len(args))]
ai = newargs[i]
if ai.dtype == float:
ai[0] = 1.2+ai[0]*3.45
elif ai.dtype == bool:
ai[0] = not ai[0]
# else panic!
rv2 = batoid.RayVector(*newargs)
assert rv != rv2
# Repeat, but force comparison on device
rv2 = rv.copy()
rv._rv.x.syncToDevice()
rv._rv.y.syncToDevice()
rv._rv.z.syncToDevice()
rv._rv.vx.syncToDevice()
rv._rv.vy.syncToDevice()
rv._rv.vz.syncToDevice()
rv._rv.t.syncToDevice()
rv._rv.wavelength.syncToDevice()
rv._rv.flux.syncToDevice()
rv._rv.vignetted.syncToDevice()
rv._rv.failed.syncToDevice()
assert rv == rv2
for i in range(len(args)):
newargs = [args[i].copy() for i in range(len(args))]
ai = newargs[i]
if ai.dtype == float:
ai[0] = 1.2+ai[0]*3.45
elif ai.dtype == bool:
ai[0] = not ai[0]
# else panic!
rv2 = batoid.RayVector(*newargs)
assert rv != rv2
@timer
def test_asGrid():
rng = np.random.default_rng(5772156)
for _ in range(10):
backDist = rng.uniform(9.0, 11.0)
wavelength = rng.uniform(300e-9, 1100e-9)
nx = 1
while (nx%2) == 1:
nx = rng.integers(10, 21)
lx = rng.uniform(1.0, 10.0)
dx = lx/(nx-2)
dirCos = np.array([
rng.uniform(-0.1, 0.1),
rng.uniform(-0.1, 0.1),
rng.uniform(-1.2, -0.8),
])
dirCos /= np.sqrt(np.dot(dirCos, dirCos))
# Some things that should be equivalent
grid1 = batoid.RayVector.asGrid(
backDist=backDist, wavelength=wavelength,
nx=nx, lx=lx, dirCos=dirCos
)
grid2 = batoid.RayVector.asGrid(
backDist=backDist, wavelength=wavelength,
nx=nx, dx=dx, dirCos=dirCos
)
grid3 = batoid.RayVector.asGrid(
backDist=backDist, wavelength=wavelength,
dx=dx, lx=lx, dirCos=dirCos
)
grid4 = batoid.RayVector.asGrid(
backDist=backDist, wavelength=wavelength,
nx=nx, lx=(lx, 0.0), dirCos=dirCos
)
theta_x, theta_y = batoid.utils.dirCosToField(*dirCos)
grid5 = batoid.RayVector.asGrid(
backDist=backDist, wavelength=wavelength,
nx=nx, lx=(lx, 0.0), theta_x=theta_x, theta_y=theta_y
)
rays_allclose(grid1, grid2)
rays_allclose(grid1, grid3)
rays_allclose(grid1, grid4)
rays_allclose(grid1, grid5)
# Check distance to chief ray
cridx = (nx//2)*nx+nx//2
obs_dist = np.sqrt(np.dot(grid1.r[cridx], grid1.r[cridx]))
np.testing.assert_allclose(obs_dist, backDist)
np.testing.assert_allclose(grid1.t, 0)
np.testing.assert_allclose(grid1.wavelength, wavelength)
np.testing.assert_allclose(grid1.vignetted, False)
np.testing.assert_allclose(grid1.failed, False)
np.testing.assert_allclose(grid1.vx, dirCos[0])
np.testing.assert_allclose(grid1.vy, dirCos[1])
np.testing.assert_allclose(grid1.vz, dirCos[2])
# Check distribution of points propagated to entrance pupil
pupil = batoid.Plane()
pupil.intersect(grid1)
np.testing.assert_allclose(np.diff(grid1.x)[0], dx)
np.testing.assert_allclose(np.diff(grid1.y)[0], 0, atol=1e-14)
np.testing.assert_allclose(np.diff(grid1.x)[nx-1], -dx*(nx-1))
np.testing.assert_allclose(np.diff(grid1.y)[nx-1], dx)
# Another set, but with odd nx
for _ in range(10):
backDist = rng.uniform(9.0, 11.0)
wavelength = rng.uniform(300e-9, 1100e-9)
while (nx%2) == 0:
nx = rng.integers(10, 21)
lx = rng.uniform(1.0, 10.0)
dx = lx/(nx-1)
dirCos = np.array([
rng.uniform(-0.1, 0.1),
rng.uniform(-0.1, 0.1),
rng.uniform(-1.2, -0.8),
])
dirCos /= np.sqrt(np.dot(dirCos, dirCos))
grid1 = batoid.RayVector.asGrid(
backDist=backDist, wavelength=wavelength,
nx=nx, lx=lx, dirCos=dirCos
)
grid2 = batoid.RayVector.asGrid(
backDist=backDist, wavelength=wavelength,
nx=nx, dx=dx, dirCos=dirCos
)
grid3 = batoid.RayVector.asGrid(
backDist=backDist, wavelength=wavelength,
nx=nx, lx=(lx, 0), dirCos=dirCos
)
# ... but the following is not equivalent, since default is to always
# infer an even nx and ny
# grid4 = batoid.RayVector.asGrid(
# backDist=backDist, wavelength=wavelength,
# dx=1/9, lx=1.0, dirCos=dirCos
# )
rays_allclose(grid1, grid2)
rays_allclose(grid1, grid3)
cridx = (nx*nx-1)//2
obs_dist = np.sqrt(np.dot(grid1.r[cridx], grid1.r[cridx]))
np.testing.assert_allclose(obs_dist, backDist)
np.testing.assert_allclose(grid1.t, 0)
np.testing.assert_allclose(grid1.wavelength, wavelength)
np.testing.assert_allclose(grid1.vignetted, False)
np.testing.assert_allclose(grid1.failed, False)
np.testing.assert_allclose(grid1.vx, dirCos[0])
np.testing.assert_allclose(grid1.vy, dirCos[1])
np.testing.assert_allclose(grid1.vz, dirCos[2])
# Check distribution of points propagated to entrance pupil
pupil = batoid.Plane()
pupil.intersect(grid1)
np.testing.assert_allclose(np.diff(grid1.x)[0], dx)
np.testing.assert_allclose(np.diff(grid1.y)[0], 0, atol=1e-14)
np.testing.assert_allclose(np.diff(grid1.x)[nx-1], -dx*(nx-1))
np.testing.assert_allclose(np.diff(grid1.y)[nx-1], dx)
for _ in range(10):
# Check nrandom
rays = batoid.RayVector.asGrid(
backDist=backDist, wavelength=wavelength,
lx=1.0, nx=1,
nrandom=1000, dirCos=dirCos
)
np.testing.assert_allclose(rays.t, 0)
np.testing.assert_allclose(rays.wavelength, wavelength)
np.testing.assert_allclose(rays.vignetted, False)
np.testing.assert_allclose(rays.failed, False)
np.testing.assert_allclose(rays.vx, dirCos[0])
np.testing.assert_allclose(rays.vy, dirCos[1])
np.testing.assert_allclose(rays.vz, dirCos[2])
# Check that projected points are inside region
pupil = batoid.Plane()
pupil.intersect(rays)
np.testing.assert_allclose(rays.z, 0.0)
np.testing.assert_array_less(rays.x, 0.5)
np.testing.assert_array_less(rays.y, 0.5)
np.testing.assert_array_less(-0.5, rays.x)
np.testing.assert_array_less(-0.5, rays.y)
assert len(rays) == 1000
@timer
def test_asPolar():
rng = np.random.default_rng(5772156)
for _ in range(10):
backDist = rng.uniform(9.0, 11.0)
wavelength = rng.uniform(300e-9, 1100e-9)
inner = rng.uniform(1.0, 3.0)
outer = inner + rng.uniform(1.0, 3.0)
nrad = rng.integers(1, 11)
naz = rng.integers(10, 21)
dirCos = np.array([
rng.uniform(-0.1, 0.1),
rng.uniform(-0.1, 0.1),
rng.uniform(-1.2, -0.8),
])
dirCos /= np.sqrt(np.dot(dirCos, dirCos))
rays = batoid.RayVector.asPolar(
backDist=backDist, wavelength=wavelength,
outer=outer, inner=inner,
nrad=nrad, naz=naz,
dirCos=dirCos
)
np.testing.assert_allclose(rays.t, 0)
np.testing.assert_allclose(rays.wavelength, wavelength)
np.testing.assert_allclose(rays.vignetted, False)
np.testing.assert_allclose(rays.failed, False)
np.testing.assert_allclose(rays.vx, dirCos[0])
np.testing.assert_allclose(rays.vy, dirCos[1])
np.testing.assert_allclose(rays.vz, dirCos[2])
assert len(rays)%6 == 0
# If we set inner=0, then last ray should
# intersect the center of the pupil
inner = 0.0
rays = batoid.RayVector.asPolar(
backDist=backDist, wavelength=wavelength,
outer=outer, inner=inner,
nrad=nrad, naz=naz,
dirCos=dirCos
)
assert len(rays)%6 == 1
pupil = batoid.Plane()
pupil.intersect(rays)
np.testing.assert_allclose(rays.x[-1], 0, atol=1e-14)
np.testing.assert_allclose(rays.y[-1], 0, atol=1e-14)
np.testing.assert_allclose(rays.z[-1], 0, atol=1e-14)
@timer
def test_asSpokes():
rng = | np.random.default_rng(5772156) | numpy.random.default_rng |
import cv2
import numpy as np
from matplotlib import pyplot as plt
def image_show(name, image, resize=1):
H, W = image.shape[0:2]
cv2.namedWindow(name, cv2.WINDOW_NORMAL)
cv2.imshow(name, image.astype(np.uint8))
cv2.resizeWindow(name, round(resize*W), round(resize*H))
def draw_screen_rect(image, point1, point2, color, alpha=0.5):
x1, y1 = point1
x2, y2 = point2
image[y1:y2,x1:x2,:] = (1-alpha)*image[y1:y2,x1:x2,:] + (alpha)*np.array(color, np.uint8)
def draw_boxes(image, boxes, color=(0, 0, 255)):
for box in boxes:
x0, y0, x1, y1 = int(box[0]), int(box[1]), int(box[2]), int(box[3])
cv2.rectangle(image, (x0, y0), (x1, y1), color, 1)
def draw_proposals(image, proposals, color=(0, 0, 255)):
proposals = proposals.detach().numpy()
for i in range(proposals.shape[0]):
box = proposals[i, 1:5]
x0, y0, x1, y1 = int(box[0]), int(box[1]), int(box[2]), int(box[3])
score = proposals[i, 5]
label = proposals[i, 6]
cv2.rectangle(image, (x0, y0), (x1, y1), color, 1)
cv2.putText(image, "%.2f"%score, (x0, y0), 0, 0.3, (255, 0, 0))
def instances_to_color_overlay(instances, image=None, color=None):
height,width = instances.shape[1:]
overlay = np.zeros((height,width,3),np.uint8) if image is None else image.copy()
num_masks = len(instances)
if num_masks==0:
return overlay
if type(color) in [str] or color is None:
#https://matplotlib.org/xkcd/examples/color/colormaps_reference.html
if color is None: color='summer' #'cool' #'brg'
color = plt.get_cmap(color)(np.arange(0,1,1/num_masks))
color = np.array(color[:,:3])*255
color = np.fliplr(color)
#np.random.shuffle(color)
elif type(color) in [list,tuple]:
color = [ color for i in range(num_masks) ]
for i in range(num_masks):
mask = instances[i]
overlay[mask != 0] = color[i]
return overlay
def mask_to_outer_contour(mask):
pad = np.lib.pad(mask, ((1, 1), (1, 1)), 'reflect')
contour = (~mask) & (
(pad[1:-1,1:-1] != pad[:-2,1:-1]) \
| (pad[1:-1,1:-1] != pad[2:,1:-1]) \
| (pad[1:-1,1:-1] != pad[1:-1,:-2]) \
| (pad[1:-1,1:-1] != pad[1:-1,2:])
)
return contour
def mask_to_inner_contour(mask):
pad = | np.lib.pad(mask, ((1, 1), (1, 1)), 'reflect') | numpy.lib.pad |
# Copyright 2019-2021 ETH Zurich and the DaCe authors. All rights reserved.
# Tests reduce expansions for FPGA
import dace
import numpy as np
from dace.fpga_testing import fpga_test
def create_reduce_sdfg(wcr_str, reduction_axis, sdfg_name, input_data, output_data, dtype):
'''
Build an SDFG that perform the given reduction along the given axis
:param wcr_str: reduction operation to perform
:param reduction_axis: the axis on which operate
:param sdfg_name:
:param input_data:
:param output_data:
:return:
'''
sdfg = dace.SDFG(sdfg_name)
###########################################################################
# Copy data to FPGA
copy_in_state = sdfg.add_state("copy_to_device")
input_data_shape = input_data.shape
output_data_shape = output_data.shape
sdfg.add_array('A', input_data_shape, dtype)
in_host_A = copy_in_state.add_read('A')
sdfg.add_array("device_A",
shape=input_data_shape,
dtype=dtype,
storage=dace.dtypes.StorageType.FPGA_Global,
transient=True)
in_device_A = copy_in_state.add_write("device_A")
copy_in_memlet = dace.Memlet("A[{}]".format(",".join([f"0:{i}" for i in input_data_shape])))
copy_in_state.add_memlet_path(in_host_A, in_device_A, memlet=copy_in_memlet)
###########################################################################
# Copy data from FPGA
copy_out_state = sdfg.add_state("copy_from_device")
sdfg.add_array("B", output_data_shape, dtype)
sdfg.add_array("device_B",
shape=output_data_shape,
dtype=dtype,
storage=dace.dtypes.StorageType.FPGA_Global,
transient=True)
out_device = copy_out_state.add_read("device_B")
out_host = copy_out_state.add_write("B")
copy_out_memlet = dace.Memlet("B[{}]".format(",".join([f"0:{i}" for i in output_data_shape])))
copy_out_state.add_memlet_path(out_device, out_host, memlet=copy_out_memlet)
########################################################################
# FPGA State
fpga_state = sdfg.add_state("fpga_state")
r = fpga_state.add_read("device_A")
w = fpga_state.add_write("device_B")
red = fpga_state.add_reduce(wcr_str, reduction_axis, 0, schedule=dace.dtypes.ScheduleType.FPGA_Device)
fpga_state.add_nedge(r, red, dace.Memlet(data="device_A"))
fpga_state.add_nedge(red, w, dace.Memlet(data="device_B"))
######################################
# Interstate edges
sdfg.add_edge(copy_in_state, fpga_state, dace.sdfg.sdfg.InterstateEdge())
sdfg.add_edge(fpga_state, copy_out_state, dace.sdfg.sdfg.InterstateEdge())
sdfg.validate()
return sdfg
@fpga_test(assert_ii_1=False)
def test_reduce_sum_one_axis():
A = np.random.rand(8, 8).astype(np.float32)
B = np.random.rand(8).astype(np.float32)
sdfg = create_reduce_sdfg("lambda a,b: a+b", [0], "reduction_sum_one_axis", A, B, dace.float32)
from dace.libraries.standard import Reduce
Reduce.default_implementation = "FPGAPartialReduction"
sdfg.expand_library_nodes()
sdfg(A=A, B=B)
assert np.allclose(B, np.sum(A, axis=0))
return sdfg
@fpga_test()
def test_reduce_sum_all_axis():
A = np.random.rand(4, 4).astype(np.float32)
B = np.random.rand(1).astype(np.float32)
sdfg = create_reduce_sdfg("lambda a,b: a+b", (0, 1), "reduction_sum_all_axis", A, B, dace.float32)
from dace.libraries.standard import Reduce
Reduce.default_implementation = "FPGAPartialReduction"
sdfg.expand_library_nodes()
sdfg(A=A, B=B)
assert np.allclose(B, np.sum(A, axis=(0, 1)))
return sdfg
@fpga_test()
def test_reduce_sum_4D():
A = np.random.rand(4, 4, 4, 12).astype(np.float64)
B = np.random.rand(4, 4).astype(np.float64)
sdfg = create_reduce_sdfg("lambda a,b: a+b", [2, 3], "reduction_sum_4D", A, B, dace.float64)
from dace.libraries.standard import Reduce
Reduce.default_implementation = "FPGAPartialReduction"
sdfg.expand_library_nodes()
sdfg(A=A, B=B)
assert np.allclose(B, np.sum(A, axis=(2, 3)))
return sdfg
@fpga_test(assert_ii_1=False)
def test_reduce_max():
A = np.random.rand(4, 4).astype(np.float32)
B = np.random.rand(4).astype(np.float32)
sdfg = create_reduce_sdfg("lambda a,b: max(a,b)", [1], "reduction_max", A, B, dace.float32)
from dace.libraries.standard import Reduce
Reduce.default_implementation = "FPGAPartialReduction"
sdfg.expand_library_nodes()
sdfg(A=A, B=B)
assert np.allclose(B, | np.max(A, axis=1) | numpy.max |
"""
Most of the code in this file is taken from https://github.com/chrischoy/DeepGlobalRegistration/blob/master/dataloader/threedmatch_loader.py
This is dataloader used in [1-3] and we re-use it to train and test PCAM on the same dataset.
[1] <NAME>, <NAME>, <NAME>. Deep Global Registration, CVPR, 2020.
[2] <NAME>, <NAME>, <NAME>. Fully Convolutional Geometric Features. ICCV, 2019.
[3] <NAME>, <NAME>, <NAME>. 4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks. CVPR, 2019.
"""
import glob
import os
import numpy as np
import torch
from pcam.datasets.pcam_dataset import PCAMDataset
import MinkowskiEngine as ME
from pcam.tool.pointcloud import make_open3d_point_cloud
from pcam.tool.transforms import apply_transform, sample_points, ground_truth_attention
import open3d as o3d
from tqdm import tqdm
class KittiDataset(PCAMDataset):
dir_path = os.path.join(os.path.dirname(os.path.realpath(__file__)), 'split')
DATA_FILES = {
'train': os.path.join(dir_path, 'train_kitti.txt'),
'val': os.path.join(dir_path, 'val_kitti.txt'),
'test': os.path.join(dir_path, 'test_kitti.txt'),
}
MIN_DIST = 10
def __init__(self,
root,
phase,
icp_path,
voxel_size=0.3,
num_points=4096):
super(KittiDataset, self).__init__(root, phase, voxel_size, num_points)
self.icp_path = icp_path
max_time_diff = 3
self.files = []
self.kitti_icp_cache = {}
self.kitti_cache = {}
subset_names = open(self.DATA_FILES[phase]).read().split()
for dirname in subset_names:
drive_id = int(dirname)
dirname = root + '/sequences/%02d/velodyne/*.bin' % drive_id
print(dirname)
fnames = glob.glob(dirname)
assert len(fnames) > 0, f"Make sure that the path {root} has data {dirname}"
inames = sorted([int(os.path.split(fname)[-1][:-4]) for fname in fnames])
all_odo = self.get_video_odometry(drive_id, return_all=True)
all_pos = np.array([self.odometry_to_positions(odo) for odo in all_odo])
Ts = all_pos[:, :3, 3]
pdist = (Ts.reshape(1, -1, 3) - Ts.reshape(-1, 1, 3))**2
pdist = np.sqrt(pdist.sum(-1))
more_than_10 = pdist > self.MIN_DIST
curr_time = inames[0]
while curr_time in inames:
# Find the min index
next_time = np.where(more_than_10[curr_time][curr_time:curr_time + 100])[0]
if len(next_time) == 0:
curr_time += 1
else:
# Follow https://github.com/yewzijian/3DFeatNet/blob/master/scripts_data_processing/kitti/process_kitti_data.m#L44
next_time = next_time[0] + curr_time - 1
if next_time in inames:
self.files.append((drive_id, curr_time, next_time))
if phase == "train":
# curr_time += 5
curr_time = next_time + 1
else:
curr_time = next_time + 1
# Remove problematic sequence
for item in [
(8, 15, 58),
]:
if item in self.files:
self.files.pop(self.files.index(item))
def __getitem__(self, idx):
drive = self.files[idx][0]
t0, t1 = self.files[idx][1], self.files[idx][2]
key = '%d_%d_%d' % (drive, t0, t1)
filename = self.icp_path + '/' + key + '.npy'
pts1_file = self.icp_path + '/' + key + '_pts1.npy'
pts2_file = self.icp_path + '/' + key + '_pts2.npy'
fname0 = self._get_velodyne_fn(drive, t0)
fname1 = self._get_velodyne_fn(drive, t1)
if key not in self.kitti_icp_cache:
if not os.path.exists(filename):
all_odometry = self.get_video_odometry(drive, [t0, t1])
positions = [self.odometry_to_positions(odometry) for odometry in all_odometry]
# XYZ and reflectance
xyzr0 = np.fromfile(fname0, dtype=np.float32).reshape(-1, 4)
xyzr1 = np.fromfile(fname1, dtype=np.float32).reshape(-1, 4)
xyz0 = xyzr0[:, :3]
xyz1 = xyzr1[:, :3]
# work on the downsampled xyzs, 0.05m == 5cm
sel0 = ME.utils.sparse_quantize(xyz0 / 0.05, return_index=True)
sel1 = ME.utils.sparse_quantize(xyz1 / 0.05, return_index=True)
M = (self.velo2cam @ positions[0].T @ np.linalg.inv(positions[1].T)
@ np.linalg.inv(self.velo2cam)).T
xyz0_t = apply_transform(xyz0[sel0], M)
pcd0 = make_open3d_point_cloud(xyz0_t)
pcd1 = make_open3d_point_cloud(xyz1[sel1])
reg = o3d.registration.registration_icp(pcd0, pcd1, 0.2, np.eye(4),
o3d.registration.TransformationEstimationPointToPoint(),
o3d.registration.ICPConvergenceCriteria(max_iteration=200))
pcd0.transform(reg.transformation)
T_gt = M @ reg.transformation
np.save(filename, T_gt)
else:
T_gt = np.load(filename)
self.kitti_icp_cache[key] = T_gt
else:
T_gt = self.kitti_icp_cache[key]
if not os.path.exists(pts1_file):
xyzr0 = np.fromfile(fname0, dtype=np.float32).reshape(-1, 4)
xyzr1 = np.fromfile(fname1, dtype=np.float32).reshape(-1, 4)
xyz0 = xyzr0[:, :3]
xyz1 = xyzr1[:, :3]
np.save(pts1_file, xyz0)
np.save(pts2_file, xyz1)
else:
xyz0 = | np.load(pts1_file) | numpy.load |
import cv2
from bresenham import bresenham
# from PIL import Image, ImageDraw
import matplotlib.pyplot as plt
import cv2
import numpy as np
# from multiprocessing import Process, Queue
from threading import Thread as Process
from queue import Queue
from collections import Counter
w_occ = 2.0
thresh_floor = -0.3
def average_plane_gridmap(xs, updates):
mx, Mx = np.min(xs[:, 0]), np.max(xs[:, 0])
my, My = np.min(xs[:, 1]), np.max(xs[:, 1])
width = 500
height = 500
xs[:, 0] = width * (xs[:, 0] - mx) / (Mx - mx)
xs[:, 1] = width * (xs[:, 1] - my) / (My - my)
a = 0
imgs = []
for b in | np.cumsum(updates) | numpy.cumsum |
# coding: utf-8
# pylint: disable=R0914
"""tests aero cards"""
import os
from collections import defaultdict
import unittest
from io import StringIO
from typing import Tuple, Optional, Any
import numpy as np
from cpylog import SimpleLogger
import pyNastran
from pyNastran.bdf.bdf import BDF, CORD2R, BDFCard, SET1, read_bdf
from pyNastran.bdf.test.test_bdf import run_bdf
from pyNastran.bdf.cards.aero.aero import (
AEFACT, AELIST, AEPARM,
CAERO1, CAERO2, CAERO3, CAERO4, #CAERO5,
PAERO1, PAERO2, PAERO4, #PAERO3, PAERO5,
AESURF, AESURFS,
AELINK, AECOMP,
SPLINE1, SPLINE2, #, SPLINE3, SPLINE4, SPLINE5
build_caero_paneling
)
from pyNastran.bdf.cards.aero.dynamic_loads import AERO, FLFACT, FLUTTER, GUST, MKAERO1, MKAERO2
from pyNastran.bdf.cards.aero.static_loads import AESTAT, AEROS, CSSCHD, TRIM, TRIM2, DIVERG
from pyNastran.bdf.cards.test.utils import save_load_deck
IS_MATPLOTLIB = False
if IS_MATPLOTLIB:
import matplotlib.pyplot as plt
ROOTPATH = pyNastran.__path__[0]
MODEL_PATH = os.path.join(ROOTPATH, '..', 'models')
#test_path = os.path.join(ROOTPATH, 'bdf', 'cards', 'test')
COMMENT_BAD = 'this is a bad comment'
COMMENT_GOOD = 'this is a good comment\n'
class TestAero(unittest.TestCase):
"""
The Aero cards are:
* AEFACT
* AELINK
* AELIST
* AEPARM
* AESTAT
* AESURF / AESURFS
* AERO / AEROS
* CSSCHD
* CAERO1 / CAERO2 / CAERO3 / CAERO4 / CAERO5
* FLFACT
* FLUTTER
* GUST
* MKAERO1 / MKAERO2
* PAERO1 / PAERO2 / PAERO3
* SPLINE1 / SPLINE2 / SPLINE4 / SPLINE5
"""
def test_aestat_1(self):
log = SimpleLogger(level='warning')
model = BDF(log=log)
lines = ['AESTAT 502 PITCH']
card = model._process_card(lines)
card = BDFCard(card)
size = 8
card = AESTAT.add_card(card)
card.write_card(size, 'dummy')
card.raw_fields()
def test_aecomp_1(self):
"""checks the AECOMP card"""
#sid = 10
#aesid = 0
#lalpha = None
#lmach = None
#lschd = None
#sid = 5
#aesid = 50
#lalpha = 12
#lmach = 15
name = 'WING'
list_type = 'AELIST' # or SET1, CAEROx
aelist_ids = [75, 76]
card = ['AECOMP', name, list_type] + aelist_ids
bdf_card = BDFCard(card, has_none=True)
aecomp1 = AECOMP.add_card(bdf_card, comment='aecomp card')
aecomp1.validate()
aecomp1.write_card()
#label = 'ELEV'
#cid1 = 0
#alid1 = 37
#aesurf = AESURF(aesid, label, cid1, alid1)
#aefact_sid = alid1
#Di = [0., 0.5, 1.]
#aefact_elev = AEFACT(aefact_sid, Di)
#aefact_sid = lalpha
#Di = [0., 5., 10.]
#aefact_alpha = AEFACT(aefact_sid, Di)
#aefact_sid = lmach
#Di = [0., 0.7, 0.8]
#aefact_mach = AEFACT(aefact_sid, Di)
#aefact_sid = lschd
#Di = [0., 15., 30., 45.]
#aefact_delta = AEFACT(aefact_sid, Di)
log = SimpleLogger(level='warning')
model = BDF(log=log)
data = ['AELIST', 75, 1001, 'THRU', 1075, 1101, 'THRU', 1109, 1201, 1202]
model.add_card(data, data[0], COMMENT_BAD, is_list=True)
data = ['AELIST', 76, 2000, 'THRU', 2010]
model.add_card(data, data[0], COMMENT_BAD, is_list=True)
#model.add_aesurf(aesurf)
#model.add_aefact(aefact_elev)
#model.add_aefact(aefact_alpha)
#model.add_aefact(aefact_mach)
#model.add_aefact(aefact_delta)
aecomp1.safe_cross_reference(model)
aecomp1.uncross_reference()
aecomp1.cross_reference(model)
aecomp1.write_card()
aecomp1.uncross_reference()
aecomp1.write_card()
model.validate()
save_load_deck(model)
#-----------
aecomp2 = AECOMP(name, list_type, aelist_ids, comment='cssch card')
aecomp2.validate()
aecomp2.write_card()
list_type = 'INVALID'
aecomp3 = AECOMP(name, list_type, aelist_ids, comment='cssch card')
with self.assertRaises(RuntimeError):
aecomp3.validate()
name = 'MYCOMP'
list_type = 'AELIST'
lists = 10
model.add_aecomp(name, list_type, lists)
lists = 42.0
with self.assertRaises(TypeError):
AECOMP(name, list_type, lists)
def test_aefact_1(self):
"""checks the AEFACT card"""
data = ['AEFACT', 97, .3, 0.7, 1.0]
log = SimpleLogger(level='warning')
model = BDF(log=log)
model.add_card(data, data[0], COMMENT_BAD, is_list=True)
data = ['AEFACT', 97, .3, 0.7, 1.0]
model.add_card(data, data[0], COMMENT_BAD, is_list=True)
data = ['AEFACT', '98', '.3', '0.7', '1.0']
model.add_card(data, data[0], COMMENT_GOOD, is_list=True)
msg = '$this is a bad comment\nAEFACT 97 .3 .7 1.\n'
aefact97 = model.aefacts[97]
aefact98 = model.aefacts[98]
self.assertTrue(all(aefact97.fractions == [.3, .7, 1.0]))
self.assertTrue(all(aefact98.fractions == [.3, .7, 1.0]))
out = aefact97.write_card(8, None)
self.assertEqual(msg, out)
msg = '$this is a good comment\nAEFACT 98 .3 .7 1.\n'
out = aefact98.write_card(8, None)
self.assertEqual(msg, out)
#data = ['AEFACT', 99, .3, 0.7, 1.0, None, 'cat']
#with self.assertRaises(SyntaxError):
#model.add_card(data, data[0], comment_good, is_list=True)
#data = ['AEFACT', 100, .3, 0.7, 1.0, 'cat']
#with self.assertRaises(SyntaxError):
#model.add_card(data, data[0], comment_good, is_list=True)
#data = ['AEFACT', 101, .3, 0.7, 1.0, 2]
#with self.assertRaises(SyntaxError):
#model.add_card(data, data[0], comment_good, is_list=True)
fractions = [1., 2., 3.]
aefact = AEFACT(200, fractions, comment='')
aefact.validate()
aefact.write_card()
#model = BDF()
#aefact.cross_reference(model)
#aefact.write_card()
#aefact.uncross_reference()
#aefact.write_card()
def test_aelink_1(self):
log = SimpleLogger(level='warning')
model = BDF(log=log)
idi = 10
label = 'CS'
independent_labels = ['A', 'B', 'C']
linking_coefficients = [1.0, 2.0]
aelink = AELINK(idi, label, independent_labels, linking_coefficients, comment='')
assert aelink.aelink_id == idi
with self.assertRaises(RuntimeError):
aelink.validate()
str(aelink)
aelink.write_card()
card = ['AELINK', idi, label, independent_labels[0], linking_coefficients[0],
independent_labels[1], linking_coefficients[1], independent_labels[2]]
with self.assertRaises(AssertionError):
model.add_card(card, 'AELINK')
card = ['AELINK', idi, label, independent_labels[0], linking_coefficients[0],
independent_labels[1], linking_coefficients[1]]
model.add_card(card, 'AELINK', comment='cat')
#print(model.aelinks[idi])
assert model.aelinks[idi][0].comment == '$cat\n', 'comment=%r' % str(model.aelinks[idi][0].comment)
#-------------------------------
idi = 11
label = 'LABEL'
independent_labels = ['pig', 'frog', 'dog']
linking_coefficients = []
aelink2 = model.add_aelink(idi, label, independent_labels, linking_coefficients)
with self.assertRaises(RuntimeError):
model.validate()
aelink2.linking_coefficients = [1.0, 2.0, 3.0]
assert aelink2.linking_coefficients == [1., 2., 3.]
#-------------------------------
idi = 'ALWAYS'
label = 'LABEL'
independent_labels = ['pig', 'frog', 'dog']
linking_coefficients = [1.0, 2.0, 3.0]
model.add_aelink(idi, label, independent_labels, linking_coefficients)
model.validate()
model.cross_reference()
def test_aelink_2(self):
log = SimpleLogger(level='warning')
model = BDF(log=log)
idi = 31
label = 'LABEL'
independent_labels = ['pig', 'frog', 'dog']
linking_coefficients = [1.0, 2.0, 3.0]
model.add_aelink(idi, label, independent_labels, linking_coefficients)
save_load_deck(model, run_renumber=False)
def test_aelist_1(self):
"""checks the AELIST card"""
log = SimpleLogger(level='warning')
model = BDF(log=log)
data = ['AELIST', 75, 1001, 'THRU', 1075, 1101, 'THRU', 1109, 1201, 1202]
model.add_card(data, data[0], COMMENT_BAD, is_list=True)
elements = list(range(1001, 1076)) + list(range(1101, 1110)) + [1201, 1202]
aelist = AELIST(74, elements)
aelist.validate()
aelist.write_card()
aelist75 = model.aelists[75]
#print(aelist.elements)
#print(elements)
self.assertTrue(elements == aelist75.elements)
elements = list(range(1001, 1076)) + list(range(1101, 1110)) + [1108, 1202]
data = ['AELIST', 76, 1001, 'THRU', 1075, 1101, 'THRU', 1109, 1108, 1202]
model.add_card(data, data[0], COMMENT_BAD, is_list=True)
aelist76 = model.aelists[76]
#print(aelist76 .elements)
#print(elements)
self.assertFalse(elements == aelist76.elements)
elements = list(set(elements))
elements.sort()
self.assertTrue(elements == aelist76.elements)
elements = [1000, 1000, 1000, 2000, 1000, 2000]
aelist = AELIST(75, elements)
aelist.clean_ids()
str(aelist.write_card())
elements = 42
AELIST(76, elements)
elements = 42.0
with self.assertRaises(TypeError):
AELIST(77, elements)
def test_aeparm_1(self):
"""checks the AEPARM card"""
aeparm_id = 100
aeparm = AEPARM.add_card(BDFCard(['AEPARM', aeparm_id, 'THRUST', 'lb']),
comment='aeparm_comment')
model = BDF(debug=False)
aeparm = model.add_aeparm(aeparm_id, 'THRUST', 'lb', comment='aeparm_comment')
assert aeparm.aeparm_id == aeparm_id
aeparm.validate()
aeparm.cross_reference(None)
aeparm.uncross_reference()
aeparm.safe_cross_reference(None)
aeparm.write_card()
save_load_deck(model)
# def test_aestat_1(self):
# def test_aesurf_1(self):
def test_aesurfs_1(self):
"""checks the AESURFS cards"""
aesid = 6001
label = 'ELEV'
list1 = 6002
list2 = 6003
card = ['AESURFS', aesid, label, None, list1, None, list2]
bdf_card = BDFCard(card, has_none=True)
log = SimpleLogger(level='warning')
model = BDF(log=log)
model.add_card(bdf_card, 'AESURFS', comment='aesurfs',
is_list=True, has_none=True)
aesurfs = AESURFS(aesid, label, list1, list2, comment='aesurfs')
str(aesurfs)
aesurfs.write_card()
model.add_set1(6002, [1, 2, 3])
model.add_grid(1, [0., 0., 0.])
model.add_grid(2, [0., 0., 0.])
model.add_grid(3, [0., 0., 0.])
model.validate()
save_load_deck(model)
def test_aero_1(self):
"""checks the AERO card"""
acsid = 0.
velocity = None
cref = 1.0
rho_ref = 1.0
aero = AERO(velocity, cref, rho_ref, acsid=acsid, sym_xz=0, sym_xy=0,
comment='aero card')
with self.assertRaises(TypeError):
aero.validate()
assert aero.is_symmetric_xy is False
assert aero.is_symmetric_xz is False
assert aero.is_anti_symmetric_xy is False
assert aero.is_anti_symmetric_xz is False
#aero.set_ground_effect(True)
#assert aero.is_symmetric_xy is False
#assert aero.is_symmetric_xz is False
#assert aero.is_anti_symmetric_xy is True
#assert aero.is_anti_symmetric_xz is False
#aero.set_ground_effect(False)
#assert aero.is_symmetric_xy is False
#assert aero.is_symmetric_xz is False
#assert aero.is_anti_symmetric_xy is False
#assert aero.is_anti_symmetric_xz is False
aero = AERO(velocity, cref, rho_ref, acsid=acsid, sym_xz=1, sym_xy=1,
comment='aero card')
assert aero.is_symmetric_xy is True
assert aero.is_symmetric_xz is True
assert aero.is_anti_symmetric_xy is False
assert aero.is_anti_symmetric_xz is False
aero = AERO(velocity, cref, rho_ref, acsid=acsid, sym_xz=-1, sym_xy=-1,
comment='aero card')
assert aero.is_symmetric_xy is False
assert aero.is_symmetric_xz is False
assert aero.is_anti_symmetric_xy is True
assert aero.is_anti_symmetric_xz is True
aero.set_ground_effect(True)
def test_aero_2(self):
"""checks the AERO card"""
acsid = 0
velocity = None
cref = 1.0
rho_ref = 1.0
aero = AERO(velocity, cref, rho_ref, acsid=acsid, sym_xz=0., sym_xy=0,
comment='aero card')
with self.assertRaises(TypeError):
aero.validate()
aero = AERO(velocity, cref, rho_ref, acsid=acsid, sym_xz=0, sym_xy=0.,
comment='aero card')
with self.assertRaises(TypeError):
aero.validate()
aero = AERO(velocity, cref, rho_ref, acsid=acsid, sym_xz=0, sym_xy=0.,
comment='aero card')
with self.assertRaises(TypeError):
aero.validate()
aero = AERO(velocity, cref, rho_ref, acsid=None, sym_xz=0, sym_xy=0,
comment='aero card')
aero.validate()
aero.write_card()
aero.raw_fields()
model = BDF()
aero.cross_reference(model)
aero.write_card()
aero.raw_fields()
aero.uncross_reference()
aero.write_card()
aero.raw_fields()
def test_aeros_1(self):
"""checks the AEROS card"""
#acsid = 0.
#velocity = None
cref = 1.0
bref = 2.0
sref = 100.
acsid = 0
rcsid = 0
aeros = AEROS.add_card(BDFCard(['AERO', acsid, rcsid, cref, bref, sref]))
aeros = AEROS(cref, bref, sref, acsid, rcsid, sym_xz=0, sym_xy=0,
comment='aeros card')
aeros.validate()
aeros.write_card()
aeros.raw_fields()
acsid = None
rcsid = None
sym_xz = None
sym_xy = None
aeros = AEROS(cref, bref, sref, acsid, rcsid, sym_xz=sym_xz, sym_xy=sym_xy,
comment='aeros card')
aeros.validate()
aeros.write_card()
aeros.raw_fields()
cref = 1
bref = 2
sref = 3
acsid = 42.
rcsid = 43.
sym_xz = 44.
sym_xy = 45.
aeros = AEROS(cref, bref, sref, acsid, rcsid, sym_xz=sym_xz, sym_xy=sym_xy)
with self.assertRaises(TypeError):
aeros.validate()
def test_caero1_paneling_nspan_nchord_1(self):
"""checks the CAERO1/PAERO1/AEFACT card"""
log = SimpleLogger(level='warning')
model = BDF(log=log)
cref = 1.0
bref = 1.0
sref = 1.0
model.add_aeros(cref, bref, sref, acsid=0, rcsid=0, sym_xz=0, sym_xy=0, comment='')
pid = 1
igroup = 1
p1 = [0., 0., 0.]
p4 = [1., 15., 0.]
x12 = 1.
x43 = 1.
model.add_paero1(pid, caero_body_ids=None, comment='')
eid = 10000000
caero = model.add_caero1(eid, pid, igroup, p1, x12, p4, x43,
cp=0, nspan=3, lspan=0, nchord=2, lchord=0, comment='')
npoints, nelements = caero.get_npanel_points_elements()
npoints_expected = 12 # 4*3
nelements_expected = 6 # 2*3
x, y = caero.xy
chord_expected = np.array([0., 0.5, 1.])
span_expected = np.array([0., 1 / 3, 2 / 3, 1.])
assert np.allclose(x, chord_expected)
assert np.allclose(y, span_expected)
assert npoints_expected == npoints
assert nelements_expected == nelements
def test_caero1_paneling_nspan_lchord(self):
"""checks the CAERO1/PAERO1/AEFACT card"""
fig, ax = _setup_aero_plot()
log = SimpleLogger(level='warning')
model = BDF(log=log)
cref = 1.0
bref = 1.0
sref = 1.0
model.add_aeros(cref, bref, sref, acsid=0, rcsid=0, sym_xz=0, sym_xy=0, comment='')
pid = 1
igroup = 1
p1 = [0., 0., 0.]
p4 = [1., 15., 0.]
x12 = 1.
x43 = 1.
model.add_paero1(pid, caero_body_ids=None, comment='')
eid = 10000000
chord_aefact_id = 10000
model.add_aefact(chord_aefact_id, [0., 0.5, 1.0])
caero = model.add_caero1(eid, pid, igroup, p1, x12, p4, x43,
cp=0,
nspan=3, lspan=0,
nchord=0, lchord=chord_aefact_id, comment='')
model.cross_reference()
npoints, nelements = caero.get_npanel_points_elements()
npoints_expected = 12 # 4*3
nelements_expected = 6 # 2*3
assert npoints_expected == npoints
assert nelements_expected == nelements
del model.caeros[eid]
del model.aefacts[chord_aefact_id]
points, elements = caero.panel_points_elements()
x, y = caero.xy
chord_expected = np.array([0., 0.5, 1.])
span_expected = np.array([0., 1 / 3, 2 / 3, 1.])
assert np.allclose(x, chord_expected)
assert np.allclose(y, span_expected)
if IS_MATPLOTLIB:
caero.plot(ax)
fig.show()
def test_caero1_paneling_transpose(self):
fig, ax = _setup_aero_plot()
log = SimpleLogger(level='warning')
model = BDF(log=log)
cref = 1.0
bref = 1.0
sref = 1.0
model.add_aeros(cref, bref, sref, acsid=0, rcsid=0, sym_xz=0, sym_xy=0, comment='')
#['CAERO1', '2000', '2000', '0', '15', '10', '1', '0', None, '7.314386', '0.', '-0.18288', '1.463854', '8.222755', '1.573341', '-0.18288', '0.365963']
#card_lines = [
#'CAERO1,2000,2000,0,15,10,1,0,1',
#'+,7.314386,0.,-0.18288,1.463854,8.222755,1.573341,-0.18288,0.365963',
#]
#model.add_card(card_lines, 'CAERO1', comment='', ifile=None, is_list=False, has_none=True)
eid = 2000
#caero = model.caeros[eid]
#print(caero.get_stats())
pid = 1
igroup = 1
p1 = [7.3, 0., 0.]
p4 = [8.2, 1.6, 0.]
x12 = 1.4
x43 = 0.3
model.add_paero1(pid, caero_body_ids=None, comment='')
caero = model.add_caero1(
eid, pid, igroup, p1, x12, p4, x43,
cp=0, nspan=5, lspan=0, nchord=2, lchord=0, comment='')
caero.validate()
x, y = caero.xy
x_expected = np.array([0., 0.5, 1.])
y_expected = np.array([0., 0.2, 0.4, 0.6, 0.8, 1.])
assert np.allclose(x, x_expected)
assert np.allclose(y, y_expected)
#print(caero.get_stats())
caero.cross_reference(model)
all_control_surface_name, caero_control_surfaces, out = build_caero_paneling(model)
box_id_to_caero_element_map_expected = {
2000: np.array([0, 3, 4, 1]),
2001: np.array([1, 4, 5, 2]),
2002: np.array([3, 6, 7, 4]),
2003: np.array([4, 7, 8, 5]),
2004: np.array([ 6, 9, 10, 7]),
2005: np.array([ 7, 10, 11, 8]),
2006: np.array([ 9, 12, 13, 10]),
2007: np.array([10, 13, 14, 11]),
2008: np.array([12, 15, 16, 13]),
2009: np.array([13, 16, 17, 14]),
}
for key, data in out.box_id_to_caero_element_map.items():
assert np.array_equal(data, box_id_to_caero_element_map_expected[key])
all_control_surface_name, caero_control_surfaces, out = build_caero_paneling(model)
if IS_MATPLOTLIB:
caero.plot(ax)
fig.show()
#x = 1
def test_caero1_paneling_multi(self):
"""checks the CAERO1/PAERO1/AEFACT card"""
fig, ax = _setup_aero_plot()
log = SimpleLogger(level='warning')
model = BDF(log=log)
cref = 1.0
bref = 1.0
sref = 1.0
model.add_aeros(cref, bref, sref, acsid=0, rcsid=0, sym_xz=0, sym_xy=0, comment='')
pid = 1
igroup = 1
p1 = [0., 0., 0.]
p4 = [1., 15., 0.]
x12 = 1.
x43 = 1.
model.add_paero1(pid, caero_body_ids=None, comment='')
eid = 1000
chord_aefact_id = 10000
model.add_aefact(chord_aefact_id, [0., 0.5, 1.0])
caero1a = model.add_caero1(eid, pid, igroup, p1, x12, p4, x43,
cp=0,
nspan=3, lspan=0,
nchord=0, lchord=chord_aefact_id, comment='')
eid = 2000
p1 = [1., 16., 0.]
p4 = [1., 30., 0.]
x12 = 1.
x43 = 1.
caero1b = model.add_caero1(eid, pid, igroup, p1, x12, p4, x43,
cp=0,
nspan=3, lspan=0,
nchord=2, lchord=0, comment='')
model.cross_reference()
npoints, nelements = caero1a.get_npanel_points_elements()
npoints_expected = 12 # 4*3
nelements_expected = 6 # 2*3
assert npoints_expected == npoints
assert nelements_expected == nelements
del model.caeros[eid]
del model.aefacts[chord_aefact_id]
#points, elements = caero.panel_points_elements()
#x, y = caero.xy
#chord_expected = np.array([0., 0.5, 1.])
#span_expected = np.array([0., 1 / 3, 2 / 3, 1.])
#assert np.allclose(x, chord_expected)
#assert np.allclose(y, span_expected)
if IS_MATPLOTLIB:
caero1a.plot(ax)
caero1b.plot(ax)
fig.show()
x = 1
def test_caero1_paneling_nspan_nchord_2(self):
"""checks the CAERO1/PAERO1/AEFACT card"""
log = SimpleLogger(level='warning')
model = BDF(log=log)
cref = 1.0
bref = 1.0
sref = 1.0
model.add_aeros(cref, bref, sref, acsid=0, rcsid=0, sym_xz=0, sym_xy=0, comment='')
# basic
pid = 1
igroup = 1
p1 = [0., 0., 0.]
p4 = [1., 15., 0.]
x12 = 1.
x43 = 1.
fig, ax = _setup_aero_plot(fig_id=None)
unused_paero = model.add_paero1(pid, caero_body_ids=None, comment='')
eid = 1000
aelist_id = 10
aesurf_id = 10
caero = model.add_caero1(eid, pid, igroup, p1, x12, p4, x43,
cp=0, nspan=3, lspan=0, nchord=1, lchord=0, comment='')
x, y = caero.xy
chord_expected = np.array([0., 1.])
span_expected = np.array([0., 1 / 3, 2 / 3, 1.])
assert np.allclose(x, chord_expected)
assert np.allclose(y, span_expected)
elements = [1001, 1003, 1005]
unused_aelist = model.add_aelist(aelist_id, elements)
label = 'FLAP'
cid1 = 0
alid1 = aelist_id
unused_aesurf = model.add_aesurf(
aesurf_id, label, cid1, alid1, cid2=None, alid2=None,
eff=1.0, ldw='LDW', crefc=1.0, crefs=1.0, pllim=-np.pi/2., pulim=np.pi/2.,
hmllim=None, hmulim=None, tqllim=None, tqulim=None, comment='')
model.cross_reference()
points, elements = caero.panel_points_elements()
if IS_MATPLOTLIB:
caero.plot(ax)
fig.show()
def test_caero3_paneling(self):
"""checks the CAERO3/PAERO1/AEFACT card"""
fig, ax = _setup_aero_plot()
log = SimpleLogger(level='warning')
model = BDF(log=log)
cref = 1.0
bref = 1.0
sref = 1.0
model.add_aeros(cref, bref, sref, acsid=0, rcsid=0, sym_xz=0, sym_xy=0, comment='')
pid = 1
igroup = 1
p1 = [0., 0., 0.]
p4 = [1., 15., 0.]
x12 = 1.
x43 = 1.
#model.add_paero1(pid, caero_body_ids=None, comment='')
ncontrol_surfaces = 0
nbox = 7
x = []
y = []
model.add_paero3(pid, nbox, ncontrol_surfaces, x, y, comment='')
eid = 1000
list_w = None
caero = model.add_caero3(eid, pid, list_w, p1, x12, p4, x43,
cp=0, list_c1=None, list_c2=None, comment='')
caero.validate()
caero.cross_reference(model)
npoints, nelements = caero.get_npanel_points_elements()
npoints_expected = 24 # (2+1)*(7+1)
nelements_expected = 14 # 2*7
# hardcoded
nchord_elements = 2
nchord_points = nchord_elements + 1
x2, y2 = caero.xy
#chord_expected = np.array([0., 0.5, 1.])
#span_expected = np.array([0., 1 / 3, 2 / 3, 1.])
#assert np.allclose(x, chord_expected)
#assert np.allclose(y, span_expected)
assert npoints_expected == npoints
assert nelements_expected == nelements
points, elements = caero.panel_points_elements()
if IS_MATPLOTLIB:
caero.plot(ax)
fig.show()
x = 1
def test_caero4_paneling(self):
"""checks the CAERO4/PAERO4 card"""
fig, ax = _setup_aero_plot()
log = SimpleLogger(level='warning')
model = BDF(log=log)
cref = 1.0
bref = 1.0
sref = 1.0
model.add_aeros(cref, bref, sref, acsid=0, rcsid=0, sym_xz=0, sym_xy=0, comment='')
pid = 1
igroup = 1
p1 = [0., 0., 0.]
p4 = [1., 15., 0.]
x12 = 1.
x43 = 1.
#model.add_paero1(pid, caero_body_ids=None, comment='')
eid = 100
caero = model.add_caero4(eid, pid, p1, x12, p4, x43,
cp=0, nspan=2, lspan=0, comment='')
docs = []
caocs = []
gapocs = []
paero = model.add_paero4(pid, docs, caocs, gapocs,
cla=0, lcla=0, circ=0, lcirc=0, comment='')
paero.validate()
caero.validate()
caero.cross_reference(model)
npoints, nelements = caero.get_npanel_points_elements()
npoints_expected = 6 # 4*3
nelements_expected = 2 # 2*3
x, y = caero.xy
#chord_expected = np.array([0., 0.5, 1.])
#span_expected = np.array([0., 1 / 3, 2 / 3, 1.])
#assert np.allclose(x, chord_expected)
#assert np.allclose(y, span_expected)
assert npoints_expected == npoints
assert nelements_expected == nelements
if IS_MATPLOTLIB:
caero.plot(ax)
fig.show()
x = 1
def test_caero5_paneling(self):
"""checks the CAERO4/PAERO4 card"""
fig, ax = _setup_aero_plot()
log = SimpleLogger(level='warning')
model = BDF(log=log)
cref = 1.0
bref = 1.0
sref = 1.0
model.add_aeros(cref, bref, sref, acsid=0, rcsid=0, sym_xz=0, sym_xy=0, comment='')
pid = 1
igroup = 1
p1 = [0., 0., 0.]
p4 = [1., 15., 0.]
x12 = 1.
x43 = 1.
#model.add_paero1(pid, caero_body_ids=None, comment='')
eid = 100
nspan = 10
caero = model.add_caero5(eid, pid, p1, x12, p4, x43, cp=0,
nspan=nspan, lspan=0, ntheory=0, nthick=0, comment='')
caoci = []
paero = model.add_paero5(pid, caoci, nalpha=0, lalpha=0,
nxis=0, lxis=0, ntaus=0, ltaus=0, comment='')
paero.validate()
caero.validate()
caero.cross_reference(model)
npoints, nelements = caero.get_npanel_points_elements()
npoints_expected = (nspan + 1) * 2
nelements_expected = nspan # 2*1
assert npoints_expected == npoints
assert nelements_expected == nelements
#x, y = caero.xy
#chord_expected = np.array([0., 0.5, 1.])
#span_expected = np.array([0., 1 / 3, 2 / 3, 1.])
#assert np.allclose(x, chord_expected)
#assert np.allclose(y, span_expected)
all_control_surface_name, caero_control_surfaces, out = build_caero_paneling(model)
box_id_to_caero_element_map_expected = {
100: np.array([0, 2, 3, 1]),
101: np.array([2, 4, 5, 3]),
102: np.array([4, 6, 7, 5]),
103: np.array([6, 8, 9, 7]),
104: np.array([ 8, 10, 11, 9]),
105: np.array([10, 12, 13, 11]),
106: np.array([12, 14, 15, 13]),
107: np.array([14, 16, 17, 15]),
108: np.array([16, 18, 19, 17]),
109: np.array([18, 20, 21, 19]),
}
assert len(box_id_to_caero_element_map_expected) == len(out.box_id_to_caero_element_map)
for key, data in out.box_id_to_caero_element_map.items():
expected_data = box_id_to_caero_element_map_expected[key]
assert np.array_equal(data, expected_data)
points, elements = caero.panel_points_elements()
if IS_MATPLOTLIB:
caero.plot(ax)
fig.show()
x = 1
def test_caero7_paneling(self):
"""checks the CAERO7/PAERO7T card"""
fig, ax = _setup_aero_plot()
log = SimpleLogger(level='warning')
model = BDF(log=log)
cref = 1.0
bref = 1.0
sref = 1.0
model.add_aeros(cref, bref, sref, acsid=0, rcsid=0, sym_xz=0, sym_xy=0, comment='')
pid = 1
igroup = 1
p1 = [0., 0., 0.]
p4 = [1., 15., 0.]
x12 = 1.
x43 = 1.
#model.add_paero7
eid = 100
chord_aefact_id = 10000
model.add_aefact(chord_aefact_id, [0., 0.5, 1.0])
label = 'panel'
nspan = 2
nchord = 4
caero = model.add_caero7(eid, label, p1, x12, p4, x43, cp=0,
nspan=nspan, nchord=nchord, lspan=0,
p_airfoil=None, ztaic=None, comment='')
model.cross_reference()
npoints, nelements = caero.get_npanel_points_elements()
npoints_expected = (nspan + 1) * (nchord + 1)
nelements_expected = nspan * nchord
#npoints_expected = 15 # 4*3
#nelements_expected = 8 # 2*3
assert npoints_expected == npoints
assert nelements_expected == nelements
points, elements = caero.panel_points_elements()
x, y = caero.xy
chord_expected = np.array([0., 0.25, 0.5, 0.75, 1.])
span_expected = np.array([0., 0.5, 1.])
assert np.allclose(x, chord_expected)
assert np.allclose(y, span_expected)
if IS_MATPLOTLIB:
caero.plot(ax)
fig.show()
all_control_surface_name, caero_control_surfaces, out = build_caero_paneling(model)
box_id_to_caero_element_map_expected = {
100: np.array([0, 5, 6, 1]),
101: np.array([1, 6, 7, 2]),
102: np.array([2, 7, 8, 3]),
103: np.array([3, 8, 9, 4]),
104: np.array([5, 10, 11, 6]),
105: np.array([6, 11, 12, 7]),
106: np.array([7, 12, 13, 8]),
107: | np.array([8, 13, 14, 9]) | numpy.array |
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